uva-dare (digital academic repository) comprehensive ... · comprehensive characterization of...

180
UvA-DARE is a service provided by the library of the University of Amsterdam (http://dare.uva.nl) UvA-DARE (Digital Academic Repository) Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA): Edam, R. (2013). Comprehensive characterization of branched polymers. General rights It is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an open content license (like Creative Commons). Disclaimer/Complaints regulations If you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library: https://uba.uva.nl/en/contact, or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible. Download date: 27 Jun 2020

Upload: others

Post on 19-Jun-2020

1 views

Category:

Documents


0 download

TRANSCRIPT

Page 1: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

UvA-DARE is a service provided by the library of the University of Amsterdam (http://dare.uva.nl)

UvA-DARE (Digital Academic Repository)

Comprehensive characterization of branched polymers

Edam, R.

Link to publication

Citation for published version (APA):Edam, R. (2013). Comprehensive characterization of branched polymers.

General rightsIt is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s),other than for strictly personal, individual use, unless the work is under an open content license (like Creative Commons).

Disclaimer/Complaints regulationsIf you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, statingyour reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Askthe Library: https://uba.uva.nl/en/contact, or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam,The Netherlands. You will be contacted as soon as possible.

Download date: 27 Jun 2020

Page 2: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Comprehensive Characterizationof Branched Polymers

Rob EdamC

omprehensive C

haracterization of Branched Polymers Rob Edam

edam_omslag_FINAL.indd 1 26-12-2012 12:50:08

Page 3: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Comprehensive Characterization of Branched Polymers

Page 4: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):
Page 5: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Comprehensive Characterization of Branched Polymers

ACADEMISCH PROEFSCHRIFT

ter verkrijging van de graad van doctor

aan de Universiteit van Amsterdam

op gezag van de Rector Magnificus

prof. dr. D.C. van den Boom

ten overstaan van een door het college voor promoties ingestelde

commissie, in het openbaar te verdedigen in de Agnietenkapel

op donderdag 21 februari 2013, te 14:00 uur

door

Rob Edam

geboren te Avenhorn

Page 6: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Promotor: Prof. Dr. Ir. P.J. Schoenmakers

Overige leden: Prof. Dr. Ir. J.G.M. Janssen

Prof. Dr. Sj. van der Wal

Prof. Dr. A.M. van Herk

Dr. W.Th. Kok

Dr. W. Radke

Dr. F.A. van Damme

Faculteit der Natuurwetenschappen, Wiskunde en Informatica

Comprehensive characterization of branched polymers; R. Edam

Printed by Universal Press, Veenendaal, The Netherlands

This research is part of the research program of the Dutch Polymer Institute (DPI), project #509.

ISBN 978-90-9027351-8

Page 7: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Contents

Chapter 1: General introduction ....................................................................................... 9

1.1 An introduction to polymers ......................................................................... 10 1.1.1 Macromolecules ........................................................................................ 11 1.1.2 Early characterization of polymers ........................................................... 11 1.1.3 Polymer structure ...................................................................................... 13 1.1.4 Branched polymers ................................................................................... 15

1.2 Characterization and separation of branched polymers ................................. 19 1.2.1 TREF, Crystaf and DSC ........................................................................... 19 1.2.2 Rheology ................................................................................................... 20 1.2.3 Spectroscopy ............................................................................................. 23

1.3 Size-exclusion chromatography with selective detection .............................. 25 1.3.1 SEC separation of branched polymers ...................................................... 25 1.3.2 SEC with on-line (micro-)viscometry ....................................................... 27 1.3.3 SEC with multi-angle laser-light-scattering detection .............................. 32 1.3.4 Application and challenges of existing methodology ............................... 33

1.4 Scope of the thesis......................................................................................... 36

Chapter 2: Hydrodynamic chromatography of macromolecules using polymer monolithic columns ........................................................................................................ 41

2.1 Introduction ................................................................................................... 42

2.2 Experimental ................................................................................................. 45 2.2.1 Chemicals and materials ........................................................................... 45 2.2.2 Instrumentation ......................................................................................... 46 2.2.3 Column preparation .................................................................................. 46

2.3 Results and discussion .................................................................................. 47 2.3.1 Preparation and characterization of monoliths for HDC........................... 47 2.3.2 HDC separation of polymers .................................................................... 51 2.3.3 Flow-rate dependence in polymer separations .......................................... 55

2.4 Conclusions ................................................................................................... 61

2.5 Appendix ....................................................................................................... 62 2.5.1 Mercury intrusion and extrusion ............................................................... 62 2.5.2 SEC separation of alkylbenzenes and solvents on monolith ..................... 64 2.5.3 Deborah numbers ...................................................................................... 66

Page 8: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Chapter 3: Branched-Polymer Separations using Comprehensive Two-Dimensional Molecular-Topology Fractionation × Size-Exclusion Chromatography......................... 69

3.1 Introduction ................................................................................................... 70

3.2 Experimental ................................................................................................. 73 3.2.1 Samples and materials .............................................................................. 73 3.2.2 Instrumentation and methods .................................................................... 74

3.3 Results and discussion .................................................................................. 75 3.3.1 Calibration curve for molecular-topology-fractionation column .............. 75 3.3.2 Branched-polymer separations ................................................................. 77

3.4 Conclusions ................................................................................................... 83

3.5 Appendix ....................................................................................................... 84

Chapter 4: Branched Polymers Characterized by Comprehensive Two-Dimensional Separations with fully Orthogonal Mechanisms ............................................................. 89

4.1 Introduction ................................................................................................... 90

4.2 Theory ........................................................................................................... 92 4.2.1 Separation techniques based on size ......................................................... 92 4.2.2 Deformation of polymers in solution ........................................................ 93 4.2.3 Reptation ................................................................................................... 96 4.2.4 Calibration curves and separation of deformed-polymers ........................ 98

4.3 Experimental ............................................................................................... 101 4.3.1 Chemicals and materials ......................................................................... 101 4.3.2 Instrumentation and operating conditions ............................................... 102 4.3.3 Columns and experimental conditions .................................................... 103

4.4 Results and discussion ................................................................................ 104 4.4.1 Flow-rate effect for columns with different pore size ............................. 104 4.4.2 Branched-polymer separations ............................................................... 108 4.4.3 Selectivity for branched polymers .......................................................... 110 4.4.4 Effect of flow rate on migration of branched polymers .......................... 113 4.4.5 Effect of temperature on migration of polymers in MTF ....................... 115

4.5 Conclusions ................................................................................................. 115

4.6 Appendix ..................................................................................................... 117 4.6.1 Comprehensive HDC×SEC experiment ................................................. 117 4.6.2 Second-dimension calibration for MTF×SEC ........................................ 118 4.6.3 Flow-rate effect in MTF×SEC ................................................................ 118 4.6.4 MTF×SEC at orthogonal conditions ....................................................... 121

Page 9: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

4.6.5 MTF×SEC-UV/MALLS on long-chain-branched polystyrene .............. 123 4.6.6 Selectivity in MTF as a function of flow rate ......................................... 124 4.6.7 Effect of temperature on MTF×SEC separations .................................... 126

Chapter 5: Z-RAFT Star Polymerization of Styrene: Comprehensive Characterization using Size-Exclusion Chromatography ........................................................................ 131

5.1 Introduction ................................................................................................. 132

5.2 Experimental Section .................................................................................. 134 5.2.1 Chemicals ............................................................................................... 134 5.2.2 Instrumentation ....................................................................................... 134 5.2.3 RAFT agent synthesis ............................................................................. 137 5.2.4 Polymerizations ...................................................................................... 140

5.3 Results and Discussion ................................................................................ 141

5.4 Conclusion .................................................................................................. 159

Summary ...................................................................................................................... 163

Samenvatting ................................................................................................................ 167

Acknowledgements ...................................................................................................... 171

Publications .................................................................................................................. 175

Page 10: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):
Page 11: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

9

Chapter 1: General introduction

Abstract

In this chapter the objective of the PhD study is introduced. Theory, concepts,

instruments and technologies for the analysis of branched polymers are presented. Also

different ways to achieve branching in the polymer structure and the impact on the

polymer properties are reviewed.

Page 12: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Chapter 1

10

1.1 An introduction to polymers

The ability to characterize polymers has been of critical importance for progress in the

field of macromolecular chemistry. It allows one to understand how a material behaves,

how it was made and how to make it better. Continuous development of polymers has

resulted in materials that are highly optimized and in the rapid proliferation of polymers

into everyday life of the 21st century. Polymers with a very wide range of physical

properties can now be produced, often at low cost. They cover an incredible application

space that continues to expand. The traditional applications, such as simple molded

items, fibers and disposable items, are still present today. More recent is the

introduction of functionalized and smart materials. Modification of the polymers can be

used to increase durability, conduct electricity or even provide self-healing properties.

These specialty materials provide higher added value and are, therefore, of great interest

for production in a commercial setting. An overview of common synthetic polymers and

their applications is presented in Table 1.

Table 1. Synthetic polymers and their application in traditional and functional materials

Material Application example

Polystyrene Coffee cups Envelope window film Insulation foam

Polyvinylchloride Piping Window lining Wire & cable insulation

Polyethylene Bags Garbage containers Artificial ice-skating floors Fishing lines Joint replacement

Polypropylene Automotive bumpers Heat-resistant food packaging

Polyester Soda bottles (polyethylene terephthalate) Clothing / fibers

Polyamide Nylon stockings

Page 13: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Introduction

11

1.1.1 Macromolecules

A landmark in history has been the discovery of covalent bonding between smaller

molecules (monomers) [1] to form polymers or ‘macromolecules’ of high molar mass

[2]. These concepts were introduced in the 1920’s by Hermann Staudinger, for which he

was awarded the Nobel Prize in 1953 [3].The term ‘polymerization’ was introduced

already in 1863 by Berthelot, who recognized the ability of unsaturated compounds to

react with themselves and yield high-boiling oligomers [4]. His work did not comprise

the formation of higher polymers. The idea of higher polymers was opposed by the

ruling misconception from crystallography that molecules had to fit in a single unit cell.

It was not until the late 1920’s that the concept of higher polymers became accepted.

Before this time the mechanism of polymerization was not well understood and was

attributed to self-assembly of small molecules by colloidal interactions [5]. Poor

understanding of molecular structure did not withhold Baekeland from producing the

first fully synthetic polymer already in 1907 [6,7].

1.1.2 Early characterization of polymers

The difficulty in obtaining experimental proof for higher polymers was one of the

reasons that it took a long time for macromolecules to become accepted. Many methods

for determining the molar mass of macromolecules were published in the years

following the introduction of the macromolecular concept [8]. This is not strange,

considering that the interpretation of most measurement techniques depends on

(assumptions about) the structure of the analyte.

Colligative properties of polymers in dilute solution can be used to determine molar

mass. The response of such properties corresponds to the mole fraction in solution as

pointed by Johannes van ‘t Hoff (Nobel Prize in Chemistry, 1901) and may be used to

obtain number-averaged molar-mass (Mn) data. Membrane osmometry has historically

been favored over other techniques, such as freezing-point-depression and vapor-

pressure measurements, because it is more practical to measure and offers better

accuracy. End-group determination may also yield Mn, provided that a selective

detection of terminal groups is possible and the polymer molecules are known to be

linear. Other techniques available for molar-mass determination are light scattering and

Page 14: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Chapter 1

12

ultracentrifugation [9]. Both techniques may be used to provide accurate (“absolute”)

molar masses, as is the case for the colligative properties described before.

Viscosity of polymer solutions has been recognized as a readily accessible and sensitive

property for molar-mass determination by so-called viscometry. It is due to the

expanded nature of the molecules in solution that viscosity is increased by most

polymers. The empirical relation between intrinsic viscosity ([η]) and relative molar

mass (Mr) was introduced by Staudinger [10] (Eq. 1).

[𝜂] = 𝐾𝑀𝑟𝑎 (1)

This equation has become known as the Mark-Houwink relation after their efforts to

improve the theory of this relation and their documentation of constants K and a for

different polymer-solvent systems at given temperatures [11,12,13]. The simplicity of

capillary viscometry for determining molar mass resulted in a high popularity of this

method and documentation of Mark-Houwink constants for many polymer-solvent

systems [14]. Viscometric methods are relative measurements, because the relation

between molar mass and viscosity needs to be determined for each different polymer at

each set of conditions (solvent and temperature). Relations between polymer melt

viscosity and molar mass were also investigated. Determination of molar mass with

much better precision was possible due to the higher viscosity of the pure polymer than

of a polymer-containing solution, but the empirical relations were found only to hold for

relatively low molar masses [15,16,17].

The macromolecular structure of polymers was supported by published work on the

application of these techniques for polymers. Polymer science and related analytical

capabilities expanded rapidly once the scientific community accepted the existence of

macromolecules. Research into polymerization reactions and mechanisms thereof

increased throughout the 1930’s. This revolutionized polymer synthesis and quickly

resulted in the first commercial production of polystyrene, polyesters,

polyvinylchloride, polyethylene and polyamides. Development of polymer-

characterization techniques was driven by the need to support polymer production and

studies into new synthesis routes and application fields. In 1953 Flory wrote ‘Principles

of polymer chemistry’, an overview of both polymer chemistry, as well as

Page 15: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Introduction

13

characterization methods for polymers, which is still considered an important reference

work [8]. Flory’s contributions to the theory of polymers in solution (Flory-Huggins

solution theory and excluded volume) earned him the Nobel Prize in Chemistry in 1974.

According to IUPAC the modern definition for macromolecule or polymer is: "A

molecule of high relative molecular mass, the structure of which essentially comprises

the multiple repetition of units derived, actually or conceptually, from molecules of low

relative molecular mass” [18]. Different types of polymer may be identified depending

on their origin. Most common are synthetic polymers and natural- or biopolymers.

Examples of natural polymers include proteins, starch, cellulose and DNA. The

emphasis throughout the work presented in this thesis will be on synthetic polymers.

Table 2. Different levels of polymer structure

Polymer Additives

Micro- level

(molecular)

Relative molar mass (MMD) (Relative) Monomer content (CCD) Functionality (end groups) Branching / Topology

Structure and concentrations

Meso-level (morphology)

Crystallinity

Self-assembly Particle size distribution Mixing and compatibilization Orientation

Spatial distribution Migration behavior

Macro-level (polymer properties)

Density Glass transition temperature Melting point Optical properties

Solubility Strength Viscosity (melt)

Effects of additives, such as plasticizers, fillers, reinforcing agents, stabilizers, anti-static agents, colorants, on polymer properties

1.1.3 Polymer structure

The characteristics of polymeric materials are the results of many structural features

(Table 2). It is for this reason that characterization is not straightforward and that

understanding of the material properties requires information on more than a single

structural feature. The basic structure of a polymer is determined by the chemistry of the

repeat units and how they are linked together (micro-level). Structural features at the

Page 16: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Chapter 1

14

meso- and macro-level depend on the molecular features, but also on the processing

conditions of the material. Polymers are heterogeneous materials and so the distribution

of micro-structural features is important as well.

A very important parameter is the number of repeat units in a chain, which is also

known as the degree of polymerization. It has a large impact on polymer properties

(macro-level) and is typically expressed as the relative molar mass (Mr). A molar-mass

distribution (MMD) is invariably present in synthetic polymers due to the stochastic

nature of polymerization reactions. This does result in molecules with different Mr being

formed even when reaction conditions are kept identical. A common metric for the

MMD in polymers is the polydispersity index (Eq. 2), which is defined as the ratio of

weight averaged to number-averaged molar mass (Mw and Mn respectively).

𝑃𝐷𝐼 = 𝑀𝑤𝑀𝑛

(2)

Optimization of polymerization conditions makes it possible to control Mr and MMD

and obtain polymers with targeted properties. Reversely, measuring Mr and MMD may

provide information on the polymerization conditions, in particular the termination

reactions [19]. Details on various types of polymerization reactions can be found in

textbooks on polymer chemistry [e.g. 8,20].

Chemistry is the broadest variable in polymer structure. Polymers with different

monomer chemistries have vastly different properties and application areas. Co-

polymers can be created with monomers of different chemistry, which are appropriately

referred to as co-monomers. The chemical-composition distribution (CCD) may deal

with overall composition (inter-chain composition), as well as distribution within chains

(intra-chain distribution). Examples include randomness and block-length distribution.

Tacticity is an intra-molecular form of stereochemistry and may therefore also be

considered part of the CCD. When the chemistry of individual repeat units has affects

reactivity or structure this is classified as “functionality”. Typical examples are reactive

end groups and pendant groups on the backbone.

Page 17: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Introduction

15

Fig. 1. Schematic representation of various types of chain structures, including linear, long-chain-branched,

short-chain-branched, cyclic, network, comb, brush, dendritic and star polymers

1.1.4 Branched polymers

Branching and topology are other important aspects of the polymer structure. Polymers

with branching may be obtained through the addition of (multi-functional) co-

monomers, post-reaction processing or ‘back-biting’ side-reactions taking place during

polymerization [21]. There are many variations possible to the linear structure, resulting

in branched polymers with many different forms (Fig. 1). The most common

applications of branched polymers take advantage of the melt rheology and solid-state

material properties that are unique for these materials. These macro-level effects can be

explained by the characteristics at the meso- and micro-structural level. Especially the

level of (inter-molecular) chain entanglement and crystallinity are affected by branching

properties, which affects material properties related to stretching, deformation or flow

of the polymer.

Changes on the molecular level as a result of branching include a higher number of end

groups, shorter back-bone length and a more compact structure relative to linear

polymers. Branched polymer with chemically different or modified end groups can be

used as highly effective functional materials. The compact molecular structure of

branched molecules gives rise to the melt and material properties corresponding to a

Page 18: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Chapter 1

16

combination of shorter chain length but higher molar mass. It is also an important

handle in the characterization of branched polymers using dilute-solution techniques,

which will be explained later. The main classes of branched polymers are presented in

Table 3.

Table 3. Different types of branched polymers and the properties

Type Effects and applications Chemical pathways Examples

Long-chain branching

Melt rheology modification

Increased toughness

Back-biting in ethylene and acrylate polymerization

Co-polymerization

Light Cross-linking [22]

LDPE, polypropylene, polycarbonate [23], polystyrene, nylon, PMMA [24]

Short-chain branching

Reduction in crystallinity

Improved material properties

Back-biting in ethylene polymerization

Co-polymerization

Polyolefins, LLDPE

Star Model component in rheology research

Multi-functional macro-monomers

Functional materials

Core-first

Multi-functional initiator

Thermo-responsive polymer [25] Low-viscosity inkjet ink [26]

Light-switchable coatings [27]

Combs/brush Model component in rheology research Functional materials

Macro-monomer polymerization [28]

Polyelectrolites [29] Biomimetic materials [30]

Dendrimers / Hyperbranched polymers

Multi-functional macro-monomers Functional materials [31]

Drug delivery [32]

OLEDs [33]

Short-chain branching (SCB) is a property that is almost exclusively associated with

polyolefins. This is because in other polymers the functionality of pendant groups is

different from the backbone and it is reflected in the CCD. Unlike other forms of

branching, the impact of short-chain branches on polymer properties is mainly a result

of interference with crystallinity at the microscopic level (meso scale). The most

common application of SCB is in the modification of linear high-density polyethylene.

With Ziegler-Natta catalysts linear low-density polyethylene may be produced by co-

polymerization of ethylene with alpha-olefins, ranging from propylene to 1-hexadecene,

Page 19: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Introduction

17

to introduce SCB. With contemporary single-site and metallocene catalysts it is possible

to precisely control the degree and distribution of SCB in LLDPE polymers and, thus, to

produce materials with highly optimized properties. An increase in SCB density results

in lower crystallinity and lower density of the material. These are important

characteristics of linear low-density polyethylene, where ‘linear’ in the name refers

merely to the absence of long-chain branching (LCB). It is generally accepted that very

short branching introduces rubber-like behavior (e.g. ethylene-propylene rubbers),

whereas longer chains as obtained by copolymerizing 1-hexene or 1-octene provides

elasticity and other properties beneficial for LLDPE films [34]. Low-density

polyethylene (LDPE) is produced by free-radical polymerization at high pressure and

contains both SCB and LCB as a result of back-biting. This is a side-reaction where in a

propagation step the free radical at a terminal methylene group is transferred to a

methylene group somewhere in the chain by hydrogen abstraction. Branches of random

length and at random position are created in this way. LDPE combines the distinct

advantages of LCB polymers with a lower density than linear high-density polyethylene

(HDPE).

Advantages of LCB polymers are higher zero-shear viscosity, improved melt strength,

reduced melt fracture, reduced melt viscosity at high shear rates (i.e. shear thinning) and

extensional thickening. Polymers with LCB have superior processing properties and

they can be used for demanding applications such as blow molding, blown-film

formation and closed-cell foam production. Long-chain branching has an effect on

viscosity through entanglement of the polymer molecules. Above the critical molecular

weight Mc , which marks the onset of chain entanglement, the melt viscosity of

polymers increases no longer linearly with mass but with Mr3.4 [35,36]. The average

length of the chain segments between entanglements Me can be determined using

experimental techniques [37,38]. An overview of Me values for many polymers has

been established based on rheology and small-angle neutron scattering (SANS)

measurements on linear and short-chain-branched model compounds [39]. For

amorphous polymers the critical molecular weight Mc ≈ 2 Me. The chemical

composition of the polymer backbone has a large effect on the onset of entanglement.

Therefore, the effects of LCB may differ for polymers with different chemistries

through the effect on Me. Branches in LCB-polymers should be longer than Me to affect

Page 20: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Chapter 1

18

the rheology of the material. In practice long-chain branches will have a significant

chain length relative to the backbone of the polymer. Polyolefins with LCB are created

using free-radical polymerization, but may also be obtained in metallocene catalyzed

polymerization. Using constraint geometry catalysts (CGC) it is possible to produce and

incorporate chains with vinyl terminal groups into the final polymer [40,41,42]. The

typical branching frequency for CGC and other metallocene polyethylenes is less than 1

long chain branch per polymer [43], while in LDPE between 3 and 7 long chain

branches are common. LCB in CGC polyethylene will be longer (1300 – 1600 carbon

atoms) than LCB in LDPE, which has branches with 200 – 300 carbon atoms in the

backbone [44,45,46,47,48]. Other pathways for the introduction of LCB are the use of

multi-functional co-monomers [24] or multi-functional initiators. Cross-linking after

reaction can also be used to introduce LCB, for instance by addition of peroxides or

irradiation. Treatment of HDPE and LLDPE with gamma-irradiation has been

performed to induce LCB successfully [22]. A too high degree of cross-linking will

result in network or gel formation, which will compromise the melt behavior of the

material.

LCB is introduced in most commercially produced polymers by chemistry that adds

branches at random locations on the backbone. The polymerization processes for

polymers with controlled and regular LCB (star, comb and brush polymers) are usually

not cost effective for the production of commodity plastics, because of the need for

high-purity monomers or expensive reactants. These materials are typically produced

using multi-step reactions, in which macro-monomers or multi-functional cores are

coupled using anionic polymerization or controlled polymerization reactions, such as

atom-transfer radical-polymerization (ATRP) [49], nitroxide mediated polymerization

(NMP) [50] or reversible addition-fragmentation chain-transfer polymerization (RAFT)

[51]. Only the use for specialty applications or functional materials justifies the cost

involved in producing these materials (Table 3). The ability to create polymers with

well-defined branching topologies and branch lengths is important for studies into the

rheological behavior of polymers [37,38,52]. In this way the effect of increased

branching frequency and branch length on various rheological and material properties

can be determined. Results from this type of research are used to design new materials

with optimized properties.

Page 21: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Introduction

19

In dendrimers and hyperbranched polymers the branching functionality is included in

the main polymerization process, rather than a variation to linear polymerization. Most

often such polymers are produced using condensation polymerizations. The emphasis is

on chemical functionality of the material and most dendrimers are used as functional

materials [31].

1.2 Characterization and separation of branched polymers

Nowadays several techniques are available for the characterization of branched

polymers. The effectiveness generally depends on the type of branching, as well as the

impact on the measurement by other structural properties of the polymer and the

distribution thereof. In certain cases it is therefore desirable or even necessary to add a

separation step before measurements are performed on the polymer.

1.2.1 TREF, Crystaf and DSC

Measurements on crystallization behavior and rheological properties of polymers are

common in quality control, production and application-related testing. These tests are

highly sensitive towards the impact of branching on the macro level properties. The

impact of branching on crystallinity and melt-behavior was described in the section on

polymer structure above. Techniques that are often applied are differential scanning

calorimetry (DSC), temperature-rising elution fractionation (TREF) and crystallization

analysis fractionation (Crystaf). In TREF the polymer is first loaded on a stationary

phase and subsequently eluted as temperature is increased [53]. The loading step is

performed by having the polymer crystallize slowly out of solution. The polymer

eluting from the stationary phase upon temperature increase may either be fractionated

or subject to concentration detection for characterization of the redissolution behavior.

TREF was developed in the early 1980’s and has been widely applied to characterize

the short-chain-branching distribution (SCBD) and tacticity, but it may also be used to

fractionate by chemical composition for certain polyolefins. In more recent applications

the analysis of TREF fractions by, for instance, size-exclusion chromatography (SEC)

has been automated [54]. Crystaf was developed in the 1990’s and is used to monitor

the crystallization of polymer in solution when the temperature is decreased [55].

Crystaf is preferred over TREF, because the analysis can generally be performed at

higher cooling rates, provided the desired information on polymer composition can still

Page 22: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Chapter 1

20

be obtained. The suitability of either technique depends on specific crystallization

behavior. It is known that the crystallization and dissolution delays for ethylene and

propylene polymers are different, which implies that the separation of polyethylene and

polypropylene is only possible with TREF. Another complication is the “supercooling”

of crystallizable materials in solution when the solution is cooled down faster than

nucleation in solution occurs [56,57]. Crystallization steps should be performed at

sufficiently slow so as to prevent co-crystallization. These effects have been illustrated

in a comparison between TREF, Crystaf and DSC for the analysis of LLDPE and blends

with polypropylene [58].

Results for Crystaf analysis of an LDPE and an LLDPE resin are compared in Fig. 2

[59]. Crystaf and TREF results are typically presented in the same way with differential

polymer concentrations in solution on the y-axis and temperature on the x-axis. For

Crystaf analysis the results have been measured starting at 95°C down to 30°C in 1,2,4-

trichlorobenzene (TCB). For LLDPE a typical bi-modal distribution is observed. The

mode near 80°C corresponds to crystalline polyethylene segments in the polymer,

whereas the broad mode below 75°C represents the amorphous material. Only one

single mode is observed for LDPE in the amorphous region as a result of both SCB and

LCB. Crystallization behavior is influenced not only by the amount of co-monomer (i.e.

degree of branching), but also by the distribution and block-length of segments with

different crystalline properties. Therefore, crystallization techniques are the method of

choice for characterizing modern LLDPE polymers. These may be prepared using

multiple metallocene catalysts or in a multi-stage reactions, resulting in complex

distribution of SCB. Crystaf and related techniques are the first choice for monitoring

catalyst efficiency in production processes or for investigating unexpected changes in

polymer performance.

1.2.2 Rheology

Measurements of viscosity and the behavior of polymer melts are among the most

sensitive methods known for characterizing LCB in polymers. Rheological experiments

allow for direct characterization of macro-level properties. Different types of

measurements are performed, depending on the shear-rate regime of interest [60].

Page 23: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Introduction

21

Fig. 2. CRYSTAF results for typical LDPE (1) and LLDPE (2) materials [59]

Dynamic-mechanical analysis (DMA) can be performed to obtain detailed information

on stress-strain relations typically in the range between 0.1 and 100 s-1 using rotational

viscometers. Zero-shear viscosity is obtained from the viscosity value at an arbitrary

low shear value, typically 0.1 s-1. Elastic properties (e.g. shear storage- and loss

modulus) and dampening (tan δ) may be investigated by oscillatory viscometry in

frequency-sweep experiments. All these parameters have been compared against

structural properties for polyethylene and were found to be affected by SCB and LCB in

distinct ways [37,61]. Measurements with an extensional rheometer are used to test for

strain-hardening behavior, and uniaxial and biaxial elongation [62]. Branching often

improves strain-hardening and biaxial-elongational properties of polymers. Therefore,

extensional rheology can be used for quality control of LLDPE and other branched

polymers. DMA at shear rates < 0.1 s-1 is rarely used for purposes other than studies on

creep behavior of polymers. Capillary viscometers are used for measurement at shear

rates > 100 s-1. Applications include the measurement of polymer melt-flow-rate (MFR,

also referred to as melt flow index in case of polyethylenes) and determination of

intrinsic viscosity of polymers in dilute solution. Solution measurements using capillary

viscometry will be described in more detail later (see section Size-exclusion

chromatography with selective detection).

Page 24: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Chapter 1

22

Fig. 3. Trends in shear-dependence of melt viscosity for polyethylene polymers

with different degrees of branching by DMA [45]

The effect of long-chain branching on viscosity is demonstrated in a comparison of

rheology curves for polyethylenes with different LCB frequency (Fig. 3) [45]. These

materials were prepared using a constrained-geometry catalyst, which is a metallocene-

type catalyst that allows for accurate control of LCB in the polymer [61,63]. An

increased zero-shear viscosity and a shear-thinning effect at high shear rate are observed

for polymers with higher branching frequencies. A metric that is used to express shear-

rate sensitivity is the ratio of melt-flow indices obtained with two different loads. The

measurement of melt-flow indices is performed at standardized conditions (ASTM D-

1238), where the melt flow through a capillary is measured with either 2.18 or 10 kg of

load on the piston driving the polymer. For polyethylene this measurement is typically

performed at 190°C.

Investigation of LCB using rheology curves is complicated, because the viscosity and

the shear-rate dependence thereof are also influenced by other properties of the

polymer. Comparing polymers with different MMDs is difficult. An increase in the

molar mass will result in a higher viscosity, irrespective of the shear rate. Changes in

the polydispersity will affect shear-rate-dependent viscosity, with an increase in PDI

resulting in changes comparable to those observed for polymers with increased LCB

frequency. The presence of additives (Table 2) will also affect rheology curves. It is

known that additives can have an unexpected impact on rheology that interferes with the

Page 25: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Introduction

23

measurement. Rheological measurements, therefore, are most useful when performed on

pure polymers with comparable characteristics. Access to a number of comparable pure

reference materials with known architecture is highly desirable for interpretation of the

results in terms of relative differences. Comparison of molar-mass data and zero-shear

viscosity for such a set of data provides very sensitive detection of LCB in the polymer

[43].

1.2.3 Spectroscopy

Information obtained from spectroscopic techniques can be used to elucidate the micro-

level structure of polymers. Infrared detection is traditionally used for monitoring the

chemical composition and it can be used to discriminate between repeat units and

branch points. It was used already in 1940 by Fox and Martin to prove branching in

polyethylene polymers [64]. The only common application for branching-selective

detection with IR today, however, is for the determination of SCB in polyolefins by

selective detection of C-H bonds on secondary and primary carbon atoms [65]. Short-

chain-branching frequency is reported as the number of methyl groups per 1000 carbon

atoms. Most often information on the SCB distribution of a polymer rather than an

average SCB frequency is desired. Such information can be obtained by infrared

analysis of the fractionated polymer or by using a hyphenated technique, such as SEC-

FTIR. Deslauriers et al. demonstrated SEC-FTIR with a precision of ±0.5

Methyl/1000C under optimized conditions for ethylene 1-olefin copolymers with ethyl

and butyl branches [65]. Partial least squares regression was used to build a calibration

between a selected spectral region and reference data on SCB frequency. Precision of

FTIR detection depends on the training set used to build a model. Either levels of ethyl

en butyl branches beyond that of the training set or inclusion of different functionality

will reduce the accuracy of the model. On-line coupling with chromatographic

techniques reduces the sensitivity of FTIR, because of the dilute solutions inherent to

most forms of chromatography [66,67]. An alternative to dilute-solution detection in

flow cells is available in the form of on-line polymer deposition on a germanium disk

using an LC-transform interface [68]. Polymer composition may be detected more

sensitively in this way without interference by the solvent, but the precision and

accuracy of the method leave to be desired [69].

Page 26: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Chapter 1

24

Both SCB and LCB may be studied by NMR spectroscopy. In case of 13C NMR

quantitative results well below 1 in 104 carbon atoms have been reported for polyolefins

with good precision using modern techniques [61]. It is possible to distinguish between

branches of different length up to hexyl side-groups and report their frequency

independently [48,70]. Branching frequency may be reported per molecule or an

arbitrary number of carbon atoms, provided molar-mass information is available. Most

quantitative results have been obtained by measurement of polymer solutions, but melt

analysis by magic-angle spinning NMR has also been reported [66]. Unfortunately,

measurement of the backbone atoms near or at low-abundance branch points requires

very long measurement times in 13C NMR. Fractionation and even on-line coupling

with HPLC or SEC is possible, but this is only practical for 1H NMR for reasons of

sensitivity and speed [71]. LC-NMR is used more often for screening of chemical

composition [72] than for characterizing LCB.

Mass-spectrometric characterization of branched polymers is limited to a specific

number of applications, despite its proliferation for polymer characterization in general

[73]. Soft ionization techniques, such as matrix-assisted laser/desorption ionization

(MALDI) and electrospray ionization (ESI), in combination with high-resolution mass

spectrometry (e.g. time-of-flight mass spectrometry, ToF-MS) are most useful for the

analysis of dendrimers [74]. These techniques are not applicable for polyolefins and

traditional random LCB polymers, because their molar mass is too high and branching

does not induce distinct mass differences of fragments. Mass spectrometry can be

applied successfully for branched polymers with moderate molecular weight and

sufficient ionizability. Products of condensation polymerization, including dendrimers

and hyperbranched polymers, are often amenable for characterization using mass

spectrometry [75,76]. Most mass-spectrometry applications for polymers deal with the

analysis of chemical-composition distributions, which includes the use of

multifunctional initiators and repeat units ultimately resulting in branched polymers.

Hyphenation of various types of liquid chromatography with ESI-ToF-MS provides a

strong combination for these polymers [77].

Page 27: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Introduction

25

1.3 Size-exclusion chromatography with selective detection

Separations are important in many techniques for the characterization of polymer

microstructure and are essential when studying the distribution in polymer properties.

Size-exclusion chromatography (SEC) is one of the most-common techniques in the

characterization of polymers. Since its introduction the 1960’s [78,79] SEC has been

used for the characterization of molar mass and MMD of polymers. In combination with

selective-detection techniques, such as on-line laser-light scattering and viscometry, the

degree of branching may be studied as a function of molar mass. The sensitivity of these

techniques is highest for LCB polymers, but other types of branching may be

investigated as well. A general requirement is that the polymers under consideration are

well dissolved and do not significantly differ from random-coil behavior in solution.

Different configurations of SEC with selective detection may be applied to obtain

comparable information of branched polymers. Preference for any separation or detector

configuration depends on specific strengths and tolerances. Separation and different

forms of detection are presented in the following sections to introduce the

considerations for common configurations of SEC with selective detection.

1.3.1 SEC separation of branched polymers

Separation in SEC is achieved through size-selective migration of polymers in dilute

solution through a column packed with porous particles [80]. The separation is entropic

in nature and interactions between the polymer and the column packing should be

negligible. Large polymer molecules are selectively excluded from pore space in the

SEC column. Their reduced access to the stagnant mobile phase in the pores results in

elution before materials that can enter the pore volume driven by random diffusion. The

relevant size parameter is that of the free molecule in solution and is referred to as the

hydrodynamic size or volume of the polymer [81].

Separation in SEC is an indirect result of molar mass and branching through their

impact on hydrodynamic size. It is therefore important to understand how experimental

and molecular properties affect the relation between size and mass. The theory for

solution behavior of flexible-chain linear polymers has been described in detail by Flory

and Casassa [8, 82]. They found that random-coil statistics could be used to describe the

relation between molar mass and ‘coil dimensions in solution’ (simply referred to as

Page 28: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Chapter 1

26

polymer size from here on) for ideal polymers. Application of random-coil statistics can

be used to describe many other structure-property relations of real polymers

appropriately using scaling laws [83]. The relation between polymer size r and molar

mass may be described using the general scaling law shown as Eq. 3, with empirical

constants a and b correcting for polymer-solvent specific behavior (with b = 0.5 for a

random coil).

𝑟 = 𝑎 𝑀𝑏 (3)

Scaling laws can be used, for instance, to describe mass dependency of intrinsic

viscosity using the Mark-Houwink relation (Eq. 1) over a molar-mass range of several

orders in magnitude [84]. Branching in polymers will interfere with the scaling behavior

between hydrodynamic size rh and molar mass M (Fig. 4) [85,86].

Fig. 4. Schematic representation of polymer structure in solution

An increasing level of (long-chain) branching will result in a reduced freedom of the

chain and therefore a smaller size in solution. Another effect is the increase in segment

density, which generally results in a lower intrinsic viscosity. The differences in scaling

behavior between linear and branched polymers i.e. different relation between molar

mass and polymer size, may result in co-elution of polymers with different molar mass

when linear and branched molecules are present. Branched polymers will generally

elute from the SEC column together with linear polymers with lower molar mass (but

identical hydrodynamic size) due to their more compact coil structure. Local

polydispersity in SEC [87,88,89] as a result of branching has been studied by several

experts. Its presence was proven experimentally by careful consideration of the results

from on-line detection techniques that provide either number- or weight-average molar

mass at each elution increment. The calculation of local polydispersity is typically not

Identical M – different topology

Identical rh – different topology

Page 29: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Introduction

27

included in the workflow of multi-detector SEC techniques and only possible with the

additional effort of setting up a universal calibration. This highlights one of the

fundamental limitations of multi-detector SEC and supports the need for better

separation techniques that can resolve linear and branched materials.

