- 70 -

POLYINSERTION and ROMP

I Polyinsertion

Assignment of tasks

Synthesis of isotactic polystyrene (it-PS) with the heterogeneous Ziegler-catalyst TiC14/(iBu)3A1 in

heptane as solvent.

Literature

1. H. G. Elias: Bd. 1, 1. Auflage, Wiley-VCH-Verlag, Weinheim, 2005.

2. Compr. Polym. Sci., Vol. 4, Part II, 1. Aufl., Pergamon Press GmbH 1989

Content

1. Theoretical basics

1.1. Ziegler-Natta catalysts

1.2. Mechanisms

1.3. Industrially produced polymers

2. Description of the experiment

2.1. Safety

2.2. Chemicals and equipment

2.3. Experimental procedure

3. Questions

- 71 -

1 Theoretical basics

1.1 Ziegler-Natta catalysts

In the last few years, transition metal-based catalysts have gained great importance, especially for the

polymerization of ethylene at low pressures, as well as for the synthesis of polypropylene.

Furthermore, they offer a wide range of applications in the preparation of stereoregular polymers.

Among the technically most important catalysts in this area are the so-called Ziegler-catalysts (also

named Ziegler-Natta-catalysts). Systems, which are made by mixing organometallic compounds of

transition group elements IV-VIII with metals alkyls or metals hydrides of the groups I – III of the

periodic system, are referred as Ziegler-catalyst. A typical Ziegler-catalyst is formed, for example,

by the reaction of TiCl4 with Et3Al. These catalysts is heterogeneous, because they precipitate as a

fine suspension in an organic solvent (for example from heptane). At the beginning of catalyst

research, this heterogeneity was assumed to be responsible for catalyst activity (“catalytic surfaces”),

however, Kaminsky et al. found that also soluble (homogeneous) systems display similar activities.

Such homogeneous Ziegler-catalysts can be generated through the combination of, e.g.,

bis(cyclopentadienyl)titanium(IV)

dichloride (Cp2TiCl2, a metallocene catalyst) with

diethylaluminiumchloride (Et2AlCl).

A few further important catalytic systems:

Et2AlCl/TiCl3 heterogeneous

Et2AlCl/VCl4/anisole homogeneous

Et2AlCl/V(acac)3 homogeneous

Et2AlCl/Cr(acac)3 homogeneous

Cp2ZrMe2/alumoxane homogeneous

Besides the Ziegler-catalyst, the so-called "Phillips-catalyst" (CrO3/SiO2/A12O3) is of technical

importance, especially in the polymerization of ethylene.

1.2 Mechanisms

The polymerization occurs at the transition metal-carbon bond. The active species and the reaction

mechanism are, with the exception of Phillips-catalysts, mostly clarified. The growth step can

principally take place over a mono- or bimetallic mechanism.

- 72 -

Monometallic mechanism

In the so-called monometallic mechanism (Fig. 1) it is assumed that the olefin approaches first to a

vacant site of the transition metal with its π-bond, and then coordinates to it. The coordinated

monomer is then inserted into the metal-carbon bond via a four-membered transition state.

Fig. 1: Monometallic mechanism.

The main group metal complex is not involved into the chain growth reaction; it is only used for the

alkylation of the transition metal complex ("monometallic"). There are (idealized) separated ion

pairs. In fact, however, these ion pairs are in reality never completely separated from each other, and

the termination and transfer reactions can be easily explained via the following reaction scheme:

Termination caused by β-hydride elimination:

Transfer to the monomer:

Molecular weight control by H2:

- 73 -

Bimetallic mechanism

In the bimetallic mechanism (Fig. 2) both metal atoms are involved in the reaction. The π-electron of

the olefin interacts first with the orbitals of the transition metal, wherein an electron-deficient

compound is formed. The free rotation of the only partially resolved C-C double bond remains

rescinded, and there is also no free rotation around the metal-carbon bond. Therefore, the substituent

R remains fixed in the further reaction steps with respect to its position relative to the methyl group

of the last inserted monomer unit. By ring formation the free residual valences are saturated. The

overlap of electrons at C(1) and C(3) forms a σ-bond. At the same time the Al-C(3) bond is broken

and the starting complex can be formed again with an extended polymer chain.

Fig. 2: Bimetallic mechanism.

The general principles of such a mechanistic model can be applied to both homogeneous and

heterogeneous catalysis. The all-accepted fact is that, in the case of heterogeneous catalysis, the

catalytically active sites on the crystal surface of the heterogeneous contact are built from originally

defects presented in the crystal structure. If any α-olefin, e.g., styrene is used instead of ethylene as

monomer, there is the possibility of the formation of various stereoregular polymer chains (Fig. 3),

such as isotactic (it), syndiotactic (st) chains and atactic (at) for those that do not have

stereoregularity in the polymer chains. Chains, in which all the side-group carbon atoms have the

same absolute configuration (RRRR or SSSS) are called isotactic. In syndiotactic chains, the

configuration alternates along the chain (RSRS etc.). By means of the zig-zag-(also Natta-) projection

used in polymer chemistry, these regular and the non-regular (R and S are randomly distributed)

- 74 -

atactic forms can be described. The stereoregularity of polymers has a very strong influence on their

physical properties. Atactic polymers, for example, are generally amorphous, and their glass

temperatures are relatively low and extend as freeze-range over several degrees. However, the iso-

and syndiotactic polymers generally can be crystallized; their melting points Tm are high and well-

defined, also the solubility is greatly reduced due to the high crystallinity. The various forms can be

characterized by both IR- and NMR.

Fig 3: Natta-projection.

The following Table summarizes some of the properties (G. Natta, 1959).

Table 1. Comparison of the properties of stereoregular and atactic polymers.

product solid state Tm /

° C

Tg /

° C

density /

g·cm-3

solubility* in

diethyl ether

solubility* in

toluene

PP

at amorphous -20 0,85 s ss

it crystalline 158 - 160 -10 0,93 ds s

PB

at amorphous -24 0,87 s ss

it crystalline 126 - 128 0,91 ds s

PS

at amorphous 70 - 100 1,04 s ss

it crystalline 230 - 231 1,08 ds s

* s: soluble; ds: difficultly soluble; ss: slightly soluble.