1.3.2 SEC with on-line (micro-)viscometry

Capillary viscometry has been used for calculation of molar mass since the early

discovery of the Mark-Houwink relation for polymers. Before the advent of on-line

detectors in the 1980’s, Mark-Houwink relations had to be established by measurement

of solution viscosity using, for instance, Ubbelohde viscometers. With the introduction

of differential viscometry it became possible to hyphenate viscometers with separation

techniques [80]. Viscometers based on the Wheatstone-bridge design have been

commercialized and have become widely available for viscosity measurement in SEC

[90]. Most commercial detectors use a Wheatstone bridge constructed made with four

steel capillaries with matched restriction. For the work presented in the rest of this

section a novel micro-sized viscometer has been used. This detector was made available

by Polymer Laboratories and Micronit in an effort to address the challenges experienced

with traditional commercial viscometers [91]. The Wheatstone bridge of this detector

has a total volume of only 8 µL and has been created on a glass chip, which allows for

tight engineering specifications and a perfectly balanced bridge. At a flow rate of 100

µL/min the viscometer operates at a shear rate of 3000 s-1, which is the standard for

commercial capillary viscometers. With the reduced detector bridge volume this

detector can match cell volumes encountered in contemporary light scattering and

concentration detectors. A complete set of miniaturized detectors allows also for

“miniaturized” separations. Therefore, SEC columns with dimensions of 4.6 mm ID ×

250 mm were used.

With differential viscometry the specific viscosity can be measured on-line. In

combination with on-line concentration detection it will allow calculation of intrinsic

viscosity at each elution volume (Fig. 5). For polymers with known Mark-Houwink

constants the molar mass can also be calculated at each elution volume. This approach

is not practical for the analysis of branched polymers, because the Mark-Houwink

parameters change with branching properties and frequency. However, other approaches

Page 30: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Chapter 1

28

that do not require Mark-Houwink parameters may be used to characterize branched

polymers using SEC with viscometry.

Fig. 5. Instrument configuration for SEC with on-line viscometry as used for universal calibration.

1.3.2.1 Universal calibration

Regular molar-mass calibrations, prepared using narrow standards, have limited

applicability. Corrections for other polymer systems can only be made when Mark-

Houwink constants are known for both calibrant and analyte. A universal calibration

method was introduced by Grubistic [92]. Knowledge on Mark-Houwink parameters of

the analyte is no longer required for molar-mass calculation when an on-line viscometer

is used. Intrinsic viscosity may be used to calculate molar mass directly when a column

calibration is available in terms of hydrodynamic volume (Vh). This is possible because

of the direct proportionality between Vh and the product of intrinsic viscosity [η] and

molar mass (M) (Eq. 4).

𝑉ℎ ∝ [𝜂]𝑀 (4)

Validity of the universal calibration for polymers of different architecture and

composition has been demonstration by the good correlation for all polymers in a plot of

[η]M against elution volume [84,92]. Accuracy of the results obtained by universal

calibration is challenged by the sensitivity of this calibration principle to experimental

imperfections. For samples with narrow MMD the incomplete separation is incorrectly

interpreted, resulting in a higher PDI and “anomalies” in Mark-Houwink plots. Better

results are obtained using the concentration and viscometer signals from the setup in

Fig. 6. For samples with broad MMD acceptable results could be obtained. Also these

results were extremely sensitive to changes in absolute retention time (correction using

flow-marker possible) and inter-detector delay volume. Changes in the room

Page 31: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Introduction

29

temperature suffice to compromise the accuracy of universal calibration for systems that

are not fully thermostatted, such as the setup used in this study. Good results with

acceptable accuracy may be obtained using universal calibration performed under well-

controlled conditions.

Fig. 6. Instrument configuration for triple-detection SEC.

1.3.2.2 Triple detection SEC

With on-line light-scattering detection the molar mass of polymers can be measured

directly. For polymers in dilute solution the weight-average molar mass may be

calculated from the intensity of the scattered light using the Rayleigh-Gans-Debye

approximation [80,86]. A practical complication is the angular dependence of scattering

as a result of destructive interference of scattered light from molecules in solution larger

than roughly 1/20 times the wavelength of the light. The applicable size is the root-

mean-square radius of the polymer, also referred to as radius of gyration (rg). A

correction is generally applied to obtain corrected values for M and rg through iterative

calculations [93].

In triple-detection SEC both a light scattering and viscometer are added to the detector

array. In the original configuration of triple detection SEC a right-angle laser-light-

scattering detector is used [93]. With measurement of light scattering at 90° the

traditional problems with signal noise at low angles are avoided, but a correction for

angular dependence is required. This is achieved using an estimate of rg calculated using

the viscometer data, estimated M and the Flory-Fox equation. The detector

Page 32: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Chapter 1

30

configuration allows for calculation of both M and [η] at every elution volume without

the need for column calibration. This prevents issues and limitations inherent to the

universal calibration with respect to absolute elution-volume differences. The sensitivity

to errors in inter-detector delay or band broadening remains. In Fig. 7 the effect of inter-

detector band broadening in a non-optimized setup is demonstrated for the analysis of

six-arm star polystyrenes with narrow MMD [94]. Broadening in the detector signals for

the RALLS and viscochip was caused by splitting of the flow towards the differential

refractive index (dRI) detector before the RALLS detector (in contrast to the

configuration in Fig. 6). This resulted in an unrealistic increase in both M and [η] at

higher elution volumes. The RALLS signal was found to be broadened by 2 seconds for

a narrow-standard peak with a width at half height of 36 seconds on the dRI signal.

With the appropriate detector configuration as displayed in Fig. 6 good results have

been obtained without artifacts resulting from inter-detector band broadening. Z-RAFT

six-arm star polystyrenes were analyzed using triple-detection SEC with UV absorption

for concentration detection (Fig. 8 and Fig. 9). The extent of inter-detector band

broadening was minimal due to the small UV detector-cell volume of only 2.5 µL. Most

of the polystyrene polymers were found to have an extremely narrow MMD (i.e. PDI <

1.1), with the exception of polymerization products obtained at very high levels of

conversion. Absolute molar-mass results obtained using triple detection were used for

confirmation in studies into the molar-mass offset in conventionally calibrated SEC by

polymers with known branching topology [94,95]. The results of this work are treated in

more detail in Chapter 5.

The traditional strength of triple-detection SEC lies in the possibility of absolute molar-

mass detection for polymers with relatively low molar mass. A RALLS detector is

simpler by design (less expensive) and can be built with a smaller detector-cell volume

relative to the more complex forms of light-scattering detection. In modern applications

the uncertainties introduced by angular correction and estimation of rg using the Flory-

Fox equation may be alleviated by using a dual-angle detector. Above an arbitrary mass

or estimate of rg the low-angle signal is used, which is much less sensitive to angular

dependence.

Page 33: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Introduction

31

Fig. 7. Mark-Houwink plot; example of triple-detector data subject to inter-detector band broadening.

(a) linear PS1683, (b) 6-arm star polystyrene polymers with different molar mass but uniform arm length

Fig. 8. Chromatograms of narrow-MMD six-arm star polymers and a broad-MMD reference; (a) linear PS1683, (b) 6-arm star PS polymers, (c) 6-arm star PS polymer obtained at high monomer conversion

Fig. 9. Mark-Houwink plot for narrow-MMD six-arm star polymers and a broad-MMD reference

Page 34: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Chapter 1

32

1.3.3 SEC with multi-angle laser-light-scattering detection

The different relation between molar-mass and intrinsic viscosity of branched polymers

is clearly observable in the Mark-Houwink plot. Six-arm star polymers have higher

molar mass and lower intrinsic viscosity than linear polystyrene with an identical

hydrodynamic size. The difference in solution properties of branched polymers relative

to those of linear polymers can be detected using SEC with selective detectors. Multi-

angle laser-light scattering (MALLS) is another selective detector that was not

introduced yet, but is commonly used in the characterization of branched polymers. Due

to the added information of scattering at multiple angles relative to the incident light the

angular dependence may be solved to obtain rg directly at every elution volume,

provided that the particle is large enough to yield appreciable angular dependence.

Calculation of rg does not require any other detector signal and is therefore not affected

by the experimental imperfections of multi-detector arrays, such as inter-detector

volumes and inter-detector band-broadening.

Relative differences in solution behavior of polymers are often expressed as contraction

ratios based on either MALLS detection (Eq. 5) or viscometry (Eq. 6). The subscripts B

and L indicate data for branched and linear reference polymer respectively, comparing

data of identical molar mass as indicated as the subscript M.

𝑔 = ��𝑟𝑔�𝐵

2

�𝑟𝑔�𝐿2�𝑀

(5)

𝑔′ = �[𝜂]𝐵[𝜂]𝐿

�𝑀

(6)

Differences in rg and [η] between linear and branched polymers may be small and hard

to observe in log-plots in comparison with plots of contraction ratio vs. molar mass.

Theoretical models for long-chain-branching frequency based on the relative changes

compared to linear polymers were derived for random-coil polymers even before SEC

with on-line detection became available [96]. Nowadays contraction ratios have been

tabulated for many branched polymers under different solvent conditions [86]. Plots of

contraction factors, rg or [η] as a function of molar mass provide important information

on the branching distribution and are often indicative of the polymerization mechanism

Page 35: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Introduction

33

related to the inclusion of branching. The relation between the parameters g and g’ has

been of great interest, because the models for branching frequency are based on g. The

relation between both parameters is not straightforward and varies within polymers as a

function of molar mass. SEC-MALLS and triple-detection SEC with a MALLS detector

may be used to investigate this relation on-line [97,98].

1.3.4 Application and challenges of existing methodology

Measurement of differences in rg and intrinsic viscosity with SEC in combination with

selective detection techniques is particularly useful for polymers with a low degree of

long-chain branching. Branched polystyrenes that have been used throughout this thesis

were analysed using triple-detection SEC (Fig. 10 and Fig. 11) and SEC-MALLS-dRI

(Fig. 12). Both techniques demonstrate good signal quality for high-molar-mass

polymers, because of the high light-scattering intensity. Contraction is observed in rg

and intrinsic viscosity measurements of the branched materials and increases towards

increasing molar mass, which indicates an increase in long-chain branching. At the low

molar-mass end the data quality is not so good, in particular for the MALLS data. Data

for the low-LCB polymer is of similar quality as the linear reference and the scatter in rg

is caused by the small angular dependence of the light scattered by the smaller

molecules.

Anomalous results are observed for the polystyrene with high LCB. The material that is

eluting later from the SEC columns is responsible for the upward curvature in the

conformation plot (Fig. 12). A change of the curve for LCBps in the Mark-Houwink

plot towards higher molar mass is observed at the low-mass end, which is indicative of

SCB in case of a good SEC separation [99].This phenomenon is known as anomalous

late elution or late elution in SEC and occurs specifically for branched materials.

Detailed investigation of the experimental parameters in the SEC separation and

comparison with field-flow fractionation (FFF) was performed for polystyrenes and

acrylates [100] as well as for LDPE [101]. It was concluded that the high molar-mass

tail of branched polymers is retained in the SEC column and slowly elutes together with

the molecules of low molar mass.

Page 36: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Chapter 1

34

Fig. 10. Chromatograms of broad-MMD linear and branched polystyrene samples. (a) linear PS1683, (b) low-LCB PS1500-10, (c) LCB PS PA2258-123 / PSbranch

Fig. 11. Mark-Houwink plot for broad-MMD linear and branched polystyrene samples

Fig. 12. Conformation plot of linear and branched polystyrene samples

Page 37: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Introduction

35

The separation of this high-LCB polystyrene was performed using FFF, which separates

also the large molecules in solution very well [102] (Fig. 13). In the same figure an

overlay is provided of the SEC and asymmetrical flow field-flow fractionation (AF4)

results. It is clear that the material on the high molar-mass end is not separated by SEC.

As a result of the incomplete separation in SEC the eluent fractions will be

polydisperse. Overestimation of rg is promoted by the higher sensitivity of the MALLS

for larger polymers, as the calculated value over the average population is a z-average.

Polymers with very-high molar mass fractions that are not well separated using SEC are

preferably separated using FFF or another technique that does not suffer from problems

with late-elution of branched or high-molar-mass materials. Separation techniques that

do include light scattering will provide the end user with data that makes it possible to

recognize problems with late elution, whereas in universal calibration this is not

observed unless significant material is observed to elute after the column void volume

using the concentration detector. In practice the amount of late-eluting material is very

small and it is unlikely that this is detected using a concentration detector. A broader

overview of complications in SEC with on-line light scattering and viscometry has been

provided by Mourey [103].

Fig. 13. SEC-MALS and AF4-MALS of the same highly branched polystyrene

10

100

1000

1.0E+04 1.0E+05 1.0E+06 1.0E+07 1.0E+08 1.0E+09

Rg (n

m)

Molar Mass (g/mol)

LCBps SEC PS1683 AF4 LCBps AF4

Page 38: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Chapter 1

36

1.4 Scope of the thesis

The aim of this work is to explore new technology for the characterization of branched

polymers, not limited by the traditional boundaries of common applied analytical

techniques. Initial results on molecular topology fractionation [104] served as an

inspiration to explore this separation further. The mechanism behind this fractionation

was still open for multiple explanations, because separation conditions could often not

be defined or studied systematically. Monolithic columns were prepared specifically to

address this issue. Columns for MTF were applied in a two-dimensional separation with

a size-based separation to study and optimize a true separation by topological properties

of the polymer.

Chapter 2 deals with the preparation of monolithic columns and their optimization for

polymer separations. Monolithic stationary phases have received much attention as an

alternative for packed beds for interaction chromatography. The highly interconnected

network of channels in polymeric monoliths provides an excellent environment for

hydrodynamic separations. Monoliths with different macropore sizes were prepared and

the materials were studied in an effort to understand the porous structure. It was

concluded that hydrodynamic chromatography was the prevailing separation mechanism

based on the confirmation of a unimodal pore-size distribution and a continuous flow-

through nature of the pores.

Chapter 3 details the application of multi-dimensional separations with selectivity based

on topology. The idea to separate a polymer based on its hydrodynamic size and

topology in a comprehensive two-dimensional separation is demonstrated for the first

time. A star polymer was used for the branching-selective separation. This serves as a

model compound for LCB polymers.

In Chapter 4 the application of MTF is considered in more detail and the mechanism of

separation is discussed. A systematic study on the selectivity is conducted using

columns with different channel sizes. Knowledge obtained in Chapter 2 on the pore

structure and separation characteristics of the columns was taken into account. Columns

used in this study provided better efficiency compared to previously used MTF

columns, which were short in length and were packed with polydisperse silica. The

Page 39: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Introduction

37

flow-rate effect on migration has been investigated thoroughly for both linear and

branched polymers.

In Chapter 5 the synthesis and analysis of branched polymers with well-defined

topology is presented. It is demonstrated that for polymers prepared with well-defined

topology the molar mass can be calculated from conventional SEC experiments. The

application is compared with results from theoretical studies for correction factors and

experimental results from other researchers. Absolute molar-masses were calculated for

the star-branched polymers for validation of the predicted molar mass using both

correction factors and theoretical molar mass for specific monomer conversion in the

polymer synthesis.

References

[1] H. Staudinger, Ber. Dtsch. Dhem. Ges. 53 (1920) 1073.

[2] H. Staudinger, J. Fritschi, Helv. Chim. Acta 5 (1922) 785.

[3] R. Mülhaupt, Angew. Chem. Int. Ed. 43 (2004) 1054.

[4] M. Berthelot, Lecons de chimie professes en 1864 et 1865, Societe chimique de Paris, 1866, p. 18 and

p. 148.

[5] T. Graham, Philos. Trans. R. Soc. London 151 (1861) 183.

[6] L.H. Baekeland, US Pat. 942 699, 1907.

[7] L.H. Baekeland, Ind. Eng. Chem. 1 (1909) 202.

[8] P.J. Flory, Principles of Polymer Chemistry, Cornell University Press, Ithaca, NY, 1953.

[9] T. Svedberg, K.O. Pedersen, The Ultracentrifuge, Clarendon Press, Oxford, 1940.

[10] H. Staudinger, W. Heuer, Ber. Dtsch. Chem. Ges. 63 (1930) 2222.

[11] H. Mark, Der feste Korper, Hirzel, Leipzig, 1938, p. 103

[12] R. Houwink, J. Prakt. Chem. 157 (1940) 15.

[13] P. Kratochvil. U.W. Suter, in Compendium of Macromolecular Nomenclature, The Purple Book,

Chapter 3, 1st ed., W.V. Metanomski, Eds., Blackwell Science, 1991. / P. Kratochvil, U.W. Suter, Pure

& Appl. Chem. 61 (1989) 211.

[14] M. Kurata, Y. Tsunashima, in Polymer Handbook, 4th ed., J. Brandrup, E.H. Immergut, E.A. Grulke,

eds., Wiley-Interscience, New York, 1999.

[15] J.R. Schaefgen, P.J. Flory, J. Am. Chem. Soc. 70 (1948, 2709.

[16] P.J. Flory, J. Am. Chem. Soc. 62 (1940) 1057.

[17] T.G. Fox, P. J. Flory, J. Am. Chem. Soc. 70 (1948) 2384.

Page 40: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Chapter 1

38

[18] A.D. Jenkins, P. Kratochvil, R.F.T. Stepto, U.W. Suter, Pure Appl. Chem. 68 (1996) 2287.

[19] L.H. Sperling, Introduction to physical polymer science, 4th edition, Wiley, 2006, p. 108.

[20] C.E. Carraher Jr., Polymer Chemistry, 5th ed., Marcel Dekker, New York, NY, 2000.

[21] A.J. Peacock, A. Calhoun, Polymer Chemistry: Properties and Applications, Carl Hanser Verlag,

Munich, 2006, Chapter 5.5.

[22] B.D. Dickie, R.J. Koopmans, J. Polym. Sci., Part C: Polym. Lett. 28 (1990) 193.

[23] Dow Calibre 600 polycarbonate tech note, www.dowengineeringplastics.com

[24] C. Jackson, Y. Chen, J.W. Mays, J. Appl. Pol. Sci. 59 (1996) 179.

[25] A. Hirao, R. Inushima, T. Nakayama, T. Watanabe, H.-S. Yoo, T. Ishizone, K. Sugiyama, T. Kakuchi,

S. Carlotti, A. Deffieux, Eur. Polym. J. 47 (2011) 713.

[26] B.-J. de Gans, L. Xue, U.S. Agarwal. U.S. Schubert, Macromol. Rapid Commun. 26 (2005) 310.

[27] P.A.P. Geelen, Light Switchable Coatings, PhD Thesis http://repository.tue.nl/638048, Technische

Universiteit Eindhoven, 2008.

[28] K. Ito, S. Kawaguchi, in: J. Roovers, (ed.), Poly(macromonomers) homo- and copolymerization, Adv.

Polym. Sci. 142 (1999) 129.

[29] C.M. Fernyhough, R.N. Young, A.J. Ryan, L.R. Hutchings, Polymer 47 (2006) 3455.

[30] A. Papagiannopoulos, T.A. Waigh, A. Fluerasu, C.M. Fernyhough, A.J. Madsen, J. Phys.: Condens.

Matter 17 (2005) 279.

[31] F. Vögtle, G. Richardt, N. Werner, Dendrimer Chemistry, Wiley-VCH, Weinheim, 2009, Chapter 8:

Special properties and potential applications.

[32] R. Haag, Angew. Chem. 116 (2004) 280.

[33] L. A. Khotina, L. S. Lepnev, N.S. Burenkova, P.M. Valetsky, A.G. Vitukhnovsky, J. Luminescence 110

(2004) 232.

[34] P. Gupta, G.L. Wilkes, A.M. Sukhadia, R.K. Krishnaswamy, M.J. Lamborn, S.M. Wharry, C.C. Tso,

P.J. DesLauriers, T. Mansfeld, F.L. Beyer, Polymer 46 (2005) 8819.

[35] T.G. Fox, V.R. Allen, J. Chem. Phys. 41 (1964) 344.

[36] P.C. Hiemenz, Polymer Chemistry, Marcel Dekker, New York, 1984, Chapter 2.

[37] D.J. Lohse, S.T. Milner, L.J. Fetters, M. Xenidou, N. Hadjichristidis, R.A. Mendelson, C.A. García-

Franco, M.K. Lyon, Macromolecules 35 (2002) 3066.

[38] T.C.B. McLeish, S.T. Milner, in: J. Roovers, (ed.), Solution Properties of Branched Macromolecules,

Adv. Polym. Sci. 143 (1999) 195.

[39] L.J. Fetters, D.J. Lohse, D. Richter, T.A. Witten, A. Zirkel, Macromolecules 27 (1994) 4639.

[40] J. Huang, G.L. Rempel, Prog. Polym. Sci. 20 (1995) 459.

[41] D. Yan, W.-J. Wang, S. Zhu, Polymer 40 (1999) 1737.

[42] Q. Yang, M.D. Jensen, M.P. McDaniel, Macromolecules 43 (2010) 8836.

[43] C. Piel, F.J. Stadler, J. Kaschta, S. Rulhoff, H. Münstedt, W. Kaminsky, Macromol. Chem. Phys. 207

(2006) 26.

[44] S.-Y. Lai, J.R. Wilson, G.W. Knight, J.C. Stevens, P.-W.S. Chum, Elastic substantially linear olefin

polymers, US Patent #5,272,236.

Page 41: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Introduction

39

[45] S.-Y. Lai, J.R. Wilson, G.W. Knight, J.C. Stevens, Elastic substantially linear olefin polymers, US

Patent #5,278,272.

[46] K.W. Swogger, G.W. Knight, S.-Y. Lai, unpublished data.

[47] D.C. Bugada, A. Rudin, Eur. Polym. J. 23 (1987) 847.

[48] T. Usami, Y. Gotoh, S. Takayama, J. Appl. Polym Sci. 43 (1991) 1859.

[49] K. Matyjaszewski, T.E. Patten, J.H. Xia, J. Am. Chem. Soc. 119 (1997) 674.

[50] C.J. Hawker, A.W. Bosman, E. Harth, Chem. Rev. 101 (2001) 3661.

[51] J. Chiefari, Y.K. Chong, F. Ercole, J. Kristina, J. Jeffery, T.P.T. Le, R.T.A. Mayadunne, G.F. Meijs,

C.L. Moad, G. Moad, E. Rizzardo, S.H. Thang, Macromolecules 31 (1998) 5559.

[52] B. J. Bauer, L. J. Fetters, Rubber Chem. Technol. 51 (1978) 406.

[53] L. Wild, T. Ryle, D. Knobeloch, I. R. Peat, J. Polym. Sci., Polym. Phys. Ed. 20 (1982) 441.

[54] A. Ortin, B. Monrabal, J. Suancho-Tello, Macromol. Symp. 257 (2007) 13.

[55] B. Monrabal, J. Appl. Polym. Sci. 52 (1994) 491.

[56] G.J. Glöckner, J. Appl. Polym. Sci., Appl. Polym. Symp. 45 (1990) 1.

[57] L. Wild, Adv. Polym. Sci. 98 (1990) 1.

[58] C. Gabriel, D. Lilge, Polymer 42 (2001) 297.

[59] H.J. de Jonge, R. Dingemanse, unpublished Crystaf results on research samples of LDPE and LLDPE

provided by Dow Chemical.

[60] L.H. Sperling, Introduction to physical polymer science, 4th edition, Wiley, 2006, Chapter 10: Polymer

viscoelasticity and rheology.

[61] P.M. Wood-Adams, J.M. Dealy, A.W. deGroot, O.D. Redwine, Macromolecules 33 (2000) 7489.

[62] M.H. Wagner, H. Bastian, P. Hachmann, J. Meissner, S. Kurzbeck, H. Münstedt, F. Langouche, Rheol.

Acta 39 (2000) 97.

[63] J.C. Stevens, J. Stud. Surf. Sci. Catal. 89 (1994) 227.

[64] T.J. Fox, A.E. Martin, Proc. R. Soc. Londern A. 175 (1940) 208.

[65] P.J. DesLauriers, D.C. Rohlfinger, E.T. Hsieh, Polymer 43 (2002) 159.

[66] S.J. Kok, Th. Hankemeier and P.J. Schoenmakers, J. Chromatogr. A 1098 (2005) 104.

[67] C. Piel, E. Jannesson, A. Qvist, Macromol. Symp. 2009 (282) 41.

[68] S.J. Kok, N.C. Arentsen, P.J.C.H. Cools, Th. Hankemeier, P.J. Schoenmakers, J. Chromatogr. A 948

(2002) 257.

[69] S.J. Kok, C.A. Wold, Th. Hankemeier, P.J. Schoenmakers, J. Chromatogr. A 1017 (2003) 83.

[70] J.C. Randall, J. Macromol. Sci., Rev. Macromol. Chem. Phys. C29 (1989) 201.

[71] W. Hiller, H. Pasch, T. Macko, M. Hoffmann, J. Glanz, M. Spraul, U. Braumann, R. Streck, J. Mason,

F. van Damme, J. Magn. Reson. 183 (2006) 309.

[72] H. Pasch, L.-C. Heinz, T. Macko, W. Hiller, Pure Appl. Chem. 80 (2008) 1747.

[73] S.M. Weidner, S. Trimpin, Anal. Chem. 80 (2008) 4349.

[74] F. Vögtle, G. Richardt, N. Werner, Dendrimer Chemistry, Wiley-VCH, Weinheim, 2009, Chapter 7:

Characterization and analysis.

[75] J.E. Klee, Eur. J. Mass Spectrom. 11 (2005) 591.

Page 42: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Chapter 1

40

[76] J.K. Gooden, M.L. Gross, A. Mueller, A.D. Stefanescu, K.J. Wooley, J. Am. Chem. Soc. 120 (1998)

10180.

[77] M.W.F. Nielen, F.A. Buijtenhuijs, Anal. Chem. 71 (1999) 1809.

[78] J. Porath, P. Flodin, Nature 183 (1959) 1657.

[79] J.C. Moore, J. Polym. Sci. A 2 (1964) 835.

[80] A.M. Striegel, J.J. Kirkland, W.W. Yau, D.D. Bly, Modern Size-Exclusion Liquid Chromatography,

Wiley, New York, 2nd ed., 2009.

[81] I. Teraoka, Macromolecules 37 (2004) 6632.

[82] E.F. Casassa, J. Phys. Chem 75 (1971) 3929.

[83] P.-G. de Gennes, Scaling Concepts in Polymer Physics, Cornell University Press, Ithaca (NY), 1979.

[84] C. Jackson, Y.-J. Chen, J.W. Mays, J. Appl. Polym. Sci. 61 (1996) 865.

[85] W.H. Stockmayer, M. Fixman, Ann. N.Y. Acad. Sci. 57 (1953) 334.

[86] W. Burchard, in: J. Roovers, (ed.), Solution Properties of Branched Macromolecules, Adv. Polym. Sci.

143 (1999) 113.

[87] A.E. Hamielec, A.C. Ouano, J. Liq. Chromatogr. 1 (1978) 111.

[88] S.T. Balke, T.H.Mourey, J. Appl. Polym. Sci. 81 (2001) 370.

[89] M. Gaborieau, J. Nicolas, M. Save, B. Charleux, J.-P. Vairon, R.G. Gilbert, P. Castignolles, J.

Chromatogr. A 1190 (2008) 215.

[90] Haney, M. (1985). The differential viscometer. I: A new approach to the measurement of specific

viscosities of polymer solutions. J. Appl. Polym. Sci. 30, 3023–3036.

[91] M. Blom, R. van ‘t Oever, P. Claes, S. O’Donohue, A. v.d. Berg, ‘A micro differential viscosity

detector for polymer separation systems’. In: MicroTAS 2005 Conference -9th International Conference

on Miniaturized Systems for Chemistry and Life Sciences, 9-13 October 2005, Boston, MA, USA. pp.

988-990. Micro total analysis systems 2005. Transducer Research Foundation. ISBN 9780444511003

[92] Z. Grubistic, R. Rempp, H. Benoit, J. Polym. Sci. B, 5 (1967) 753.

[93] M.A. Haney, C. Jackson, W.W. Yau, In: Proceedings of the 1991 international GPC symposium; 1991.

p. 49–63.

[94] D. Boschmann, R. Edam, P.J. Schoenmakers. P. Vana, Polymer, 49 (2008) 5199.

[95] D. Boschmann, R. Edam, P.J. Schoenmakers, P. Vana, Macromol. Symp., Vol. 275-276 (2009), p. 184-

196

[96] B.H. Zimm, W.H. Stockmayer, J. Chem. Phys., 17 (1949) 1301.

[97] W.-J. Wang, S. Kharchenko, K. Migler, S. Zhu, Polymer, 45 (2004) 6495.

[98] P. Tackx, J.C.J.F. Tacx, Polymer 39 (1998)3109.

[99] T. Sun, P. Brant, R.R. Chance, W.W. Graessley, Macromolecules, 34 (2001) 6812.

[100] S. Podzimek, T. Vlcek, C. Johann, J. Appl. Polym. Sci., 81 (2001) 1588.

[101] T. Otte, T. Klein, R. Brüll, T. Macko, H. Pasch, J. Chromatogr. A, 1218 (2011) 4240.

[102] D. Roessner, W.-M. Kulicke, J. Chromatogr. A 687 (1994) 249.

[103] T.H. Mourey, International Journal of Polymer Anal. Charact., 9 (2004) 97.

[104] D.M. Meunier, P.B. Smith, S.A. Baker, Macromolecules, 38 (2005) 5313.

Page 43: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

41

Chapter 2: Hydrodynamic chromatography of

macromolecules using polymer monolithic columns

Abstract

The selectivity window of size-based separations of macromolecules was tailored by

tuning the macropore size of polymer monolithic columns. Monolithic materials with

pore sizes ranging between 75 nm and 1.2 μm were prepared in-situ in large I.D.

columns. The dominant separation mechanism was hydrodynamic chromatography in

the flow-through pores. The calibration curves for synthetic polymers matched with the

elution behavior by HDC separations in packed columns with ‘analyte-to-pore’ aspect

ratios (λ) up to 0.2. For large-macropore monoliths, a deviation in retention behavior

was observed for small polystyrene polymers (Mr < 20 kDa), which may be explained

by a combined HDC-SEC mechanism for λ < 0.02. The availability of monoliths with

very narrow pore sizes allowed investigation of separations at high λ values. For high-

molecular weight polymers (Mr > 300,000 Da) confined in narrow channels, the

separation strongly depended on flow rate. Flow-rate dependent elution behavior was

evaluated by calculation of Deborah numbers and confirmed to be outside the scope of

classic shear deformation or slalom chromatography. Shear-induced forces acting on the

periphery of coiled polymers in solution may be responsible for flow-rate dependent

elution.

Page 44: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Chapter 2

42

2.1 Introduction

Liquid chromatography (LC) is an invaluable analytical separation technique for the

characterization of synthetic polymers and bio-macromolecules. Large molecules with

relative molecular weights up to several millions can be separated, provided that they

are well dissolved in the mobile phase [1,2]. Size-exclusion chromatography (SEC),

hydrodynamic chromatography (HDC) and flow field-flow fractionation (F4) are often

used in the analysis of macromolecules. The separation conditions are typically mild

(moderate temperatures and shear stress), leaving the molecules intact for further

characterization (e.g. light scattering, viscometry, spectroscopy), separation, or

collection of fractions. Each of these techniques separates the analytes by size in

solution and enthalpic interactions between analytes and stationary surfaces must be

negligible. When this is the case, the physical properties of the stationary phase, rather

than the surface chemistry, are of paramount importance in creating a suitable

hydrodynamic environment for separation.

As opposed to SEC, HDC separations are based on partitioning within the transient

mobile phase [3,4,5]. The separation is a result of partitioning induced by surface-

exclusion in flow-through pores and hydrodynamic forces on the polymer in laminar

flow. Small analyte molecules can sample the low-velocity flow regions near the

stationary-phase surface that cannot be sampled by larger analytes. The latter are

excluded from the channel surface, because of both steric and hydrodynamic effects. An

overview of conditions and requirements of separations techniques for macromolecule

characterization is provided in Table 1. Hydrodynamic separations are ideally

performed in very narrow open (tubular) channels, because of their well-described

geometry, which allows rigorous theoretical description and calibration [6], and the

absence of eddy diffusion. The selectivity in HDC depends on the aspect-ratio (λ = r /

R) that relates the size of the analyte molecule (radius r) to the size of the flow-through

channel (radius R). For solutes moving through open-tubular channels with laminar

(Poiseuille) flow (i.e. a parabolic flow profile), the migration rate can generally be

expressed as the residence time of an analyte polymer or particle (tp) relative to the

migration time of a small-molecule marker (tm) as defined in Eq. 1 where τ is the

relative retention (with τ = 1 for a flow marker). In the basic form with C = 1 Eq.1

Page 45: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Hydrodynamic chromatography of macromolecules using polymer monolithic columns

43

describes solute migration based on surface exclusion only. This is the dominant effect

for low values of λ. C is a variable used for including hydrodynamic effects. Its value

varies between 1 and 5.3 depending on solute type and model assumptions [7].

𝜏 = 𝑡𝑝𝑡𝑚

= 11+2𝜆−𝐶𝜆2

(1)

Table 1. Description and boundary conditions for selected size-based macromolecule separations.

SEC HDC MTF

Principal requirements

Stagnant pore volume. Transient mobile phase + inhomogeneous flow profile (e.g. Poiseuille flow).

Obstructed flow for analyte molecules.

Critical dimensions Stagnant-pore size related to size of analyte molecules in solution.

Channel diameter 5 to 50 times the diameter of analyte molecules in solution.

0.02 < λ < 0.2

Channel diameter less than 2.5 times the diameter of analyte molecules in solution.

λ > 0.4

Implementation Porous particles; monoliths with bimodal pore-size distributions.

Open-tubular columns (≤ 2 µm inner diameter); packed columns (non-porous particles; ≤ 2 µm particle diameter), monoliths ≤ 1 µm channel diameter).

Columns packed with sub-micron (non-porous) particles; monoliths (ca. 0.1 µm channel diameter).

Selectivity Molecular size (flow-rate independent).

Molecular size (largely flow-rate independent).

Molecular size, branching (flow-rate dependent).

Stationary-phase characterization

Particle-size measurement (Coulter counter, SEM, FFF); MIP; Inverse SEC

Particle-size measurement; MIP

MIP, permeability

Linear (interstitial) velocity

0.5 mm/s 1 to 2 mm/s 0.05 mm/s

Typical column dimensions

300 × 7.5 mma 150 × 4.6 mm (packed columns)b

150 × 4.6 mm

Volumetric flow rate 1 mL/min 1 mL/min (packed columns)b

10 µL/min

Typical analysis time

10 mina 4 min 180 min

a Often several columns are used in series. b Typical dimensions of open columns for HDC would be 500 mm × 1 µm I.D. and the flow rate would be of

the order of 10 nL/min. Such experiments are highly impractical.

Page 46: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Chapter 2

44

Separations of particles in open-tubular columns are extremely difficult to perform, due

to the exceptionally narrow column diameters needed (internal diameter of the order of

1 µm) and the resulting brutal requirements on injection, detection and other aspects of

the instrumentation [8]. HDC can more conveniently be performed on columns packed

with non-porous particles. In such columns, the inter-particle space serves as a network

of narrow channels where the hydrodynamic separation takes place [9]. For packed

beds, the dimensions of R scale with the particle size. Columns with narrow and

uniformly sized flow-through channels require homogeneous packing of very small

particles, which is notoriously difficult. Packing capabilities for small particles dictate

the lower limit of selectivity attainable in packed-column chromatography. HDC has

been demonstrated using 1-µm non-porous particles where a value of R = 213 nm was

obtained [10]. Alternative stationary phases that provide suitable flow-through

characteristics may be applied to perform HDC. As a result of advances in micro

fabrication, chips and pillar-structured micro channels have been used with increasing

success to perform hydrodynamic separations [11,12]. However, R values suitable for

the separation of synthetic polymers are difficult to realize even with the most-advanced

contemporary fabrication technologies.

Monolithic columns, which have become increasingly popular as separation media for

LC [13], can also be considered for HDC. Hydrodynamic separations can be performed

in the macropores, which offer a highly interconnected network of flow-through pores

in the monolith. In contrast to the well-defined structure of packed beds with uniform

particles, the structure and porous properties of monoliths may vary with the type of

material and the preparation conditions. Although many different formulations and

preparation techniques for monoliths have been presented in recent years [14], silica

monoliths [15] and organic-polymer monoliths [16,17] have become most wide-spread

in liquid chromatography. Separations of polystyrenes with low dispersity based on

SEC-type partitioning have been demonstrated using silica monoliths featuring a

bimodal pore-size distribution (PSD) [18]. However, the small volume of stagnant

mobile phase in mesopores in comparison with the much larger external volume in the

flow-through pores (εi/εe << 1) limits the resolution and sample capacity for SEC

separations on this type of monolith. The ratio εi/εe is even more unfavorable for

Page 47: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Hydrodynamic chromatography of macromolecules using polymer monolithic columns

45

polymeric monoliths due to the absence of mesopores (microglobules in the polymeric

material) and thus the absence of stagnant zones in the column [19].

Separations of synthetic polymers by HDC using organic-polymer monoliths have been

investigated in this work. Polystyrene-co-divinylbenzene (PS-DVB) was selected as the

material of the monoliths based on its mechanical strength, solvent compatibility and

low susceptibility for enthalpic interactions with synthetic polymers. Due to the low

degree of dimensional shrinkage during polymerization, PS-DVB columns can be

prepared successfully in-situ in wide-bore stainless steel columns [20], which allows

usage in a manner analogous to contemporary high-performance SEC. We will attempt

to elucidate the separation mechanism by relating the observed selectivity to the

morphology and the pore-size distribution.

2.2 Experimental

2.2.1 Chemicals and materials

Styrene (PS, >99.5%), divinylbenzene (DVB, ~80%), dodecanol (98%), and azodiiso-

butyrodinitrile (AIBN, 98%) were purchased from Sigma-Aldrich (Zwijndrecht, The

Netherlands). Tetrahydrofuran (THF, 99.8% unstabilized HPLC grade), diethyl ether

(99.5%), and toluene (99.7%) were obtained from Biosolve (Valkenswaard, The

Netherlands). Ethanol (99.7%) was obtained from BDH Chemicals (Poole, England).

2,6-di-tert-butyl-4-methylphenol (ionol, 99%) was acquired at Acros (Geel, Belgium).

Polystyrene and poly(methyl methacrylate) standards with low dispersity and relative

molecular weights (Mr) ranging between 580 Da and 3.7 MDa were obtained from

Polymer Laboratories (Church Stretton, UK).

The monomers were purified by passing them over activated basic alumina followed by

a distillation under reduced pressure. AIBN was refluxed in diethylether for 30 min, re-

crystallized, and dried under vacuum before use. Helium 5.0 (99,999% Praxair,

Vlaardingen, The Netherlands) was used to degas the HPLC mobile phase prior to use.

The polymer standards were dissolved in THF.

Page 48: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Chapter 2

46

Stainless-steel column hardware (100 mm × 4.6 mm I.D. and 250 × 4.6 mm I.D.; SS

grade 316), including end fittings, and 2-μm frits was purchased from Restek

(Bellefonte, PA, USA).

2.2.2 Instrumentation

HPLC experiments were performed on a Shimadzu LC system (‘s Hertogenbosch, The

Netherlands) consisting of a system-controller (SCL10a), a micro-pump (LC10Advp), a

column oven (CTO7), and a UV detector (SPD10AVvp). Data acquisition was

performed using ClassVP software. Separations were performed applying 5-μL

injections, with the column placed in the oven thermostatted at 50°C. The flow rate was

varied between 10 and 500 μL/min to record calibration curves on different monolithic

materials. UV detection was performed at 260 nm or 280 nm.

Porosity data were obtained by using Pascal 140 and 440 mercury-intrusion

porosimeters (CE Instruments, Milan, Italy) for low- and high-pressure analysis,

respectively. The pore-size distribution was calculated using Pascal software using a

model based on the Washburn equation [21] assuming cylindrical pores and a surface-

contact angle of 140° for mercury with the monolith. The samples for mercury-intrusion

porosimetry (MIP) were obtained by extruding the monolithic columns from their steel

cladding by removing one end fitting of the column and applying a flow. The monolith

was cut into coarse pieces and dried overnight under vacuum.

2.2.3 Column preparation

Monolithic columns were prepared in-situ in 4.6-mm I.D. stainless-steel columns. The

composition of the polymerization mixture was 20% styrene, 20% divinylbenzene

(w/w). The percentage of toluene was varied in between 10 and 24% (w/w) to control

the pore size; dodecanol was used to make up to the composition (60% w/w minus the

toluene content). After purging the polymerization mixture with Helium for 10 min. it

was transferred into the column, closed by stainless-steel disks in lieu of porous frits.

Polymerization was performed in a water bath (with Neslab RTE-140 water circulator,

Thermo, Waltham, MA, USA) for 24 hours at 80°C. After completion of the

polymerization reaction, the stainless-steel disks were replaced by porous frits and the

columns were flushed with at least 50 column volumes of THF at 50°C and 10 µL/min.

Page 49: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Hydrodynamic chromatography of macromolecules using polymer monolithic columns

47

2.3 Results and discussion

2.3.1 Preparation and characterization of monoliths for HDC

To make the polymer HDC separations compatible with conventional detectors for the

characterization of macromolecules, such as refractive-index detection, viscometry, and

static light-scattering, the monoliths were developed in wide-bore (4.6 mm I.D.)

columns. No covalent bonding of the monolith with the wall was required since the

cross-linked polymer was significantly more swollen in the SEC mobile phase (THF).

For a “small” molecule (ionol) symmetric peak shapes were observed, indicating the

absence of channeling effects.

To create monoliths with macropores that give inter-particle space of comparable

dimensions to columns packed with sub-3 μm particles [7], the porogen ratio in the

polymerization mixture was adjusted while the monomer composition was kept

constant. A detailed description of pore formation and the effect of porogen

composition on the phase separation and consequently on pore and globule size is

provided by Eeltink et al. [22]. Figure 1 shows the intrusion curves (A) and the volume

distributions (B) of the monolithic materials as determined with mercury-intrusion

porosimetry (MIP). The macropore size of the monolithic materials decreased with

increasing toluene content in the reaction mixture. Remarkably, the monoliths with the

smallest mode pore size (< 500 nm) appear to have a bimodal pore-size distribution.

This is probably an artifact of the MIP measurements, due to compression effects of the

semi-flexible monoliths during the intrusion process. In the MIP experiment dried

monolith (under vacuum) is immersed in mercury and subsequently pressurized. At

initial conditions mercury does not protrude the pores. During the intrusion process the

macropores are filled with mercury at the pressure required to overcome the surface

tension of mercury to enter the pores. For the material with the largest pores (sample 1

with a macropore diameter of 1200 nm) this occurs at approximately 1.2 MPa. For

monoliths with smaller pores higher pressures are required, because the intrusion

pressure is inversely related to the pore size. However, these materials are compressed

before the onset of pore intrusion, as shown in Fig. 1a, and this will result in an

increasing bias to smaller pore size and even an apparent bimodal pore size (Fig. 1b).

Page 50: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Chapter 2

48

Fig. 1. (a) Intrusion curves and (b) pore-size distributions of monoliths with different macropore size as determined with mercury-intrusion porosimetry. Numbers correspond to materials depicted in Table 2.

Page 51: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Hydrodynamic chromatography of macromolecules using polymer monolithic columns

49

In the Appendix (section 2.5) it is discussed how extrusion data obtained by MIP may

be used to confirm sample compression during intrusion measurements. Caution should

be exercised in interpretation of the PSD from Fig. 1b, because this may be influenced

by the extent of compression at the moment of mercury intrusion. This may result in the

apparent narrow distribution, particularly for pores larger than the mode of PSD, as

observed for materials 6 and 7.

Flow-restriction measurements with THF were used to compare macropore sizes for

monolithic columns without errors introduced by compression of the monolith. The

Hagen-Poiseuille equation (Eq. 2) can be used to relate changes in flow resistance to

macropore-size, under the assumption that the monoliths have narrow pore-size

distributions. It relates backpressure (∆P) and average linear mobile-phase velocity (u0)

in cylindrical channels to solvent viscosity (η), column length (L), and channel radius

(r). This relationship has been demonstrated to hold for the pores in acrylic and styrenic

monoliths [23].

∆𝑃𝑢0

= 8η𝐿𝑟2

(2)

The ∆P/u0 ratio was determined for material 4, which was selected as reference for its

balance between pore size and compression effects. Under the assumption that the

morphology remains the same, Eq. 2 was used to convert the changes in ∆P/u0 ratio to

macropore size (diameter DP) for the other materials with r = DP/2. Table 2 summarizes

mode pore sizes as determined with mercury-intrusion porosimetry (Dmip) and flow-

resistance measurements (DP). The deviation between Dmip and DP becomes larger for

monoliths with smaller pores. This is indicative for compression effects in MIP.

The microscopic images obtained with scanning electron microscopy (SEM; see Fig. 2)

show the typical globular structures of the monoliths prepared with different porogen

composition. It was observed that monoliths with sub-micron pores have the same

globular structure as their highly-permeable counterparts, but the domain size (i.e. the

length scale of both pore and globular support) is different. Surface roughness of the

fused globular structure for sample 1 provides some void space with dimensions

significantly smaller than the through pores of 1.2 µm. Exclusion from such pores may

Page 52: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Chapter 2

50

contribute to the separation (SEC mechanism), but because the void volume is

obviously low compared to εe this contribution will be small. For monoliths with sub-

micron pores no large through pores were observed. Therefore, the mobile phase must

be flowing through the sub-micron pores, thereby providing a suitable environment for

HDC of polymers.

Fig. 2. Scanning electron micrographs of polymer monoliths prepared with different porogen ratios. (a) material 1: 10% toluene, 50% dodecanol, 20% PS, 20% DVB, (b) material 6: 18% toluene, 42% dodecanol, 20% PS, 20% DVB.

Table 2. Porous properties of monolithic materials as obtained with mercury-intrusion porosimetry and pressure measurements.

Monolithic material Wt% toluene in polymerization mixture

Mode pore size (nm) MIP Dmip

Mode pore size correction using Poiseuille, DP

1 10 1170 1194

2 12 550 571

3 14 305 321

4 15 258 258*

5 16 216 241

6 18 127 162

7 20 93 126

8 22 50 104

9 24 28 75

*reference value in DP calculation

Page 53: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Hydrodynamic chromatography of macromolecules using polymer monolithic columns

51

2.3.2 HDC separation of polymers

Polystyrene (PS) and polymethylmethacrylate (PMMA) standards were used to study

the separation performance of PS-DVB monoliths with different pore sizes. Figure 3

shows overlaid chromatograms obtained for individual PS standards obtained on a 100

mm × 4.6 mm I.D. monolithic column with DP of 258 nm (material 4) operating at flow

rates of 300 μL/min and 100 µL/min. Good peak symmetry, As = b / a < 1.24 (with b =

the peak width of the tail at 10% of peak height and a = the peak width at the front at

10% of the peak height) was observed. The peak width at half height for 20 kDa PS was

6.1 s for the 300 µL/min separation, yielding a (minimum) plate height of 18 µm.

Backpressure over the monolith was 120 bar for THF at 50°C at 300 µL/min.

Fig. 3. Hydrodynamic chromatographic separation of polystyrene standards on a 100 mm × 4.6 mm I.D.

polymer monolithic column with 260 nm macropores. Peak identification: 1 = ionol, 2 = 20 kDa PS, 3 = 200 kDa PS, 4 = 1120 kDa PS. Flow rates: a = 300 μL/min, b = 100 µL/min. Mobile phase: 100% THF at 50°C.

Compared to the best plate-height values, about 6 µm for HDC separations reported on

columns packed with 2.7-µm particles at a linear velocity of 0.5 mm/s or higher, the

peaks are significantly broader [7]. Since the mass-transfer contribution to the total peak

width can be neglected in HDC, peak dispersion for polymers can be attributed to the

Page 54: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Chapter 2

52

large eddy-diffusion contribution induced by the column inhomogeneity. No significant

changes in polymer separation efficiency have been observed with changes in the

mobile-phase velocity (Fig. 3) or macropore size of the different monolithic materials.

Ionol is commonly used as a marker for the mobile-phase volume and its dimensionless

retention was defined as τ = 1. Different elution volumes were observed for other low-

molecular-weight flow markers, such as benzene, toluene, and alkylbenzenes.

Alkylbenzenes were found to elute earlier with increasing molecular weight, supporting

a separation based on size rather than a separation based on (adsorption) interactions.

Similar behaviour was observed for commercially available SEC columns with PS-DVB

cross-linked porous packings (Appendix, section 2.5.2). Low-molecular-weight non-

polar markers can adsorb onto or diffuse into the cross-linked PS-DVB phase. In case of

the ionol both processes are unfavourable, because of its polarity. Different behavior of

the flow marker may cause an offset, which should be taken into account when

comparing phases with different cross-link densities or permeabilities. Monolithic

columns compared in this work were all prepared with the same monomer-to-cross-

linker ratio and they all behaved comparably.

High flow-rates could not be used on all monolithic materials, because of the high

backpressures generated in the narrow macropores and the concomitant risk of phase

compression. Separations of polystyrene standards were obtained with flow rates

ranging from 300 µL/min (material 2 and 3) down to 20 µL/min for material 9. The

effect of macropore size on the retention behaviour and on the selectivity window is

demonstrated by the calibration curves depicted in Figure 4. Monoliths with different

macropore sizes show selectivity across different molecular-weight ranges. Columns

with narrower macropores (and thus lower permeabilities) separate smaller polymers.

This concurs with the expectation of HDC being the dominating retention mechanism as

postulated in the introduction. Selectivity for the different monolithic materials is very

similar between 0.75 < τ < 0.95, but the corresponding molecular-weight ranges differ

by more than one order of magnitude. For each monolith the effective range of

separation covers at least 2 orders of magnitude in polystyrene molecular weight. For

values of τ < 0.75 differences in the shapes of the calibration curves were observed. For

the materials with larger macropores (materials 3 through 6) the separation window

Page 55: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Hydrodynamic chromatography of macromolecules using polymer monolithic columns

53

extended down to τ = 0.65, which is extraordinary for HDC-type separations.

Separations at the upper end of the calibration curve have been observed to be flow-rate

dependent in previous studies in which packed columns were used [7,10]. Comparison

of the calibration curves in a universal format provides a better means to evaluate this

hypothesis using monolithic columns. In a universal calibration graph the aspect ratio λ

is displayed on the y-axis, which allows for a direct comparison of HDC-type

separations irrespective of macropore size or molecular weight of the analyte polymer.

Fig. 4. Effect of macropore size of monolithic columns on HDC selectivity for polymers with Mr ranging

between 990 Da and 3.7 MDa. Numbers correspond to materials depicted in Table 2. Monolith materials 2 and 3 were operated at 300 µL/min, materials 5 through 8 at 50 µL/min. and material 9 at 20 µL/min.

The size of the flow-through channel and that of the solute molecules in solution must

be known to calculate λ. Neither is obvious in the case of monolithic columns and

dissolved synthetic polymers. Irregular shapes of the macropores and uncertainties

about the morphology prevent a straightforward calculation of the hydraulic radius (i.e.

the surface-to-volume ratio), which has been successfully used to calculate the

equivalent capillary size for packed beds with non-porous particles [7]. The mode of

pore size from MIP is expected to be less accurate when either the pore-size distribution

in the monolith is broad or when compression occurs during MIP before the mode of

Page 56: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Chapter 2

54

pore size is reached. Therefore macropore size DP as determined from flow-restriction

measurements was used in calculation of λ (Table 2). This is appropriate, because

backpressure depends on the restriction in the flow-through pores where HDC takes

place by definition.

Polymers in solution do not behave as hard spheres, but as flexible chains following

random coil statistics. Excluded volume of the polymer chain contributes to the coil size

and varies with solvent and polymer chemistry [24]. The distance of exclusion near a

surface has been used successfully in modeling retention behavior. This size is

commonly referred to as the effective size and is conveniently defined relative to the

radius of gyration for linear random-coil polymers [25] as

𝑟𝑒𝑓𝑓 = √𝜋2𝑟𝑔 (3)

The relation between molecular weight (M) and radius of gyration (rg) in THF as

obtained using light scattering [26] was substituted in Eq. 3. The effective size (reff) of

PS and PMMA polymer standards was calculated using Eq. 4 and Eq. 5.

𝑟𝑒𝑓𝑓,𝑃𝑆 = √𝜋2

0.0118 𝑀0.600 (4)

𝑟𝑒𝑓𝑓,𝑃𝑀𝑀𝐴 = √𝜋2

0.0110 𝑀0.596 (5)

The same calibration curves for columns with various pore sizes in Fig. 4 are presented

in the form of a universal HDC calibration plot in Fig. 5a. A theoretical curve for HDC

on packed columns (calculated using Eq. 1 and C = 2.7) is provided for reference

purposes [9]. Experimental data match the theoretical curve for HDC separation best for

solutes in the center of the selectivity window of the columns (around λ = 0.1). The

slope in this central region is identical for all curves, which suggests that the balance

between size exclusion and hydrodynamic effects is identical to that encountered with

HDC in capillaries and packed beds.

The experimental curves do not coincide with the theoretical curve, with an offset

towards lower elution volumes that increases with macropore size. This offset is

Page 57: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Hydrodynamic chromatography of macromolecules using polymer monolithic columns

55

believed to result from additional size-exclusion effects. For λ < 0.1 size exclusion of

the polymer from the walls of flow-through channels is the main mechanism of

separation [6]. Modeled retention assumes surface exclusion in cylindrical channels.

Globular morphology and a distribution of the pore sizes (PSD) of the monolith,

however, provide an increased volume for SEC effects. For macropores with a large

average diameter this may result in increased selectivity at low λ. The broad PSD for

materials 1 and 2 (Fig. 1B) and increased selectivity of material 2 for λ < 0.02 (Fig. 5a)

illustrate this effect on monolithic columns. Size-exclusion effects other than wall

exclusion in flow-through pores observed for λ < 0.02 decrease with macropore size and

account for < 5% in elution volume for all monoliths. This effect is different from

exclusion in HDC using columns packed with non-porous particles, which is limited to

the geometric exclusion volume of spheres and scales with particle size [27]. It is

dependent on the morphology of the monolith and may, therefore, be reduced further by

optimization of the column-preparation process.

2.3.3 Flow-rate dependence in polymer separations

Flow-rate dependent elution behavior was observed for polymers separated at λ ~ 0.2

and above (Figs. 5 and 6). Hydrodynamic interactions (particle rotation, drag, flow-

induced radial force, etc.) become significant for solutes approaching the flow-through

channel size and depend on both flow rate and solute characteristics [9]. Only when

these contributions hold universally, retention will scale with λ and a single constant

can be used to account for hydrodynamic interactions in Eq. 1 (e.g. C = 2.7, assuming

rotating, non-draining behaviour of polymers in cylindrical channels according to

Dimarzio & Guttman [28]). However, this universality fails for λ > 0.4 and the

selectivity becomes dependent on either macropore or polymer size (Fig. 5a). For

materials 5 through 8 the calibration curve for monoliths with smaller macropores

demonstrates stronger reversal due to stronger retardation by hydrodynamic effects. The

same calibration curves acquired at 20 µL/min (Fig. 5b) closely resemble the theoretical

curve, which predicts strong retardation at λ > 0.2 after the assumption of non-draining

polymer coils. At λ = 0.4 reversal of the calibration curves towards higher τ values is

observed. Both PS and PMMA polymers are present as random coils under good-

solvent conditions and their flow-rate dependent elution behaviour is identical (Fig. 6).

Page 58: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Chapter 2

56

Fig. 5. Universal retention plot showing the calibration curves on monoliths with different macropore size. (a) Materials and LC condition similar as in Fig. 4. (b) Reversal of calibration curves for material 5 through 8

when operating at a flow rate of 20 μL/min.

Page 59: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Hydrodynamic chromatography of macromolecules using polymer monolithic columns

57

Fig. 6. Flow-rate dependent calibration curves of PS and PMMA polymers on monolith material 7 (a) and corresponding chromatograms for PS standards 1.1 MDa, 523 kDa, 200 kDa, 71 kDa, 20 kDa, 7 kDa and 2

kDa at a flow rate 50 μL/min (b). Column dimensions: 250 mm × 4.6 mm I.D. monolithic column.

Page 60: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Chapter 2

58

Flow-rate dependent elution of high-molecular weight polymers has been observed for

separations under wall-exclusion (HDC-like) conditions in other studies

[7,10,29,30,31]. It has been attributed to either deformation or elongation of the

polymer coil. The time-averaged coil size measured perpendicular to the flow direction

will decrease when the polymer molecules are subjected to shear stress. To describe

these effects the Deborah number (De) can be introduced [29]. De expresses the ratio of

hydrodynamic (elongation) forces to Brownian (relaxation) forces. For dilute polymer

migrating through packed beds it can be described as follows

𝐷𝑒 = 𝐾𝑑𝑒𝑏ν𝑑𝑝

6.12 Φ η 𝑟𝑔3

𝑅 𝑇 (6)

where Kdeb is a constant (with a typical value of 6 [29]), ν is the superficial solvent

velocity, dp the particle size of the packing, Φ the Flory-Fox parameter, η the solvent

viscosity, rg the radius of gyration of the polymer, R the gas constant and T the absolute

temperature.

Application of Eq. 6 for monoliths is complicated, because reference data only exist for

packed beds [29,32]. In the elongation factor in Eq. 6 (Kdeb ν /dp) the particle size can

be replaced by the hydrolic radius (i.e. the radius of a capillary with an identical

surface-to-volume ratio). For a packed bed of non-porous monodisperse particles Rh =

2/9 dp assuming a porosity of 0.4 [5,7]. This relation was used successfully in

comparing HDC selectivity between packed beds and capillary columns, but may be

used for monoliths as well. For monoliths Rh = DP / 2 was used. Kdeb is a constant that

accounts for the effect of pore structure on elongation. It is determined semi-empirically

by matching selectivity changes in HDC for well characterized systems with De = 0.5

[32]. Since Kdeb could not be established accurately for monoliths, the typical value for

particle-packed beds was used.

Random spherical coils prevail at low values of De. The onset of polymer deformation

is commonly assumed to occur around a value of De of 0.1. At still higher values (De >

0.5) the chains become completely elongated, resulting in a separation mechanism

termed “slalom chromatography” to picture the migration of flexible, stretched polymer

chains through the interstitial channels of the support [31]. Liu et al. describe a system

Page 61: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Hydrodynamic chromatography of macromolecules using polymer monolithic columns

59

with λ values on the order of 0.1 (dp = 15 µm, Rh = 3.3 µm, polystyrene rg = 125 to 450

nm). On the 4.6-mm I.D. column used the onset of slalom chromatography was

observed for flows in excess of 0.1 mL/min. The present separations on monoliths differ

significantly from those described by Liu on packed columns in terms of analyte

molecular weight (De ÷ rg3) and aspect ratio (λ). Uliyanchenko et al. reported on slalom

chromatography for polymers in the same molecular-weight range as used in the present

study. They used contemporary HPLC conditions (dp = 1.7 µm, Rh = 0.38 µm) [30] with

a flow rate of 1 mL/min on 4.6-mm I.D. columns, which corresponded to De = 0.6 for

the 2.0-MDa PS.

Deborah values were calculated for separations on monoliths with different macropore

sizes (see Appendix, section 2.5.3). At the point where the calibration curves in Fig. 5

show a reversal towards higher elution volumes the De values were almost always much

lower than 0.1. Thus, the present observations are not akin to the slalom

chromatography described elsewhere [31]. Conventionally, De numbers are calculated

for channels much larger than the diameter of the polymer coil (λ < 0.2). In that case the

elongation (Kdeb × ν /dp) can be assumed not to depend on the coil size. In the present

study we consider phenomena that occur for much higher λ values. Clearly, the

straightforward calculation of De values does not suffice to describe the observations in

such narrow channels, where the shear stress caused by the Poiseuille flow profile only

affect the periphery of the polymer coil and rotation of the coil is largely prohibited.

Very large polymers with λ ≈ 1 elute faster than the average fluid velocity (τ = 1; see

Fig. 5). This suggests that the polymer coils are “reptating” [33,34] through the

stationary-phase channels without significant restriction. Higher flow rates cause an

increase in the migration rate, which suggests that chain segments of the reptating coil

move towards the faster-moving central part of the Poiseuille flow profile (assuming

that the non-draining assumption holds). It appears that they no longer possess the

spherical coil geometry that prevails under equilibrium conditions at De < 0.1 in the

absence of constriction. The chromatographic selectivity arising from coil-reptation-

based elution is large and expected to cover the complete elution window of HDC. This

is supported by calibration curves obtained at different flow rates for materials 5

through 8 (cf. λ > 0.4 range in Fig. 5). It is not expected that a fully flexible polymer

such as polystyrene will uncoil at conditions of moderate constriction (λ ≈ 1), because

Page 62: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Chapter 2

60

of fast relaxation by Brownian motion under the conditions used here. In reptation or

translocation of charged polymers and biomaterials, however, complete elongation may

readily occur as a result of reduced flexibility in the polymers, highly constricted pores

or conditions featuring much slower relaxation due to Brownian motion [35, 36, 37, 38].

A different mechanistic explanation is therefore desired for flow-rate sensitive polymer

separation in monoliths.

A useful concept from the theory of flow-rate-dependent migration in HDC is “stress-

induced diffusion” (SID) [9,39]. This concept implies that polymers in Poiseuille flow

migrate away from the channel walls, driven by the lower entropy as a result of

elongation and reduced orientation by shear stress in this region. Migration towards the

channel center (and avoiding the elongating shear forces) leads to an increase in entropy

[40]. This effect is strongest at high shear rates and for high molecular weights. The

same arguments can be applied to reptating coiled polymers in confined channels.

Relaxation towards a spherical coil sampling the full channel diameter (natural trend to

increased entropy) will result in strong internal forces near the channel walls (induced

decrease in entropy). This effect is in agreement with the results for polymers eluted

from confined channels in monoliths in Fig. 5. Higher Mr polymers eluting at identical λ

from larger macropores get stronger deformed by SID due to their longer relaxation

times and the calibration curve demonstrates less reversal. The mechanism described

here is also in agreement with topology based separation by MTF [41,42]. Branched

polymers with identical hydrodynamic size but increased segment may exhibit stronger

resistance to SID compared to linear polymers under identical conditions. The

mechanism of an entropy-barrier was postulated before [41], but emphasized the role of

migration through orifices as compared to SID which takes place in continuous narrow

channels.

Page 63: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Hydrodynamic chromatography of macromolecules using polymer monolithic columns

61

2.4 Conclusions

Monolithic columns for separations of macromolecules were successfully prepared in-

situ in wide bore (4.6-mm I.D.) stainless-steel columns. The selectivity window

depended strongly on the size of the macropores tuned by the ratio of porogens. HDC is

the dominant mechanism of separation, since the mesoporous volume required for SEC

was too small. Also, calibration curves match with elution behavior as expected for

HDC separation up to λ = 0.2. Only for large-macropore monoliths, a deviation in

retention behavior is observed for small polymers (Mr < 20 kDa), which may be

explained by a combined HDC-SEC mechanism for λ < 0.02.

Macropores with much smaller hydrolic radii relative to packed columns were obtained

and therefore selectivity for lower-Mr macromolecules can be obtained. Our approach

allowed the preparation of monoliths with a pore size as small as 75 nm and a selectivity

window in HDC corresponding to a theoretical column packing with 0.17 µm particles

(DP = 4/9 dp). These monoliths have limited applicability for fast size-based separations

due to their low permeability. Monoliths with 258 nm macropores yielded polymer

separations in the molecular weight-range common for SEC separations. Selectivity

equivalent to 0.6 µm particles was demonstrated on this material with only 120 bar for

THF at 0.5 mm/s on a 100 mm column (Fig. 3). Size-based separations featuring

selectivity beyond what is possible with contemporary column-packing techniques are

readily obtained. The efficiency of polymers monoliths for HDC may be improved

further by optimization of the column heterogeneity.

For high-molecular weight polymers (Mr > 300,000 Da) the separation in monoliths

with confining channels strongly depended on flow rate. This situation differs from

other flow-rate dependent in that the shear rate is not identical throughout mobile phase

sampled by the coil. Response to the high shear rate experienced in the polymer-coil

periphery was suggested to result in departure from thermodynamic equilibrium

geometry and flow-rate dependent elution. This hydrodynamic-based explanation was

found to be in semi-quantitative agreement with experimental results for linear

polystyrene polymers.

Page 64: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Chapter 2

62

2.5 Appendix

In this supporting information extrusion data is provided from mercury intrusion

porosimetry. It is explained how this information may be helpful to confirm

compression of monolithic samples during porosimetry measurements.

Separation of alkylbenzenes on cross-linked polystyrene-co-divinylbenzene monoliths

and SEC-particles is presented to demonstrate the absence of adsorption effects and

diffusion of small molecules into the stationary phase compared to non-porous silica

columns.

The calculation of Deborah numbers is explained for polymer separations on monolithic

columns. Threshold values for molecular weight and λ are presented for the separation

conditions that were used in obtaining calibration curves for monolithic columns with

various macropore sizes.

2.5.1 Mercury intrusion and extrusion

Mercury extrusion data for two monoliths is presented in support of the discussion on

compression of monoliths. During the intrusion measurement the pressure was

increased up to 300 MPa. At this pressure porosity in pores with a diameter down to 5

nm can be measured. Porosity data for monolithic materials 7 and 8 (Table 2) was

obtained during both pressure increase and decrease and is presented in Fig. S-1.

Once the pressure is decreased, mercury will be extruded from pores again driven by its

surface tension. The pressure where extrusion will always be somewhat lower compared

to the intrusion pressure. Compression of the material during intrusion measurement

will result in a higher pressure required for mercury intrusion, because the pores become

smaller when the material is compressed. If the compression is a reversible process, the

sample will reassume its equilibrium dimensions once it has been intruded by the

mercury under high pressure. Little or no effect of compression is expected for the

extrusion pressure. The higher pressure difference between intrusion and extrusion

pressure for material 8 supports the assumption that this material suffers more

compression compared to material 7 at the moment of mercury intrusion.

The recovery may depend on actual pore geometry as well as the rate at which pressure

was reduced. For the results presented here pressure was decreased at a faster rate

Page 65: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Hydrodynamic chromatography of macromolecules using polymer monolithic columns

63

compared to the pressure increase. A study of mercury extrusion under well controlled

conditions can reveal useful information with respect to sample compression during the

intrusion measurement. Unfortunately, such data was not acquired for the work here,

because the hypothesis of compression was formed after most of the measurements

were completed.

Fig. S-1. Mercury intrusion during pressure increase and decrease

Page 66: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Chapter 2

64

2.5.2 SEC separation of alkylbenzenes and solvents on monolith

The elution for ionol, benzene, toluene and alkylbenzenes was measured to confirm that

absence of adsorption effects. Ionol, benzene, toluene, ethylbenzene, propylbenzene,

butylbenzene and hexylbenzene were diluted in THF before injection at a concentration

of about 1 mg/ml. Detection was performed by UV at 260 nm. All separations were

performed at room temperature to minimize axial diffusion. Column dimensions were

150 × 4.6 mm I.D. in each case.

(A) Monolithic material 4, DP 258 nm, 100 µL/min THF

(B) 106 Å PLgel, dp 10 µm, 200 µL/min THF

(C) Non-porous silica, dp 1.0 µm, 100 µL/min THF

The elution order in Fig. S-2 and S-3 was, from left to right, ionol, hexylbenzene,

butylbenzene, propylbenzene, ethylbenzene, toluene/benzene with the lowest peak

height for benzene. In Fig. S-4 all elute at the same volume, because the samples do not

diffuse into or adsorb onto the non-porous silica.

Fig. S-2. Separation of small molecules on cross-linked PS-DVB monolith (A)

Page 67: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Hydrodynamic chromatography of macromolecules using polymer monolithic columns

65

Fig. S-3. Separation of small molecules on cross-linked PS-DVB SEC particles (B)

Fig. S-4. Separation of small molecules on non-porous silica (C)

Page 68: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Chapter 2

66

2.5.3 Deborah numbers

The polystyrene molecular weight corresponding to a Deborah value of 0.1 was

calculated using Eq. 6. This specific value of De = 0.1 was used, because it provides the

lower limit where the effects of polymer deformation may be observed. For each

monolith the flow rate that was used to obtain its calibration curve in Fig. 5a was used.

Common variables used in calculating De were a viscosity of 0.356 Cp for THF at

50°C, a Flory-Fox parameter of 2.5⋅1023 mol-1 and fictive particle size of dp = 4/9 DP.

The results are presented in Table S-1 and Fig. S-5. The onset of deformation is reached

at increasingly lower molecular weight with smaller macropore size. However, it was

not reached within the classic HDC selectivity range for separations on monolithic

columns.

The mobile phase flow-rate directly impacts the expected onset of deformation.

Deborah scales linear with both particle size (channel size) and average linear mobile-

phase velocity u0. In practice the flow rate and thus u0 are a result from backpressure

limitations and permeability of the column. According to Hagen-Poiseuille (Eq. 2) u0

scales quadratic with increasing pore size at identical backpressure. Therefore,

deformation of analytes is more commonly observed for highly permeable stationary

phases with large interstitial pores. De > 0.1 is reached at much lower backpressure,

within the range of common separation conditions.

Table S-1. Lower-limits for polymer deformation according to Deborah-number calculation, expressed in PS molecular weight and λ.

Monolithic material

DP

(nm) Flow rate (µL/min)

De = 0.1 PS Mr (MDa)

De = 0.1 λ

1 1194

2 571 300 2.0 0.22

3 321 300 1.45 0.32

4 258

5 241 50 3.4 0.72

6 162 50 2.7 0.93

7 126 50 2.35 1.09

8 104 50 2.1 1.25

9 75 20 3.0 2.15

Page 69: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Hydrodynamic chromatography of macromolecules using polymer monolithic columns

67

Fig. S-5. Calibration curves on monoliths with different macropore size with diamonds indicating

De = 0.1 for conditions described in Table S-1.

References

[1] A.M. Striegel, W.W.Yau, J.J.Kirkland and D.D.Bly, Modern Size-Exclusion Liquid Chromatography,

Second edition, Wiley, New York, 2009.

[2] T. Chang, Adv. Polym. Sci., 163 (2003) 1.

[3] K.O. Pedersen, Arch. Biochem. Biophys., Suppl., 1 (1962) 157.

[4] E.A. DiMarzio, C.M. Guttman, J. Polym. Sci., Part B, 7 (1969) 267.

[5] A.J. McHugh, CRC Crit. Rev. Anal. Chem., 15 (1984) 63.

[6] R. Tijssen, J. Bos, M.E. Van Kreveld, Anal. Chem. 58 (1986) 3036.

[7] G. Stegeman, R. Oostervink, J.C. Kraak, H. Poppe, K.K. Unger, J. Chromatogr. 506 (1990) 547.

[8] J. Bos, R. Tijssen, M.E. van Kreveld, Anal. Chem. 61 (1989) 1318.

[9] G. Stegeman, J.C. Kraak, H. Poppe, R. Tijssen, J. Chromatogr. A 657 (1993) 283.

Page 70: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Chapter 2

68

[10] E. Venema, J.C. Kraak, H. Poppe, R. Rijssen, J. Chromatogr. A 740 (1996) 159.

[11] E. Chmela, R. Tijssen, M.T. Blom, J.G.E. Gardeniers, A. Van den Berg, Anal. Chem. 74 (2002) 3470.

[12] M. De Pra, W. De Malsche, G. Desmet, P.J. Schoenmakers, W. Th. Kok, J. Sep. Sc. 30 (2007) 1453.

[13] G. Guiochon, J. Chromatogr. A 1168 (2007) 101.

[14] D. Sykora, F. Svec, in: F. Svec, T.B. Tennikova, Z. Deyl (Eds.), Monolithic materials: preparation,

properties and applications, Chapter 20, Elsevier, Amsterdam, 2003.

[15] K. Nakanishi, N. Soga, J. Am. Ceram. Soc. 74 (1991) 2518.

[16] S. Hjertén, J.-L. Liao, R. Zhang, J. Chromatogr. 473 (1989) 273.

[17] F. Svec. J.M.J Fréchet, Anal. Chem. 64 (1992) 820.

[18] K. Ute, S. Yoshida, T. Kitayama, T. Bama, K. Harada, E. Fukusaki, A. Kobayashi, N. Ishizuka, H.

Minakuchi, K. Nakanishi, Polym. J. 38 (2006) 1194.

[19] J. Urban, S. Eeltink, P. Jandera, P.J. Schoenmakers, J. Chromatogr. A. 1182 (2008) 161.

[20] M. Petro, F. Svec, I. Gitsov, J.M.J. Fréchet, Anal. Chem. 68 (1996) 315.

[21] E.W. Washburn, Physical Rev., 17 (1921) 273.

[22] S. Eeltink, J.M. Herrero-Martinez, G.P. Rozing, P.J. Schoenmakers, W. Th. Kok, Anal. Chem. 77

(2005) 7342.

[23] C. Viklund, K. Irgum, F. Svec, J.M.J. Fréchet, Chem. Mater. 8 (1996) 744.

[24] P.J. Flory, Principles of Polymer Chemistry, Cornell University Press, Ithaca, NY, 1971.

[25] M.E. van Kreveld, N. Van den Hoed, J. Chromatogr., 83 (1973) 111.

[26] C. Jackson, Y.-J. Chen, J.W. Mays, J. Appl. Pol. Sci., 61 (1996) 865.

[27] W. Cheng, J. Chromatogr. 362 (1986) 309.

[28] E.A. DiMarzio, C.M. Guttman, J. Chromatogr. 55 (1971) 83.

[29] D.A. Hoagland, R.K. Prud’homme, Macromolecules 22 (1989) 775.

[30] E. Uliyanchenko, P.J. Schoenmakers, S. van der Wal, J. Chromatogr. A 1218 (2011) 1509.

[31] Y. Liu, W. Radke, H. Pasch, Macromolecules 38 (2005) 7476.

[32] R. Haas, F. Durst, Rheol. Acta 21 (1982) 566.

[33] R. Tijssen and J. Bos, in: F. Dondi and G. Guiochon (eds.), Theoretical Advancement in

Chromatography and Related Separation Techniques, Kluwer, Dordrecht, 1992, pp. 397-441.

[34] P.G. De Gennes, J. Chem. Phys. 55 (1971) 572.

[35] P.G. De Gennes, Science 276 (1997) 1999.

[36] W. Reisner, K.J. Morton, R. Riehn, Y.M. Wang, Z. Yu, M. Rosen, J.C. Sturm, S.Y. Chou, E. Frey, R.H.

Austin, Phys. Rev. Lett. 94 (2005) 196101.

[37] T. Su, P.K. Purohit, Phys. Rev. E 83 (2011) 061906.

[38] C.T.A. Wong, M. Muthukumar, J. Chem. Phys. 133 (2010) 045101.

[39] A.B. Metzner, Y. Cohen, C. Rangel-Nafaile, Non-Newtonian Fluid Mech. 5 (1979) 449.

[40] M. Muthukumar, A. Baumgartner, Macromolecules 22 (1989) 1937.

[41] D.M. Meunier, P.B. Smith, S.A. Baker, Macromolecules 38 (2005) 5313.

[42] R. Edam, D.M. Meunier, E.P.C. Mes, F.A. Van Damme, P.J. Schoenmakers, J. Chromatogr. A 1201

(2008) 208.

Page 71: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

69

Chapter 3: Branched-Polymer Separations using

Comprehensive Two-Dimensional Molecular-Topology

Fractionation × Size-Exclusion Chromatography

Abstract

Branching has a strong influence on the processability and properties of polymers.

However, the accurate characterization of branched polymers is genuinely difficult.

Branched molecules of a certain molecular weight exhibit the same hydrodynamic

volumes as linear molecules of substantially lower weights. Therefore, separation by

size-exclusion chromatography (SEC), will result in the co-elution of molecules with

different molecular weights and branching characteristics. Chromatographic separation

of the polymer molecules in sub-micron channels, known as molecular-topology

fractionation (MTF), may provide a better separation based on topological differences

among sample molecules. MTF elution volumes depend on both the topology and molar

mass. Therefore co-elution of branched molecules with linear molecules of lower molar

mass may also occur in this separation. Because SEC and MTF exhibit significantly

different selectivity, the best and clearest separations can be achieved by combining the

two techniques in a comprehensive two-dimensional (MTF×SEC) separation system. In

this work such a system has been used to demonstrate branching-selective separations of

star branched polymers and of randomly long-chain branched polymers. Star-shaped

polymers were separated from linear polymers above a column-dependent molecular

weight or size.

Page 72: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Chapter 3

70

3.1 Introduction

Knowledge of the relationships between polymerization conditions and functional

properties of the polymers being formed enables polymer chemists to make materials

that are largely optimized for their application. High-performance polymers meet

specific needs in the market place. The desired properties of such polymers are typically

achieved by optimizing the parameters of the polymerization process. Such an

optimization can be performed much more efficiently when key structural parameters

affecting polymer properties are understood. Meaningful structure-property

relationships can only be developed if the key structural parameters can be measured. In

the case of branched polymers, a more detailed description of branching, beyond a basic

estimate of the average number of branch points per molecule, is required. Distributions

of the molecular properties must be revealed, which requires that the molecules with

different degrees of branching be separated, ideally in combination with selective

detection techniques. Knowledge of detailed molecular characteristics and their effect

on functional properties will ultimately allow the design of high-performance polymers.