- 75 -

1.3 Industrially important polymers prepared via coordinative polymerization

HDPE, high density polyethylene

Hostalen (Hoechst), Marlex (Phillips)

vessels, bags, sheets, dishes, disposable products, cable sheathing, insulators, hip joints, ...

it-PP, it-polypropylen

Hostalen PP (Hoechst), Novolen (BASF)

temperature-resistant containers, vessels, automotive, upholstery, ...

it-PB, it-poly-l-butene

tear-resistant films, pipes, ...

poly-4-methyl-l-pentene

TPX (Mitsui)

electrical and lighting industry, temperature resistant (mp 240 ° C), medical applications

trans-1,4-polyisoprene

golf balls, medical applications (for example shoe inserts)

cis-1,4-polyisoprene und -butadiene

rubber and tire industry

2 Experimental produce

2.1 Safety: All persons being exposed to chemicals have to be instructed about the effects of

dangerous substances (toxicity, point of ignition, etc.) as well as about preventive measures. Before

the experiment is carried out, read the MSDS sheets for all the chemicals used in this laboratory and

be familiar with their safe handling. The instructions of the teaching assistant must be followed at all

times. Especially the following points are relevant:

1. Wearing of suitable protective clothing (protective goggles, glove, laboratory coat, etc.)

2. Knowledge about the safety devices (e.g., laboratory hood, fire extinguisher, emergency

shower, first aid boxes, etc.), exit

3. Controlled disposal of toxic substances in compliance with legal regulations

4. Strict ban on eating, drinking and fuming in the laboratory

- 76 -

The greatest possible care must be exercised when working with organoaluminum compounds, since

they ignite very easily on contact with air and water. All operations must, therefore, be carried out

with the complete exclusion of air and moisture and pipettes must be flushed with nitrogen.

Moreover, these substances cause wounds that are slow to heal, so that the wearing of safety goggles

is mandatory and all contact with the skin must be avoided. The pipettes are cleaned as follows: after

all organoaluminum have been run out, the pipette is filled with ether and allowed to drain again. It is

then washed with isopropanol/HCl solvents.

2.2 Chemicals and equipment

Chemicals: heptane abs., triisobutylaluminium (25% in hexane), TiCl4 (caution!), styrene (freshly

distilled), 2-propanol, methanolic HCl (ca. 10%), methanol, methyl ethyl ketone (MEK), toluene.

Equipment: Gas purification system, Schlenk line with pressure relief valve, 500 mL three-neck flask

with gas introduction, KPG-stirrer, dropping funnel with pressure balance and

three-way valve, thermometer, oil bath with temperature sensor, hotplate, extraction flask with reflux

condenser and heating mantle, heating gun, vacuum desiccator (heatable), vacuum pump, N2-

cylinder with pressure reducer.

2.3 Experiment

The apparatus is evacuated (vacuum pump, slightly heated (heat gun) and filled with N2. After

cooling down the apparatus, 50 mL of absolute heptane are added with the aid of a dropping funnel

to the flask. Under a nitrogen atmosphere 1.0 mL of TiCl4 is added by a syringe and then 25 mL of

the aluminumalkyl-solution are added drop wise over a period of 20 minutes. Since the reaction of

the two catalyst is highly exothermic, an external cooling may be necessary. After approximately 10

minutes “aging time” of the catalyst, 25 mL styrene are added to the solution at once. The reaction

mixture is heated up to 75 °C (inside temperature) for 3-4 hours. After the mixture is cooled to room

temperature, the polymerization is stopped by adding 20 mL of 2-propanol under N2 and then

100 mL of 2-propanolic HCl subsequently (thorough mixing by vigorous stirring required). The

polymer is filtered off and washed thoroughly with methanol. The crude product is boiled under

reflux with 80 mL of methyl ethyl ketone, and then portion wise 30 mL of toluene are added and

extracted for 5 hours. The residue is first decanted and then sucked off with a coarse frit. After

washing with methyl ethyl ketone, the polymer is dried at 60 ° C in a vacuum desiccator. Both the

yield of it polystyrene and the melting range are to be determinated.

3 Questions about coordinative polymerization

- 77 -

1. Why is the extraction with MEK and toluene necessary?

2. What are the molar concentrations of the catalyst components in the reaction mixture?

Calculate the ratio Ti:styrene!

3. What is the difference between Fischer-projection and Natta-(Zig-Zag-) projection?

4. What is the difference between low and high pressure PE? Physically? Chemically?

5. What is meant by a 3rd

-generation Ziegler catalyst?

6. Why can vinyl ether not be coordinative polymerized by TiCl4/Et3Al?

7. Structures of HDPE, LDPE, LLDPE, it-PP, st-PP, PB, trans-1,4-polyisoprene,

poly(4-methyl-1-pentene), cis-1,4-polybutadiene?

- 78 -

II Ring-Opening Metathesis Polymerization (ROMP)

Task

Polymerization of norbornene derivatives using the metathesis reaction and a transition metal

alkylidene catalyst.

Literature

1. R. H. Grubbs (Ed.) Handbook of Metathesis, Wiley-VCH, Weinheim, (2003)

2. M. Chanda, Introduction to Polymer Science and Chemistry: A Problem Solving Approach, CRC Press Inc.,

(2006)

3. F. J. David, Polymer Chemistry: A Practical Approach, Oxford University Press, (2004)

4. P. W. N. M van Leeuwen, Homogeneous Catalysts: Activity, Stability, Deactivation, Wiley-VCH, Weinheim,

(2011)

5. M. R. Buchmeiser, Chem. Rev. (2000), 100, 1565

Content

1. Introduction

2. Mechanism

3. Experimental part

4. Chemicals, equipment and safety

5. Experiment

6. Questions

- 79 -

1 Introduction

Today catalytic olefin metathesis, in addition to palladium catalyzed coupling reactions, is one of the most important

chemical reactions for the formation of carbon-carbon bonds. It has had an undeniable impact on various areas of

chemistry. Olefin metathesis is the exchange of alkenyl groups of two olefins in the presence of a metal alkylidene

catalyst. The results is a thermodynamically equilibrated mixture of products consisting of cis- and trans-olefins (Figure

1).

Fig. 1: General olefin metathesis reaction.

Olefin metathesis opened the door for a wide range of new methods and research areas in both organic and polymer

chemistry. One important area is the research on organometallic compounds done by Schrock, Grubbs, Katz and many

others. The need for catalytically active species of these kinds is rising ever since.

Fig. 2: Catalytic cycle of olefin metathesis.

Outstanding contributions in this field were provided by Chauvin (postulation of the right mechanism), Schrock

(synthesis and characterization of the first highly active well defined metathesis catalysts) and Grubbs (synthesis of

broadly applicable and (air) stable catalysts). In 2005 they shared the Chemistry Nobel Prize.