Spectroscopic techniques (e.g. Fourier-transform infrared, FTIR, or nuclear magnetic

resonance, NMR) and physical measurements (e.g. light scattering or viscometry) are

used on a routine basis to characterize the overall (or average) molecular structure of

polymers. Using hyphenated techniques (typically combinations of a chromatographic

separation with one or more spectroscopic or physical methods) more information

concerning the distributed properties may be obtained. Size-exclusion chromatography

(SEC) with light scattering and/or viscometry detection is commonly used to

characterize long-chain branching (LCB) in high-molecular-weight polymers [1,2,3].

The characterization of LCB in polymers is of particular interest, because of the

influence of LCB on processing properties, such as zero-shear viscosity and melt

strength. Branching factors based on the Zimm-Stockmayer theory [4] may be

calculated when a linear-polymer (reference) sample with identical chemistry or its

Mark-Houwink parameters are available. These can subsequently be converted to

branching frequencies if assumptions are made regarding the functionality of the

branching points and the average branch length. SEC with selective detection is,

however, not able to fully characterize branched polymers. Separation by size of the

Page 73: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Branched-Polymer Separations using Comprehensive 2D MTF × SEC

71

unperturbed chain in solution yields fractions containing molecules with equal

hydrodynamic volumes, but with different topologies and molecular weights. This

distribution cannot be characterized by selective detection techniques. For example,

light scattering only provides the weight-average molecular weight for the ensemble of

chains eluting in each SEC fraction. Molecular-weight polydispersity at a given SEC

elution volume was recently confirmed by comparing selective-detection techniques

that yielded different types of molecular-weight averages (weight average from light

scattering and number average from viscometry, [5]). The authors demonstrated that the

so-called local polydispersity was affected by the distribution of the degree of branching

and the functionality. NMR is an alternative technique for determining the structure and

the frequency of branch points, but the technique has some limitations. A high-field

instrument is needed to detect and quantify low levels of LCB, but discrimination of

different branch lengths is still not possible when branches are longer than a few carbon

atoms [6]. Most importantly, NMR provides only an average number of branches per

molecule.

Multi-dimensional separations can be used to study complex polymers that feature more

than one distribution simultaneously. In a comprehensive two-dimensional separation

system, denoted by the “×” sign, every part of the sample is subjected to two

independent mechanisms and the separation obtained in the first dimension is

maintained in the final two-dimensional chromatogram) [7]. The peak capacity is

increased substantially by comprehensive operation of multi-dimensional separations.

However, the separation power is only used efficiently when different selectivity in

each separation dimension allows the sample to be separated among its distributions of

interest [8,9]. Only in orthogonal separations the retention times in the different

dimensions are by definition completely independent (uncorrelated). Although most

multi-dimensional separation systems are not orthogonal, confounded distributions that

remain unresolved in a single separation step can be separated using two independent

separations with different selectivity. Therefore, complex polymers with distributions in

distinct molecular properties can successfully be resolved using multi-dimensional

systems. Separations by functionality [10] and chemical composition [11] have, for

example, been combined with separations according to size using SEC to fully elucidate

two mutually dependent distributions.

Page 74: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Chapter 3

72

Branched polymers can also be separated using combinations of independent

separations, such as interactive liquid chromatography and SEC, in a comprehensive

two-dimensional setup. Selectivity for branched versus linear polymers has resulted

from differences in the number of repeat units, number of branch points or size in

solution. Star polymers prepared by coupling living polystyrene anions were separated

by an off-line combination of temperature-gradient interaction chromatography (TGIC)

and SEC [12]. The TGIC separation is thought to be based on molecular weight, while

SEC is based on the size of molecules in solution. The relationships between molecular

weight and hydrodynamic volume are different for branched and linear polymers

allowing separations of differently branched polymers by a combination of both

methods. Similar star polymers of lower molecular weights were separated on-line by

liquid chromatography at the critical composition in combination with either SEC or

TGIC (LCCC×SEC or TGIC×LCCC [13]). In the LCCC separation, branched polymers

were separated by interaction of the apolar side-groups at the coupling agent. The

techniques described here yielded good separations for branched homo-polymers with

numerous branches and chemically different branch points or end groups. High-

molecular-weight polymers, with very little long-chain branching (LCB), or without

functional groups at the branch points or chain ends of different polarity cannot be

separated using these techniques.

For LCB polymers, complete separation may be obtained when the polymer is also

separated based on branching parameters. Such a separation has previously been

demonstrated on monolithic columns containing sub-micron macro pores [14] and on

columns packed with sub-micron particles [15]. Both separation systems featured sub-

micron flow channels. Polymers above a stationary-phase dependent molecular weight

become retained at low flow rates. Branched polymers were found to elute much later

than linear ones of the same molecular weight. This separation method was termed

molecular-topology fractionation (MTF) and it was thought to result from the topology-

dependent relaxation-time spectrum of polymers in dilute solution [15]. The word

topology reflects the geometrical structure of the polymer molecules, more specifically

the branch length, frequency and functionality of the branch points. Separation of

branched polymers by MTF can only be applied to samples with very narrow

molecular-weight distributions, since the degree of polymerization also affects the

Page 75: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Branched-Polymer Separations using Comprehensive 2D MTF × SEC

73

retention. Off-line fractionation of LCB polymer by SEC and re-injection of the

fractions in MTF was used to demonstrate the differences in selectivity of the two

techniques for LCB polymers [15]. Similar to the comprehensive two-dimensional

separation systems (described in the previous paragraph) for separating star polymers,

samples featuring LCB could be resolved when the separation dimensions display

significantly different selectivity towards long-chain branching and hydrodynamic size.

In this paper, the separation of long-chain branched polymers using MTF×SEC will be

demonstrated. Knowledge of the relationship between molecular weight, hydrodynamic

size and branching will be used to interpret the selectivity in MTF separations. The

separation of polymers with similar hydrodynamic size, but different topologies is

demonstrated for star polymers with narrow molecular-weight distributions. Results on

the separation of randomly long-chain-branched polymers and star polymers will be

used to discuss the selectivity of MTF and the applicability MTF×SEC for the

separation of complex samples of branched polymers.

3.2 Experimental

3.2.1 Samples and materials

The eluent for MTF and SEC separations was non-stabilized HPLC-grade

tetrahydrofuran (THF; Biosolve, Valkenswaard, The Netherlands); it was continuously

degassed by purging with helium 5.0 (99,999% Praxair, Vlaardingen, The Netherlands).

Sample polymers were dissolved in HPLC-grade THF stabilized with 250 ppm butyl-

hydroxylated toluene to prevent degradation by radicals. Narrowly distributed linear

polystyrene standards (Polymer Laboratories, Church Stretton, UK) were used to study

retention behaviour. These standards were dissolved at concentrations of 0.5 mg/mL. A

nominal three-arm star polystyrene sample was obtained from Polymer Source (Dorval,

Canada) and used at a concentration of 1.0 mg/mL. This star polymer was synthesized

by coupling of anionically polymerized arms with a tri-functional agent (α,α’,α’’-

trichloromesitylene). The manufacturer specified a nominal molar mass of 1,480 kg/mol

for the precursor arms. However, thorough analysis using size-exclusion

chromatography with low-angle light scattering and differential viscometry revealed an

arm molar-mass closer to 1,250 kg/mol. The sample composition was determined from

Page 76: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Chapter 3

74

the same experiment. Integration of the concentration signal revealed ~5% to be

uncoupled precursor, ~45% linear polymer with double the precursor molecular weight

and a remainder of three-arm coupling product. A small amount of higher-coupling

products as a result of lithium-halide exchange [16,22] was evident from the overall

molecular weight of the star-polymer sample as estimated by SEC with light-scattering

detection. A four-arm coupling side-product by lithium-halide exchange is expected to

have all arms coupled in one functional centre. The concentration of this large-molecule

fraction could not be determined quantitatively by SEC. The reaction scheme of the

coupling and analysis results have been presented by Meunier et al. [15]. Polystyrene

with a high LCB frequency was obtained from the Dow Chemical Company (Midland,

MI, USA). The Mark-Houwink plot and information on the molecular-weight

distribution of this material can be found in the supplementary information of this

article. Details regarding the preparation of this high-LCB sample can be found

elsewhere [17].

A custom-made 150 mm × 4.6 mm I.D. column packed with 10-µm 106 Å PLgel

particles by Polymer Laboratories was used for fast SEC as the second dimension

separation at a flow rate of 750 µL/min. The MTF-column packing consisted of a

polydisperse mixture of particles in the range of 0.1 to 1 µm (Admatech, Aichi, Japan).

Particle-size-distribution data provided by the supplier revealed that the average particle

diameter was 0.5 µm and the half-width of the distribution was about 0.3 µm. The

particles were functionalized with C8 chains to facilitate the packing procedure. A 150

mm × 4.6 mm I.D. column was packed by Diazem (Midland, MI, USA) using an

identical procedure as that used previously for packing columns for MTF [15].

3.2.2 Instrumentation and methods

Comprehensive two-dimensional MTF×SEC was performed on a system assembled in-

house. Basic components of the system were two LC10ADvp pumps (Shimadzu, ‘s

Hertogenbosch, The Netherlands) to perform isocratic separations in the two

dimensions, along with an SCL10a system controller (Shimadzu) for interfacing with

the data-acquisition computer. Either 10 or 20 µL injections of the samples were

performed by a SIL9a autosampler and columns were kept at 50°C in a CTO7 column

oven (both from Shimadzu). Detection in MTF×SEC experiments was performed using

Page 77: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Branched-Polymer Separations using Comprehensive 2D MTF × SEC

75

a Spectroflow 757 (ABI, Ramsey, NJ, USA) UV-absorbance detector equipped with an

8-µl flow cell. Data acquisition was typically performed at 5 Hz, recording the signals

of both detectors. A capillary UV detector was used (Linear UVIS 200, Linear

Instruments, Reno, NV, USA) to record the data for the calibration curve in Fig. 1. The

detector wavelength of UV detectors was set to 260nm, close to the absorption

maximum of polystyrene in tetrahydrofuran.

Modulation in comprehensive two-dimensional separations was accomplished with an

air-actuated VICI two-position 10-port valve (Valco, Schenkon, Switzerland). This

valve was operated using a high-speed switching accessory. The digital valve interface

(DVI; Valco) was connected to the SCL10a system controller. The 10-port valve was

plumbed for symmetrical dual-loop modulation [11]. Two injection loops of equal

volume (43 or 92 µL) were used. From the moment of injection on the MTF column,

the 10-port valve was switched either every 2, 2.67 or 4 minutes in order to inject 40

µL from the first dimension (running at 20, 15 or 10 µL/min respectively) at the SEC

column. Instrument control and data acquisition were achieved with ClassVP v7.4

build15 software (Shimadzu). Exported data were processed in Matlab v7.3 (The

Mathworks, Natick, MA, USA) using in-house written software for data folding and

visualization of two-dimensional colour plots.

3.3 Results and discussion

3.3.1 Calibration curve for molecular-topology-fractionation column

Linear polystyrene standards with a well-defined molecular-weight distribution (MWD)

are readily available, in contrast to well-characterized branched polymers with high

molecular weights. Therefore, linear polystyrenes were used to determine retention

behaviour in MTF as a function of molecular weight. The elution volume at the peak

maximum is plotted against the logarithm of the peak molecular weight in Fig. 1.

Reversal of the curve is observed around 200 kg/mol. The molecular weight where such

a reversal occurs will be referred to as the critical molecular weight Mcrit for reversal.

The elution order for polymers below Mcrit was consistent with that observed for

polystyrenes separated on columns packed with 1-µm, non-porous particles and can be

explained as hydrodynamic chromatography [18]. The interest in MTF stems from the

Page 78: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Chapter 3

76

elution region above Mcrit, because in this range the selectivity for branching (molecular

topology) has been observed [14, 15]. Although branched molecules are more

effectively retained than linear ones (section 3.2), the flow-rate effect on retention of

linear molecules may be used as a benchmark for the MTF selectivity of the column.

Fig. 1. MTF calibration curve for linear polystyrenes; obtained at a flow rate of 20 µL/min, at 10 µL/min.

Retention times of linear polymers above Mcrit were measured at two different flow

rates. The influence of flow rate on retention volume is much larger for high molar

masses, i.e. above Mcrit. Elution-order reversal has also been observed for polystyrene

standards in hydrodynamic chromatography (HDC) on columns packed with 1-µm non-

porous particles [18], but in that case the effect is very much smaller than observed for

MTF. In HDC the reversal in the calibration curve has been explained by shear

deformation of the polymers in solution [18]. After such a deformation the radius of the

polymer molecules perpendicular to the direction of flow is effectively smaller

compared to its unperturbed state. As a result the deformed molecules can get closer to

the channel walls, where the linear velocity is lower, and elute later from HDC columns.

Reversal due to polymer deformation is expected to be observed most strongly at high

shear and thus high flow rates. This is indeed observed in HDC, but not in the present

MTF system, where the effect is strongest at the lowest flow rates (Fig. 1). Our

calibration curves (molecular weight vs. elution volume) are thus not in agreement with

HDC data. However, our results are in agreement with observations in previous MTF

studies [14]. Thus, the separation mechanisms in HDC and MTF are based on different

principles.

Page 79: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Branched-Polymer Separations using Comprehensive 2D MTF × SEC

77

One important difference between the more conventional chromatographic separation

techniques (SEC, HDC, or field-flow fractionation, FFF) and MTF is the aspect ratio

(λ), defined as the ratio of the effective radius of the polymer in solution and the radius

of the channel that it is migrating through. Hydrodynamic separation techniques (such

as HDC) are typically operated below λ = 0.2 [19], whereas branching selectivity in

MTF is obtained only at values of λ that exceed this value. HDC theory predicts that for

large values of λ the forces resulting from rotation and solvent lagging (inertia) will

reduce the migration rate of the polymer, ultimately resulting in elution volumes greater

than the column volume. Shear alignment or deformation at such high values of λ may

be responsible for decreasing retention with increasing flow rate for large polymers

(above Mcrit). However, this is unlikely in MTF considering that the linear velocity of

the mobile phase is several times lower for MTF than in HDC with 1-µm particles [18].

A quantitative comparison of λ values for the different separation systems cannot be

made, because absolute values of the average diameter of the flow-through channels are

hard to obtain for the column used in this study. The flow path in particle packed beds is

much more complex than that in open-tubular channels, for which HDC theory was

derived. Successful attempts to relate hydrodynamic retention in particle packed beds

with retention in capillaries were made by using the hydraulic radius to define the

interstitial channel diameter [18, 20, 21]. However, the polydisperse packing material of

the present MTF column complicates the use of the classical concepts. Stationary

phases with well-defined channel parameters will have to be used to for a robust

comparison of HDC and MTF in terms of the aspect ratio.

3.3.2 Branched-polymer separations

Because branched polymers and linear polymers of the same hydrodynamic size co-

elute in SEC, triple-detection SEC can only be used to obtain the average number of

branches per molecule at any given elution volume. Therefore, branching properties

cannot be fully characterized when polymers are separated by hydrodynamic size only.

Comprehensive two-dimensional separation by hydrodynamic size and by branching

properties will be used to demonstrate this point. MTF is used in the first dimension to

fractionate polymers that vary in molecular weight and/or branching properties. This

choice for MTF in the first dimension is dictated by the experimental conditions. MTF

Page 80: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Chapter 3

78

is operated at flow rates between 10 and 20 µL/min on a 150 mm × 4.6 mm I.D.

column, resulting in analysis times of one or several hours. Therefore, MTF is

convenient as a (slow) first-dimension separation, but it cannot be applied as a (fast)

second-dimension separation. In MTF×SEC, 120 fractions of 40 µL each were collected

using the two-way 10-port switching valve. These fractions were injected and analysed

in real time on a fast SEC column. The same number of fractions was collected,

irrespective of the first-dimension flow rate. The time used for collection and second-

dimension separation was adapted to the first-dimension flow rate. By keeping the

number of fractions and the second-dimension flow rate constant, we were able to

directly compare the resulting chromatograms in terms of (MTF) resolution in relation

to the hydrodynamic size (SEC retention volume) of the molecules.

A sample of a star polymer, prepared by coupling anionically polymerized linear

polystyrene [22], was used for our studies. Because the PS-precursors possess a very

narrow molecular-weight distribution, the sample exhibits a nearly discrete relationship

between molecular weight and topology (the number of branches connected to the

coupling point in the molecule). The molecular weight of the PS-precursor was

determined to be 1,250 kg/mol [15]. In the star synthesis of the star polymers, coupling

was performed by reaction of the living ends of the precursor polymers with a tri-

functional coupling agent. Besides a three-arm star molecule, some unreacted linear

polymer remains and linear two-arm polymers are formed, as well as some higher order

coupling products. The presence of a four-arm star was first demonstrated using one-

dimensional MTF with low-angle-light-scattering detection [15]. More details on the

synthesis and composition of the star polymer can be found in the experimental section.

Linear polymers with molar masses comparable to the coupling products of the

precursor polymer were injected for reference purposes.

Coupling of one, two or three precursor polymers (arms) used for the star-polymer

sample would result in the peaks as observed in figure 2a, b and c if the MTF separation

would be based solely on molecular weight. In the chromatogram of the star sample in

Fig. 3a, which was obtained using identical experimental conditions, two peaks (1.60

and 2.68 mL) are observed at MTF elution volumes higher than any of the peaks

observed in Fig. 2. The elution volumes corresponding to peak-maxima have been

Page 81: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Branched-Polymer Separations using Comprehensive 2D MTF × SEC

79

summarized in Table 1 for both dimensions. Because retention of branched molecules is

expected to be higher in MTF, it can be tentatively concluded that the peak in Fig. 3a at

VMTF = 1.6 mL is due to the three-arm star-shaped coupling product. Comparison of

VSEC values suggests that the hydrodynamic size of the three-arm star is close to that of

the linear polymer of 2,536 kg/mol. Both the increased retention in MTF and the

decreased elution volume in size-exclusion chromatography compared to linear polymer

of identical mass can be explained by branching. The last peak eluting in Fig. 3a is

consistent with a higher order star as the peak has nearly the same SEC retention

volume as the three-arm star, but is retained much longer in the MTF column. The

probability of such products being formed decreases with increasing functionality, but

the presence of a peak corresponding to the four-arm coupling product is clearly visible

in Fig. 3a.

At lower MTF flow rates the components of the star-polymer sample were better

separated. This is illustrated in Fig. 3b and 3c where flow rates of 15 and 10 µL/min

were used. At low flow rates the calibration curves in MTF become less steep (Fig.1 )

and branched components are retained much longer. Because of the very slow

molecular diffusion of high molecular-weight polymers we do not anticipate increased

band broadening at very low flow rates. Indeed, peak broadening is hardly affected by

the long residence time in the MTF column (Fig. 3). Comparison of the peak widths in

Fig. 3 with those of the linear polystyrene standards (with Mw/Mn 1.03 – 1.04) in Fig. 2

shows that the peak widths of branched polymers are not significantly greater than those

of narrowly distributed linear standards. The observed broadening may be due to the

limited efficiency of the column. Furthermore, it is known that overloading occurs

easily in HDC. Therefore, overloading may also be a threat when using MTF. The low

porosity (ε = 0.3) of the column may well aggravate the loadability issues.

To assess whether shear degradation was occurring in the system, polymer elution was

studied as MTF flow rate was varied. It was speculated that at relatively high flow rates

in MTF shear-induced degradation (i.e. chain scission) of the polymer could occur.

Because even partial degradation of the polymer is likely to have a significant effect on

the hydrodynamic-size distribution of the polymer, MTF×SEC provides information on

the likelihood of chain scission. Neither increase in SEC elution volume nor tailing in

Page 82: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Chapter 3

80

the SEC dimension towards lower molecular weights was observed as MTF flow rate

was increased. Thus, polymer molecules do not appear to be shear degraded as a result

of MTF separation. Shear degradation in the SEC separation has been addressed in the

supporting information of this article. No significant evidence for shear degradation that

might impair the integrity of MTF×SEC was found. It is much more difficult to

establish whether or not the polymer molecules are deformed during the MTF

separation. If they are, it is likely that the molecules relax to their unperturbed shapes

before they are analysed by SEC or characterized by light scattering.

Table 1. Peak maxima in MTF and SEC for different first-dimension flow rates.

MTF 20 µL/min MTF 15 µL/min MTF 10 µL/min

Vmax (mL) MTF SEC MTF SEC MTF SEC

1,373 kg/mol 1.08 1.43

2,536 kg/mol 1.24 1.35

3,742 kg/mol 1.24 1.31

1-arm linear polymer 1.00 1.47 1.12 1.46 1.20 1.47

2-arm linear polymer 1.16 1.37 1.40 1.36 1.72 1.37

1.60 1.34 2.12 1.34 3.28 1.34

4-arm star polymer 2.68 1.33 > 3.5 > 3.5

Another example of the separation of a branched polymer is presented by the separation

of a broadly distributed polystyrene (PDI = 3.3, see supplementary information) with

random long-chain branching (LCB) in Fig. 4a. For a sample with a considerable degree

of LCB (MTF flow rate 20 µL/min) a low-concentration tail towards higher MTF

elution volume is observed which is considerably different from that of the three-arm

star polymer sample. However, the star sample contained discrete populations of

branched species which could be separated into discrete peaks in the MTF separation.

On the other hand, the broadly distributed PS contains a nearly continuous distribution

of branched components varying in the number of branch points and branch lengths.

The fact that peaks in the MTF separation tail to larger elution volumes, while the SEC

separation becomes constants, suggests that this distribution of branching may result in

separation in the MTF direction. Elution of this material in the SEC dimension was

compared to that of the linear polymers shown in Fig. 2. The peak maximum of the

Page 83: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Branched-Polymer Separations using Comprehensive 2D MTF × SEC

81

branched PS in SEC for an MTF elution volume of 1.24 mL was 1.47 mL. This is

considerably different from the 1.35 mL and 1.31 mL that were found for linear

polymer (table 1).

Fig. 2. (left). Comprehensive two-dimensional MTF×SEC of linear polystyrene standards with MTF at 20 µL/min. Nominal molecular weights (a) Mp 1373 kg/mol, (b) 2536 kg/mol, (c) 3742 kg/mol,

(a)/(b)/(c) 126.7 kg/mol (internal-reference peak in top-left corner).

Fig. 3. (right). Comprehensive two-dimensional MTF×SEC of linear and star-branched polymers. (a) MTF at 20 µL/min, (b) MTF at 15 µL/min, (c) MTF at 10 µL/min.

Page 84: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Chapter 3

82

Fig. 4. Separations of a polystyrene sample with a broad MWD and a high degree of LCB

(a) MTF×SEC, (b) SEC×SEC

An important question is whether or not the samples are fully eluted from the MTF

column (featuring sub-µm flow-through channels). Recovery may be negatively

affected if the flow rate is decreased in order to increase resolution. At 15 µL/min the

four-arm star polymer is no longer observed to elute within about five column volumes

(Fig. 2b). The chromatograms in Fig. 2 were integrated over MTF volumes from 0.5 to

3.5 mL and SEC volumes from 1.15 to 1.7 mL. Compared to MTF performed at 20

µL/min, only 89% of the sample was eluted at 15 µL/min in the same retention window.

For 10 µL/min this relative recovery drops to 80%. The sample that is not recovered is

expected to elute after the elution window as a result of increased retention. The

separation was not extended long enough to observe all the branched polymers at flow

rates below 20 µL/min. Therefore, the run length was increased in subsequent

experiments for recovery studies (Fig. 5a). Furthermore, these experiments were all

performed at 20 µL/min.

Fig. 5. Separations of the star-polymer sample (a) MTF×SEC, (b) SEC×SEC

Page 85: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Branched-Polymer Separations using Comprehensive 2D MTF × SEC

83

To assess absolute sample recovery in the MTF×SEC system, the MTF column was

replaced by a SEC column (V0 = 1.2 mL; Fig. 4b and 5b). The experimental conditions

were equal to those for MTF×SEC, except that the first-dimension separation was run

until only 1.5 times the total permeation volume had passed through the first-dimension

SEC column. No polymer is expected to elute after this point. This showed that in the

MTF×SEC set-up linear polymers with high molecular weight (Fig. 2) and the LCB

polystyrene (Fig. 4) were all recovered quantitatively (> 95%). The star polymer sample

was recovered for 92% (average of triplicate MTF×SEC measurements) when

integrated over MTF volumes from 0.5 to 4.7 mL (Fig. 5a). When the integration was

extended to a volume of 7.2 mL the recovery was also found to be quantitative (>95%).

3.4 Conclusions

Molecular-topology fractionation (MTF) provides branching-selective separation. The

technique can be used to separate molecules according to their degree of long-chain

branching, but only for samples with extremely narrow molecular-weight distributions.

In all other cases, the effect of branching on retention in MTF is confounded with the

effect of molecular weight. A solution to this problem has been found by combining

MTF and size-exclusion chromatography into a comprehensive two-dimensional

separation system. This MTF×SEC technique was used to clearly demonstrate the

branching-selective separation obtained by MTF for a sample of (narrowly distributed)

star-shaped polystyrenes. MTF×SEC was also applied to a broadly distributed

polystyrene sample that featured a high degree of long-chain branching (LCB).

Although some selectivity was observed, the separation may need to be improved if we

are to obtain quantitative measures for LCB. However, even in the present, immature

state, the fractionation of LCB polymers may prove to be useful in predicting

rheological properties of polymers.

Only high-molecular-weight polymers were separated using MTF for this study. The

range of applicability of MTF is limited to the range above the reversal molecular

weight (Mcrit), which in turn depends on the diameter of the flow-through-channels.

Several improvements are foreseen in the near future. The presently used MTF column

was packed with polydisperse particles. It is difficult to obtain such columns, let alone

Page 86: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Chapter 3

84

pack them reproducibly. Even the repeatability of nominally identical columns is poor.

It is also difficult to use these columns to perform fundamental studies on MTF, because

accurate information regarding the size of the inter-particle (flow-through) channels is

cannot be obtained. Because it is difficult to accurately characterize the channel

dimensions in these packed columns, the relationship of the former with elution

behaviour is challenging to evaluate. Columns packed with mono-disperse particles are

needed to sensibly compare hydrodynamic chromatography (HDC) and MTF. However,

because the two techniques operate in different regimes of the aspect ratio (size of

molecules compared with that of the flow channels) and because the effects of changes

in the flow rate were found to be opposite, we believe that HDC and MTF are based on

different separation mechanisms. Columns that are well packed with uniform sub-

micron particles are also difficult to obtain. Monolithic stationary phases with well-

characterized sub-micron flow-through pores may be a viable alternative. The use of

such monolithic columns for MTF separations will be reported elsewhere.

3.5 Appendix

MTF column parameters

The column volume and efficiency were determined by injection of 5 µL of a 1000-ppm

solution of ethylbenzene. At a flow rate of 20 µL/min THF and a column-oven

temperature of 50°C ethylbenzene eluted at 38.1 minutes. Therefore, the MTF column

volume (V0) was 762 µL, the efficiency of the separation was 3400 plates per meter.

The porosity of the packing was calculated by dividing the ethylbenzene elution volume

by the theoretically calculated volume of the empty column (150 x 4.6 mm) and was ε =

0.30.

Characterization of long-chain-branched polystyrene sample

The long-chain-branched (LCB) polystyrene sample was characterized using size-

exclusion chromatography (SEC) with multi-angle light scattering (MALS) and on-line

viscometry detection. The SEC columns used were three mixed-B columns (300x7.5

mm each; 10-µm particles) from Polymer Labs (Church Stretton, UK). Stabilized THF

Page 87: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Branched-Polymer Separations using Comprehensive 2D MTF × SEC

85

(J.T. Baker, Deventer, The Netherlands) was used as the mobile phase at a flow rate of 1

mL/min.

The weight-average molecular weight of the LCB polymer (measured by SEC-MALS)

was 810 kg/mol with a polydispersity of PDI = 3.3. The presence of long-chain

branching at high molecular weights is illustrated by the reduction in intrinsic viscosity

in the Mark-Houwink plot in Fig. 1.

Fig. S1. Mark-Houwink plot for the long-chain branched polystyrene used in this article

and a linear reference polystyrene polymer.

Verification of SEC at elevated flow rates

SEC was performed at two and a half times the recommended flow rate in the

MTF×SEC experiment. The impact of separation at elevated flow rates was validated by

performing SEC separations comparable to those in a two-dimensional experiment at

the recommended and elevated flow rates.

SEC was performed at 300 and 750 µL/min on a 150 mm x 4.6 mm I.D. column with

10-µm PLgel particles with a pore size of 106 Å. The porosity of the frits in this column

was 5 µm. The mobile phase was non-stabilized tetrahydrofuran (Biosolve,

Valkenswaard, The Netherlands) and separations were performed at 50°C. The injection

volume was 5 µL of polymer solution. Four samples and one blank were injected in

duplicate. Polystyrenes with peak molecular weights of 7,450, 3,742, 2,536 and 1,373

kg/mol (Polymer laboratories, Church Stretton, UK) were dissolved in tetrahydrofuran

individually at a concentration of 0.1 mg/mL. The samples with 3,742, 2,536 and 1,373

Page 88: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Chapter 3

86

kg/mol polystyrene were all used with an additional 0.2 mg/mL of 126.7 kg/mol

polystyrene (reference standard). All four samples and the blank contained

approximately 250 ppm butyl-hydroxylated toluene to prevent degradation by radicals.

Detection was performed using a Spectroflow 757 (ABI, Ramsey, NJ, USA) UV-

absorbance detector equipped with an 8-µl flow cell and set for detection at 260 nm.

The chromatograms have been overlaid in Fig. S2. An x-axis multiplier was chosen to

have this x-axis display the elution volume. Peak assignment for Fig. S2 from left to

right: 7,450, 3,742, 2,536, 1,373 and 126.7 kg/mol linear polystyrene, ionol, injection-

solvent related peak.

Fig. S2. UV absorbance of high molecular weight polystyrenes at 750 µL/min (offset 0 mAU) and 300

µL/min (offset 15 mAU). Retention times are annotated in red for 7,450 kg/mol PS, ionol and an injection-solvent related peak.

For all high-molecular-weight PS polymers a shift towards higher elution volume is

observed when separated at 750 µL/min. This shift is small compared to the separation

of the individual standards and therefore has a small effect on the separation. The shift

in elution volume may possibly be explained by the slow diffusion of high-molecular-

weight polymers, being responsible for incomplete inclusion of the polymer in the pores

of the packing material. If any shear degradation were to occur, this would be expected

to result in significant tailing and changes in the peak shape. Only the peak front of the

7,450 kg/mol appears to be deformed at 750 µL/min. Absolute molecular-weight

determination techniques, such as low-angle laser light scattering, can be used to

discriminate between poor chromatography or shear degradation. Because fast SEC is

not used for absolute-molecular-weight determination, this discussion is beyond the

Page 89: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Branched-Polymer Separations using Comprehensive 2D MTF × SEC

87

scope of the present article. Based on the results in Fig. S2 we conclude that peak

elution volumes for polystyrene polymers up to a molecular weight of 7,450 kg/mol

may be used to compare hydrodynamic size parameters at 750 µL/min. under the

conditions used for MTF×SEC.

References

[1] T.H. Mourey, Int. J. Polym. Anal. Charact. 9 (2004) 97.

[2] S. Pang, A. Rudin, in T. Provder (Editors), Chromatography of Polymers (ACS Symposium Series, No.

521), American Chemical Society, Washington, DC, 1993, p. 254.

[3] K.D. Caldwell, in H.G. Barth, J.W. Mays (Editors), Modern Methods of Polymer Characterization,

Wiley, New York, 1991, p. 113.

[4] B.H. Zimm, W.H. Stockmayer, J. Chem. Phys. 17 (1949) 1301.

[5] M. Gaborieau, J. Nicolas, M. Save, B. Charleux, J.-P. Vairon, R.G. Gilbert, P. Castignolles, J.

Chromatogr. A 1190 (2008), 215.

[6] P.M. Wood-Adams, J.M. Dealy, A.W. deGroot, O.D. Redwine, Macromolecules 33 (2000) 7489.

[7] P.J. Schoenmakers, P. Marriott, J. Beens, LC-GC Eur. 16 (2003) 335.

[8] J.C. Giddings, J. Chromatogr. A 703 (1995) 3.

[9] P.J. Schoenmakers, G. Vivó-Truyols, W.M.C. Decrop, J. Chromatogr. A 1120 (2006) 282.

[10] X. Jiang, A. v.d. Horst, V. Lima, P.J. Schoenmakers, J. Chromatogr. A 1076 (2005) 51.

[11] A. v.d. Horst, P.J. Schoenmakers, J. Chrom. A 1000 (2003) 693.

[12] J. Gerber, W. Radke, Polymer 46 (2005) 9224.

[13] K. Im, Y. Kim, T. Chang, K. Lee, N. Choi, J. Chromatogr. A 1103 (2006) 235.

[14] D.M. Meunier, S.A. Baker, P.B. Smith, Macromolecules 38 (2005) 5313.

[15] D.M. Meunier, T.M. Stokich Jr., D. Gillespie, P.B. Smith, Macromol. Symp. 257 (2007) 56.

[16] R. Matmour, A. Lebreton, C. Tsitsilianis, I. Kallitsis, V. Héroguez, Y. Gnanou, Angew. Chem. Int. Ed.

44 (2005) 284.

[17] J.L. Hahnfeld, W.C. Pike, D.E. Kirkpatrick, T.G. Bee, in R. Quirk (Editor), Applications of Anionic

Polymerization Research (ACS Symposium Series, No. 696), American Chemical Society, Washinton,

DC, 1996, p. 167.

[18] E. Venema, J.C. Kraak, H. Poppe, R. Tijssen, J. Chromatogr. A 740 (1996) 159.

[19] R. Tijssen, J. Bos, in F. Dondi, G. Guiochon (Editors), Theoretical Advancement in Chromatography

and Related Separation Techniques, Kluwer, Dordrecht, 1992, p. 424.

[20] G. Stegeman, R. Oostervink, J.C. Kraak, H. Poppe, K.K. Unger, J. Chromatogr. 506 (1990) 547.

[21] G. Stegeman, J.C. Kraak, H. Poppe, R. Tijssen, J. Chromatogr. A 657 (1993) 283.

[22] T. Altares Jr., D. P. Wyman, V. R. Allen, K. Meyersen, J. Polym. Sci., Part A : Polym. Chem. 3 (1965)

4131.

Page 90: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):
Page 91: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

89

Chapter 4: Branched Polymers Characterized by

Comprehensive Two-Dimensional Separations with Fully

Orthogonal Mechanisms

Abstract

Polymer separations under non-conventional conditions have been explored to obtain a

separation of long-chain branched polymers from linear polymers with identical

hydrodynamic size. In separation media with very narrow flow-through channels (of the

same order as the size of the analyte molecules in solution) the separation and the

elution order of polymers are strongly affected by the flow rate. At low flow rates the

largest polymers are eluted last. At high flow rates they are eluted first. By tuning the

channel size and flow rate, conditions can be found were separation becomes

independent of molar mass or size. Other differences between polymer molecules are

revealed, such as the extent of long-chain branching. This type of separation is referred

to as molecular-topology fractionation (MTF) at critical conditions. MTF involves

partial deformation of polymer coils in solution. The increased coil density and

resistance to deformation can explain the different retention behavior of branched

molecules. Much higher efficiency and selectivity were obtained by MTF in columns

than with traditional membrane fractionations. MTF in combination with size-exclusion

chromatography (SEC) was applied for the separation of branched polymers. Branching

selectivity was demonstrated for three- and four-arm “star” polystyrenes of 3 to 5 × 106

g/mol molar mass. Baseline separation could be obtained between linear polymer, Y-

shaped molecules, and X-shaped molecules in a single experiment at constant flow rate.

For randomly branched polymers the branching selectivity inevitably results in an

envelope of peaks, because it is not possible to fully resolve the huge numbers of

different branched and linear polymers of varying molar mass. Separations performed

by comprehensive two-dimensional MTF×SEC revealed the presence of branched

polymers that could not be discerned with one-dimensional SEC in combination with

mass-selective detectors, such as light scattering or viscometry.

Page 92: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Chapter 4

90

4.1 Introduction

Branching that is accidentally or purposefully introduced in (high-molar-mass)

polymers may be advantageous. Long chain branching in thermoplastics improves melt

strength and flow, which allows for faster processing and unique applications [1].

Through the introduction of branching a favorable balance may be obtained between

modulus (i.e. stress-strain relation), viscosity, and elongation behavior [2,3,4]. A major

challenge up to this day remains the analysis of long-chain-branched (LCB) polymers,

because a distribution of different topologies (or “qualitative geometries”) [5,6] is

confounded with a molar-mass distribution (MMD). In many polymer samples both

linear molecules and molecules with various degrees of branching are present,

depending on the polymerization conditions. Unequivocally demonstrating the

properties of branched-polymeric materials can only be achieved by synthesis and

physical testing of model compounds with well-described branching topologies [7].

Branching may also be introduced by post-synthesis blending of linear polymers with

LCB molecules. Although the positive effects of branched polymers remain after

blending with other polymers, no existing techniques can specifically characterize the

properties of branched molecules. Recent theories on structure-property relationships

for branched polymers emphasize the role of the intra-molecular structure [8]. For

material characterization it is, therefore, important that polymers can be separated

according to their structure and that molecules can be discriminated based on their

topology. However, conventional polymer-analysis techniques cannot be used to

perform such separations for LCB polymers. Separations by either branches or end

groups based on interaction chromatography [9,10] may be possible for polymers of low

to moderate molecular weight with chemically different end groups [11]. High-

molecular-weight short-chain-branched (SCB) polyolefins may also be analyzed with

gradient liquid chromatography [12]. While spectroscopic techniques offer the best

possibility to identify functional groups, they only provide information on population

averages of the sample. Hyphenation of size-exclusion chromatography (SEC) with

NMR or FTIR spectroscopy has been applied successfully to investigate distributions in

terms of functionality [13] or SCB frequency [14]. Studying the extent of LCB using

this approach is extremely difficult, because the low frequency of functional groups (i.e.

branch points) would require an exceptional sensitivity and dynamic range [15].