- 80 -

In 1971, Y. Chauvin postulated that the olefin adds to the metal carbon double bond via a [2+2] cycloaddition. The

resulting intermediate is a metalla-cyclobutane species, which reacts to the product olefin and a new metal alkylidene via

a [2+2] cycloreversion. All steps in this reaction, in principle, are reversible. Thus, the product can be transformed back

to the starting material. Therefore, a driving force is needed to achieve high conversions and constantly shift the

equilibrium to the product side. This is illustrated in detail in Figure 2.

First observations of this kind of reactions were made in the 1950s when strange side products occured in the

polymerisation of ethylene in the presence of various metals. In early attempts, compounds like MoO3, WCl6, WOCl4 or

Re2O7 were used to selectively catalyze olefin metathesis. In addition, an alkylating agent had to be present (e.g., SnR4,

AlR3, etc.). These systems were highly active (but not selective). Another striking disadvantage was that they were

relatively short living and sensitive for impurities containing functional groups. In many cases, the real catalytically

active species remains unknown until today.

In 1964 Fischer synthesized the first metal-carbon double bond (carbene). The so called Fischer-carbenes are stabilized

by π-donors (Figure 3). Thus, these carbenes have a singlet configuration.

Fig. 3: Fischer-Carbene.

In 1974 Schrock prepaired the first metal-carbene without neighboring π-donors and with a transition metal in its highest

oxidation state. His alkylidenes (Figure 4) differ from Fischer-carbenes in that they possess a triplet configuration of the

metal carbon bond. Schrock synthesized complex 2 (Figure 4) by treating tantalum pentachloride with neopentyl lithium.

Fig. 4: First examples of a Schrock-carbene (alkylidene).

Through α-H-abstraction one equivalent of neopentane is lost and the new alkylidene forms. Schrock consequentially

recognized the unstable character of pentaalkyl substituted tantalum and proposed the formation of alkylidenes by this

mechanism. Over the years new and more active and stable catalysts were prepaired with great effort (Schrocks catalysts,

Figure 5). Grubbs made the invention of air (bench-top) stable rutheniumcarbenes (Figure 6), which set a new landmark

in the applicability of these catalysts. They are made by oxidation of Ru(II)-precursors. They complement to Schrocks

catalysts in their properties, because in general they are less active but also less sensitive. First and foremost they are

more stable to protic functional groups like alcohols or water. Schrock-alkylidenes in return have a better tolerance

towards functional groups containing sulfur, nitrogen or phosphorus.

- 81 -

Fig. 5: General structure of tungsten- or molybdenum-alkylidene catalysts.

RuR

Cl

Cl

L

L

Ru

P(Cy)3

P(Cy)3

Cl

Cl RuCl

ClP(Cy)3

NNMesMes

Grubbs I

Ru

P(Cy)3Cl

ClO Ru

Cl

ClO

NNMesMes

Grubbs-Hoveyda I

Grubbs II

Grubbs-Hoveyda IIRu

CF3COO

CF3COOO

NNMesMes

Buchmeiser-Grubbs-Hoveyda

Fig. 6: General structure and important examples of Grubbs-catalysts.

- 82 -

Olefin Metathesis Reactions

Some olefin metathesis reactions are shown in the following schemes.

nn

Rn

Rn

XX X

x yz

Ring Opening Metathesis Polymerization (ROMP)

1-Alkyne Polymerization

Cyclopolymerization

nn

n

+

Acyclic Diene Metathesis Polymerization (ADMET)

R

R'+ R

R'

+Crossmetathesis

R +R'

R R'

Cross-Ene-Yne-Metathesis

X

R

n

X Rn

RingclosingEne-yne-Metathesis

X

R +

X

R

Cross-Ene-Diyne-Metathesis

R +

RRing opening

Cross-metathesis

XTandem-

Ringopening CrossmetathesisX

X

Ringclosing metathesis X

+

Fig. 7: Examples for metathesis reactions.

One important aim of such catalytic reactions is the selective formation of E- and Z-double bonds. In general, E-double

bonds are thermodynamically favored. In the case of moderately controlled reactions a mixture of E- und Z- configured

products is formed. Another important factor is the control of tacticity in stereoregular polymers. Besides Mo- and W- ,

- 83 -

some highly selective Ru-catalysts have been reported. Normally, the driving forces for the reactions shown in Figure 7

are release of volatile molecules (ethylene, etc.), entropic effects, release of ring strain or the formation of highly

conjugated systems.

2 ROMP: Mechanisms

Ring opening metathesis polymerization (ROMP) is a reaction where mostly strained double bonds are opened by the

catalyst (better: initiator) and rearranged subsequently with other olefins to form chains. Basically, it follows a chain-

growth mechanism. Usually, a monocyclic (e.g., cyclopentene, cyclooctene, cyclooctadiene etc.) or polycyclic (e.g.,

norbornene, dicyclopentadiene etc.) monomer with higher ring strain is used. The general mechanism is shown in Figure

8.

Fig. 8: Mechanism of the ring opening metathesis polymerization.

Besides the mentioned growth and termination of a polymer chain, several side reactions are also of importance.

Particularly undesired terminations, which end the reaction in an unpredictable manner are responsible for a wide range

of products and a broad molecular weight distribution.

- 84 -

Fig. 9: Undesired terminations that can occur in ROMP.

RR

R R

n/2

R R

n/2

R R

RR

R R

n/2

R R

n/2

R R

R

R

[cat.]

n

cis-syndio tactic

cis-iso tactic

trans-iso tactic

trans-syndio tactic

Fig. 10: Formation of different polymer structures of poly-Norbornadienenes through ROMP.

The determining factor for the physical properties of polymers is their microstructure. For instance, the ROMP of

substituted norbornadienenes can produce four different regular structures of the polymer or a mixture of them. Cis- and

trans- double bonds as well as iso- and syndiotactic incorporation of the five membered repeat units is possible. With

chiral substrates, the microstructure can be even more complicated.

- 85 -

Whether regular or mixed structures are formed strongly depends on the applied catalyst system. The following schemes

show the addition of monomer to different catalysts and the consequences for the configuration of the double bond and

tacticity.

Fig. 11: Monomer addition in the polymerization of substituted norbornadienenes using a MAP-catalyst.

Fig. 12: Monomer addition to the 1st-generation Grubbs catalysts.