Page 93: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Branched-Polymers Characterized by Comprehensive 2D Separations with Fully Orthogonal Mechanisms

91

Polymers of high molar mass and moderate to low degree of branching are typically

separated based on their hydrodynamic size using SEC or field-flow fractionation

(FFF), often followed by selective detection using on-line viscometry and/or light

scattering [16,17]. Results for branched polymers are commonly reported as so-called

contraction ratios based on radius of gyration (rg, Eq. 1, [18]) or intrinsic viscosity ([η],

Eq. 2, [19]).

𝑔 = ��𝑟𝑔�𝐵

2

�𝑟𝑔�𝐿2�𝑀

(1)

𝑔′ = �[𝜂]𝐵[𝜂]𝐿

�𝑀

(2)

where B refers to branched polymers and L to the linear-equivalent reference polymer

and the subscript M indicates molecules of equal mass. LCB has a strong impact on the

solution properties of macromolecules, such as the relation between hydrodynamic size,

molar mass and intrinsic viscosity. Contraction ratios can be used to estimate the

branching frequency and to obtain information on the topology [20] when information

on polymer chemistry and linear reference polymers are available. This methodology

has developed over the years into the most popular method for LCB analysis [21].

Nevertheless, the separation by SEC is based on the hydrodynamic size of the analyte

molecules and is only indirectly related to branching and topology. This is a limitation

and a source of errors inherent to this method. As in conventional SEC analysis, a

significant bias may be accepted in practice, especially when comparing similar

polymers (prepared by identical chemistries). Algorithms exist to estimate the branching

frequency for tri- and tetra-functional branching based on the Zimm-Stockmayer theory

[18], but failure to separate by topology prevents such an approach from successfully

discriminating between branching functionality and frequency. The relationship

between molar mass and size in solution is affected by the topology and this implies that

a fraction of given size will be polydisperse when a branching distribution is present

[22,23].

The ability to separate polymers according to their topology and degree of LCB would

clearly benefit the characterization of branched polymers. Potentially interesting for this

Page 94: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Chapter 4

92

purpose are separations that exploit differences in what has been referred to [24] as

polymer dynamics in solution. In this study the application of molecular-topology

fractionation (MTF) [25,26] has been explored for the separation of branched polymers.

This technique is based on the migration of polymers in dilute solution through

chromatographic columns with very narrow flow channels. Unlike fractionation under

conditions of strong confinement that require the coil to unwind (e.g. reptation), the

separation is based on continuous migration of the coiled polymers. This renders MTF

less sensitive to clogging of the pores. The size of the polymer in solution has an effect

on MTF as well and, therefore, the separation by branching properties will be

confounded with the molar-mass distribution. Therefore, comprehensive two-

dimensional MTF×SEC (after nomenclature in [27]) separations were used to

independently study the selectivities due to branching and due to hydrodynamic size

[28]. In the present study key variables, such as the pore size and the flow rate, have

been optimized in an attempt to obtain orthogonal separation mechanisms. Accurate

information on the pore size will be used to provide a better definition of the MTF

separation and predict its application range. Flow-rate gradients have been explored to

enhance the applicability of the technique.

4.2 Theory

4.2.1 Separation techniques based on size

Polymers in dilute solution are present as coils. For ideal polymers behaving as perfect

random-flight chains the time-averaged coil size scales with the square root of the molar

mass. Deviations from this scaling law for real polymers are implied by limited

flexibility in the backbone, excluded volume by the chain itself and solvent adsorbed by

the coil due to enthalpic interactions [29,30]. A relation where size follows a power law

of mass is often still valid across broad molar-mass ranges, provided that composition

and structure of the polymer remain constant.

The equilibrium size of polymers in solution provides a robust basis for SEC and HDC

separations. Wall exclusion from the stationary-phase surface based on coil-size of

dissolved polymers is the driving force in both separations (steric exclusion). In SEC

smaller polymers selectively populate the stagnant volume in narrow pores by diffusion

Page 95: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Branched-Polymers Characterized by Comprehensive 2D Separations with Fully Orthogonal Mechanisms

93

from adjacent convective channels [31,32]. In packed beds with porous particles the

porous properties can be optimized to provide selective exclusion and convective

transport takes place in the interstitial space between the particles. In HDC large

polymers are excluded from the slow-moving solvent layers near the walls in convective

pores [33,34,35]. Selectivity scales with the aspect-ratio (λ) that relates the size of the

solute molecules (radius r) to the size of the flow-through channel (radius rc) as λ = r /

rc. Besides steric exclusion, which increases the migration rate for larger polymers,

hydrodynamic interactions in convective flow will affect the polymer migration rate.

For most flexible-chain polymers with M > 10 kg/mol the polymer coil behaves as if

impermeable to flow (i.e. non-draining behavior) under the mild conditions of SEC or

viscometry [16,36,37]. Friction in shear flow due to non-draining behavior of the

analyte will generally result in retardation and counteract the exclusion effect at higher

λ values [38,39,40]. Hydrodynamic interaction is specific to the conditions used and

depends on both λ and absolute size. A detailed breakdown of hydrodynamic effects for

polymers in shear flow has been provided by Tijssen et al. [41] and Stegeman et al.

[42]. Migration in HDC can be described using Eq. 3 where migration rate (τ) is defined

as residence time of the polymer (tp) relative to the residence time of a flow marker (tm)

and expressed as a function of λ and a constant C describing hydrodynamic interaction.

𝜏 = 𝑡𝑝𝑡𝑚

= 11+2𝜆−𝐶𝜆2

(3)

4.2.2 Deformation of polymers in solution

Under HDC conditions shear stress on the solute may become significant and result in

flow-rate-dependent elution behavior [42]. The effective size (r) may decrease when the

molecules are subjected to shear stress above a certain threshold that may be related to

the Deborah number (De) [24,43]. De is defined as the product of effective elongation

(𝜀̇) and the longest relaxation time of the polymer (τrel) . The effect of elongation may

become detectable in HDC for Deborah numbers exceeding 0.1, while for De > 0.5

severe elongation may occur. Separation in this latter domain does result in elution

behavior that differs significantly from that of HDC and is referred to as slalom

chromatography (SC) [44]. Deborah numbers can be calculated using either molar mass

Page 96: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Chapter 4

94

(Eq. 4) or radius of gyration (Eq. 5), depending on the experimental conditions and

available data on the polymer [24,45].

𝐷𝑒 = 𝜀̇𝜏𝑟𝑒𝑙 = 𝐾𝑑𝑒𝑏ν𝑑𝑝

0.42 η𝑠 [η] 𝑀𝑅 𝑇

(4)

𝐷𝑒 = 𝜀̇𝜏𝑟𝑒𝑙 = 𝐾𝑑𝑒𝑏ν𝑑𝑝

6.12 Φ η𝑠 𝑟𝑔3

𝑅 𝑇 (5)

Kdeb is a constant related to the geometry of the pores (with a typical value of 6), ν is the

superficial solvent velocity, dp the particle size of the packing, Φ the Flory-Fox

parameter, ηs the solvent viscosity, [η] the polymer intrinsic viscosity, rg the polymer

radius of gyration, R the gas constant and T the absolute temperature. The Flory-Fox

equation (Eq. 6) is used to transform Eq. 4 into Eq. 5.

[𝜂]𝑀 = 63/2Φ𝑟𝑔3 (6)

It is important to note that the Flory-Fox parameter is a measure of hydrodynamic

interaction and depends on solvent conditions, molar mass and branching of the

polymer. For example, values ranging from Φ = 1.8 × 1023 mol-1 for linear polymers to

Φ = 3.5 × 1023 mol-1 for branched polymers have been observed, while at θ-conditions

(indicated by the subscript 0) a value of Φ0 = 2.8 × 1023 mol-1 is common [46,47]. When

studying molecules of varying topology in good solvents we prefer to use Eq. 4,

avoiding the assumptions inherent to Eq. 5.

A problem with the application of Deborah numbers for branched polymers is in the

treatment of polymer relaxation. The polymer relaxation τrel (Eq. 7) is based on a model

by Zimm for a chain of beads connected by ideal springs [48,49].

𝜏𝑟𝑒𝑙 = 𝐶𝑍η𝑠 [η] 𝑀𝑅 𝑇

(7)

The constant CZ corrects for hydrodynamic interaction (e.g. draining behavior) of the

polymer. Branching and topology effects are not included in the model and correct

treatment should therefore not be assumed. Notice that according to Eq. 7 relaxation for

polymers with identical hydrodynamic volumes is identical. Linear and branched

Page 97: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Branched-Polymers Characterized by Comprehensive 2D Separations with Fully Orthogonal Mechanisms

95

polymers in dilute solution can be expected to respond differently to stress. It is known

that branching leads to increased segment density and reduced internal freedom of

motion for random-coil polymers in solution [50,51]. The entropy decrease resulting

from deformation of a branched molecule will be greater than that for the deformation

of a linear polymer. Therefore, branched polymers are expected to deform less than

linear polymers under identical stress. A size-dependent separation may then be applied

to achieve branching selectivity, dependent on the level of stress on the molecules (i.e.

on the flow rate).

The aspect ratio and Deborah number provide convenient metrics to compare separation

techniques based on size and dynamic properties of the polymers. In Fig. 1 techniques

are indicated at λ and De values corresponding to typical operating conditions. Arrows

in the insert indicate how λ and De values respond to changes in the separation

conditions, such as increasing the flow rate and decreasing the particle size (dp). Molar

mass has an indirect effect on both λ and De through its impact on the radius. Ultra-

high-pressure SEC separations are by definition operated at higher flow rates and with

smaller particles. Complex multi-mode separations result for samples with high molar

mass [52]. Some uncertainty is introduced in the assessment of elongation for λ > 0.3

(shaded region in Fig. 1), because shear stress experienced by the polymer is no longer

continuous and its elongation character is reduced. In Poiseuille flow shear stress will

mainly affect the periphery of the coiled polymer with λ > 0.3 and rotation is largely

prohibited. This situation no longer meets the assumptions in calculation of Deborah

numbers i.e. steady elongation against relaxation of the entire coil, but it is expected that

deformation as a result of shear forces will still occur. Hydrodynamic interaction of

polymers is significant for λ > 0.3 and MTF separations can be obtained under these

conditions. The upper limit of λ for MTF separations is not strictly defined. The dashed

line in Fig.1 puts an approximate limit at λ = 1, but MTF separations with linear

polymers up to λ = 2 have been performed.

Page 98: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Chapter 4

96

Fig. 1. Classification of separation techniques based on Deborah number and aspect ratio. Arrows in the insert

indicate changes implied by variation of experimental conditions.

4.2.3 Reptation

Separation techniques which are performed at conditions associated with MTF are

reviewed for similarities that can explain the topology sensitivity obtained at different

flow rates. Different mechanisms can be identified for polymer migration through

strongly confining media i.e. λ > 1. Sieving, entropic-barrier transport, and reptation can

be distinguished based on channel geometry and rigidity of the solute [53]. Random-coil

polymers in dilute solution with equilibrium sizes larger than the flow-through channels

through which they migrate will be continuously squeezed into a stretched

conformation. This condition is most similar to the tube-like diffusion path of molecules

as described in the theory of reptation [41,54]. This model finds its origin in the

description of the rheological behavior of melted polymers, where it is used to describe

motion, diffusion, and viscosity successfully [7,55]. Modifications to the theory have

been described for polymers in dilute solution, specifically for the case of separating

polymers by their degree of branching [56]. The barrier energy and critical flux required

to overcome the osmotic pressure under strong and weak confinement was derived for

ideal-star and randomly branched chains. Shortcomings of the theory impose serious

Page 99: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Branched-Polymers Characterized by Comprehensive 2D Separations with Fully Orthogonal Mechanisms

97

limitations on its applicability for real chains. For critical-flux calculations the flow

needed to overcome diffusion of a polymer segment is considered, while treating the

molecule as free-draining (i.e. interaction of each polymer segment with flow is not

affected by other segments in the molecule). Because non-draining conditions are more

likely for real chains, shear inside the coil domain will be low, resulting in smaller drag

forces on the chains in comparison with free-draining conditions. Thus, flow-induced

migration through strongly confining pores, resulting in unwinding of the polymer and

in molar-mass insensitivity for linear chains, will not take place for real polymers. It

was later pointed out that the critical flux for linear and branched chains under strong

confinement will be identical and cannot be used to achieve separation, because of the

progressive nature of the drag force once the first segments of a chain have entered the

pore [57].

In the weak-confinement case deformation and moderate stretching are considered for

polymers in solution. Most theoretical work takes into account constriction by the pore

walls alone, whereas for real polymers hydrodynamic interactions are present as well.

The forces induced by solvent shear on the polymer contribute to deformation and can

be controlled externally by adjusting the flow rate. Polycarbonate or mica filtration

membranes prepared by fast-atom bombardment and track-etching have been used to

study reptation of synthetic polymers. Flow-rate-dependent rejection of polymers with

equilibrium dimensions close to or larger than the membrane pores has been described

by Long and Anderson [58]. They confirmed that polymer migration through pores in a

mica membrane at higher flow rates was due to deformation rather than degradation for

the range 1 < λ < 2. Selective rejection of branched-polymers was considered in a

follow-up article [59]. A greater rejection of comb and star polymers relative to linear

polymers was attributed to deformability of the polymers. Unfortunately, the branched

samples used in this study had different molecular weights and high dispersities.

Challenges with membrane separations are the limited separation efficiency and low

sample capacity (concentrations of 160 ppm w/w had to be used). It was observed that

high concentrations (above the overlap limit) were needed for polymers with λ ≈ 1 to

diffuse through the membrane when using osmotic pressure only [60,61]. Therefore

concentration build-up on membranes in flow-driven separations may present a

problem, because this would alter the migration behavior of the polymer [62]. The

Page 100: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Chapter 4

98

results obtained for flow-rate dependent polymer rejection are most relevant to the

separations considered here, since the conditions and findings are in good agreement

with the observations for molecular-topology fractionation (MTF).

4.2.4 Calibration curves and separation of deformed-polymers

The impact of polymer deformation on migration can be very different depending on the

separation technique and corresponding conditions. Whether a useful separation may be

obtained for polymers with different deformability is assessed by comparing the

calibration curves as a function of polymer equilibrium size (Fig. 2). SEC (pore

exclusion) and HDC (wall exclusion) separate non-deformed macromolecules and result

in decreasing residence times for analyte molecules with increasing size. SEC by

definition takes place in pores that are not subject to convective transport. Pores in

stationary phases for SEC are typically smaller than the flow-through channels and may

be optimized independently from the flow-through-channel size. The channel size

(related to the particle diameter) may vary, but λ is generally below 0.1 for polymers

separated by SEC. Modern phases offer both high porosity, which ensures a broad

separation window (e.g. 0.5 < τ < 1), and a high mechanical strength, which allows

separation at higher flow rates. In case high-molar-mass polymers are separated using

small particles (i.e. small flow-through channels) λ may be high enough for a seamless

transition into HDC to occur [63,64]. A continuous SEC-HDC separation is the result,

with the largest polymers eluting first. However, if λ increases beyond about 0.35 a

strong reversal of the HDC calibration curve is observed (Fig. 2). Unlike rigid particles,

which will be significantly retarded for λ > 0.4, polymers will respond to shear stress

either through deformation or degradation. Deformation is broadly defined and may

comprise many effects, such as compression, elongation or increased flow draining of

the coil periphery. In the MTF region (above λ ≈ 0.35; see Fig.2) the behavior of non-

rigid polymers may be used to discriminate between different architectures.

Deformation of polymers results in departure from the HDC calibration curve, which

applies for rigid solutes, with λ corresponding to the non-deformed-polymer. All

molecules will be deformed, but linear molecules more so than branched ones. The

linear molecules, therefore, elute earlier (indicated by the gray horizontal arrows in Fig.

2).

Page 101: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Branched-Polymers Characterized by Comprehensive 2D Separations with Fully Orthogonal Mechanisms

99

Fig. 2. Schematic calibration curves for SEC, HDC, MTF and SC. Arrows indicate the effect of flow-induced polymer deformation.

Hydrodynamic interactions of polymers play an important role in flow-induced

deformation. This is supported by the observation that linear polymers with equilibrium

dimensions of the order of the channel size elute much faster at increased flow rates

[65]. In the absence of deformation the polymer lags the solvent in its surrounding due

to non-draining behavior (i.e. impermeability to flow). Especially in monoliths or

packed beds with highly interconnected flow-through channels this results in τ > 1 for

polymers with λ ≈ 1. At elevated flow rate τ = 0.7 was observed, which is possible only

by depletion of the slower-moving solvent layers near the stationary phase surface (Fig.

3). The effect does not occur for smaller polymers that do not have sufficient

hydrodynamic interaction relative to the fast internal relaxation, rotation and

translational diffusion. Only for large polymers will a higher shear strain near the

surface result in a higher internal stress, thereby making conformations that occupy this

region unfavorable. To think of this effect as stress-induced diffusion or stress-induced

deformation depends on whether or not migration of the entire coil perpendicular to the

direction of flow is achieved. Separation due to stress-induced deformation is a more-

accurate description for the aspect ratios considered in MTF.

Page 102: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Chapter 4

100

Fig. 3. Stress-induced deformation presented schematically. (a) Deformation absent at low flow rate;

(b) depletion of high-shear region near channel surface at high flow rate.

Higher entropic elasticity of branched polymers was suggested as a qualitative

explanation for topology selectivity. Different possible interpretations of polymer

deformation prevent a more accurate description at this moment. Deformation may be

explained as selective population of polymer conformations. After all, the spherical

equilibrium dimensions represent the average of many instantaneous aspherical

conformations at a time scale longer than the longest relaxation time of the polymer

[66,67]. This supports the entropic nature of (stress-induced) deformation. Differences

in flow permeability are reflected in the viscosity-shielding ratio [21], the Flory-Fox

parameter, and ratios of viscosity radius and radius of gyration [16] in Poiseuille flow

under traditional separation conditions. Most published work on deformation under flow

conditions focuses on the coil-stretch transition in elongational flow. The shear-rate

dependent coil-stretch transition for DNA was found to agree very well with predictions

based on Brownian dynamics for random coils [68]. Experiments on polystyrene,

however, demonstrated that the extended length under flow conditions did not exceed

twice the radius of gyration and was generally lower than predicted [69,70].

Experimental evidence from light scattering and birefringence measurements on the

absence of a coil-stretch transition for polystyrene were later suggested to be biased and

not selective [68,71]. Furthermore, it was suggested that shear levels were simply too

low for the polymers considered and the experiments therefore failed to provide

conclusive results.

Page 103: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Branched-Polymers Characterized by Comprehensive 2D Separations with Fully Orthogonal Mechanisms

101

In slalom chromatography (SC) coil-stretch transition interferes with the accelerated

migration by wall-exclusion of the polymer. Stretched molecules are retarded in the

tortuous interstitial space by frequent conformational changes and changes in flow

direction through the stationary phase packing. In the SC region, the extent of

deformation could potentially result in a different elution volume for linear and

branched molecules. Successful application of SC is unlikely, because it is expected that

the selectivity (length of the arrows in Fig. 2) is limited. Conditions where wall-

exclusion and slalom chromatography co-exist and their effects on migration cancel out

do not exist. Instead it was observed that flow rate could be used to obtain coil-stretch

transition for different molar masses in agreement with Deborah-number calculations.

Once this transition was reached elution volumes increased quickly [52].

4.3 Experimental

4.3.1 Chemicals and materials

The eluent for MTF and SEC separations was non-stabilized tetrahydrofuran (THF,

HPLC-grade, Biosolve, Valkenswaard, The Netherlands). The eluent was degassed by

purging with helium 5.0 (99.999% Praxair, Vlaardingen, The Netherlands). Sample

polymers were dissolved in THF stabilized with 250 mg/L butyl-hydroxylated toluene

to prevent degradation by radicals. Narrowly distributed linear polystyrene standards

(Polymer Laboratories, Church Stretton, UK) with molar masses (M) between 1,990 and

3.74 × 106 g/mol with polydispersity indices (PDI) no larger than 1.05 were used to

study retention behaviour. These standards were dissolved at concentrations between

0.1 and 1 mg/mL. A nominal “three-arm star” (or Y-shaped) polystyrene sample was

obtained from Polymer Source (Dorval, Canada) and used at a concentration of 1.0

mg/mL. Synthesis of the “star” polymer was by coupling of anionically polymerized

arms with a tri-functional agent (α,α’,α’’-trichloromesitylene). Analysis using SEC

with light scattering and viscometry revealed an arm molar-mass of 1,250 kg/mol and a

composition of 5% uncoupled precursor, 45% linear two-arm coupling product and a

remainder of three-arm coupling product [26]. Suspected side products were a four-arm

star polymer formed by lithium-halide exchange with all arms coupled in one functional

centre (X-shaped) [72,73]. The concentration of this large-molecule fraction could not

be determined quantitatively by SEC.

Page 104: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Chapter 4

102

Polystyrenes with broad molar-mass distributions were obtained from the Dow

Chemical Company (Midland, MI, USA). Dow polystyrene 1683 (weight-average molar

mass (Mw) 250 kg/mol, PDI 2.5) was used as a linear reference material. LCB

polystyrene (Mw 810 kg/mol, PDI 3.3, SEC-MALLS [28]) and low-LCB polystyrene

(Mw 310 kg/mol, PDI 5) were used for analysis of branched polymers. Long-chain

branching at high-molar mass is confirmed by the reduced intrinsic viscosity in the

Mark-Houwink plot (Fig. 7). The LCB polystyrenes were prepared by coupling of

polystyryl anions with di- and tri-functional benzyl chlorides as published elsewhere

[74]. Comb polystyrene (kindly donated by Dr. C. Fernyhough, University of Sheffield)

has a backbone molar mass of around 200 kg/mol and approximately 30 randomly

placed branches of 70 kg/mol. The synthesis technique of the comb polymer has been

described in [75].

4.3.2 Instrumentation and operating conditions

HPLC experiments were performed on a Shimadzu LC system (‘s Hertogenbosch, The

Netherlands) consisting of a system-controller (SCL10a), two micro-pumps

(LC10ADvp), a column oven (CTO7), autosampler (SIL9a), UV detector

(SPD10AVvp) and right-angle laser light scattering (RALLS) detector model LD600

(Viscotek, Houston, TX, USA). UV detection was performed simultaneously at 260 nm

and 214 nm. Modulation for comprehensive two-dimensional separation was performed

with a VICI two-position 10-port valve (Valco, Schenkon, Switzerland) with a high-

speed switching accessory and digital valve interface. The 10-port valve was plumbed

for symmetrical dual-loop modulation [76]. From the moment of injection on the 1D

column, the 10-port valve was switched at regular intervals between 1 and 3 minutes in

order to inject first-dimension effluent on the 2D SEC column. Instrument control and

data acquisition were achieved with ClassVP v7.4 build15 software (Shimadzu).

Exported data were processed in Matlab v7.3 (The Mathworks, Natick, MA, USA)

using in-house written software for data folding and visualization of two-dimensional

colour plots.

Triple-detection SEC was performed using the Shimadzu LC system plumbed for 1D

chromatography. The detection array consisted of a UV detector (SPD10AVvp),

RALLS detector (LD 600) and chip-based on-line viscometer (Polymer Laboratories /

Page 105: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Branched-Polymers Characterized by Comprehensive 2D Separations with Fully Orthogonal Mechanisms

103

Micronit, Enschede, The Netherlands). Data acquisition and processing was performed

with PLCirrus (Polymer Laboratories, v3.0) based on triple-detection SEC principles

[1].

4.3.3 Columns and experimental conditions

Wide-bore columns (4.6-mm I.D.) were used for all separations. The sample volume

injected on the 1D column was between 5 and 25 μL. Monolithic columns with narrow

macropore sizes were prepared in columns of 100, 150 and 250 mm length according to

the procedure published previously [65]. Custom-made columns (Polymer Laboratories)

were used for fast 2D SEC. A 150-mm long column packed with 10-µm 106 Å PLgel

particles (V0 = 1.9 mL) was used at 750 µL/min. Two 100-mm long columns packed

with 5-µm 105 Å PLgel particles were used in series only for the 2D separation in

HDC×SEC at 600 µL/min.

Chromatograms in the HDC×SEC mode (Fig. 5, Fig. S-1) were acquired with two 150

mm 1D monolithic column in series (V0 = 3.1 mL) at 10 µL/min. 160 2D chromatograms

were obtained during a runtime of 480 minutes at 50°C. Flow-rate studies in MTF×SEC

(Fig. 6) were performed on a 250 mm monolithic 1D column (V0 = 2.6 mL) with Dpore

126 nm and a 150 mm 106 Å 2D column, with both columns operated at 40°C. 200 2D

chromatograms were obtained by injection of 30 µL 1D effluent fractions at a

modulation interval matched to the 1D flow rate. MTF×SEC at conditions with minimal

molar mass selectivity (Fig. 7) was achieved using two 150 mm monolithic columns

(Dpore = 126 nm, 30 µL/min) and a 150 mm 106 Å 2D column. 80 2D chromatograms

were obtained during a runtime of 120 minutes at 50°C.

Light scattering was used in most 2D experiments. It allows for overlapped 2D

injections, because a solvent signal is not present. This is beneficial in experiments

where higher 1D flow rates are used and the time required to complete the 2D separation

is rate limiting. More second-dimension chromatograms can be obtained when using the

RALLS signal.

Triple-detection SEC was performed at room temperature with a flow rate of 0.3

mL/min. A set of two minimix B (10-µm particles) and one minimix C (5-µm particles)

columns (each 250 mm long) was used.

Page 106: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Chapter 4

104

4.4 Results and discussion

4.4.1 Flow-rate effect for columns with different pore size

Monolithic columns with well-controlled macropore sizes were prepared by in-situ

polymerization of polystyrene and divinylbenzene. In thermodynamically favorable or

‘good’ solvents, such as tetrahydrofuran for polystyrene, polymers readily dissolve and

can be separated free from enthalpic interaction with the column. The selectivity for

hydrodynamic separations on monolithic columns has been studied for linear polymers

[65]. A flow-rate effect on migration rate was observed and stress-induced diffusion

(SID) was presented as the mechanism responsible for this effect when separating

synthetic polymers in macropores close to unperturbed-polymer dimensions. The

hypothesis of SID playing an important role in MTF separations will be tested with the

results obtained in this work on branched-polymer separations. After presenting the

results we provide a detailed discussion on the mechanism.

Channel dimensions of the columns used in the present work have been optimized for

MTF separation. Separation by a HDC mechanism according to unperturbed-polymer

dimensions was obtained at low flow rates. This is demonstrated by the calibration

curves obtained with narrow-molar-mass polystyrenes for columns with pore sizes

(Dpore) ranging from 160 nm down to 75 nm (Fig. 4, Table 1). At 20 µL/min reversal of

the calibration curve is observed for high molar masses. This is in agreement with HDC

separation of rigid solutes (solid spheres) where hydrodynamic interaction at λ > 0.4

will reduce the migration rate. The retardation for high- molar-mass polymers is

generally reduced when the flow rate is increased to 50 µL/min. This was also observed

for micro-porous membranes where the rejection of large polymers decreased at higher

flow rates [58]. Calibration curves in Fig. 4 indicate that only the hydrodynamic effects

for λ approaching 1 are affected, because the selectivity for molecular weights below

the point of reversal is maintained. Wall exclusion-effects and coil dimensions that

induce these effects apparently have not changed for polymers below the reversal molar

mass. Under certain conditions the molar-mass selectivity diminishes above the reversal

point. Hydrodynamic interactions and calibration-curve reversal depend on the aspect

ratio λ, rather than on the molar mass. Thus, we should preferably speak of a reversal

(or critical) size. In practice, we may refer to a critical molar mass. In the present case

Page 107: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Branched-Polymers Characterized by Comprehensive 2D Separations with Fully Orthogonal Mechanisms

105

this is a linear-polystyrene-equivalent molar mass. The effective radius for wall-

exclusion separations [77] is used in calculating λ and is given in Eq. 8 for polystyrene

in THF [78].

𝑟𝑒𝑓𝑓 = √𝜋2𝑟𝑔 = √𝜋

20.0118 𝑀0.600 (8)

In MTF experiments it has been observed that branched polymers are ‘retained’ longer

than linear polymers for λ > 0.4 [41,28]. At optimized experimental conditions a

separation may then be performed where linear polymers above a critical molar mass

co-elute, while branched materials elute later from the column and co-elute with linear

polymers of lower molecular weight. In a comprehensive MTF×SEC separation the co-

eluting species can be separated and distributions in terms of hydrodynamic size and

branching will be obtained.

Monolithic columns with three different flow-through-pore sizes were considered for

MTF in MTF×SEC separations. Small pores are required to obtain λ values high

enough to allow MTF separations of polymers below 1000 kg/mol. A special test was

designed to establish the molecular weight at the point of reversal in the calibration

curve. Broad-MWD polystyrene was analyzed in a comprehensive two-dimensional

separation with the monolith in the first dimension (1D) and a regular SEC column in

the second dimension (2D). Separation in the ‘HDC×SEC-mode’ was obtained for

monolith 7 (see Table 3) with Dpore = 126 nm at a flow rate of 10 µL/min (Fig. 5). The

ionol peak originating from the sample solvent marks the void volume in both the 1st

and 2nd dimensions at τ = 1.00 and Vsec = 2.4 mL, respectively. The earliest eluting

polymeric material from the monolith (τ = 0.69) was used to determine the critical molar

mass of reversal. Mcrit, (Table 1) is the peak molar mass in the 2D SEC separation of the

first fraction containing polymer. Two-dimensional separations for monolith 8 and 9, as

well as the calibration curve for the 2D SEC separation are presented in section 4.6.1 of

the Appendix. Calibration-curve reversal for separation at 10 µL/min occurs at roughly

identical values of λ (Table 1), which are very close to the expected value of 0.37 based

on the Dimarzio-Guttman retention model for HDC of unperturbed polymers (Eq. 3

with C = 2.7).

Page 108: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Chapter 4

106

Fig. 4. Calibration curves for narrow polystyrene standards obtained on monoliths

at 20 µL/min (a) and 50µL/min (b).

Page 109: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Branched-Polymers Characterized by Comprehensive 2D Separations with Fully Orthogonal Mechanisms

107

Fig. 5. Calibration plot obtained by MTF×SEC for a broad standard 1F = 10 µL/min

(PS1683; Mw = 250 kg/mol, PDI = 2.5) using monolith 7 in the first dimension.

Table 1. Reversal molar masses for monoliths determined by HDC×SEC at 10 µL/min.

Monolithic ID Dpore (nm) Mcrit (kg/mol) λ

6 160 [700]* [0.4]*

7 126 355 0.36

8 104 260 0.36

9 75 207 0.39

*Approximate values obtained from calibration curve at 20 µl/min

Comprehensive-two-dimensional chromatography is highly useful for exploring the

migration behavior in MTF. Not only does it provide more information than a

calibration curve based on the injection of narrow-MWD standards, it also allows the

characterization of samples with a high polydispersity. The 2D chromatogram gives a

qualitative impression of the calibration curve in a single experiment (Fig. 5).

Therefore, the flow-rate effect was examined by MTF×SEC with 1D flow rates (1F)

between 10 and 75 µL/min. A shorter 2D column with packing optimized for separation

of large polymers was used (supplementary information, S2). Linear polymers with

molecular weights above Mcrit were separated on a monolith with Dpore = 126 nm at 10

µL/min (Fig. 6a) and at 30 µL/min (Fig. 6b). A sample of three polystyrene standards of

1.37⋅106, 2.56⋅106 and 3.74⋅106 g/mol was used, which for this monolith corresponds to

aspect ratios in the range 0.80 < λ < 1.46. Higher flow rates result in a transition from

Page 110: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Chapter 4

108

polymers separated under equilibrium conditions (HDC) to polymers separated in a

deformed state (MTF) (Fig. 6, Fig. S-4). The three peaks corresponding to the narrow

standards merge into a single peak in 1D and molecular-weight independence is

achieved for these high-molecular-weight materials. For the monolith with Dpore = 126

nm a flow rate of 1F = 30 µL/min was used in subsequent experiments to suppress the

molar-mass selectivity. A similar suppression of molar-mass selectivity above Mcrit was

obtained with a Dpore = 104 nm monolith, but at a higher flow rate. In 2D experiments

with this column (L = 100 mm) the lowest degree of molar-mass selectivity was

obtained for 1F = 50 µL/min (Fig. S-6). The calibration curves in Fig. 4b confirm this

trend, but do reveal little retention above Mcrit. The small 1D column volume is limiting

the number of 2D chromatograms and thus the resolution of the 2D experiment.

However, the use of long columns with narrow pores is experimentally challenging. The

pressure drop that is required for operating longer monolithic columns with Dpore = 104

nm or smaller is so high as to cause irreversible damage by compression of the

stationary phase. Additional results on MTF×SEC at various flow rates for both column

types are presented in the supplementary information, section S3.

Fig. 6. A mixture of three narrow-MMD polystyrenes separated on an MTF column with Dpore = 126 nm at

different flow rates. (a) 10 µL/min (b) 30 µL/min.

4.4.2 Branched-polymer separations

Conditions for MTF separation with minimal molar-mass selectivity for linear polymers

above Mcrit were established. Branched polymers with different topology were analyzed

at those conditions using MTF×SEC to assess branching-selectivity in MTF (Fig. 7). A

linear reference prepared by mixing Dow1683 with the narrow standards from Fig. 6

was used to cover a wide molar-mass range. Only little retardation for the highest

Page 111: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Branched-Polymers Characterized by Comprehensive 2D Separations with Fully Orthogonal Mechanisms

109

molar-mass polymers was observed in Fig. 7a. Such small difference may be the result

of inaccuracy of the flow or the porous properties of the column (similar columns were

used, see section 4.3.3). Star-branched polystyrene prepared by coupling of 1250

kg/mol linear ‘arms’ was mixed with the linear reference. Base-line separation of the 3-

arm (Y-shaped) and 4-arm (X-shaped) branched coupling products from the linear

materials is obtained (Fig.7b). The linear 2-arm coupling product and single arm

polystyrene elute together with the linear materials. The 4-arm star, which is a by-

product from the coupling reaction, is base-line separated from the 3-arm star. This

separation provides a dramatic demonstration of the separation of high molar-mass,

branched polymers with only a single branching point from linear polymers with a

broad range in molar mass and hydrodynamic size. An overview of the elution volumes

in both dimensions is given in Table 2. Calibration of the 2D separation with linear

polymers was used to calculate λ values for the branched material eluting from the MTF

column (supplementary information, S2).

Retardation of polymers with higher branching frequency was observed already at

smaller hydrodynamic size relative to long-chain branched (LCB) star polymer.

Random long-chain branched material (LCB PS, Fig. 7c) and a comb polymer with

controlled long-chain branching (Fig. 7d) were separated at the same conditions as those

used in Fig.7a and 7b. The results of analyses by SEC with triple detection are provided

in Fig. 8 for reference. For both the separations of LCB PS and Comb polymers by

MTF×SEC a tail is observed in the MTF direction. This is the expected result for the

LCB PS, because here the degree of branching increases with molecular weight. In case

of the comb the tail may reflect a cross-linking byproduct of the synthesis. The comb

itself (VMTF = 2.48 mL) is hardly retained, most likely because its aspect ratio (λ) is too

low for significant hydrodynamic interactions to occur. In the UV chromatogram a

small amount of polystyrene with a smaller hydrodynamic size than the bulk of the

sample can also be observed (Fig. S-7). This material is not separated from the bulk in

the 2D SEC separation or in the triple-detection analysis. Most likely this is a uncoupled

linear precursor that has remained in the comb sample as a side-product.

Page 112: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Chapter 4

110

The branched materials retarded in MTF have different hydrodynamic sizes depending

on their topology. In Fig. 9 an overlay with 2D-SEC peak maxima from Fig. 7 is

presented on top of the linear reference polymer. LCB and comb polymers start to be

retained at lower hydrodynamic sizes than the star polymers. This implies that stress-

induced deformation effects are less effective in counteracting the hydrodynamic effects

for polymers with higher degree of branching. A plausible explanation is that polymers

with higher segment density are less susceptible to deformation. Segment density in

solution is inversely related to intrinsic viscosity, which is given in Fig. 8. Lower

intrinsic viscosity for polymers above log M = 6 correlates well with the lower λ for

material retarded in MTF (Table 2).

4.4.3 Selectivity for branched polymers

A better look at the separation conditions is needed to understand the separation

selectivity for branched polymers. We will assume that polymers with higher segment

densities than linear polymer will deform to a lesser extent under stress and , therefore,

resemble HDC behaviour. Material eluting later than linear polymers above Mcrit at λ >

0.4 will have a higher segment density and/or a larger hydrodynamic size. In the case of

3- and 4-arm star polymers the elution is affected by segment density only, because

hydrodynamic size (e.g. λ) is identical. For the randomly branched LCB polymer

branching and hydrodynamic size both increase, indicating that molar mass increases

for material eluting later from the MTF column. However, when segment density is too

high to allow for deformation and hydrodynamic size is large then polymers may elute

very late or not at all. The tail for both LCB and comb polystyrene is indicative of very

dense polymer (possibly crosslinked) that is not completely eluting. Applicability of the

present separation conditions is limited to conditions that allow polymers to elute from

the MTF column within reasonable time. This may be achieved by using MTF columns

with pore size matched to polymers of interest or by changing the conditions to make

also more dense polymers at higher λ elute.

While material eluting slowly from the MTF column can be explained as material with

exceptional high coil density, it can also be argued that this is the result of polymer

degradation. The light-scattering signal from RALLS divided by a concentration signal

(UV) was used to estimate molar-mass changes for material eluting from the MTF

Page 113: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Branched-Polymers Characterized by Comprehensive 2D Separations with Fully Orthogonal Mechanisms

111

column. High angular dependence of the RALLS signal makes it impossible to

quantitatively compare LS/UV ratios without correction for angular dependence, which

strongly depends on polymer size. However, it is possible to use the LS/UV ratio for a

qualitative comparison when dealing with polymers of identical size (e.g. eluting at

identical 2tr). The LS/UV ratio for polymers in Fig. 7 is presented in Fig. S-7. In all

cases material eluting later from the MTF column was found to have a higher LS/UV

ratio, which is indicative of higher molar mass. MTF×SEC-MALLS was performed to

obtain accurate molar mass following the separation of LCB PS on the monolithic

column with Dpore = 104 nm (Supplementary Information, S5). The gradual increase in

molar mass was confirmed and material up to the highest mass present in this polymer

as measured in Fig. 8 was found back in fractions eluting later from the MTF column.