3 Chemicals, Equipment and Safety

Equipment:

Beaker 20 mL, Beaker 200 mL, heat gun, Schlenk flask 50 mL, suction filter, stirring bars, filter

paper, glas stopper, spatula, pipette, syringe, scintillation vials

Chemicals:

MW (g/mol)

Grubbs Catalyst 1st-gen. (RuCl2(PCy3)2CHPh) 822,96

5-Norbornen-2-yl-acetate 152,19

dichloromethane, methanol, ethyl vinyl ether, chloroform-d

3.1 Safety

Work under high vacuum bears the danger of imploding glasware and has to be done in closed fume

hoods. Ethyl vinyl ether as well as methanol are highly flamable and have to be protected from

- 86 -

ignition sources. The exposure of the chemicals used in this experiment to atmosphere must be

avoided. Dichloromethane and chloroform are suspected cancerogens. Methanol is toxic by any

exposure (skin, lung etc.). Norbornene and its derivates are flamable and have to be kept away from

ignition sources. Since other data for the used monomer is not available, it has to be considered as

highly dangerous. Prevent exposure and inhalation of the fumes. The applied ruthenium compound is

flamable and should be handled with great care. Avoid any contact with skin.

3.2 Experiment

Handling of the catalyst: The transition metal complex has to be stored in the fridge (2-8 °C).

Minimize its exposure to the atmosphere and/or humidity to prevent decomposition of this expensive

chemical. Before opening the bottle, it should reach room temperature to minimize water

condensation. Weighing should be carried out as quickly as possible and catalyst containers need to

be kept close when not used. Thus, dry glassware and solvents are required for this experiment. All

manipulations have to be conducted under a nitrogen atmosphere using Schlenk techniques.

The reaction vessel has be heated and evacuated to eliminate residual water and oxygen. 20 mL of

dry dichloromethane are added under a stream of nitrogen. The monomer (ca. 1.00 g, 3.29 mmol) is

added into the flask the same way. Use a scintillation vial for weighing and rinse thoroughly with dry

dichloromethane. Note the exact used amounts of catalyst and monomer. Now weigh in the catalyst

(ca. 54 mg, 0.0329 mmol, 1 mol-%) and dissolve in 2 mL dry dichloromethane. Transfer the solution

quickly and completely into a syringe. Add the catalyst solution as quickly as possible and in one

single shot into the heavily stirred reaction mixture. Close the flask with a stopper. The reaction is

being stirred for one hour at room temperature. After that time a small portion of the reaction mixture

(approx. 2 mL) is taken out by a syringe and added under heavy stirring to 20 mL of methanol. Note

your observations. To the rest of the reaction mixture 2 mL of ethyl vinyl ether is added. Stirr the

reaction for another 15 minutes. For isolation of the polymer, the reaction mixture has to be added

dropwise to heavily stirred 300 mL of methanol. The polymer should precipitate. After addition, stirr

for another 10 minutes and filter the product. Wash the polymer with some methanol. Residual

solvent is removed applying high vacuum. Use 10 mg of the dry polymer and dissolve it in 10 mL of

THF for GPC analysis. 20 mg of the dry polymer are dissolved in 0.6 mL of chloroform-d for NMR

analysis.

- 87 -

4 Questions

1. What was the visual difference you observed when precipitating the polymer for the first

and second time? Explain.

2. What is ethyl vinyl ether used for in this experiment and what is being formed after addition?

Write down the reaction equations for the reactions in this experiment and explain why

ethyl vinyl ether is a good candidate for the needed purpose. Would 1-pentene be an

alternative? Why/(not)?

3. Why has the catalyst solution to be added as quickly as possible? Clarify the role of

temperature, mixing and concentration of monomer solution in this regard.

4. Calculate the theoretical values for molecular weight of the synthesized polymer chains.

Compare them to the experimentally found values determined by GPC analysis. Explain any

deviations. Why, in general, can an experiment deliver much higher or smaller values

compared to the theoretical ones?

5. Do you see any possible way to reuse the catalyst? What is necessary to accomplish this?

6. Name some simple ways to prepare (in this experiment) polymers with higher solubility?

Name factors which play a crucial role.

7. Which influences can an applied catalyst system have on the reaction process and the

product? Why do expensive and sensitive systems still play an important role?

8. What is the striking structural feature of transition metal alkylidene complexes? What

significant difference would you expect from the NMR spectrum of a propagating species to

the parent catalyst?

9. Assign the observed signals you see in the 1H-NMR of the polymer and explain the

differences to the spectrum of the monomer.

88  

Experiment 6: Emulsion Polymerization 

 

Objective 

Styrene  is polymerized  in an emulsion using dodecyl hydrogen sulfate sodium salt as an emulsifier and potassium persulfate as the  initiator.   Samples are drawn from the reactant solution  in regular intervals  in order  to  generate diagrams of  the  conversion  as well  as  the  reaction  rate  versus  the reaction time.   

 

References 

1) H.‐G. Elias, Makromoleküle Bd. 1, Edition 6, Wiley‐VCH Verlag, Weinheim, 1999 

2) P. J. Flory, Principles of Polymer Chemistry, Cornell, University Press, Ithaca, 1953 

3) B. Tieke, Makromolekulare Chemie, Edition 2, Wiley‐VCH Verlag, Weinheim, 2005 

4) W. V. Smith, H. Ewart, J. Chem. Phys. 16(6), 592 (1948) 

5) W. D. Harkins, J. Am. Chem. Soc. 69, 1428 (1947) 

 

Content 

1. Theoretical Background 

2. Experimental Part 

3. Questions 

   

89  

1. Theoretical Background 

The process of emulsion polymerization is of vital significance for the fabrication of various industrial 

polymers  such  as  polychloroprene,  poly(vinyl  acetate),  polytetrafluoroethylene  and  poly(vinyl 

chloride) as well as “cold rubber” (styrene/butadiene copolymers).   The technological development 

of this method started  in the 1920s and has since gained ever‐increasing  importance resulting  in a 

recent global production of several million tons per year.   

The essential components of an emulsion polymerization are the following. 

Monomer (insoluble in water) 

Water 

Surfactant 

Initiator (radical forming agent, soluble in water) 

In most  cases anionic  surfactants  (e.g.  salts of  fatty acids,  salts of alkyl hydrogen  sulfates,  salts of 

alkyl  sulfonic  acids)  are  used,  while  cationic  (quaternary  ammonium  salts,  e.g.  cetyltrimethyl 

ammonium bromide) or non‐ionic surfactants  (often high molecular weight) are rarely applied.   All 

types of surfactants comprise both hydrophilic and hydrophobic groups.   When highly diluted,  the 

surfactants  can  be  completely  dissolved  in water.   However,  at  concentrations  above  the  critical 

micelle concentration  (cmc), the molecules of  the emulsifier aggregate  into micelles.   This process, 

which  is driven by  thermodynamic principles,  is  accompanied by  a  significant drop  in  the  surface 

tension  of  the  system.    The  emulsion  polymerization  is  generally  performed  at  surfactant 

concentrations above the cmc.   

Water‐soluble peroxo salts (e.g. potassium persulfate) are the classical choice for the initiator of the 

polymerization reaction, even though organic hydroperoxides (e.g. cumene hydroperoxide) are also 

frequently used.   Redox  initiators are of particular  importance  in  industrial processes,  since  these 

compounds can induce polymerization even at low temperatures.   

The progress of a typical emulsion polymerization can be divided into three phases distinguished by 

their characteristic profiles of the reaction rate over time (see Figure 1):  

(I) increasing reaction rate 

(II) constant reaction rate 

(III) decreasing reaction rate. 

 

Figure  1

transitio

Figure 1: D

Harkin a

processe

initial re

At  the  b

~4.3 nm

of mono

emulsifie

micelles 

formed 

the mice

number 

emulsion

monome

no  relev

polymer

monome

monome

limited 

transform

of the re

 

1  further  ill

on between t

Development o

s well as Sm

es occurring 

servations, t

beginning  of

) as well as m

omer, howev

er  (see  Figu

by diffusion

in this proce

elles.  Howev

(~1010 per c

n) present in

er droplets a

vance  due  t

rization  the 

er molecules

er  droplets 

conditions). 

m into so‐ca

eaction and t

ustrates  tha

the first and 

of the reaction 

ith and Ewa

at  a molec

the essential

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92  

 

a) The aqueous phase enables temperature regulation during the polymerization reaction. 

b) Redox initiators can be applied, which enable polymerization reactions to proceed at comparably 

low temperatures, yet keeping the reaction rate relatively high. 

c) High degrees of polymerization can be achieved due to the small probability of chain termination.  

This can be further regulated by the controlled addition of chain transfer agents.   

d) Remaining monomer can be removed by steam distillation. 

e) The obtained latex can be directly subjected to further applications (paints, glues, coatings). 

 

On  the  downside,  however,  a  frequently  problematic  extraction  of  the  emulsifier  as  well  as  the 

potentially high degree of branching of the polymer chains have to be taken  into account as major 

disadvantages of the method.  

 

Kinetics and Mechanism 

A  hallmark  of  the  emulsion  polymerization  process  is  that  this  method  yields  higher  degrees  of 

polymerization  than  those  accessible  under  comparable  conditions  in  bulk  or  suspension 

polymerization  reactions.    The  kinetics  and  the  mechanism  of  emulsion  polymerization  are, 

therefore, distinct from other radical polymerization methods. The reaction rate vw(L) in an individual 

latex particle is given by equation (1). 

(1)  [M][P*]k)(v Ww L  

vw(L): reaction rate of the polymerization in the latex particle 

kw: rate constant of the polymerization 

[M]: concentration of monomer in the latex particle 

[P*]: concentration of radicals in the latex particle 

The  measurable  reaction  rate  vw  of  the  entire  reaction  batch  is  represented  by  the  sum  of  the 

reaction rates in all isolated latex particles.  Assuming a narrow size distribution of the latex particles 

the reaction rate can be described as follows: 

93  

(2) A

wwN

nN[M]kv  

vw: reaction rate of the polymerization 

n: average number of free radicals per latex particle 

N: number of latex particles per unit volume of the emulsion 

NA: Avogadro constant 

In  equation  (2),  it  is  further  assumed  that  the  polymerization  occurs  exclusively  within  the  latex 

particles, i.e. there is no considerable amount of polymer forming either in the aqueous phase or in 

the monomer droplets.  For the determination of vW the factors included in equation (2) have to be 

expressed as properties, which are experimentally accessible. This is particularly difficult in the case 

of N  and n.    The most  established quantitative model  for  the description of  the  kinetics  and  the 

mechanism of the emulsion polymerization was derived by Smith and Ewart.    It  is particularly well‐

suited for systems showing a behavior consistent with the Harkin model.   

The Harkin model is based on the following considerations: After a short phase of particle generation 

(phase I) the reaction rate becomes constant in phase (II). Therefore, regarding the factors included 

in equation (2), not only the monomer concentration [M] and the number of latex particles per unit 

volume  [N],  but  also  the  number  of  free  radicals  within  the  latex  particles  have  to  be  constant.  

However, according to the steady state approximation the number of these radicals will only remain 

constant, when equal amounts of radicals are formed and consumed in a given period of time.   

The  following assumptions will be made: Once a radical  is  located within a  latex particle,  it cannot 

leave  this  environment  again.    If  a  second  radical  enters  the  same  latex  particle,  an  immediate 

recombination of the two will take place due to the small radius of the latex particle.  An individual 

latex particle,  therefore,  contains either one or no  radical at any given  time,  corresponding  to an 

average number of radicals per  latex particle of n = ½.   With additional assumptions regarding  the 

number of latex particles equation (3) can be derived: 

(3)  5

3

S5

2

A

ww [S])(a)N

σb(

2

1[M]kv  

b: system constant in the range of 0.37‐0.53 

σ: inflow/intake velocity of the radical into the latex particle 

µ: constant volume increase of the latex particle 

94  

aS: surface area required by one surfactant molecule 

[S]: concentration of the emulsifier 

Combining  all  constant  parameters  included  in  equation  (3)  into  a  single  constant  K  leads  to  a 

simplified representation as given by equation (4): 

(4)  5

3

w K[M]([S])v  

On  closer examination of equation  (4)  it becomes obvious,  that  the  reaction  rate of  the emulsion 

polymerization can be raised even without  increasing the temperature, monomer concentration or 

initiator concentration – simply by adding a higher amount of the surfactant. 

The degree of polymerization Pn of a polymerization reaction is defined as the ratio between the sum 

of all reaction rates associated with processes leading to an increase in the chain length and the sum 

of reaction rates ascribed to those processes resulting in the termination of an individual chain.  The 

latter can occur either by direct  termination or by chain  transfer  to monomer, solvent, or  initiator 

molecules (but not to polymer chains!).   