Fig. 7. 2D Chromatograms of polystyrene polymers separated by MTF×SEC with 1F 30 µL/min. (a) Linear polymers 20 – 3740 kg/mol; (b) linear and star polymers; (c) LCB PS; (d) comb PS.

Page 114: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Chapter 4

112

Table 2. Elution volume and aspect ratio for polymers of different topology in MTF×SEC (V0,MTF = 3.1 mL).

MTF SEC MTF linear reference

Vmax (mL) τ Vmax (mL) λ τ 3-arm star 3.02 0.97 1.28 0.88 0.78

4-arm star 4.41 1.42 1.28 0.87 0.78

LCB 3.02 0.97 1.38 0.53 0.78

3.38 1.09 1.37 0.55 0.78

3.60 1.16 1.37 0.56 0.77

4.37 1.41 1.36 0.58 0.77

5.09 1.64 1.35 0.60 0.77

Comb 2.48 0.80 1.42 0.43 0.77

3.38 1.09 1.41 0.47 0.77

5.04 1.63 1.38 0.54 0.77

Fig. 8. Mark-Houwink plot of linear and branched polystyrene samples. Dow PS1683 (1), star [26] (2), low-LCB PS (3), LCB PS (4), comb (5).

Page 115: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Branched-Polymers Characterized by Comprehensive 2D Separations with Fully Orthogonal Mechanisms

113

Fig. 9. Linear polymer separated by MTF×SEC;

overlay of peak maxima in 2D light-scattering signal for star (+), LCB (o) and comb (x) polymers.

4.4.4 Effect of flow rate on migration of branched polymers

The flow rate applied in MTF separation can be used to change migration behavior for

branched polymers in a similar way as it was used to obtain molecular-weight

independent elution for linear polymers. MTF×SEC experiments were performed with

MTF flow rates up to 75 µL/min on the star polymer and two LCB polymers with

different degrees of branching (Supplementary information, S6). At 75 µL/min the star

polymer and the polymer with a low degree of LCB could be completely eluted within a

single column volume. These results support that flow rate can be used to control

migration rates for both linear and branched polymers and influence their recovery.

Only polystyrene with material that is highly branched or even cross-linked did not

readily elute at these conditions.

Polymers with a low degree of branching are not well separated in the MTF separation

at higher flow rates. In order to obtain good separation for materials subject to much

different extent of retardation on the MTF column a flow-rate gradient may be applied.

It was observed in experiments at constant flow rate that little separation was obtained

for polymers eluting after the column void volume (V0). An MTF×SEC experiment was

performed in which the flow rate was increased gradually from 10 µL/min to 20 µL/min

between 150 and 250 minutes or once the elution volume approached V0 (Fig. 10). A

Page 116: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Chapter 4

114

complete separation resulted, in which well-resolved peaks were observed for the

single-arm precursor up to the 4-arm star. Even a high molar-mass coupling product can

be discerned, which has a slightly smaller hydrodynamic size. The elution of highly-

branched materials with a smaller hydrodynamic size than earlier eluting material was

also observed in constant flow rate experiments for three-arm star polymer (Fig. S-9)

and LCB polystyrene (Fig. S-10).

Fig. 10. MTF×SEC separation of star-polymer sample using a flow-rate gradient; (1) unreacted single-arm

polymer (2) two-arm linear coupling product (3) 3-arm star polymer (4) 4-arm star polymer (5) higher coupling product.

The star polymer separated in Fig. 10 could even be fractionated by topology in a 1D-

MTF experiment. Such a separation is unlikely for other branched polymers under the

conditions used for this separation, because linear and branched polymers may co-elute

as a result of the low flow rate. Operating at conditions with minimal selectivity for

linear polymers provides the most powerful application. The optimal experiment would

therefore start at conditions with minimal selectivity for linear chains. Once linear

materials have eluted the flow rate may be ramped up to elute branched material with

higher segment density from the column.

Page 117: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Branched-Polymers Characterized by Comprehensive 2D Separations with Fully Orthogonal Mechanisms

115

4.4.5 Effect of temperature on migration of polymers in MTF

The effect of flow rate on selectivity in MTF is very clear and can be understood. It

provides direct control over the levels of shear and stress that polymers in solution are

subjected to. Temperature as a parameter to control deformation was not considered in

detail, but it may certainly be used for this purpose considering the low speed of

separation. Higher temperatures induce faster polymer relaxation (τrel, eq. 7) through

faster Brownian motion and lower solvent viscosity. The migration of polymer above

Mcrit will be slower at higher temperatures because of less deformation. This trend was

confirmed in a comparison of linear and star polymers separated at both 50 °C and room

temperature. However, the effect of temperature on retention proved rather small, even

at low flow rates (Supplementary section S7). Great changes in polymer relaxation

times cannot be achieved within the limits of practical separation conditions. Flow rate

is a more effective parameter, exerting a greater effect on migration and selectivity.

4.5 Conclusions

Molecular-topology fractionation (MTF) is a term used to denote separations of

branched and linear polymers as a result of selective deformation. MTF separations

combine characteristics of HDC and reptation. Polymers were separated on monolithic

column with flow-through channels only slightly larger than the polymer itself. At such

conditions polymer molecules experience strong hydrodynamic interactions, resulting in

deformation and increased migration rates. MTF separations were used successfully to

fractionate polymers by their topology in a comprehensive two-dimensional separation

with size-exclusion chromatography (SEC) in the second dimension (MTF×SEC).

Selectivity based on topology is introduced through faster relaxation of branched

polymers subject to shear deformation. At optimized conditions the effects of

hydrodynamic interaction and deformation for linear polymers compensate for each

other. Such conditions allows for an orthogonal separation of polymers by their

hydrodynamic size and branching properties above Mcrit.

Branched polystyrenes with λ between 0.4 and 0.9 were separated from linear polymers

with identical hydrodynamic size. A relation was observed between the aspect ratio of

branched polymers retarded in MTF and coil density in solution. The absence of

migration effects resulting from polymer properties other than topology with an effect

Page 118: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Chapter 4

116

on coil density was not rigorously validated in this study. It would be interesting to

assess the impact of chemical composition and short-chain branching on migration for

application of MTF to polyolefins and polar synthetic polymers. Several results support

the hypothesis of molecular relaxation as the decisive property for selectivity in MTF,

such as increased retention above Mcrit at higher temperature or the higher flow rates

needed for molar-mass-independent elution from monoliths with narrower flow-through

channels.

MTF×SEC was used to investigate MTF separations preferably on long 1D columns for

better separation efficiency. Lengthy experiments were the result and comprehensive

on-line coupling with SEC proved impossible without a significant sacrifice in terms of

separation efficiency. For practical purposes off-line fractionation may be used once the

separation conditions are known [26]. A simple SEC-MTF experiment with MTF

performed at conditions with minimal molar mass selectivity above Mcrit can be used for

a fast and inexpensive screening for branched material. In another approach a short

MTF column may be used to obtain the fraction with branched material and linear

molecules below Mcrit. A high-resolution SEC experiment with selective detection may

than be used to characterize only the branched material free from co-eluting linear

material.

A challenge for the application of MTF is still the lack of commercially available

stationary phases with suitable flow-through-channel dimensions. High diffusion and

fast relaxation of synthetic polymers require an aspect ratio (λ) close to unity for

branched molecules. Extension of deformation-selective separation of branched

polymers towards either larger polymers or polymers with longer relaxation times may

be possible even when using commercially available HDC columns. Starches and bio-

polymers may satisfy this criterion and provide interesting cases [79].

Page 119: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Branched-Polymers Characterized by Comprehensive 2D Separations with Fully Orthogonal Mechanisms

117

4.6 Appendix

4.6.1 Comprehensive HDC×SEC experiment

Monolithic columns with different pore sizes were used to obtain chromatograms at

identical conditions (see Table 1). The chromatograms obtained using each monolith in

the first dimension for HDC×SEC are presented in Fig. S-1.

Fig. S-1. HDC×SEC performed with 1D monolithic phases 7 (a), 8 (b) and 9 (c).

The sample was 0.8 mg/mL PS1683 + 0.1 mg/mL 2MDa narrow-standard PS in THF.

Two 100 mm × 4.6 mm I.D. column packed with 5-µm 105 Å PLgel were used in the

second dimension. Accurate molar-mass calibration was performed by injection of four

mixtures, each with three narrow-MMD PS standards. Calibration samples were

injected at 30 min intervals with 1F = 10 µL/min. Elution volumes corresponding to

peak maxima were used to construct a third order polynomial fit (Fig. S-2). This

calibration data were used to calculate Mcrit for each monolithic phase (Table 1).

Fig. S-2. Narrow MMD PS standards separated using HDC×SEC (a)

and calibration of the second-dimension SEC separation (b).

y = -2.5x3 + 11.8x2 - 20.6x + 18.1

3

4

5

6

7

1 1.5 2 2.5

log

M

Elution volume (mL)

(b)

Page 120: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Chapter 4

118

4.6.2 Second-dimension calibration for MTF×SEC

For MTF×SEC experiments a 2D column with a high exclusion limit (10-µm 106 Å

PLgel particles, 150 × 4.6 mm I.D.) was used to prevent overloading and anomalous-

elution behavior in the 2D-SEC separation. Accurate molar-mass calibration was

performed by injection of four mixtures, each with three narrow-MMD PS standards.

Peak maxima from the UV signal were used to construct the calibration curve (Fig. S-

3). The polynomial equation fitted to the calibration curve was used to calculate

polymer size corresponding to each elution volume in order to calculate λ values (Eq. 8 /

Table 2).

Fig. S-3. Calibration experiment and calibration curve for second-dimension of MTF×SEC separations.

4.6.3 Flow-rate effect in MTF×SEC

The transition from an HDC to an MTF-type separation at critical conditions is

demonstrated in Fig. S-4 using a comprehensive two-dimensional experiment. Linear

and star-branched polymers were separated on a 250-mm long monolithic column with

Dpore = 126 nm at 10, 15, 20 and 30 µL/min (Fig. S-4). A sample containing three linear

polystyrene standards of 1.37⋅106, 2.56⋅106 and 3.74⋅106 g/mol was used, as well as a

nominal “three-arm star” (or Y-shaped) polystyrene sample obtained from Polymer

Source (Dorval, Canada; see section 4.3.1).

A particularly challenging aspect of studies into flow-rate effects is the transfer of all 1D

effluent to the 2D separation. The flow rate and injected amount in the 2D were kept

identical to maximize the comparability. 200 Injections of 30 µL each were transferred

to the 2D in all chromatograms, irrespective of the 1D flow.

y = -251x5 + 1,897x4 - 5,720x3 + 8,597x2 - 6,443x + 1,933

2

3

4

5

6

7

1 1.5 2

log

M

Elution volume (mL)

(b)

Page 121: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Branched-Polymers Characterized by Comprehensive 2D Separations with Fully Orthogonal Mechanisms

119

For the chromatogram with 1F = 30 µL/min only one minute is available for each 2D

chromatogram. An experimental problem is the overlap or wrap-around in the UV

signal for these short sampling intervals. Signals near the void volume of the 2D column

interfere with the high-molar-mass peaks in the subsequent 2D chromatogram.

Fig. S-4. Transition of the 1D separation mode from HDC to MTF.

Linear polymer at 10 (a), 15 (b), 20 (c) and 30 µl/min 1F (d); three-arm “star” polymer at 10 (e), 15 (f), 20 (g) and 30 µl/min 1F (h).

Experiments were performed with RALLS detection using 150 mm 1D columns to study

selectivity at higher flow rates for linear polymers. The sample was a mixture of nine

narrow-MMD linear PS standards in the range 200 – 3740 kg/mol. Separations on

monolithic material 7 were performed with 1F between 75 and 10 µL/min (Fig. S-5). A 1D flow rate higher than 33 µL/min does not significantly change the selectivity or bring

additional advantages other than analysis-time reduction. Such high flow rates are not

practical for comprehensive 2D separations, because adjustments to the second

dimension are required to deal with the larger 1D flow. These will result in either a

reduced separation efficiency or a lower sensitivity. For 1F of 50 and 75 µL/min part of

the 1D effluent is lost between 2D injections.

Page 122: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Chapter 4

120

Fig. S-5. Flow-rate effect for linear polystyrene on a 150 × 4.6 mm I.D. monolith with Dpore = 126 nm.

1F = 75 (a), 50 (b), 33 (c), 22 (d), 15(e) and 10 (f) µl/min.

Flow-rate effects were also investigated for a 100 mm monolith with smaller pores (Fig.

S-6). Molar-mass selectivity can be suppressed at comparable or slightly higher flow

rates relative to a Dp = 126 nm monolith. At a flow rate in between 33 and 50 µL/min a

separation can be obtained with minimal molar-mass selectivity. The narrow-pores of

this monolith induced higher operating pressures. A backpressure of 13 MPa was

measured for separation at 50 µL/min with THF at 50°C.

Page 123: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Branched-Polymers Characterized by Comprehensive 2D Separations with Fully Orthogonal Mechanisms

121

Fig. S-6. Flow-rate effect for linear polystyrene on a 100 × 4.6 mm I.D. monolith with Dpore = 104 nm.

1F = 50 (a), 33 (b), 22 (c), 15 (d), and 10 (e) µl/min.

4.6.4 MTF×SEC at orthogonal conditions

All detector signals for the separations shown in Fig. 7 (see section 4.4.3) are presented

in Fig. S-7. The detector array consisted of a Shimadzu dual-wavelength UV detector

and a Viscotek right-angle laser light scattering (RALLS) detector coupled in series. In

the bottom row the light-scattering signal divided by the UV absorption signal at 214

nm is presented to give an indication of changes in molar mass. The angular dependence

for 90° light scattering is significant for the polymers considered here. Regardless of the

reduced scattering intensity for large solutes, the signal is most sensitive for high molar-

mass polymers. A comparison of the LS/UV ratio at identical 2tr yields a qualitative

indication of molar-mass changes. The ratio is sensitive to inter-detector delay and

inter-detector band broadening.

Page 124: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Chapter 4

122

Fig. S-7. Polystyrene separated by MTF×SEC at 30 µL/min; consecutive detector signals from top to bottom: UV 260nm, UV 214nm, 90° light scattering and light scattering / UV 214nm ratio (indicated near color bar).

(a) linear polymers (b) linear and star polymers (c) LCB polymer Mw 810 kg/mol (d) comb polymer

Page 125: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Branched-Polymers Characterized by Comprehensive 2D Separations with Fully Orthogonal Mechanisms

123

4.6.5 MTF×SEC-UV/MALLS on long-chain-branched polystyrene

An experiment was performed where the RALLS detector in the MTF×SEC-

UV/RALLS setup was replaced by a MALLS detector. For the 1D a 150 mm × 4.6 mm

I.D. column with Dpore = 104 nm monolith (monolith 8) was used with 1F = 30µL/min.

The 2D was identical to other MTF×SEC experiments (150 mm × 4.6 mm I.D. 10 µm

106 PLgel with 2F = 750 µL/min). 25 µL of 1 mg/mL LCBps were injected. Fractions of

90 µL each were transferred to the 2D separation. Results of this experiment are

presented in Fig. S-8.

Fig. S-8. 2D plots for UV absorption (a) and the 90° light-scattering signal (b), as well as molar mass for MTF

fractions from the MTF×SEC-UV/MALLS experiment between 1.1 and 1.9 mL in the 1D (c).

41.0x10

51.0x10

61.0x10

71.0x10

1.2 1.4 1.6 1.8 2.0

Mol

ar M

ass

(g/m

ol)

Volume (mL)

Molar Mass vs. Volume LCBps_03LCBps_04LCBps_05LCBps_06LCBps_07LCBps_08LCBps_09LCBps_10

(c)

Page 126: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Chapter 4

124

The signal from the MALLS detector was sufficient to calculate molar-masses, but not

for calculating Rg. Therefore, a conformation plot with results of the different fractions

could not be created. The increase in molar mass for materials eluting at the same

hydrodynamic volume (in the 2D) supports the hypothesis that material eluting later

from the MTF column has an increasing degree of branching.

4.6.6 Selectivity in MTF as a function of flow rate

MTF×SEC Experiments were performed with linear (Fig. S-5) and branched polymers

(Fig. S-9 through Fig. S-11) at different 1D flow rates. A 150 mm × 4.6 mm I.D. column

with Dpore 126nm with V0 = 1.65 mL was used. Experimental conditions are presented

in Table S-1.

Red +++ was added as a marker for 2D-peak maxima to 2D chromatograms of branched

samples as a visual aid to help establish whether material is still eluting from the 1D

column.

Fig. S-9. “Star” polymer separated at different flow rates in 1D MTF.

75 (a), 50 (b), 33 (c), 22 (d), 15(e) and 10 µL/min (f)

Page 127: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Branched-Polymers Characterized by Comprehensive 2D Separations with Fully Orthogonal Mechanisms

125

Fig. S-10. LCB Polymer separated at different flow rates in 1D MTF.

75 (a), 50 (b), 33 (c), 22 (d), 15(e) and 10 µL/min (f).

Fig. S-11. Polymer with little LCB separated at different flow rates in 1D MTF.

75 (a), 50 (b), 33 (c), 22 (d), 15(e) and 10 µL/min (f). A problem with the 2D pump prevented completion of the experiment at 10 µl/min (f).

Page 128: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Chapter 4

126

Table S-1.: Experimental conditions for the separations in Fig. S-9, S-10 and S-11.

1D flowrate (µL/min)

2D time (min)

2D injection volume (µL)

Total time min.

(2D chromatograms)

Total volume 1D (mL)

75 1.33 100* 80 (60) 6

50 1.33 66.6* 120 (90) 6

33 1.33 34 180 (135) 6

22 1.33 30 266 (200) 6

15 2 30 400 (200) 6

10 3 30 600 (200) 6

* Incomplete sampling is expected due to the use of 45 µL transfer loops.

4.6.7 Effect of temperature on MTF×SEC separations

Separations of linear and star-branched polystyrene polymers by MTF×SEC were

performed under identical conditions, but at room temperature and 50°C different

temperatures. For the 1D a 100 mm × 4.6 mm I.D. column with Dpore = 104 nm

(monolith 8) was used with 1F = 10 µL/min. The 2D was a 250 mm × 4.6 mm I.D., 10

µm Mini-mixed B column with 2F = 600 µL/min. 25 µL of sample solution were

injected. 60 Consecutive fractions of 50 µL were transferred to the 2D.

2D Chromatograms of the separations are provided in Fig. 12 and Fig. 13.

Dimensionless elution volume (τ) is provided for a convenient comparison of elution

volumes in the first-dimension (table S-2) and the second-dimension (table S-3).

Table S-2.: First-dimension temperature dependence of polymer separations in Fig. S-12 and S-13

Elution volume MTF (mL) τMTF

Label Sample 25°C 50°C 25°C 50°C

1 ionol 1.1 1.1 1 1

2 9.9 kg/mol PS 1.05 1.05 0.95 0.95

3 197 kg/mol PS 0.8 0.8 0.73 0.73

4 3742 kg/mol PS 1.25 1.4 1.14 1.27

5 ionol 1.15 1.15 1 1

6 2-arm linear PS 1.2 1.3 1.09 1.18

7 3-arm “Star” PS 1.65 1.95 1.50 1.77

Page 129: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Branched-Polymers Characterized by Comprehensive 2D Separations with Fully Orthogonal Mechanisms

127

Table S-3.: Second-dimension temperature dependence of polymer separations in Fig. S-12 and S-13

Elution volume SEC (mL) τSEC

Label Sample 25°C 50°C 25°C 50°C

1 ionol 3.04 2.94 1 1

2 9.9 kg/mol PS 2.59 2.52 0.85 0.86

3 197 kg/mol PS 2.21 2.14 0.73 0.73

4 3742 kg/mol PS 1.81 1.76 0.60 0.60

5 ionol 3.18 3.09 1 1

6 2-arm linear PS 1.87 1.82 0.62 0.62

7 3-arm “Star” PS 1.84 1.79 0.61 0.61

Fig. S-12. Room-temperature separation of narrow-MMD linear standards (a)

and a three-arm “Star” Polymer (b).

. Fig. S-13. Separation of narrow-MMD PS standards (a) and a three-arm “Star” Polymer (b) at 50°C.

Page 130: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Chapter 4

128

References

[1] C. Harper, Handbook of Plastics, Elastomers, and Composites, McGraw-Hill, New York, 3rd ed., 1996.

[2] G.S. Grest, L.J Fetters, J.S. Huang, D. Richter, Adv. Chem. Phys. 94 (1996) 67.

[3] N. Hadjichristidis, M. Xenidou, H. Iatrou, M. Pitsikalis, Y. Poulos, A. Avgeropoulos, S. Sioula, S.

Paraskeva, G. Velis, D. J. Lohse, D. N. Schulz, L. J. Fetters, P. J. Wright, R. A. Mendelson, C. A.

Garcıa-Franco, T. Sun, C. J. Ruff, Macromolecules 33 (2000) 2424.

[4] D. J. Lohse, S. T. Milner, L. J. Fetters, M. Xenidou, N. Hadjichristidis, R. A. Mendelson, C. A. García-

Franco, M. K. Lyon, Macromolecules 35 (2002) 3066.

[5] J.B. Listing, Vorstudien zur topologie, Vandenhoeck und Ruprecht, Göttingen, 1848, pp. 67.

[6] P.G. Tait, Nature 27 (1883) 316.

[7] T.C.B. McLeish, S.T. Milner, Adv. Polym. Sci. 143 (1999) 195.

[8] D.J. Read, D. Auhl, C. Das, J. den Doelder, M. Kapnistos, I. Vittorias, T.C.B McLeish, Science 330

(2011) 1871.

[9] J. Gerber, W. Radke, Polymer 46 (2005) 9224.

[10] K. Im, Y. Kim, T. Chang, K. Lee, N. Choi, J. Chrom. A 1103 (2006) 235.

[11] X. Jiang, A. van der Horst, V. Lima, P.J. Schoenmakers, J. Chromatogr. A 1076 (2005) 51.

[12] T. Macko, R. Brüll, R.G. Alamo, F.J. Stadler, S. Losio, Anal. Bioanal. Chem. 399 (2011) 1547.

[13] W. Hiller, H. Pasch, T. Macko, M. Hoffmann, J. Glanz, M. Spraul, U. Braumann, R. Streck, J. Mason,

F. van Damme, J. Magn. Reson. 183 (2006) 309.

[14] C. Piel, E. Jannesson, A. Qvist, Macromol. Symp. 2009 (282) 41.

[15] P.M. Wood-Adams, J.M. Dealy, A.W. deGroot, O.D. Redwine, Macromolecules 33 (2000)7489.

[16] W. Burchard, in: J. Roovers, (ed.), Solution Properties of Branched Macromolecules, Adv. Polym. Sci.

143 (1999) 113.

[17] P.M. Cotts, in: A. M. Striegel (ed.), Multiple Detection in Size-Exclusion Chromatography, ACS Symp.

Ser. 893, American Chemical Society, Washington, DC, 2005, pp. 52.

[18] B.H. Zimm, W.H. Stockmayer, J. Chem. Phys., 17 (1949) 1301.

[19] B.H. Zimm, R.W. Kilb, J. Polym. Sci. 37 (1959) 19.

[20] T.H. Mourey, Int. J. Polym. Anal. Charact. 9 (2004) 97.

[21] A.M. Striegel, W.W. Yau, J.J. Kirkland, D.D. Bly, Modern Size-Exclusion Liquid Chromatography,

John Wiley & Sons, Hoboken (NJ), 2nd ed., 2009.

[22] S.T. Balke, T.H. Mourey, J. Appl. Polym. Sci. 81 (2001) 370.

[23] M. Gaborieau, J. Nicolas, M. Save, B. Charleux, J.-P. Vairon, R.G. Gilbert, P. Castignolles, J.

Chromatogr. A 1190 (2008) 215.

[24] D.A. Hoagland, R.K. Prud’homme, Macromolecules 22 (1989) 775.

[25] D.M. Meunier, P.B. Smith, S.A. Baker, Macromolecules 38 (2005) 5313.

[26] D.M. Meunier, T.M. Stokich Jr., D. Gillespie, P.B. Smith, Macromol. Symp. 257 (2007) 56.

[27] Philip J. Marriott, Peter Schoenmakers, Ze-ying Wu, LC-GC Europe 25 (2012) 266.

Page 131: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Branched-Polymers Characterized by Comprehensive 2D Separations with Fully Orthogonal Mechanisms

129

[28] R. Edam, D.M. Meunier, E.P.C. Mes, F.A. Van Damme, P.J. Schoenmakers, J. Chromatogr. A 1201

(2008) 208.

[29] P.J. Flory, J. Chem. Phys. 17 (1949), 303.

[30] P.J. Flory, Principles of Polymer Chemistry, Cornell University Press, Ithaca, NY, 1971.

[31] A.M. Striegel, W.W.Yau, J.J.Kirkland and D.D.Bly, Modern Size-Exclusion Liquid Chromatography,

Second edition, Wiley, New York, 2009.

[32] T. Chang, Adv. Polym. Sci., 163 (2003) 1.

[33] K.O. Pedersen, Arch. Biochem. Biophys., Suppl., 1 (1962) 157.

[34] E.A. DiMarzio, C.M. Guttman, J. Polym. Sci., Part B, 7 (1969) 267.

[35] A.J. McHugh, CRC Crit. Rev. Anal. Chem., 15 (1984) 63.

[36] W. R. Krigbaum and P. J. Flory, J. Polymer Sci., 11 (1953) 37.

[37] H. Yamakawa, Modern Theory of Polymer Solutions, Harper & Row, New York, 1971.

[38] E.A. DiMarzio, C.M. Guttman, J. Polym. Sci. B 7 (1969) 267.

[39] E.A. DiMarzio, C.M. Guttman, Macromolecules 3 (1970) 131.

[40] R. Tijssen, J. Bos, M. E. van Kreveld, Anal. Chem. 58 (1986) 3036.

[41] R. Tijssen, J. Bos, in: F. Dondi, G. Guiochon (Eds.), Theoretical Advancement in Chromatography and

Related Separation Techniques, Dordrecht, Kluwer, 1992, p. 397.

[42] G. Stegeman, J.C. Kraak, H. Poppe, R. Tijssen, J. Chromatogr. A 657 (1993) 283.

[43] R. Haas, F. Durst, Rheol. Acta 21 (1982) 566.

[44] Y. Liu, W. Radke, H. Pasch, Macromolecules 38 (2005) 7476.

[45] C.D. DeLong, D.A. Hoagland, Macromolecules 41 (2008) 4887.

[46] T. Konishi, T. Yoshizaki, H. Yamakawa, Macromolecules 24 (1991) 5614.

[47] B.S. Farmer, K. Terao, J.W. Mays, International Journal of Polymer Anal. Charact. 11 (2006) 3.

[48] B.H. Zimm, J. Chem. Phys. 24 (1956) 269.

[49] S.F. Sun, Physical chemistry of macromolecules, John Wiley, Hoboken, New Jersey, 2nd ed., 2004.

[50] W.H. Stockmayer, M. Fixman, Ann. N.Y. Acad. Sci. 57 (1953) 334.

[51] J.F. Douglas, J. Roovers, K.F. Freed, Macromolecules 23 (1990) 4168.

[52] E. Uliyanchenko, P.J. Schoenmakers, S. van der Wal, J. Chromatogr. A 1218 (2011) 1509.

[53] D. Nykypanchuk, H.H. Strey, D.A. Hoagland, Science 297 (2002) 987.

[54] P.G. De Gennes, J. Chem. Phys. 55 (1971) 572.

[55] M. Doi, S.F. Edwards, The theory of polymer dynamics, 1986, Oxford.

[56] C. Gay, P.G. de Gennes, E. Raphaël, F. Brochard-Wyart, Macromolecules 29 (1996) 8379.

[57] T. Sakaue, E. Raphaël, P.-G. de Gennes, F. Brochard-Wyart, Europhys. Lett. 72 (2005) 83.

[58] T. D. Long, J. L. Anderson, J. Polym. Sci. Polym. Phys. Ed., 22 (1984) 1261.

[59] R.P. Adamski, J. L. Anderson, J. Polym. Sci. B 25 (1987) 765.

[60] G. Guillot, L. Léger, F. Rondelez, Macromolecules 18 (1985) 2531.

[61] G. Guillot, Macromolecules 20 (1987) 2600.

[62] Q.T. Nguyen, J. Neel, J. Membr. Sci. 14 (1983) 111.

[63] G. Stegeman, J.C. Kraak, H. Poppe, J. Chromatogr. 550 (1991) 721.

Page 132: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Chapter 4

130

[64] Uliyanchenko, SEC-HDC demonstration, choose article where this is shown

[65] R. Edam, S. Eeltink, D.J.D. Vanhoutte, W.Th. Kok, P.J. Schoenmakers, J. Chromatrogr. A 1218 (2011)

8638.

[66] D.E. Kranbuehl, P.H. Verdier, J. Chem. Phys 67 (1977) 361.

[67] M. G. Davidson, W. M. Deen, J. Membr. Sci. 35 (1988) 167.

[68] T. Perkins, D.E. Smith, S. Chu, Science 276 (1997) 2016.

[69] M. J. Menasveta, D. A. Hoagland, Macromolecules 1991,24, 3427-3433

[70] L. Li, R.G. Larson, Macromolecules 33 (2000) 1411.

[71] D.E. Smith, H.P. Babcock, S. Chu, Science 283 (1999) 1724.

[72] R. Matmour, A. Lebreton, C. Tsitsilianis, I. Kallitsis, V. Héroguez, Y. Gnanou, Angew. Chem. Int. Ed.

44 (2005) 284.

[73] T. Altares Jr., D. P. Wyman, V. R. Allen, K. Meyersen, J. Polym. Sci., Part A : Polym. Chem. 3 (1965)

4131.

[74] J.L. Hahnfeld, W.C. Pike, D.E. Kirkpatrick, T.G. Bee, in R. Quirk (Editor), Applications of Anionic

Polymerization Research (ACS Symposium Series, No. 696), American Chemical Society, Washinton,

DC, 1996, p. 167.

[75] C.M. Fernyhough, R.N. Young, A.J. Ryan, L.R. Hutchings, Polymer 47 (2006) 3455.

[76] A. v.d. Horst, P.J. Schoenmakers, J. Chrom. A 1000 (2003) 693.

[77] M.E. van Kreveld, N. Van den Hoed, J. Chromatogr., 83 (1973) 111.

[78] C. Jackson, Y.-J. Chen, J.W. Mays, J. Appl. Pol. Sci., 61 (1996) 865.

[79] F. Vilaplana, R.G. Gilbert, Macromolecules 43 (2010) 7321.

Page 133: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

131

Chapter 5: Z-RAFT Star Polymerization of Styrene:

Comprehensive Characterization using Size-Exclusion

Chromatography

Abstract

Reversible Addition-Fragmentation Chain Transfer (RAFT) polymerizations of styrene

in bulk at 80°C using tri-, tetra-, and hexafunctional trithiocarbonates, in which the

active RAFT-groups are linked to the core via the stabilizing Z-group, were studied in

detail. These Z-RAFT star polymerizations of styrene showed excellent molecular

weight control up to very high monomer conversions and star sizes of more than 200

kDa. The application of high pressure up to 2600 bar was found to significantly increase

the relative amount of living star polymer. Not even at very high monomer conversions

and for large star molecules, a shielding effect of growing arms hampering the RAFT

process could be identified. Absolute molecular weights of star polymers using a

conventionally calibrated SEC setup were determined with high precision by using a

mixture of linear and star-shaped RAFT agents. When using phenylethyl as the leaving

R-group, well-defined star polymers that perfectly match the theoretical predictions

were formed. However, when using benzyl as the leaving group, a pronounced impact

of monomer conversion on the star polymer topology was observed and pure star

polymers with the expected number of arms could not be obtained.

Page 134: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Chapter 5

132

5.1 Introduction

The precise tailoring of macromolecules on a molecular level is a major key for

controlling the polymer properties. Within this context, the control of macromolecular

topology is an ongoing research theme [1]. Among these topologies, star polymers are

of special interest since years, because of their distinct rheological behavior arising from

their spatial shape both in solution and melt, which is exploited, e.g., in oils and

lubricants for automotives [2,3], in adhesives [4], and for flocculation [5]. In addition,

star polymers are becoming increasingly important for life sciences, where they e.g. find

applications in the field of drug release [6], serve as unimolecular polymeric micelles

[7,8], and are used as nucleic acid delivery vectors [9]. A lot of effort was put into the

investigation of properties of stars [10,11] as well as into the development of new

methods for their synthesis [12]. The rise of controlled radical polymerization ignited

enormous research activities in the field of topological polymer design, as these

methods allow the preparation of samples with narrowly distributed and controlled

molecular weights of a wide array of different monomers and under various reaction

conditions. Especially Reversible Addition-Fragmentation Chain Transfer (RAFT)

polymerization [13-17] has proven to be extremely versatile. In this method,

propagating macroradicals are in equilibrium with the dormant polymeric RAFT

compounds via reversible chain transfer and all chains have thus an equal probability to

grow which results in relatively narrow chain length distributions. Core-first star

polymers can easily be produced via RAFT polymerization when using multifunctional

RAFT agents that, in addition to controlling the process, predetermine the final polymer

topology [18,19]. When targeting very well defined star polymers, a RAFT agent design

has to be chosen, in which the stabilizing group (so called Z-group) constitutes the core

(see Scheme 1) [20-25]. This Z-RAFT star polymerization approach effectively

prevents extensive coupling reactions between star polymers as well as side-production

of linear material, which occur when connecting the RAFT-groups to the core via its

reinitiating leaving group (so called R-group) [18,19,23,26-29]. For a detailed

description of the mechanistic underpinnings of core-first RAFT star polymerizations,

the reader is referred to reference [25].

Page 135: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Z-RAFT Star Polymerization of Styrene: Comprehensive Characterization using SEC

133

Scheme 1. Main equilibrium of Z-RAFT star polymerization.

In Z-RAFT star polymerization, the growing radical center sits at the end of a linear

chain (i.e., the arm) and the equilibrating reaction occurs near the center of the star,

where the thiocarbonylthio-moieties are located throughout the entire reaction. As a

matter of fact, the controlling reaction is increasingly shielded by the surrounding

polymer segments. It was, however, experimentally found that Z-RAFT star

polymerization of acrylates is well controlled up to relatively high monomer

conversions and up to star molar masses of over one million Da [25]. We therefore

scrutinized earlier reported arguments about the detrimental steric shielding of growing

arms, which was accused to increasingly hamper the RAFT process [20,21,30-32]. In

order to quantify this shielding for the first time, we performed Monte Carlo simulations

of polymer chain pairs that mimic the steric situation occurring in Z-RAFT star

polymerization, showing that the shielding is not sufficiently large to impede the RAFT

process [33,34]. We also modeled the initial transfer reaction in Z-RAFT star

polymerization by pseudo-kinetic Monte Carlo simulations [35].

Our motivation for comprehensively study Z-RAFT star polymerization is driven by our

efforts in designing well-defined unimolecular nano-carriers, which base on star

polymers as templates [36]. We thus comprehensively studied 6-arm Z-RAFT star

polymerization of various acrylates [25], in which we identified intermolecular transfer

to polymer as side reaction that induces star-star coupling at high monomer conversions.

Based on a detailed kinetic analysis of this transfer-to-polymer reaction, we were able to

develop guidelines for poly(acrylate) stars of very uniform structure. The objective of

the present work is to in-depth characterize 3-arm, 4-arm, and 6-arm Z-RAFT star

polymerization of styrene in order to obtain very homogenous star polymers from this

important monomer. By exploiting the distinct mechanistic features of Z-RAFT star

Page 136: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Chapter 5

134

polymerization, we develop a novel and relatively easy method for characterizing

absolute molecular weights and true numbers of arms of the generated star polymers.

5.2 Experimental Section

5.2.1 Chemicals

Dipentaerythritol hexakis(3-mercaptopropionate) was obtained from Wako Chemicals

and used without further purification. The initiator 1,1′-azobis(cyanocyclohexane)

(ACCN, Aldrich) was used as received. Styrene (≥ 99.0 %, Fluka) was purified by

passing through a column filled with inhibitor remover for 4-tert-butylcatechol

(Aldrich). Column-chromatographic purification of the RAFT agent was performed

using silica gel (Merck, Kieselgel 60) and technical grade n-pentane, ethyl acetate and

CH2Cl2. Tetrahydrofuran was used as the eluent in size-exclusion chromatography

(THF, Carl Roth, Rotipuran, stabilized with 2,6-di-tert-butyl-4-methylphenol). It was

used as received for all experiments using refractive-index and UV detection. Non-

stabilized HPLC-grade THF from Biosolve (Valkenswaard, The Netherlands) was

filtered over a 20 nm ceramic filter (Anodisk 47 from Whatman, Maidstone, England)

and continuously purged with helium 5.0 (99,999 %, Praxair, Vlaardingen, The

Netherlands) for the triple-detection SEC measurements. All other chemicals were

purchased from Aldrich and used without further purification.

5.2.2 Instrumentation

Molecular weight distributions were determined by size-exclusion chromatography

(SEC) using a JASCO (Tokyo, Japan) AS-2055-plus autosampler, a Waters 515 HPLC

pump (Milford, MA, USA), three PSS-SDV columns (Mainz, Germany) with nominal 5

µm particle size and pore sizes of 105, 103 and 102 Å, a Waters 2410 refractive index-

detector, a Viskotek (Houston, TX, USA) VE3210 UV/VIS detector, and THF at 35°C

as the eluent at a flow rate of 1.0 mL·min–1. 50 µL of polymer solution with a

concentration of approximately 3 mg/mL were injected. The SEC setup was calibrated

with polystyrene standards of narrow polydispersity (Mp = 410 to 2 000 000 g mol–1)

from PSS.