(5) )v(v

vP

TA

wn

 

vA: sum of the reaction rates of all processes terminating the chain 

vT: sum of the rates of all chain transfer reactions 

As the concentration of the emulsifier directly  influences vw,  it also has an  immediate effect on the 

degree  of  polymerization.    In  contrast  to  all  other  radical  polymerization  processes,  the 

recombination of radical chain ends is inhibited in emulsion polymerization, since the chains exist in 

isolated latex particles and are therefore effectively separated from each other.   

Moreover,  in  its final stages the process of emulsion polymerization shows a behavior analogous to 

the Norrish‐Trommsdorf effect, which  is known from bulk polymerization.   As a result, the reaction 

rate and the degree of polymerization are comparably higher.   

   

95  

2. Experimental Part 

The goal of this experiment is to prepare polystyrene by polymerization of styrene in emulsion.  For 

that  purpose,  dodecyl  hydrogen  sulfate  sodium  salt  and  potassium  persulfate  are  used  as  the 

surfactant and initiator, respectively.  Plots of the conversion as well as the reaction rate versus the 

reaction time should be obtained. The conversion  is determined gravimetrically at various stages of 

the reaction.  The results shall be discussed with a special emphasis on the kinetics of the reaction.   

 

Chemicals: 

‐ Styrene (destabilized and freshly distilled) 

‐ Water  

‐ Dodecyl hydrogen sulfate sodium salt 

‐ Potassium persulfate 

‐ Hydroquinone (0.02% in water) 

 

Equipment: 

‐ Oil bath  

‐ Round‐bottomed flask 

‐ Hot‐plate magnetic‐stirrer device 

‐ Reflux condenser 

‐ Thermometer 

‐ Magnetic stirring bars 

‐ Sample dishes  

‐ Glass vials 

‐ Syringes and needles 

‐ Plastic pipettes 

‐ Analytical balance 

‐ Vacuum drying oven 

 Procedure: 

Water  (50 mL), emulsifier  (1 g) and styrene  (5 g) are  filled  into a  round‐bottomed  flask of 100 mL 

capacity.  The mixture is heated to 70°C under stirring in an oil bath.  After an equilibration period of 

approximately 30 minutes the polymerization is started by the addition of the initiator dissolved in 4 

96  

mL water  (t = 0 min).   During the course of the next two hours, samples of 2 mL reactant solution 

each are drawn in regular intervals according to the specifications in table 1.   

Table 1.  Sample identifier and reaction time at which the sample was taken. 

Sample 

identifier E1  E2  E3  E4  E5  E6  E7  E8  E9  E10  E11 

t/min  2  4  6  10  15  20  30  45  60  90  120 

 

These samples are  immediately pipetted  into glass vials containing 2 mL hydroquinone solution for 

stabilization  and  are  subsequently  transferred  to  a  vacuum  drying  oven  to  remove  all  volatile 

components.    Afterwards,  the  solid  content  is  determined  by  gravimetric  analysis.    All  relevant 

masses and mass differences are calculated and documented according to table 2.   

Table 2.  Evaluation of the obtained sample weights and determination of the conversion. 

Sample 

identifier 

m0 

 

(dish) 

m1 

 

(dish + 

hydroquinone) 

m2

 

(dish + 

hydroquinone 

+ dispersion 

before 

drying) 

m2‐m1 

(msample) 

m3 

 

(dish + 

dispersion 

after drying) 

m3‐m0 

 

(msolid) 

Conversion 

E1       

E2       

E3       

E4       

E5       

E6       

E7       

E8       

E9       

E10       

E11       

 

Evaluation: 

Plots of conversion versus time. 

1) Besides the polymer molecules the isolated solid additionally contains residual emulsifier.  In order 

to  determine  the  conversion  (conv)  of  the  reaction  accurately,  the  surfactant  content  has  to  be 

97  

subtracted from the total weight of the solid material.  This calculation can be performed according 

to the following equation: 

conv = msolid

mM0

· 1

1+  mE0

mM0

· mtot

msample

·100% 

msolid:  weight of the solid 

mE0:  weight of emulsifier used in the reaction batch 

mM0:  weight of monomer used in the reaction batch 

mtot:  total weight of the reaction batch 

msample: weight of the sample  

 

2)  Calculate  conversions  for  all  samples  taken  during  the  reaction  and  plot  the  results  over  the 

reaction time.   

 

Plots of reaction rate versus time. 

3) Determine the reaction rates at the various time steps by constructing tangents on the conversion 

vs. time curve.  List the obtained reaction rates in a table, plot and discuss the results.   

   

98  

3. Questions 

1) Which effects can be potentially caused by the presence of oxygen traces in the emulsion?  What 

could  be  an  explanation  for  another  increase  in  the  reaction  rate  during  the  final  stages  of  the 

polymerization (Take into account that the reaction is a radical polymerization)?   

2) Why is the coagulation of latex particles inhibited? 

3) What is the average radical concentration in the latex particles under the following assumptions? 

The radicals reach the latex particles by diffusion.  This process determines the reaction rate. 

Whenever  two  radicals  are  located  in  the  same  latex  particle  they  will  recombine 

immediately.   

4) Describe the principle of a redox initiator and list a number of examples. 

5)  Compare  the  characteristics  of  emulsion  polymerization  and  suspension  polymerization. Name 

further examples for technologically relevant polymerization procedures.   

1

Versuch 6

Electropolymerization of Conducting Polymers

Assignment of tasks:

1. The theoretical and experimental aspects of the electrochemistry and electropolymerization of

conducting polymers shall be mediated.

2. Voltammetry is introduced as a tool for the synthesis of polythiophene films

3. The electrochromic behavior of an electropolymerised PEDOT film is studied by means of

charging/ discharging cycles.

4. A consistent analysis and evaluation of electrochemical data shall be performed to gain access to

the values of the HOMO and LUMO levels

References:

[1] György Inzelt, Conducting Polymers - A New Era in Electrochemistry, 2nd Edition, Springer, 2012.

[2] Jürgen Heinze, Bernardo A. Frontana-Uribe, and Sabine Ludwigs, Electrochemistry of Conducting

Polymers - Persistent Models and New Concepts, Chem. Rev., 2010, 110, 4724–4771.

[3] Matthias Rehahn., Elektrisch Leitfähige Kunststoffe, Chemie unserer Zeit 2003, 37, 18-30.

[4] Alan MacDiarmid, Synthetische Metalle: eine neue Rolle für organische Polymere, Angew. Chem.,

2001, 113, 2649-2659.

[5] Jean-Luc Bredas and G.Brian Street, Polarons, bipolarons, and solitons in conducting polymers, Acc.

Chem. Res. 1985, 18, 309–315.

[6] Allen J. Bard and Larry R. Faulkner, Electrochemical Methods – Fundamentals and Applications, John

Wiley & Sons ; 2nd Edition., 2001.

[7] Carl H. Hamann and Wolf Vielstich, Elektrochemie, Wiley-VCH Verlag GmbH & Co. KGaA, 4th Edition,

2005.

2

1. Theoretical Background 1.1 Conducting polymers

In the year 2000 the scientists Alan G. MacDiarmid, Alan J. Heeger, and Hideki Shirakawa received the

Nobel Prize in chemistry for their discovery and development of conducting polymers (CPs). Their

discovery of the electrical conductivity of the organic material polyacetylene upon doping with iodine

was the key step in the modern development of conducting polymer science. From the late 1970s up to

now a variety of new CPs (Figure 1) has been introduced based on different monomers like pyrroles,

thiophenes, anilines or aromatic hydrocarbons.

Figure 1: Structures of common conducting polymers; polyacetylene 1, poly(paraphenylenevinylene) 2, polythiophene 3, polypyrrole 4, polyaniline 5

The important features which all of them share are alternating π- and σ-bonds along the polymer

backbone resulting in a π-conjugation. The electronic structure and the electronic properties of

conjugated polymers can be explained by the molecular orbital model. In ethylene two sp2 hybridized

carbons combine resulting in an occupied π- and an unoccupied π*-orbital, as shown in Figure 2.

Interaction with a uniform π-bond results in a splitting of the orbitals. A polymer with n sp2 hybridized

carbons has likewise n/2 π- and n/2 π*-orbitals, the distance in-between them is negligible and so they

can be described as bands. Also the distance between the highest occupied π- (HOMO, also Valence

Band, VB, in analogy to the band theory) and the lowest unoccupied π*-orbital (LUMO, also Conduction

Band, CB) which is called band gap (Eg) decrease with increasing number of repeating units.

3

Figure 2: Schematic explanation of the formation of energy bands in conjugated polymers: Transition from the atomic orbital of an individual sp2 carbon atom to the molecular orbitals of ethylene and finally formation of the band structure in polyacetylene. [3]

As Eg is still so large, that electrons cannot easily be promoted from the Valence Band to the Conduction

band just by thermal energy at room temperature, conjugated polymers are semi-conductors or

insulators in the neutral state. However, upon oxidation (extraction of an electron, formation of a radical

cation, Figure 3, right) or reduction (uptake of an electron, formation of a radical anion, Figure 3 left) the

conductivity of such materials is dramatically increased. The oxidation and reduction process is often

called p- and n-doping process, respectively. Thus, conductive polymers are often called p-type (hole

transport) or n-type (electron transport) semi-conductors.

Figure 3: Structure of a neutral polythiophene (middle) as well as a radical cation (oxidized form, right) and radical anion (reduced form, left).

4

During oxidation electrons are extracted from the HOMO. On the other hand, the reduction of the

polymer is coupled to an uptake of electrons by the LUMO. In both cases, i.e. upon reduction and

oxidation, charges are generated due to the uptake/extraction of electrons. Therefore, the reduction and

oxidation process is often called charging.

In the literature the term polaron is also found for the mono-ionic forms (radical cation and radical

anion) and bipolaron is used for di-ionic forms. These charged species (radical mono-anion and di-ion;

polaron and bipolaron) are stabilized through a delocalization of the charge/electron over the

conjugated π-system of several monomer units of the polymer. The neutral form exhibits a benzoid-like

structure, whereas the charged states reveal a quinoid-like structure (Figure 4a). Thus, in the doped

polymer both structures are present. This change in the electronic structure is followed by a geometric

reorganization which causes a local upward shift (Δε) of the HOMO and downward shift of LUMO levels,

respectively, see Figure 4b, which results in a decrease of the band gap. This may also serve as an

explanation for the increased conductivity.

Figure 4: a) chemical structure of the neutral state, polaron and bipolaron of polythiophene, b) change of the electronic structure upon doping

As the color of a conducting polymer is defined by the band gap (absorption correlates to an excitation of

an electron from the HOMO to the LUMO), the change of the band gap will also evoke a color change.

Thus, conducting polymers are electrochromic materials.

Electrochromic materials are compounds that undergo a color change upon switching the redox-state of

the species. A variety of organic compounds show electrochromic behavior. For example, molecular

based materials that show electrochromism are viologens or metal complexes based on phthalocyanine

ligands. In particular polythiophenes and polyanilines are widely used as materials for electrochromic

devices due to their high stability and simple preparation as well as their well-established processability.

5

The optical properties of these materials can be tuned by the choice of appropriate thiophene or aniline

monomers.

Typical colors of a polythiophene film in the neutral and the p-doped state (oxidized form) are red and

blue/green, respectively. Polymers based on PEDOT (poly(3,4-ethylenedioxythiophene)) are of particular

interest because of their low oxidation potentials (high lying HOMO level) as well as their transparency

and high conductivity (hole transport) in the p-doped state. PEDOT polymers are often used in

electrochromic displays, namely in the form of the complex PEDOT:PSS (PSS = polystyrenesulfonate). In

this material PEDOT is present in its oxidized form. The polyanion PSS acts as stabilizer in the complex

with the p-doped PEDOT and ensures electroneutrality. In addition, the PSS part ensures the formation

of a stable aqueous dispersion of this complex which makes it an industrially applicable and solution-

processable form of PEDOT. Because of its high conductivity and transparency (transmission of light is

possible) PEDOT:PSS has found its application as printable electrode in organic solar cells for example.

Organic electrochromic materials have already been applied in anti-glare car rearview mirrors, in

controllable light reflective/transmissive devices, protective eyewear, smart windows (used in

automotive industry and buildings) and sunglasses. One interesting and promising application is the use

as long-term display of information due to the low energy demand of such types of displays.

1.2 Voltammetry / Electropolymerization

Voltammetry:

Voltammetry is one of the most common electroanalytical methods to study the redox-behavior of

electro-active compounds. In particular, cyclic voltammetry (also linear sweep voltammetry) has been

proven as a versatile tool for the characterization of electro-active species in aqueous and non-aqueous

solvents. The electro-active species can be either dissolved in the electrolyte or be present in the solid

state.

In a cyclic voltammetric experiment a linear potential scan with a constant scan rate (v) is performed in a

certain potential window. At the end of the potential window (Eλ) the sign of the scan direction is

inverted and the potential is linearly decreased (with the same v) until the start potential is reached

again (Figure 5 a): the potential cycle is “closed”. During this potential sweep, the current is recorded and

plotted vs. the applied potential. A typical I-E curve, a so called cyclic voltammogram, of a dissolved

redox-species is depicted in Figure 5 b).

From the corresponding I-E curves several characteristic data are obtained:

redox-potentials (thermodynamic parameters) and

peak currents (diffusion coefficients, kinetic parameters, etc.)

6

Figure 5: a) Cyclic potential sweep and b) resulting cyclic voltammogram in the presence of a redox-active species in solution (voltammogram for the simplest electron transfer reaction: A A+ + e-)

The formal potential can be estimated from the half wave potential E1/2 by determining the peak

potentials of the oxidation ( ) and reduction (

) in the forward and backward scan, respectively, in

the I-E curve (Figure 5 b) according to eq. (1)

|

|

This value is an excellent approximation for the formal potential: E1/2 = E0

The measurements are conducted with a three electrode setup (Figure 6) which consists of a stationary

working electrode (WE), a counter electrode (CE, also known as auxiliary electrode) and a reference

electrode (RE). The redox-active species is present in solution or deposited as film on the working

electrode (in the case of polymers). The use of a reference electrode allows the potential control. The

experiment is controlled and monitored by a potentiostat. The potential of the working electrode against

the counter electrode is carefully controlled by the potentiostat, so that the potential difference ΔE

between the working electrode and the reference electrode is precisely defined and corresponds to the

potential value specified by the user. The current flows between the WE and CE.

The reference electrode is important to define the point of origin of the potential scale. Standardized

reference electrodes as the standard (or normal) hydrogen electrode (SHE or NHE), the saturated

calomel electrode (SCE), or the Ag/AgCl (silver chloride coated silver wire immersed into a KCl solution)

system consist of a redox couple of a known concentration in a separated electrolyte filled compartment

connected to the main cell via a semi-permeable membrane. Here, the potential depends only on the

concentration of the redox-active couple (e.g. Ag/Ag+). However, these real reference electrodes (also

known as second order electrodes) with a defined potential are only available for aqueous systems. In

𝐸𝑝𝑜𝑥

𝐸𝑝𝑟𝑒𝑑

t

switching time λ

a)

E / V

I / A

=

b)

E1/2 = E0

7

organic solvents pseudo reference electrodes as an AgCl covered silver wire are commonly used. As the

potential of these is not well defined, IUPAC recommends for organic solvents to measure an external

standard. Here the standard redox-couple ferrocene/ferrocenium (Fc/Fc+) is added, measured and all

potentials are reported against it (see, rit ner . ta J. Recommendations on reporting electrode

potentials in nonaqueous solvents Pure Appl. Chem. 1984 56 461−466). This calibration allows the

comparison of different experiments conducted in different solvent systems and with different reference

electrodes.

Figure 6: Three electrode setup for cyclic voltammetric experiments.

To ensure charge transport in solution a supporting electrolyte is necessary. The electrolyte has to be

electrochemically inert for a broad potential window and should be chemically stable (reactions with

oxidized/reduced species must be avoided). Typically tetra-alkylammonium salts are used as cations. As

anions ClO4-, BF4

-, and PF6- are commonly employed. Furthermore, the supporting electrolyte ensures the

electroneutrality in the diffusion layer in front of the working electrode (the diffusion layer corresponds

to the volume in which the oxidation/reduction takes place). In case of redox-active films, counter ions

are incorporated in the electro-active material during oxidation/reduction which also results in volume

changes of the films.

8

Electropolymerization:

Cyclic voltammetry is a powerful tool for the synthesis (electropolymerization) and characterization of

conducting polymers. A typical anodic electropolymerization takes place via a step-wise coupling of

radical cations. In particular, the electrodeposition of aromatic systems like thiophene or pyrrole has

been extensively studied. The oxidation of such monomers 1 (Figure 7) leads to the formation of radical

cations 2 followed by dimerization 3 and proton elimination. This leads to a neutral dimer 4. Longer π-

conjugated systems are oxidized at lower potentials than the monomer, therefore the dimer 4 gets

oxidized immediately. Then the same reaction cascade is repeated: The oxidized dimer 5 reacts with

other radical cations and the formation of oligomers 6 takes place. Recent studies propose that the rate

determining step seems to be the elimination of protons rather than the dimerization step. This

mechanism is widely accepted in literature. One of the best models for the polymer growth mechanism

is the so called oligomer-approach. This mechanism proposes that dimerization rates of radical cations of

the same conjugation length are higher than those of coupling products of radical cations with different

conjugation lengths. Hence, the formation of dimers, tetramers and octamers is favored.

The larger the conjugation length the easier the oxidation and, thus, the lower the oxidation potential:

the polymer is oxidized at potentials smaller than the oxidation potential of the monomer unit (see

Figure 7). When the oligomers reach a certain length, the deposition onto the electrode surface takes

place. Further polymer growth includes now several steps under solid-state conditions. All these steps

are taking place as soon as the monomer oxidation potential is reached, and so the polymer oxidation

signal is observable already in the second cycle. Obviously, the peak current of the polymer increases

with increasing number of cycles: the polymer film grows. Voltammetric methods can be used to induce

and follow the polymer growth.

Figure 7: Electropolymerization of polythiophenes, a) cyclic voltammogram of the anodic polymerization of a thiophene derivative under potentiodynamic conditions (first cycle in red), b) reaction mechanism of the anodic polymerization of thiophene.

9

During the potentiodynamic growth of the film, the polymer is oxidized and reduced (to the neutral

form) in each potential cycle which means that the polymer can be obtained as neutral film (the

polymerization stops at a potential lower than the polymer oxidation) on the electrode.

Electrochemical Characterization:

The electrochemical characterization of conducting polymer films deposited on electrodes can be

performed by means of cyclic voltammetric experiments in monomer-free electrolyte. Thus, an influence

of the monomer and further polymer growth can be excluded. Polymers show very broad oxidation and

reduction signals because no longer an one electron process in a small and uniform molecule, but

instead multiple electron processes (polaron, bipolarone) in a non-uniform material (polymerization

degree, different length of effective π-conjugation …) are taking place. The resulting curve can be

described as an overlapping of many redox-events with slightly different redox-potentials, as it is implied

by the grey curves in Figure 8, which could be summed up giving the measured curve (black) of the

oxidation of P3HT (poly(3-hexylthiophene). Hence, the determination of E1/2 is no longer possible and the

onset potential of the oxidation Eoxonset is determined instead by the interception