The triple-detector SEC setup comprised a SIL9a autosampler, LC20Advp micropump

and SCL10a system controller all from Shimadzu (Kyoto, Japan). Various columns with

Page 137: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Z-RAFT Star Polymerization of Styrene: Comprehensive Characterization using SEC

135

mixed-bed particles were used (Resipore 3 µm, Minimix-C 5 µm and Minimix-B 10

µm, 250x4.6 mm each). All of these were obtained from Polymer Laboratories (Church

Stretton, UK). The separation was performed at a flow rate of 400 µL/min and 50 µL of

sample was injected. The sample solution was prepared by dissolving the polymer at a

concentration of approximately 1.5 mg/mL in THF with 250 ppm butyl-hydroxylated

toluene (Acros, 99 %) to prevent degradation by radicals. The triple-detection array was

assembled in-house (University of Amsterdam) and comprised an LC600 90° light

scattering detector (Viscotek), an on-line viscometry detector (Viscochip, Polymer

Laboratories) and a differential refractive-index detector (RID10a, Shimadzu). The data

were acquired using a PL-datastream A/D converter (Polymer Laboratories) and

processed using PL-Cirrus v3.0 software (Polymer Laboratories). Processing of the data

was performed in compliance with the triple-detection principle [37,38].

Electrospray-ionization mass spectrometry (ESI-MS) experiments were carried out

using a Finnigan LCQ ion trap mass spectrometer (Thermo Finnigan, San Jose, CA,

USA). For further details regarding the ESI-MS setup see ref. [39].

NMR spectroscopy was performed using a Varian Mercury 200 and a Varian Unity 300

NMR spectrometer.

Elemental analysis was carried out on a Heraeus CHN-O-Rapid Analyzer and on a

METROHM 662 photometer equipped with a 636 Tiroprocessor.

Page 138: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Chapter 5

136

S

S

SR

O

OO

O

O

O

S

S

S

SR

S

SR

S

SRS

O

OO

OO

O

O

OS

SS

SS

RS

SR

S

S RS

SR

S

1,2

3,4

5,6

O

O

O

O

OOO

O

SS

SR

O

S

S

SR

O

S

S SR

O S

SS

R

O S

S

SR

OS

S

SR

7,8

7: R = 8: R =

5: R = 6: R =

3: R = 4: R =

1: R = 2: R =

Chart 1. Mono-, tri-, tetra-, and hexafunctional RAFT agents used in this study.

Page 139: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Z-RAFT Star Polymerization of Styrene: Comprehensive Characterization using SEC

137

5.2.3 RAFT agent synthesis

Hexyl-benzyl-trithiocarbonate, 1. To a solution of 1-hexanethiol (1.00 g, 8.46 mmol)

in 50 mL chloroform triethylamine (1.41 mL, 1.03 g, 10.2 mmol, 1.2 eq) was added.

After stirring the reaction mixture for one hour at room temperature, 5 ml of CS2 and

benzyl bromide (1.21 mL, 1.74 g, 10.1 mmol, 1.2 eq) were added slowly. The mixture

was stirred for 15 h and the reaction was then quenched by adding 50 mL of 10 %

hydrochloric acid. The organic phase was separated and washed two times with 50 mL

of water and dried over Na2SO4. Solvent and traces of non-reacted starting materials

were removed in vacuum. 2.41 g (99 %) of 1 were received as a yellow liquid.

1H-NMR (300 MHz, CDCl3) δ (ppm): 0.89 (t, J = 7.1 Hz, 3 H, CH3-CH2), 1.35 (m, 6 H,

CH2), 1.71 (p, J = 7.2 Hz, 2 H, -S-CH2-CH2-CH2-), 3.37 (t, J = 7.4 Hz, 2 H, S-CH2),

4.62 (s, 1 H, CH2), 7.35 (m ,5 H, Har).

13C-NMR (300 MHz, CDCl3) δ (ppm): 13.96 (CH3-CH2), 22.45 (CH2), 27.90 (CH2),

28.56 (CH2), 31.25 (CH2), 37.03 (CH2), 41.31 (CH2), 127.69 (CarH), 128.65 (CarH),

129.22 (CarH), 135.07 (Car), 223.78 (C=S).

Mass spectrometry: m/z 285.1 (M + H+), 302.2 (M + NH4+), 319.2 (M + NH3 +NH4

+),

586.3 (2 M + NH4+).

Hexyl-1-phenylethyl-trithiocarbonate, 2. The synthesis was according to that of 1, but

using (1-bromoethyl)benzene (1.39 mL, 1.88 g, 10.1 mmol, 1.2 eq) instead of benzyl

bromide. 2.49 g (97 %) of 2 were received as a yellow liquid.

1H-NMR (300 MHz, CDCl3) δ (ppm): 0.89 (t, J = 6.7 Hz, 3 H, CH3-CH2), 1.35 (m, 6 H,

CH2), 1.68 (p, J = 7.2 Hz, 2 H, -S-CH2-CH2-CH2-), 1.76 (d, J = 7.1 Hz, 3H, CH3-CH),

3.34 (t, J = 7.4 Hz, 2 H, S-CH2), 5.38 (q, J = 7.1 Hz, 1 H, CH), 7.35 (m ,5 H, Har).

13C-NMR (300 MHz, CDCl3) δ (ppm): 13.96 (CH3-CH2), 21.34 (CH3-CH), 22.44 (CH2),

27.90 (CH2), 28.56 (CH2), 31.25 (CH2), 36.79 (CH2), 50.03 (CH), 127.63 (CarH), 127.67

(CarH), 128.60 (CarH), 141.16 (Car), 223.07 (C=S).

Mass spectrometry: m/z 299.1 (M + H+), 316.2 (M + NH4+), 614.3 (2M + NH4

+).

Page 140: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Chapter 5

138

Trimethylolpropane-tris-3-(S-benzyl-trithiocarbonyl)propanoate), 3. To a solution

of trimethylolpropane-tris-(3-mercaptopropionate) (1.00 mL, 1.21 g, 3.04 mmol) in 50

mL chloroform triethylamine (1.52 mL, 1.11 g, 10.9 mmol, 3.6 eq) was added. After

stirring the reaction mixture for one hour at room temperature 5 mL of CS2 and benzyl

bromide (1.30 mL, 1.87 g, 10.9 mmol, 3.6 eq) were added slowly. The mixture was

stirred for 15 h and the reaction was then quenched by adding 50 mL of 10%

hydrochloric acid. The organic phase was separated and washed two times with 50 mL

of water and dried over Na2SO4. Solvent and traces of non reacted starting materials

were removed in vacuum. 2.73 g (99%) of 3 were received as a yellow liquid.

1H-NMR (300 MHz, CDCl3) δ (ppm): 0.88 (t, J = 7.6 Hz, 3 H, CH3), 1.47 (q, J =

7.6 Hz, 2 H, CH2), 2.79 (t, J = 7.0 Hz, 6 H, CH2), 3.62 (t, J = 7.0 Hz, 6 H, CH2), 4.05 (s,

6 H, CH2), 4.61 (s, 6 H, CH), 7.32 (m, 15 H, Har).

13C-NMR (300 MHz, CDCl3) δ (ppm): 7.34 (CH3), 23.02 (CH3-CH), 31.23 (C(CH2)3),

33.07 (CH2), 33.13 (CH2), 40.73 (CH2), 64.12 (CH2), 127.79 (CarH), 128.69 (CarH),

129.24 (CarH), 134.79 (Car), 170.96 (C=O), 221.98 (C=S).

Mass spectrometry: m/z 897.07(M + H+), 914.10 (M + NH4+).

(An alternative pathway for the synthesis of 3 is given by Stenzel and co-workers [40].)

Trimethylolpropane-tris-(3-(S-phenylethyl-trithiocarbonyl)propanoate), 4. The

synthesis was according to that of 3, but using (1-bromoethyl)benzene (1.50 mL, 2.02 g,

10.9 mmol, 3.6 eq) instead of benzyl bromide. 2.86 g (99 %) of 4 were received as a

yellow liquid.

1H-NMR (300 MHz, CDCl3) δ (ppm): 0.87 (t, J = 7.6 Hz, 3 H, CH3), 1.45 (q, J =

7.6 Hz, 2 H, CH2) 1.75 (d, J = 7.1 Hz, 9 H, CH3-CH), 2.76 (t, J = 7.0 Hz, 6 H, CH2),

3.57 (t, J = 7.0 Hz, 6 H, CH2), 4.02 (s, 6 H, CH2), 5.32 (q, J = 7.1 Hz, 3 H, CH), 7.32

(m, 15 H, Har).

Page 141: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Z-RAFT Star Polymerization of Styrene: Comprehensive Characterization using SEC

139

13C-NMR (300 MHz, CDCl3) δ (ppm): 7.33 (CH3), 21.32 (CH3-CH), 26.79 (CH), 30.95

(C(CH2)3), 33.08 (CH2), 33.15 (CH2), 40.72 (CH2), 50.36 (CH3), 64.07 (CH2), 127.66

(CarH), 127.73 (CarH), 128.64 (CarH), 140.92 (Car), 221.98 (C=S).

Mass spectrometry: m/z 956.14 (M+NH4+).

Pentaerythritol-tetrakis-(3-(S-benzyl-trithiocarbonyl)propanoate), 5, was

synthesized according to Mayadunne et al. [19].

Pentaerythritol-tetrakis-(3-(S-1-phenylethyl-trithiocarbonyl)propanoate), 6. To a

solution of pentaerythritol tetrakis(3-mercaptopropionate) (0.71 mL, 1.44 g, 5.00 mmol)

in 100 mL chloroform triethylamine (5.53 mL, 4.04 g, 40.0 mmol, 8 eq) was added.

After stirring the reaction mixture for one hour at room temperature 10 mL of CS2 and

(1-bromoethyl)benzene (3.02 mL, 4.07 g, 22.0 mmol, 4.1 eq) were added slowly. The

mixture was stirred for 15 h and afterwards the reaction was quenched by adding 100

mL of 10 % hydrochloric acid. The organic phase was separated and washed two times

with 100 mL of water and dried over Na2SO4. Solvent was removed in vacuum and the

crude product was purified on silica with CH2Cl2 (Rf = 0.38) as eluent. 2.98 g (49 %) of

6 were received as yellow oil.

1H-NMR (200 MHz, CDCl3) δ (ppm): 1.75 (d, J = 7.1 Hz, 12 H, CH3-CH), 2.76 (t, J =

7.0 Hz, 8 H, CH2), 3.56 (t, J = 7.0 Hz, 8 H, CH2), 4.02 (s, 8 H, CH2), 5.32 (q, J = 7.1 Hz,

4 H, CH), 7.32 (m, 20 H, Har).

13C-NMR (300 MHz, CDCl3) δ (ppm): 21.32 (CH3-CH), 30.92 (C(CH2)3), 32.98 (CH2),

40.92 (CH2), 50.36 (CH3), 62.52 (CH2), 127.67 (CarH), 127.73 (CarH), 128.63 (CarH),

140.87 (Car), 170.76 (C=O), 221.89 (C=S).

Mass spectrometry: m/z 1226.13 (M+NH4+)

Dipentaerythritol-hexakis-(3-(S-benzyl-trithiocarbonyl)propanoate), 7, was

synthesized as recently reported by Johnston-Hall and Monteiro [41].

Dipentaerythritol-hexakis-(3-(S-1-phenylethyl-trithiocarbonyl)propanoate), 8. To a

solution of dipentaerythritol hexakis(3-mercaptopropionate) (3.915 g, 5.00 mmol) in

Page 142: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Chapter 5

140

200 mL chloroform triethylamine (6.32 mL, 6.07 g, 60.0 mmol, 12 eq) was added. After

stirring the reaction mixture for one hour at room temperature 50 mL of CS2 and (1-

bromoethyl)benzene (4.78 mL, 6.48 g, 60.0 mmol, 12 eq) were added slowly. The

mixture was stirred for 15 h and afterwards the reaction was quenched by adding 100

mL of 10 % hydrochloric acid. The organic phase was separated and washed two times

with 100 mL of water and dried over Na2SO4. The solvent was evaporated in vacuum.

The crude product was purified via column chromatography on silica gel using

pentane:ethyl acetate (3:1; Rf = 0.38) as eluent. 4.48 g (48 %) of 8 were received as

yellow oil.

1H-NMR (300 MHz, CDCl3) δ (ppm): 1.75 (d, J = 7.1 Hz, 12 H, CH3), 2.76 (t, J = 7.0

Hz, 12 H, CH2), 3.56 (t, J = 7.0 Hz, 12 H, CH2), 4.11 (s, 12 H, CH2), 5.32 (q, J = 7.1

Hz, 6 H, CH), 7.25 (m, 30 H, Har).

13C-NMR (200 MHz, CDCl3) δ (ppm): 21.33 (CH3), 30.79 (C(CH2), 30.93 (CH2), 32.99

(CH2), 42.92 (CH2), 50.37 (CH2), 62.53 (CH2), 127.68 (CarH), 127.74 (CarH), 128.64

(CarH), 140.88 (Car), 170.77 (C=O), 221.98 (C=S).

Elemental analysis: C, 52.81; H, 5.08; S, 30.95 (theor.). C, 53.32; H, 5.38; S, 29.95

(exp.)

5.2.4 Polymerizations

Styrene was degassed via three freeze-pump-thaw cycles, transferred along with RAFT

agent and initiator into an argon-filled glove box (oxygen content below 1.5 ppm),

where stock solutions of 10 mL monomer, initiator (ACCN), and RAFT agent or RAFT

agent mixtures were prepared. For the ambient pressure experiments, ten samples of

each stock solution were filled into individual glass vials and sealed with Teflon/rubber

septa. The vials were subsequently inserted into a block heater, thermostated at

80 ± 0.1 °C. The samples were removed after preset time intervals and the reactions

were stopped by cooling the solutions in an ice bath. The reaction times were up to 144

h. Polymerizations up to pressures of 2600 bar were performed in in-house-made

pressure cells. For details see ref. [42]. Monomer to polymer conversions was

determined gravimetrically.

Page 143: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Z-RAFT Star Polymerization of Styrene: Comprehensive Characterization using SEC

141

5.3 Results and Discussion

For our studies of Z-RAFT star polymerization of styrene, we chose multifunctional

trithiocarbonates as RAFT agents (see Chart 1). Trithiocarbonates become increasingly

popular as RAFT agents, due to their facile preparation and due to the absence of

potentially disturbing rate retardation effects, which are observed with more reactive

RAFT agents such as dithiobenzoates [43]. Mayadunne et al. [19] were the first who

introduced pentaerythritol-based multifunctional trithiocarbonates as Z-RAFT star

agents. Since then, the synthesis protocols for this class of star-shaped RAFT agents

were adapted by us [25] and others [41], providing access to bi-, tri-, tetra- and hexa-

functional mediating agents. Other trithiocarbonate-typed Z-RAFT star agents used in

styrene polymerization were based on β-cyclodextrin cores [20], on hyperbranched

polymer cores [30], and on dendrimers [24]. Multifunctional dithiobenzoates for usage

in styrene polymerization were constructed as dendrimers [21] and as 1,3,5-benzene-tri-

dithiocarboxylic-esters [32]. All these RAFT agents used for Z-RAFT star

polymerization of styrene were decorated with a benzyl-moiety as the reinitiating

leaving group. This is surprising, as it is well understood that benzyl as leaving group

results in a relatively low apparent chain transfer coefficient of the associated RAFT

agent in styrene polymerization, both with trithiocarbonates [44] and with

dithiobenzoate [45]. This is due to the relatively high energy of the benzyl radical,

which slows down the fragmentation rate of the initial intermediate radical and speeds

up the undesired back-transfer within the pre-equilibrium in comparison to monomer

addition. This scenario results in a pronounced so-called hybrid behavior [46], which

describes the formation of relatively high molecular weights of the resulting polymer

after only negligible monomer conversion, X, that is, experimental molecular weight vs.

X plots show a significant intercept instead of crossing the origin. The resulting

polydispersities are consequently significantly higher than in systems with more

effective pre-equilibriums [45]. The preference for benzyl as leaving group seen in

every study into Z-RAFT star polymerization of styrene performed so far is obviously

due to the easiness of the associated RAFT agent synthesis. In an effort to optimize this

polymerization system, we consequently implemented phenylethyl as leaving group,

which induces a more effective pre-equilibrium in styrene polymerization [44]. It should

be noted that benzyl as the leaving group may unfold sufficient transfer activity in other

Page 144: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Chapter 5

142

monomer systems, such as acrylates, due to a pronouncedly different fragmentation

selectivity of the RAFT intermediate of the pre-equilibrium.

When using RAFT agents 1, 3, 5, and 7 at, e.g., ca. 1 mmol∙L–1 of RAFT-group

concentration, intercepts of the experimental number average molecular weight, nM ,

vs. X traces of around 8000 g∙mol–1 were observed (not shown). This finding is in

agreement with literature reports about benzyltrithiocarbonate-mediated styrene

polymerizations, in which similar intercepts were found [20,32,47]. The Z-RAFT star

polymerization of styrene using RAFT agents 4, 6, and 8, which carry a phenylethyl

moiety revealed - as anticipated - that the hybrid-behavior is largely reduced in

comparison to benzyl as the leaving group. Nevertheless, a minor hybrid behavior could

still be observed, especially with low RAFT agent concentrations. In Figure 1a, the

intercept values 𝑀𝑛,0% are depicted on the example of 8-mediated 6-arm star

polymerization. The other RAFT agents showed very similar behavior. It can clearly be

seen that the intercept is below 4000 g∙mol–1, even for RAFT agent concentrations

below 1 mmol∙L−1, and approaches zero with increasing RAFT agent concentration. The

polymerizations were performed at 80 °C, which we identified as optimal. Since styrene

is a slowly propagating monomer [48] and usage of vast amounts of initiator is not

advisable, as it drastically increases the amount of terminated polymer, reaction times in

which full monomer conversion were reached lasted up to several days. It was hence

necessary to use the slowly decomposing initiator ACCN, which has about the same

fragmentation rate at 80 °C as has AIBN at 60 °C [49].

It is tempting to use the intercepts for obtaining average chain-transfer constants for the

initial RAFT step via plotting the inverse number average degree of polymerization at

zero monomer conversion, 1/𝑃𝑛,0% , against the RAFT agent concentration, as has been

demonstrated by Barner-Kowollik and co-workers [50,51]. However, this approach is

beset by problems in the case of star polymers, as the molecular weights obtained using

SEC calibrated with linear standards differ significantly from true molecular weights.

This needs to be addressed in the evaluation procedure, which will be presented below.

Page 145: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Z-RAFT Star Polymerization of Styrene: Comprehensive Characterization using SEC

143

0 1 2 3 4 5 6 70

1000

2000

3000

4000

5000

0.00 0.01 0.02 0.03 0.040.0

0.2

0.4

0.6

0.8

[RAFT] / mmol⋅L−1

Mn,

0% /

g⋅m

ol−1

(a) 1

/Pn,

0% (c

orr.)

[RAFT-groups] / mol⋅L−1

(b)

Fig. 1. (a) Intercepts of apparent number average molecular weight from conventional calibration using linear standards, 𝑀𝑛 vs. X traces in 8-mediated styrene bulk polymerization (6-arm star polymerization) vs. RAFT

agent concentrations at 80 °C using ACCN (cACCN = 3 mmol∙L–1) as the initiator. (b) Inverse degree of polymerization (corrected by K taken from Fig. 9 according to the procedure described in the text) at zero monomer conversion (extrapolated values) of star arm polymer vs. the concentration of trithiocarbonate

groups. The line indicates the best linear fit, forced through the origin.

The performed Z-RAFT star polymerizations using 3-, 4, and 6-armed RAFT

agents exhibited very well controlled behavior up to full monomer conversion, as is

exemplified on 8-mediated 6-arm star polymerization of styrene (see Fig. 2).

Polydispersities show minimal values of 1.07 at X = 20 % when using RAFT agent

Page 146: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Chapter 5

144

concentrations of 6.4 mmol∙L−1, which refers to 3.8×10–2 mol∙L−1 of trithiocarbonate

moieties. The slight curvature of the 𝑀𝑛 vs. X traces originates from continues

formation of dead chains (see below).

Fig. 2. Polydispersity index, PDI, and apparent number average molecular weight from conventional

calibration using linear standards, 𝑀𝑛, vs. monomer conversion in 8-mediated styrene bulk polymerization (6-arm star polymerization) at various RAFT agent concentrations at 80 °C using ACCN (cACCN = 3 mmol∙L–1) as

the initiator.

Full molecular weight distributions of the formed star polymers, as exemplified on 6-

mediated styrene polymerization (4-arm star polymerization) (see Fig. 3) are narrow and

unimodal, as expected for a well-controlled polymerization. This is in contrast to Z-

RAFT star polymerization of acrylates, in which star-star coupling side reactions were

observed after intermediate values of X [25]. The polymerization behaviors of 4-, 6, and

8-mediated polymerizations of styrene were very similar to each other, thus, only

demonstrating examples are presented.

Page 147: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Z-RAFT Star Polymerization of Styrene: Comprehensive Characterization using SEC

145

Fig. 3. SEC-distributions, wlogM, of polystyrene samples produced in 6-mediated (c6 = 9.6 mmol∙L−1) styrene bulk polymerization (4-arm star polymerization) at 80 °C using ACCN (cACCN = 3 mmol∙L–1) as the initiator,

after monomer conversion of 30 % (PDI = 1.06), 46 % (PDI = 1.08), 73 % (PDI = 1.11) and after full monomer conversion (PDI = 1. 17).

RAFT polymerization requires continuous delivery of initiating radicals, whereby dead

polymer is formed throughout the entire polymerization. Especially at low RAFT agent

concentrations and with slowly propagating monomers, such as styrene, the amount of

terminated polymer can become significant. In Z-RAFT star polymerization,

termination occurs between two growing arms (see Scheme 1), generating dead polymer

that at maximum, in the case of termination via combination, has double the chain

length of one arm polymer, which is lower than the degree of polymerization of the

complete star. Dead polymer consequently occurs completely at the low molecular

weight side of the living star polymer, as demonstrated in Fig. 4, in which 4-arm star

polymer is presented that has been formed in presence of relatively low RAFT agent

concentration. UV-detection set to 330 nm has been used to selectively detect the

trithiocarbonyl group, i.e., the living star polymer, which – after appropriate correction

[25] – can be related to the molecular weight distribution from RI-detection, which

includes both the living and the dead polymer.

It is clear, that the formation of dead polymer is an obstacle for obtaining pure and

narrowly dispersed star polymer. Terminated linear polymer can either be separated

Page 148: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Chapter 5

146

from the star polymer, e.g., via selective extraction [21], or its formation can be

minimized during the process via the following strategies: (i) The polymerizations can

be performed at high RAFT agent concentrations, which suppresses the relative

influence of terminated polymer. The maximum molecular weight, however, which can

be achieved thereby, is restricted. (ii) When performing the RAFT polymerization at

very low radical concentrations, the kinetic chain length becomes long, i.e., termination

is suppressed in comparison to propagation. This lowering of dead polymer, however, is

on the expense of polymerization rate, which can thus become considerable. The low

initiator concentrations used in the present study, for instance, yielded well-defined star

polymers with relatively low amounts of dead polymer; the reaction times, however,

were several days (e.g., see gaps in Fig. 2 which indicate overnight periods). (ii) The

kinetic chain length can also be stretched by applying high pressure, as we demonstrated

earlier for cumyldithiobenzoate-mediated polymerizations [42]. The impact of high

pressure becomes evident when quantifying the amount of dead polymer. Due to the

clear separation of dead and living polymer in Z-RAFT star polymerization (see Fig. 4),

these species can roughly be separated via multi-Gaussian fitting, yielding estimates for

the weight fraction of terminated polymer.

Inspection of Fig. 5 clearly shows that the fraction of dead polymer is largely reduced

when applying high pressure. Since samples are compared that were taken after

identical monomer conversions, they have almost identical molecular weights. As high

pressure increases the value of kp/kt, the rate of polymerization is increased as well, that

is, the reaction times for obtaining identical monomer conversion is significantly

reduced with increasing pressure. It goes without saying that the decreased amount of

terminated polymer is also reducing the polydispersity of the overall generated polymer;

the impact on the polydispersity of the living star polymer, which may be anticipated

due to the pressure dependence of the individual RAFT reactions, however, remains too

small to be detected unambiguously. For a detailed discussion of the pressure effect in

RAFT polymerization, the reader is referred to reference [42].

Page 149: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Z-RAFT Star Polymerization of Styrene: Comprehensive Characterization using SEC

147

Fig. 4. SEC-distribution, wlogM, of polystyrene samples produced in 6-mediated (c6 = 0.8 mmol∙L−1) styrene bulk polymerization (4-arm star polymerization) at 80°C using ACCN (cACCN = 3 mmol∙L–1) as the initiator, after 26% of monomer conversion. (---) RI detection (overall molecular-weight distribution); (–––) via UV

detection at 330 nm (trithiocarbonate end-groups, indicating living star polymer). The UV signal was corrected according to ref. [25] to allow comparison. The RI signal was subjected to multi-Gaussian fitting.

0 1000 2000 30000

10

20

30

w.-%

of d

ead

polym

er

p /bar

Fig. 5. Weight percent of dead polymer, w.-%, vs. applied pressure in 6-mediated (c6 = 1.2 mmol∙L−1) styrene bulk polymerization (4-arm star polymerization) at 80°C using ACCN (cACCN = 3 mmol∙L–1) as the initiator

after 25% of monomer conversion.

Page 150: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Chapter 5

148

In order to further characterize the Z-RAFT star polymerizations of styrene, we

compared molecular weights from SEC measurements to theoretical values, 𝑀𝑛𝑡ℎ𝑒𝑜

,

which were calculated using Eq. 1.

( )− ⋅

⋅ ⋅= +

+ ⋅ ⋅ ⋅ − d

0theo M monomern RAFT0 0

RAFT I 1 k t

X c MM Mc c d f e

(1)

with the monomer to polymer conversion, X, the initial monomer concentration, 0Mc ,

the initial RAFT agent concentration, 0RAFTc , the initial initiator concentration, 0

Ic , the

molecular weights of monomer, Mmonomer, and of RAFT agent, MRAFT, with d being the

number of chains that are generated in the termination process (d ≈ 1 for styrene), with

the initiator decomposition rate coefficient, kd (kd = 1.02×10–5 s–1 for ACCN [49]), and

the initiator efficiency f, which we recently determined to be around unity [52]. In many

reported studies, a simplified version of Eq. 1 is used, which does not account for the

continuous production of chains via initiation and yields straight lines for 𝑀𝑛𝑡ℎ𝑒𝑜

vs. X

traces. Such approach is, however, not advisable for slowly propagating monomers,

such as styrene, were significant amounts of additional chains are produced before

elevated monomer conversions are reached.

Inspection of Fig. 6 reveals that almost perfect agreement between molecular

weights from SEC and predicted values is found up to very high X values when using

the monofunctional trithiocarbonate 2 to obtain linear polymer. When using star-shaped

RAFT agents, however, a systematic deviation from theoretical values is observed; the

magnitude of the deviation increases with increasing numbers of arms. This effect is

well understood [53] and relates to the fact that star polymers exhibit a smaller

hydrodynamic volume in a good solvent than the linear polymers of identical molecular

weight that served as molecular-weight calibrants for the SEC setup. Star polymers are

consequently eluted later (corresponding to smaller hydrodynamic volumes). If

molecular weights were to be calculated using conventionally (linear) standards, the

obtained values would be too low. Since the studied Z-RAFT star polymerizations of

styrene exhibit well-controlled behavior, i.e. steadily increasing molecular weights and

low polydispersities up to very high monomer conversion (see Figs. 2 and 6), we

Page 151: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Z-RAFT Star Polymerization of Styrene: Comprehensive Characterization using SEC

149

conclude that the controlling reaction of macroradicals and RAFT groups near the

center of the core is fast enough to guarantee an efficient RAFT equilibrium,

independent of the number (if ≤6) and length of the growing arms. This finding is in

line with our recent simulation studies [33,34]. Apparent ceasing of star polymer

growth, reported by Stenzel and co-workers [20,24,30,31] and Gnanou and co-workers

[32], which was attributed to a loss of RAFT control due to shielding effects, was

possibly more likely due to large fractions of dead polymer because of high initiator

concentrations and high reaction temperatures, and due to arm cleavage via RAFT

reaction of small initiating radicals at elevated monomer conversions, which

counterbalance the star polymer growth.

Fig. 6. Number average molecular weight, 𝑀𝑛, by conventionally calibrated SEC vs. monomer conversion in styrene bulk polymerizations at 80°C using ACCN (cACCN = 3 mmol∙L–1) as the initiator and 2, 4, 6, and 8 (see

Chart 1) as the RAFT agents. The concentration of trithiocarbonate groups was 38 mmol∙L−1 in all cases. Lines indicate the theoretical molecular weights, calculated via Eq. 1.

The good agreement between experimental 𝑀𝑛 and theoretical 𝑀𝑛𝑡ℎ𝑒𝑜

vs. X plots for

monofunctional RAFT agent (see Fig. 6) indicates that Eq. 1 is valid and the curvature

of the plot is due to formation of dead chains. The deviations for the star polymers

therefore have to be attributed to a different effect, i.e. the reduced hydrodynamic

volume of star polymers. In order to prove this assumption, the absolute molecular

weights of the star polymers need to be known. This can either be done via light

scattering detection (see below), which is challenging for polymer of low and medium

Page 152: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Chapter 5

150

molecular weights and moreover may not be available in every laboratory, or via arm

cleavage yielding linear polymer that can be measured via conventionally calibrated

SEC [19,23,25]. We found that arm cleavage experiments, either via treatment with

amines or radical sources, give not well reproducible results and are prone to several

side reactions that alter the molecular weight distribution. For an approximate

characterization of star polymers, this might be sufficient; for a more detailed study,

however, methods with higher precision are required. We hence developed a very

straightforward method, which enables to measure absolute molecular weights of star

polymers from Z-RAFT star polymerization via conventionally calibrated SEC.

When performing a RAFT polymerization using a mixture of monofunctional

and star-shaped Z-RAFT agent, two RAFT equilibriums are established, which are

interlinked via the growing macroradicals, i.e. the individual arms (see Scheme 2).

Because of the controlled nature of RAFT polymerization, all macroradicals in the

system have approximately the same chain length and, during the polymerization, either

add to a linear polymeric RAFT agent (linear RAFT equilibrium) or to a living star

polymer (Z-RAFT star equilibrium). This situation implies that linear polymer and arm

polymer within the star at any time have identical average molecular weights, as they

are constantly exchanged via the RAFT equilibriums.

Scheme 2. The interdigitated equilibriums of simultaneously proceeding linear and Z-RAFT star polymerization. Thiocarbonylthio-moieties are indicated by circles.

Page 153: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Z-RAFT Star Polymerization of Styrene: Comprehensive Characterization using SEC

151

3.5 4.0 4.5 5.0(a)

(c)

(b)

star

star

star

linear

linear

linear

log (M / g⋅mol−1)

w logM

Fig. 7. Molecular weight (SEC) distributions, wlogM, of polystyrene (M are apparent molecular weights from conventional calibration using linear standards) generated in the presence of 19 mmol∙L−1 of linear RAFT

agent 2, 4.8 mmol∙L−1 of tetrafunctional RAFT agent 6, and 3.0 mmol∙L−1 ACCN as the initiatior at (a) 29 %, (b) 43 %, and (c) 81 % of monomer conversion.

It should be noted that this approach works best when all RAFT groups in the system

have similar chain transfer reactivity, independent whether they are in mono- or

multifunctional RAFT agents. This guarantees an even distribution of arms between the

free and the linked state and can generally be achieved by using identical RAFT agent

moieties both in mono- and multifunctional agents. Molecular-weight distributions of

polymer formed in the presence of a mixture of mono- and a multifunctional RAFT-

agent are distinctively bimodal, as shown in Fig. 7 on the example of a 4-arm star

polymerization. For such trithiocarbonate-mediated systems, the transfer activity was–

as required for this method – found as being independent on the RAFT agent

functionality [35]. Both the linear polymer (arms) and the star polymer increase steadily

in molecular weight with monomer conversion.

Page 154: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Chapter 5

152

Since the trithiocarbonate-group concentration was chosen to be identical for both

RAFT agents, the weight fraction of both types of polymer is identical, too. It can also

be seen that the polydispersity of the star polymer is smaller than that of the individual

arms, which is due to the arbitrary combination of dispersed arm polymer within one

star polymer molecule.

As the molecular weight of the linear arm polymer can accurately be determined via

conventionally calibrated SEC, the true number average molecular weight of the star

polymer can be calculated by multiplying the number average molecular weight of one

arm by the number of arms of the respective star. Both the arm and star polymers are

narrowly distributed due to the RAFT process. Thus, the number average molecular

weights are well represented by the peak molecular weight. This implies that by

dividing the peak molecular weight of the star polymer, Mp,star, by the peak molecular

weight of the linear arm polymer, Mp,arm, the apparent number of arms, as shown in Fig.

8 for 3-arm, 4-arm, and 6-arm stars, can be calculated.

It can clearly be seen that the apparent number of arms is always smaller than the

expected number, which reflects the contracted nature of the star polymers in

comparison to linear chains. 6-Arm stars appear to have only 3.94 arms, 4-arm stars

appear to have only 3.05 arms, and 3-arm stars seem to have only 2.58 arms. Further

important information drawn from Fig. 8 is that the apparent numbers of arms remain

constant throughout the polymerization. This means that the topology of the star

polymer remains unaltered, independent of monomer conversion, i.e., star-star coupling

or arm cleavage reactions at elevated X values are absent. From the apparent number of

arms, a correction factor K for the SEC setup was calculated by dividing the theoretical

number of arms (ftheory) by the apparent number of arms (fapp) (see Eq. 2). This factor

relates absolute molecular weight of a star polymer Mstar to that of a linear polymer Ml

eluting at the same hydrodynamic volume and is depicted in Fig. 9 as function of

number of arms, f. Comparison of polymers at identical molecular weight or

hydrodynamic volume is indicated by a subscript M or V respectively.

𝐾 = �𝑓𝑡ℎ𝑒𝑜𝑟𝑦𝑓𝑎𝑝𝑝

� = �𝑀𝑠𝑡𝑎𝑟𝑀𝑙

�𝑉

(2)

Page 155: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Z-RAFT Star Polymerization of Styrene: Comprehensive Characterization using SEC

153

0.0 0.2 0.4 0.6 0.8 1.02.0

2.5

3.0

3.5

4.0

4.5R =

3-arm star (4)

4-arm star (6)

Mp,

star /

Mp,

arm

monomer conversion

6-arm star (8)

Fig. 8. Ratio of peak molecular weights of star polymer and peak molecular weights of linear arm polymer

(Mp,star/Mp,arm), as obtained by conventionally calibrated SEC vs. monomer conversion for styrene bulk polymerizations at 80°C using ACCN (cACCN = 3 mmol∙L–1) as the initiator and mixtures of 2 and 4 (3-arm star

polymerization), 2 and 6 (4-arm star polymerization), and 2 and 8 (6-arm star polymerization). The overall trithiocarbonate-group concentration was around 38 mmol∙L−1 for all samples with approximately half the number of RAFT groups belonging to multifunctional RAFT agents. Horizontal lines indicate the average

value.

2 3 4 5 6 7

1.0

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8 this work Douglas' equation (semi-emp.) Radke et al. (exp.) Radke et al. (simul.)

corre

ctio

n fa

ctor

, K

number of arms, f

Fig. 9. Correction factor, K, for calculating absolute molecular weights of star polymers from values obtained using SEC with conventional calibration with linear standards. Closed circles: data from this work;

dashed line: semi-empirical equation by Douglas et al. [54]; open squares: mean values of experimental data collated by Radke et al. [55], error bars are standard deviations; dashed-dotted line: computer simulations by

Radke et al. [55,56].

Page 156: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Chapter 5

154

Branching ratios describing the reduction of the radius of gyration, rg, or of the

hydrodynamic radius, rH, of branched polymers have been subject of research for quite

some time. In order to compare our results, which were obtained via SEC separation

without on-line light scattering or viscosity detection, with branching ratios from

literature that are usually reported for identical molar mass, a calculation procedure,

e.g., starting from the viscosity branching ratio, is required. The viscosity branching

ratio g’ (see Eq. 3)

𝑔′ = �[𝜂]𝑏𝑟[𝜂]𝑙

�𝑀

(3)

is relating intrinsic viscosity [η] at identical mass of branched (index br) and linear

(index l) polymer and can be rewritten using the theory of universal calibration [57],

yielding Eq. 4, which related molecular weight of the linear and branched polymer of

identical hydrodynamic volume.

𝑔′ = � 𝑀𝑙𝑀𝑏𝑟

�𝑉

𝑎+1

(4)

The exponent a in Eq. 4 is the Mark-Houwink coefficient a of the linear polymer, i.e.,

0.700 for polystyrene in THF at 30 °C [58] as used in the present study. The correction

factor K can then be compared to branching-ratio data from other studies by combining

Eqs. 2 and 4, resulting in Eq. 5.

𝐾 = 𝑔′(−1𝑎+1) (5)

A prominent data set was reported by Douglas and co-workers [54], who calculated g’

for regular stars using the theoretical model by Stockmayer and Fixman [59]. They

found a semi-empirical relation (Eq. 6) which describes the viscosity branching ratio for

regular stars in good solvent best for ε = 0.58, which is an empirical form factor.

𝑔′ = �3𝑓−2𝑓2

�𝜀�1−0.276−0.015(𝑓−1)

1−0.276� (6)

Page 157: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Z-RAFT Star Polymerization of Styrene: Comprehensive Characterization using SEC

155

Based on this, Tsitsilianis et al. [60] described that the functionality of regular stars can

be calculated using SEC and Eqs. 4 and 6, that is, they used an approach that is similar

to the one described in this work. Inspection of Fig. 9 shows that the values obtained in

the present study are in relatively good agreement with semi-empirical g’ values

reported by Douglas et al. [54], calculated by via Eq. 6 and transformed to K values via

Eq. 5. Interestingly, the trend of our data is well matching that of Douglas’ data,

although the absolute values of our results are slightly higher.

Correction factors K for usage in conventionally calibrated SEC were also reported by

Radke et al. [55,56], who collated experimental contraction factors of star polymers that

were generated by various techniques and performed simulations of star polymer

shapes. These data are also plotted in Fig. 9. It can be seen that our results fit excellently

to the averaged experimental values by Radke et al. [55] for 3-arm stars (7 reported data

points) and 4-arm stars (6 reported data points) and that the simulated data by Radke et

al. [55,56] nicely matches Douglas’ Eq. 6. A somewhat higher discrepancy can be seen

for 6 arm stars: Our data are slightly higher than the simulated data by Radke et al. as

well as the semi-empirical data by Douglas et al., whereas the experimental values

reported by Radke et al. are significantly lower than these calculated values. This data

point originates from two samples only, which were generated via coupling of pre-

polymer and subsequent separation of grafted polymers having various arm numbers.

These laborious procedures might be a source of uncertainty. Since our method prepares

star and arm polymer simultaneously in a simple and straightforward fashion, the herein

reported data are possibly more precise. It is also gratifying to note that our data almost

perfectly follow the relative trend of the calculated data by Radke et al. and Douglas et

al.

In order to probe the precision, it seems rational to use our correction factors, K, to

estimate absolute molecular weight data by multiplying K with the molecular weights

from conventionally calibrated SEC. This approach is demonstrated in Fig. 10, in which

both the uncorrected and corrected data from conventional SEC calibration are plotted

together with the theoretically expected values. It can be clearly seen that the corrected

molecular weights almost perfectly match the 𝑀𝑛𝑡ℎ𝑒𝑜

values, suggesting that our

procedure is capable of yielding true molecular weights of star polymers. In order to

Page 158: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Chapter 5

156

finally prove that the perfect match between the corrected experimental values and the

predicted molecular weights is not a coincidence, we measured absolute molecular

weights of selected star polymer samples after SEC separation using a triple-detection

system that comprised an RI, a viscometry, and a light-scattering detector. Fig. 10

shows convincingly that the thus obtained absolute molecular weights perfectly blend

into the data obtained using the introduced correction method.

The concise picture that is obtained for Z-RAFT star polymerization of styrene up to 6

arms and using phenyl ethyl as the leaving group allows the following conclusions to be

drawn.

1. The number of arms of star polymer is constant above 30 % of monomer

conversion.

2. The number of arms is identical to the functionality of the star-shaped RAFT

agent, i.e., all RAFT groups have initiated arm growth.

3. Even at very high monomer conversions (thus yielding large star molecules),

there is no shielding effect observable that hampers the RAFT process.

Otherwise, deviations from theoretical predictions would occur.

Having now a method at hand to correctly determine molecular weights of star

polymers, we can evaluate the chain-transfer constant, CRAFT, of the initial RAFT step.

From a plot of the inverse number average degree of polymerization of one individual

arm against the concentration of trithiocarbonate groups, CRAFT can be evaluated via

linear fitting according to the procedure introduced by Barner-Kowollik and co-workers

[50,51]. Inspection of Fig. 1b shows that good linear behavior is observed in such a plot,

from which a CRAFT = 164 for phenylethyl-trithiocarbonate in styrene polymerization at

80°C can be estimated. This relatively large value is indicative of a very effective chain

transfer.

Page 159: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Z-RAFT Star Polymerization of Styrene: Comprehensive Characterization using SEC

157

0.0 0.2 0.4 0.6 0.80.0

2.0x104

4.0x104

6.0x104

8.0x104

1.0x105

conventional calibration corrected conventional calibration triple detection theoretical values

Mn /

g⋅m

ol−1

monomer conversion

Fig. 10. Number average molecular weight, 𝑀𝑛, of six-arm star polymer (data taken from Fig. 6) vs. monomer conversion, obtained via conventional SEC calibration (raw data and corrected by K given in Fig. 9) and via

triple-detection. The dashed line marks the theoretical molecular weight according to Eq. 1.

We also applied our method for obtaining apparent number of arms to Z-RAFT star

polymerizations having benzyl as the leaving group. This study was inspired by the fact

that all literature reports about Z-RAFT star polymerization of styrene used benzyl as

the leaving group. When applying exactly the same experimental conditions and

evaluation procedures as above, but using benzyl instead of phenylethyl as R-group, a

completely different picture is obtained, as can be seen in Fig. 11: The apparent arm

numbers are steadily increasing with monomer conversion and do reach the expected

and confirmed values for the anticipated arm numbers – indicated by the horizontal

dashed lines – only at very high X values, if at all. As the chemical nature of these stars

and that of the solvent are identical, the strong deviations from the star polymers

described above imply that the polymers from benzyl-typed star-shaped RAFT agents

have a distinct different topology. The data suggest that the real arm numbers are well

below the expected values and only slowly approach the expected numbers.

Page 160: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Chapter 5

158

0.0 0.2 0.4 0.6 0.8 1.0

1.5

2.0

2.5

3.0

3.5

4.0

R =

6-arm star (7) 4-arm star (5) 3-arm star (3)

Mpe

ak,s

tar /

M

peak

,linea

r

monomer conversion

Fig. 11. Ratio of peak molecular weights of star polymers and peak molecular weights of linear arm polymers (Mp,star/Mp,arm; representing the apparent number of arms in conventionally calibrated SEC) vs. monomer

conversion, from styrene bulk polymerizations at 80°C using ACCN (cACCN = 3 mmol∙L–1) as the initiator and mixtures of 1 and 3 (3-arm star polymerization), 1 and 5 (4-arm star polymerization), and 1 and 7 (6-arm star polymerization). The overall trithiocarbonate-group concentration was around 38 mmol∙L−1 for all samples

with approximately half the number of RAFT groups belonging to multifunctional RAFT agents. Horizontal lines indicate the average values from Fig. 8.

Stenzel and co-workers made similar observations in Z-RAFT star polymerizations with

benzyl-trithiocarbonates already in one of their early publications [20], in which they

found evidence for an increasing number of arms with proceeding reaction. However,

they did not quantify this effect, since they measured only apparent molecular weights

of star polymers. Surprisingly, this worrying effect was not considered since then and

benzyl-typed star-shaped RAFT agents were uncritically used by many research groups.

It may hence be that many observations, which were attributed to the mechanism of Z-

RAFT star polymerization, simply stem from an inefficient pre-equilibrium, which

apparently is highly relevant for the final topology.

It seems to be clear that the imperfect pre-equilibrium when using benzyl as the leaving

group hampers the rapid initiation of arm growth, which apparently not only affects

polydispersity, but more importantly, the topology of the final star polymer product.

This dramatic effect is due to the multifunctionality of the star-shaped RAFT agent,

which effectively needs to be initiated several times in a row before becoming a star.

Page 161: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Z-RAFT Star Polymerization of Styrene: Comprehensive Characterization using SEC

159

Unfortunately, our method for obtaining true molecular weights of star polymers is not

able to detect apparent arm numbers at very low monomer conversions, as linear and

star polymer species are not well separated in this regime. In order to fill this gap and to

study the topologically evolution of star growth also in more effective systems, detailed

theoretical and experimental studies of arm growth initiation at low monomer

conversions are underway in our laboratory.

5.4 Conclusion

Z-RAFT star polymerization of styrene leading to star polymers having 3, 4, and 6 arms

show very well controlled behavior up to very high monomer conversion. The

application of high pressure up to 2600 bar could suppress the amount of dead polymer

by more than a factor of 2.5, which is especially important for systems with low RAFT

agent concentrations, where the fraction of terminated linear polymer may become

substantial. No shielding effects were observed that would obstruct the RAFT process,

not even at very high monomer conversions (yielding large star molecules). By using a

mixture of linear and star-shaped RAFT agents, we were able to determine precise

absolute molecular weights of star polymers using a conventionally calibrated SEC

setup. When using trithiocarbonate-typed RAFT agents with phenylethyl as the leaving

group, a rapid chain-transfer of the initial RAFT step was found and well-defined star

polymers were formed, which perfectly match the theoretical predictions. However,

when using benzyl as the leaving group in the star-shaped RAFT agents, a pronounced

impact of monomer conversion on the number of arms was observed. It was found to be

impossible to synthesize pure star polymers with the expected number of arms, when

using benzyl as the leaving group.

References

[1] Tezuka Y, Oike H. Prog Polym Sci 2002;27:1069-1122.

[2] Lee JH, Goldberg JM, Fetters LJ, Archer LA. Macromolecules 2006;39:6677-6685.

[3] McLeish TCB. Chem Eng Res Des 2000;78:12-32.

[4] Hadjichristidis N, Pispas S, Pitsikalis M, Iatrou H, Vlahos C. Asymmetric star polymers: Synthesis and

properties, In: editor. Branched Polymers I, vol. 142. 1999. pp. 71-127.

[5] Li JS, Modak PR, Xiao HN. Colloids Surf, A 2006;289:172-178.

Page 162: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Chapter 5

160

[6] Qiu LY, Bae YH. Pharm Res 2006;23:1-30.

[7] Jones MC, Ranger M, Leroux JC. Bioconjugate Chem 2003;14:774-781.

[8] Jie P, Venkatraman SS, Min F, Freddy BYC, Huat GL. J Controlled Release 2005;110:20-33.

[9] Fichter TM, Zhang L, Kiick KL, Reineke TM. Bioconjugate Chem 2008;19:76-88.

[10] Likos CN. Soft Matter 2006;2:478-498.

[11] Vlassopoulos D, Fytas G, Pakula T, Roovers J. Journal of Physics-Condensed Matter 2001;13:R855-

R876.

[12] Freire JJ. Branched Polymers Ii 1999;143:35-112.

[13] Chiefari J, Chong YK, Ercole F, Krstina J, Jeffery J, Le TPT, Mayadunne RTA, Meijs GF, Moad CL,

Moad G, Rizzardo E, Thang SH. Macromolecules 1998;31:5559-5562.

[14] Barner-Kowollik C, Davis TP, Heuts JPA, Stenzel MH, Vana P, Whittaker M. J Polym Sci, Part A:

Polym Chem 2003;41:365-375.

[15] Moad G, Rizzardo E, Thang SH. Aust J Chem 2005;58:379-410.

[16] Perrier S, Takolpuckdee P. J Polym Sci, Part A: Polym Chem 2005;43:5347-5393.

[17] Moad G, Rizzardo E, Thang SH. Aust J Chem 2006;59:669-692.

[18] Stenzel-Rosenbaum M, Davis TP, Chen V, Fane AG. J Polym Sci, Part A: Polym Chem 2001;39:2777-

2783.

[19] Mayadunne RTA, Jeffery J, Moad G, Rizzardo E. Macromolecules 2003;36:1505-1513.

[20] Stenzel MH, Davis TP. J Polym Sci, Part A: Polym Chem 2002;40:4498-4512.

[21] Darcos V, Dureault A, Taton D, Gnanou Y, Marchand P, Caminade AM, Majoral JP, Destarac M,

Leising F. Chem Commun (Cambridge, U K) 2004;2110-2111.

[22] Boschmann D, Vana P. Polym Bull (Heidelberg, Ger) 2005;53:231-242.

[23] Bernard J, Favier A, Zhang L, Nilasaroya A, Davis TP, Barner-Kowollik C, Stenzel MH.

Macromolecules 2005;38:5475-5484.

[24] Hao XJ, Malmstrom E, Davis TP, Stenzel MH, Barner-Kowollik C. Aust J Chem 2005;58:483-491.

[25] Boschmann D, Vana P. Macromolecules 2007;40:2683-2693.

[26] Hong CY, You YZ, Liu J, Pan CY. Journal of Polymer Science Part a-Polymer Chemistry

2005;43:6379-6393.

[27] Chaffey-Millar H, Stenzel MH, Davis TP, Coote ML, Barner-Kowollik C. Macromolecules

2006;39:6406-6419.

[28] Zhou GC, He JB, Harruna, II. J Polym Sci, Part A: Polym Chem 2007;45:4225-4239.

[29] Liu O, Chen Y. Macromolecular Chemistry and Physics 2007;208:2455-2462.

[30] Jesberger M, Barner L, Stenzel MH, Malmstrom E, Davis TP, Barner-Kowollik C. J Polym Sci, Part A:

Polym Chem 2003;41:3847-3861.

[31] Barner-Kowollik C, Davis TP, Stenzel MH. Aust J Chem 2006;59:719-727.

[32] Dureault A, Taton D, Destarac M, Leising F, Gnanou Y. Macromolecules 2004;37:5513-5519.

[33] Frohlich MG, Vana P, Zifferer G. J Chem Phys 2007;127:-.

[34] Frohlich MG, Vana P, Zifferer G. Macromol Theory Simul 2007;16:610-618.

[35] Boschmann D., Drache M., Fröhlich M., Zifferer G., and Vana P., Polym. Prepr. (Am. Chem. Soc., Div.

Polym. Chem.) 2008, 49, 189–190

[36] Mänz M, Vana P. 2008;in preparation.

Page 163: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

Z-RAFT Star Polymerization of Styrene: Comprehensive Characterization using SEC

161

[37] Haney MA, Jackson C, Yau WW. Proceedings of the 1991 International GPC Symposium 1991;49-63.

[38] Huang Y, Peng H, Lam JWY, Xu Z, Leung FSM, Mays JW, Tang BZ. Polymer 2005;45:4811-4817

[39] Buback M, Frauendorf H, Vana P. J Polym Sci, Part A: Polym Chem 2004;42:4266-4275.

[40] Bernard J, Hao XJ, Davis TP, Barner-Kowollik C, Stenzel MH. Biomacromolecules 2006;7:232-238.

[41] Johnston-Hall G, Monteiro MJ. Macromolecules 2008;41:727-736.

[42] Arita T, Buback M, Janssen O, Vana P. Macromolecular Rapid Communications 2004;25:1376-1381.

[43] Barner-Kowollik C, Buback M, Charleux B, Coote ML, Drache M, Fukuda T, Goto A, Klumperman B,

Lowe AB, Mcleary JB, Moad G, Monteiro MJ, Sanderson RD, Tonge MP, Vana P. J Polym Sci, Part A:

Polym Chem 2006;44:5809-5831.

[44] Mayadunne RTA, Rizzardo E, Chiefari J, Krstina J, Moad G, Postma A, Thang SH. Macromolecules

2000;33:243-245.

[45] Chong YK, Krstina J, Le TPT, Moad G, Postma A, Rizzardo E, Thang SH. Macromolecules

2003;36:2256-2272.

[46] Barner-Kowollik C, Quinn JF, Nguyen TLU, Heuts JPA, Davis TP. Macromolecules 2001;34:7849-

7857.

[47] Quinn JF, Barner L, Davis TP, Thang SH, Rizzardo E. Macromolecular Rapid Communications

2002;23:717-721.

[48] Beuermann S, Buback M. Prog Polym Sci 2002;27:191-254.

[49] Initiators for High Polymers, ed. AKZO Nobel Chemicals, 2006.

[50] Theis A, Feldermann A, Charton N, Stenzel MH, Davis TP, Barner-Kowollik C. Macromolecules

2005;38:2595-2605.

[51] Johnston-Hall G, Theis A, Monteiro MJ, Davis TP, Stenzel MH, Barner-Kowollik C. Macromolecular

Chemistry and Physics 2005;206:2047-2053.

[52] Buback M, Frauendorf H, Günzler F, Huff F, Vana P. 2008; Macromolecular Chemistry and Physics

210 (2009) 1591-1599.

[53] Burchard W. Solution properties of branched macromolecules. In: Branched Polymers I, vol. 143. 1999.

pp. 113-194.

[54] Douglas JF, Roovers J, Freed KF. Macromolecules 1990;23:4168-4180.

[55] Radke W, Gerber J, Wittmann G. Polymer 2003;44:519-525.

[56] Radke W, Macromol Theory Simul 2001;10:668-675.

[57] Strazielle C, Herz J. Eur Polym J 1977;13:223-233.

[58] Strazielle C, Benoit H, Vogl O. Eur Polym J 1978;14:331-334.

[59] Stockmayer WH, Fixman M. Ann N Y Acad Sci 1953;57:334-352.

[60] Tsitsilianis C, Ktoridis A. Macromol Rapid Commun 1994;15:845-850.

Page 164: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):
Page 165: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

163

Summary

Branched polymers are different from other polymers in many different ways. Due to

their structure and properties branched polymers present a challenging class of materials

for structural analysis. The main goal of project CoBra (viz. ‘Comprehensive

characterization of Branched polymers’) has been the development of new analytical

technologies and methodology for branched polymers. Traditional characterization

techniques fail to separate long-chain-branched from linear polymers and do not

discriminate between the effects of degree of branching and topology. The approach

followed in the work described in this thesis has been the exploration and detailed study

of separations with unique selectivity towards branched polymers. The emphasis has

been on hydrodynamic separations and molecular-topology fractionation (MTF) for

high-molar-mass linear and long-chain-branching polymers. Comprehensive two-

dimensional separations have been used extensively with combinations of both new and

conventional separation modes. These experiments were used to improve understanding

of topology-sensitive separations, as well as experimental optimization ultimately

resulting in highly-selective separation of branched polymers.

The background of polymer structure and the importance of branching on material

properties are presented in chapter 1. A broad overview of different branched polymers

and their applications is provided. Classification of branched polymers is based on

molecular structure. Topology and branch length together determine the kind of

branching, as well as the impact on material properties. Common characterization

techniques for different kinds of branching are presented. The overview serves to

illustrate that the analytical needs for polymers with highly-abundant branching or low

molar masses can be properly addressed using the available characterization techniques.

Limitations with respect to conventional characterization of long-chain-branched

polymers and the distinct impact of even low levels of branching on rheology provide

the main drivers for the work presented in this thesis.

Page 166: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

164

In chapter 2 the preparation of monolithic columns and their application for polymer

separations is described. It was verified that columns could be obtained with well-

defined and uniform flow-through pores. The application of such stationary phases was

of high interest for the studies of topology-selective separations, because these

separations require flow-through channels with dimensions comparable to the size of

analyte molecules. Flow-resistance measurements and mercury-intrusion porosimetry

were performed to obtain accurate pore-size information. Based on these results and the

observed polymer separations it was concluded that the prevailing separation

mechanism was hydrodynamic chromatography (HDC).

The first demonstration of a comprehensive two-dimensional separation for high-molar-

mass polymers with identical size, but different topology is presented in chapter 3.

Branching-selective separation was performed on an MTF column with polydisperse

sub-1-µm particles. The calibration curve for this column (established using one-

dimensional separations) showed reversal of the calibration curve analogous to HDC. In

an MTF×SEC experiment (comprehensive two-dimensional liquid chromatography with

MTF in the first and size-exclusion chromatography in the second dimension) the

branching selectivity in MTF was confirmed, although the effects of size and topology

remained confounded. Another important step forward in branching-selective separation

demonstrated in this chapter is the separation of a long-chain-branched polymer with a

broad molar-mass distribution. The need for MTF columns with well-defined porous

properties is highlighted by this work, because accurate statements on the separation

mechanism were hindered by the ill-defined nature of the interstitial-channels in a bed

with polydisperse particles.

State-of-the-art separations of branched polymers in chapter 4 are the result of progress

made in terms of both column technology and understanding of polymer separations in

monoliths with extremely narrow flow-through channels. Monoliths described in

chapter 2 were used in a systematic study of experimental conditions, such as pore size,

flow rate, and hydrodynamic size and topology of analyte polymers. An overview is

presented of different separation modes for random-coil polymers in terms of the aspect

ratio (λ) and Deborah numbers. The analogy between HDC to MTF at low flow rates

and deviations at higher flows are studied using comprehensive MTF×SEC. The

Page 167: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

165

occurrence of ‘critical conditions’, where the non-equilibrium deformation of polymers

and retardation effects at high λ cancel out, is recognized as a means to enhance the

applicability of MTF separations. Within the relatively narrow window of 0.4 < λ < 0.9

the separation of linear from branched polymers is demonstrated for materials with

different branching topology.

In chapter 5 the preparation and characterization of well-defined star polymers is

described. Reversible addition-fragmentation chain transfer (RAFT) polymerization is a

living polymerization. Star polymers can be created with a pre-defined number of arms

using multi-functional RAFT agents, provided that suitable leaving groups are used.

Mixtures of linear and star polymers were prepared with the linear segments or ‘arms’

all having the same degree of polymerization. The bi-modal molar-mass distribution of

the product served as a well-defined star polymer with an internal linear reference. The

viscosity contraction ratio was indirectly used to calculate correction factors for SEC

separations calibrated with linear polymers. Results of the study were validated against

externally published work and against accurate molar masses determined using triple-

detection SEC.

Page 168: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):
Page 169: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

167

Samenvatting

Vertakte polymeren verschillen van andere polymeren in veel opzichten. Vertakte

polymeren vertegenwoordigen een bijzonder uitdagende klasse van materialen vanwege

hun structuur en eigenschappen. Het voornaamstel doel van project CoBra (acroniem

voor ‘comprehensive characterization of branched polymers’ ofwel de alomvattende

analyse van vertakte polymeren) is de ontwikkeling van nieuwe analytische technologie

en methodologie voor vertakte polymeren. Traditionele analytischetechnieken voldoen

niet om hoogmoleculair materiaal met lange vertakkingen (zogenaamde ‘long-chain-

branched polymeren’) te onderscheiden van lineair materiaal, dan wel onderscheid te

maken tussen de mate en soort van de vertakkingen. De aanpak van deze uitdaging,

zoals beschreven in dit proefschrift, is gericht op de verkenning en verdieping in

scheidingmethoden met een unieke selectiviteit voor vertakte polymeren. De nadruk

binnen dit werk ligt op de toepassing van hydrodynamische scheiding en fractionering

op basis van moleculaire topologie (MTF) voor hoogmoleculair lineair en vertakt

materiaal met lange vertakkingen. Alomvattende twee-dimensionale scheidingen zijn

uitvoerig gebruikt, met zowel nieuwe als bestaande analytische scheidingsmethoden.

Deze experimenten dienen zowel voor het verdiepen van inzicht in scheidingen met

selectiviteit voor topologie, als voor experimentele optimalisering om een effectieve

scheiding van vertakte polymeren te verkrijgen.

De achtergrond van vertakte polymeren, de moleculaire structuur en de

materiaaleigenschappen worden behandeld in hoofdstuk 1. Een brede achtergrond wordt

geschetst voor vertakte polymeren en de toepassingsgebieden hiervan. De classificering

van vertakte polymeren vindt plaats op basis van de moleculaire structuur. Topologie en

de lengte van de vertakkingen bepalen samen tot welke klasse het polymeer behoort en

wat de gevolgen zijn voor materiaaleigenschappen. Een overzicht van gangbare

analytische technieken voor verschillende klassen van vertakte polymeren wordt

gepresenteerd. Hieruit blijkt dat met de gangbare technieken in voldoende mate kan

worden voorzien in de analytische behoefte voor polymeren met een hoge mate van

vertakking of een laag moleculair gewicht. De beperkingen van deze technieken doen

Page 170: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

168

zich met name gelden voor polymeren met lange vertakkingen, die reeds bij zeer

beperkte aanwezigheid de materiaaleigenschappen beïnvloeden. Dit vormt de

belangrijkste drijfveer voor het werk dat wordt gepresenteerd in dit proefschrift.

In hoofdstuk 2 worden de bereiding van monolithische kolommen en toepassing daarvan

voor de scheiding van polymeren beschreven. De mogelijkheid om kolommen te maken

met goed gedefinieerde en uniforme doorstroomkanaaltjes wordt hierin geverifieerd.

Toepassing van dit soort stationaire fasen is van bijzondere interesse voor studies met

betrekking tot topologie-gevoelige scheidingen, omdat hiervoor een stationaire fase

gewenst is met doorstroomkanaaltjes van vergelijkbare grootte als de

polymeermoleculen in oplossing. Metingen van de stromingsweerstand en

kwikverzadigingsporosimetrie werden uitgevoerd om een nauwkeurig beeld te krijgen

van de poriegrootte. De resultaten hiervan, in combinatie met observaties voor

polymeerscheidingen op deze materialen, leidden tot de conclusie dat een

hydrodynamisch mechanisme verantwoordelijk was voor chromatografische scheiding.

Een eerste demonstratie van een alomvattende twee-dimensionale scheiding van

hoogmoleculaire polymeren met identieke hydrodynamische omvang, maar

verschillende topologie, wordt gepresenteerd in hoofdstuk 3. Vertakkingsgevoelige

scheiding werd uitgevoerd op een kolom met polydisperse deeltjes kleiner dan 1 µm. De

kalibratie van deze kolom (op basis van één-dimensionale experimenten) bevestigde de

omslag van de kalibratiecurve vergelijkbaar met hydrodynamische scheidingen. In een

MTF×SEC experiment (alomvattende twee-dimensionale scheiding met MTF in de

eeerste en “size-exclusion” chromatografie in de tweede dimensie) werd de

vertakkingsgevoeligheid voor fractionering op basis van moleculair topologie bevestigd,

ondanks dat de scheiding tevens beïnvloed werd door de hydrodynamische omvang van

de moleculen. Een belangrijke stap vooruit in de vertakkingsgevoelige scheiding wordt

ge zet met de scheiding van een polymeer met lange vertakking in combinatie met een

brede moleculaire gewichtsverdeling. De behoefte aan MTF kolommen met goed

gedefinieerde doorstroomkanaaltjes werd wederom bevestigd in dit werk, omdat een

nauwkeurige analyse van het scheidingsmechanisme niet mogelijk was bij gebrek aan

goed gedefinieerde poriën in de stationaire fase.

Page 171: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

169

De best mogelijke analytische scheidingen van vertakte polymeren in hoofdstuk 4 zijn

het resultaat van de vooruitgang die geboekt in kolomtechnologie en verbeterd inzicht in

polymeerscheidingen in monolithische kolommen met zeer nauwe

doorstroomkanaaltjes. De monolithische kolommen zoals beschreven in hoofdstuk 2

werden toegepast in een systematisch onderzoek naar de invloed van experimentele

condities, zoals de grootte van doorstroomkanaaltjes, het debiet en de hydrodynamische

straal en de topologie van de polymeermoleculen. Een overzicht van verschillende

scheidingsmechanismen die van toepassing zijn voor polymeren met een flexibele

ketenstructuur is opgesteld op basis van de relatieve polymeergrootte (λ) en

Deborahgetallen. De overeenkomst tussen hydrodynamische scheiding en MTF,

alsmede de verschillen bij hogere debieten, werden bestudeerd met MTF×SEC. Het

verschijnsel van ‘kritische condities’, waarbij de effecten van de verstoring van de

polymeeromvang onder evenwichtscondities worden opgeheven door de trage relaxatie

van relatief grote polymeermoleculen wordt aangemerkt als een mogelijkheid om de

toepasbaarheid van MTF te verruimen. Binnen een relatief klein toepassingsgebied (0.4

< λ < 0.9) wordt de analytische scheiding van lineaire en vertakte polymeren

gedemonstreerd voor materialen met verschillende topologie.

In hoofdstuk 5 word de bereiding en analyse van goed gedefinieerde sterpolymeren

beschreven. Reversibele additie-fragmentatie ketenoverdrachtspolymerisatie (RAFT) is

een vorm van levende polymerisatie. Sterpolymeren kunnen worden bereid met een

vooraf gekozen aantal armen met behulp van multifunctionele RAFT start

verbindingen, op voorwaarde dat een geschikte vertrekkende groep wordt gebruikt.

Mengsels van lineaire en stervormige polymeren kunnen worden gemaakt met een

vergelijkbare polymerisatiegraad voor alle lineaire ‘arm’ segmenten. De bimodale

molaire-massa verdeling van het product reflecteert zowel een goed gedefinieerd

sterpolymeer als een lineaire interne standaard. De relatieve viscositeitscontractie

verhouding kan indirect worden gebruikt voor een correctie op een massa’s verkregen

uit SEC op basis van een kalibratie met lineaire polymeren. De resultaten van het

gebruik van deze correctie werden gevalideerd door middel van een vergelijking met

extern gepubliceerd werk, alsmede met een zeer nauwkeurige moleculaire-massa meting

met behulp van “triple” detectie SEC.

Page 172: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

170

Page 173: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

171

Acknowledgements

The time has finally come to finish this thesis, but before I do so I would like to say

thank you to everyone who contributed to the result that lies before you. Over the time

of my thesis research I came to meet and work together with many people. I owe them

my gratitude for the great collaboration and the good times in Amsterdam during my

PhD research.

First of all I would like to thank Peter, my promotor, for his trust and support that have

made it possible to perform and complete this work. The way that you convey your

enthusiasm and engage people with analytical chemistry got me interested to continue in

this field (starting back in the first year at university for both of us, 1999, Algemene

Chemie). After various projects and courses in the analytical-chemistry group and Shell

both of us were convinced that a PhD-project was the way to move forward. Jan

Blomberg deserves a fair share in the credit here as well! I would like to mention the

many possibilities people get in the group to visit meetings, conferences and even help

organize them. They have been the best times and created a wealth of personal

development opportunities. Thank you for always being ready to join singing good-old

Dutch songs on Friday evenings. You once accused me in York of comprehensive waste

of time, but this wasn’t one of them.

Special thanks go out to members of the thesis committee: Sjoerd van der Wal, Hans-

Gerd Janssen, Alex van Herk, Wim Kok, Wolfgang Radke and Freddy van Damme. I

appreciate our discussions and the critical question with respect to the various subjects

of this thesis. Without your challenging this thesis could not have reached the level it

has now. I also appreciate the possibilities of visiting the DKI in Darmstadt (Wolfgang

Radke, Harald Pasch, Tibor Macko, Mubasher Bashir, Yonggang Liu and others, thank

you for your hospitality), DSM in Geleen, and Unilever in Vlaardingen (ice cream!).

Colleagues and friends of the analytical-chemistry group at University of Amsterdam –

the list has grown long after being around for almost seven years! Fiona Fitzpatrick and

Aschwin van der Horst, thank you for giving me the chance to work with liquid

chromatography and SEC for the first times during the bachelor internships. Simona

Popovici, I’m happy that we meet again in our new roles now you’re teaching at

Page 174: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

172

Hogeschool Zeeland. I like the student visits to Dow, you’re welcome. Xulin, Maya

Ziari, Wybren Frankema (I still don’t say RMS-radius, though you are right), thank you

for sharing the office space at the fourth floor of Roeterseiland when I just joined the

group. Many other colleagues there I would like to thank for the work we did and good

times we had. Yuli, Filippo (I will remember you surrounded by a canteen full of girls

only in Groningen), Mauro (you should have been there), Erwin (has similar problems

with English women when dressed in purple), Sonja (outclasses all of them together),

Peter Pruim & Stella (I’d better make sure the fridge is full when you are there, I

appreciate your attendance on Friday afternoons), Linda, Elena (thank you for the royal

banquet upon your arrival), Aleksandra and Daniela. Sebastiaan Eeltink, thank you not

only for teaching me how to make monoliths and guiding me in doing PhD research

when I just started, but also for being a good friend (especially when you let me win

with squash…). HPLC2006 San Francisco was one of the best symposium visits,

because of the associated holidays. Gabriel (thank you for supporting the group with

chemometrics expertise), Sonja and Frederique; thank you for joining the road trips

around SF and being part of this adventure. Wim Decrop, I’ve learned a great deal from

you with respect to two-dimensional liquid chromatography and data processing in

Matlab. Other things that come to mind are the tree W’s: waffles, Westvleteren and DJs

Wipneus & Pim. Dominique and Korneel (he can open a beer with anything, included a

printed version of J Chromatogr A.), I’m grateful for the work you did on making

monolithic and particle-packed columns. Apart from that there were the barbeques,

wok-frituren; we had a lot of fun as well. When their project was finished Siri took over

making monoliths. No wonder you are doing a PhD now in Switzerland, within a few

weeks we did some of the best experiments ever with monoliths. Then there are Petra

(jij regelde de hulptroepen bij symposia en activiteiten, ook als de Jenever op moest),

Tom and Peter Verschuren. Thank you for making the group successful as it is. Marjo,

your help with the porosimetry has been most valuable to this work, thank you! To all

of you, it has been my pleasure to run the FBI for so long. I enjoyed many Friday-

afternoon events with you of the Friday beer initiative. After the department had fallen

short of a crazy woman to serve coffee I was happy to jump in and set something up for

that as well. It’s less flattering than the previous initiative, but having access to descent

coffee at work is priceless.

Page 175: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

173

I’ve met many great people that I would like to mention that are active on the subject of

polymers through collaboration in the European Graduate School (Thank you Wibke

Dempwolf and Alex for your efforts to make EGS possible). Ellen Donkers, Patricia

Geelen, Joris Salari, Marie-Claire Hermant, Roxana Abu, Joost Leswin, Bas Staal,

Maarten Staal, thank you for the nice times (EGS and not to forget Lunteren) and

collaboration. Thanks to Phillip Vana and Daniel Boschmann (Göttingen) for

collaboration on synthesis and analysis of star polymers as part of EGS as well.

Eindhoven is home also to the Dutch Polymer Institute that has made project CoBra

possible. Through the update meetings I’ve met great collaborators within the Dutch

Polymer Institute. Joachim Loos and Kangbo Lu, thank you for providing the cryo-TEM

results and 3D mapping of monolith structure. Rob Duchateau, Wouter Gerritsen, I

appreciate the knowledge we shared on the high-temperature SEC for high-throughput

polymer synthesis.

Also I would like to acknowledge my colleagues and friends at Dow that I’ve interacted

with during and after my time at University. Freddy, Edwin and David, thank you for

making this possible, as well as for the regular contact on results and progress of this

project. I am most grateful for the possibilities you offered me to visit Dow in

Terneuzen and Midland where we worked on high-temperature 2D-LC. David Meunier,

I really appreciate the time you made available for me during the longer visit to Midland

– not only at work, but also for visiting the Loons games, traveling for football through

most of Michigan. Ted Stokich, thank you for the work on 2D-LC we did. I appreciated

the confrontation with my own culture (the Holland visit) and having shooting classes

as well. Credit for visiting Holland goes to Pat Smith as well. Pat is a great person, he

helped me with the essentials: a bicycle, good coffee (we grind beans) and a trip to a

microbrewery once in a while. Most of all thank you for your contribution to great

science in making new analytical techniques possible. Dave Walter, I appreciate the

concept lunch meeting as well as moose-burger. I remember you as an engaged project

leader and great people leader. The return favor of showing you the analytical

department and the rest of Amsterdam was therefore more than deserved. In the post-

university time I’ve learned from a number of people about how we do characterization

of (branched) polymers: Jaap den Doelder, Sjoerd de Vries, Marc Mangnus, Hans de

Jonge; I would like to thank you for your time and the contributions to this thesis.

Page 176: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

174

Albena Lederer, Marion Gaborieu, Patrice Castignolles, Bob Gilbert, Walther Burchard

and Wolfgang Radke; thank you for organizing the stimulating workshop on

characterization of branched polymers in Dresden. I have learned a lot at this meeting

about things I did not know. Thanks Anna, Susanne and Michael for your contributions

as well, I will try and get you a version of this thesis.

Various others have contributed to project Cobra. Christine Fernyhough from the

University of Sheffield. Thank you for making comb polymers available early in my

project! Another contact established at the ISPAC 2005 meeting was with Polymer

Laboratories. Adrian Williams, Steve O’Donohue and Greg Saunders. Thank you for

providing us with the second-dimension SEC columns. Many thousands of second-

dimension chromatograms have been analyzed on rock-solid columns that lasted the

entire project! Through collaboration between PL and Micronit it was possible to work

with a chip-sized viscometer. Marco Blom is gratefully acknowledged for the support

with this apparatus. We got it to work properly pretty soon as you can see in the

introduction. Small things can have huge impact, as proven again by Ben Klein

Meulekamp from our mechanical workshop. Thanks to the disks provided by you we

were able to make monoliths in wide-bore steel columns successfully.

Acknowledgements also to Johan Scholtens (Shimadzu, LC-equipment) and Jeroen de

Jong (Interscience, empty column hardware) for their engagement with this work and

going the extra mile to get us the tools to make this work possible.

It’s time to finish. I would like to thank my parents, Ton en Ria, for their support. After

you pushed me to finish up the last corrections of the manuscript I can go on a nice

holiday with the writing finished. Khanh, you’ve permitted me the time to complete this

work. Good life balance is important and you helped me to relax from time to time.

When you were not around I was able to work twice as hard and fill my micro-pauses

with improving my Gangnam-style dance. Time to show you the result, the plane is here

now for my flight to Hanoi.

Page 177: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

175

Publications

1. Fiona Fitzpatrick, Rob Edam, Peter J. Schoenmakers, “Application of the

reversed-phase liquid chromatographic model to describe the retention

behavior of polydisperse macromolecules in gradient and isocratic liquid

chromatography”, J. Chromatogr. A, 988 (2003) 53.

2. R. Edam, J. Blomberg, H.-G. Janssen, P.J. Schoenmakers, “Comprehensive

multi-dimensional chromatographic studies on the separation of saturated

hydrocarbon ring structures in petrochemical samples”, J. Chromatogr. A,

1086 (2005) 12.

3. R. Edam, D.M. Meunier, E.P.C. Mes, F.A. Van Damme, P.J. Schoenmakers,

“Branched-polymer separations using comprehensive two-dimensional

molecular-topology fractionation × size-exclusion chromatography”, J.

Chromatogr. A, 1201 (2008) 208.

Chapter 3 of this thesis

4. Daniel Boschmann, Rob Edam, Peter J. Schoenmakers, Philipp Vana, “Z-

RAFT star polymerization of styrene: Comprehensive characterization using

size-exclusion chromatography”, Polymer, 49 (2008) 5199.

5. Daniel Boschmann, Rob Edam, Peter J. Schoenmakers, Philipp Vana,

“Characterization of Z-RAFT star polymerization of butyl acrylate by size-

exclusion chromatography”, Macromol. Symp., Vol. 275-276 Issue 1 (2009)

184.

Chapter 5 of this thesis

6. R. Edam, Sebastiaan Eeltink, Dominique J.D. Vanhoutte, Wim Th. Kok, Peter

J. Schoenmakers, “Hydrodynamic chromatography of macromolecules using

polymer monolithic columns”, J. Chromatogr. A, 1218 (2011) 8638.

Chapter 2 of this thesis

Page 178: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):

176

7. James F. Griffith, William L. Winniford, Kefu Sun, Rob Edam, Jim C. Luong,

“A reversed-flow differential flow modulator for comprehensive two-

dimensional gas chromatography”, J. Chromatogr. A, 1226 (2012) 116.

8. Rob Edam, Edwin P.C. Mes, David M. Meunier, Freddy A. Van Damme, Peter

J. Schoenmakers, “Branched polymers characterized by comprehensive two-

dimensional separations with fully orthogonal mechanisms: molecular-

topology fractionation × size-exclusion chromatography”, submitted for

publication in J. Chromatogr. A, 2013.

Chapter 4 of this thesis

Page 179: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):
Page 180: UvA-DARE (Digital Academic Repository) Comprehensive ... · Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA):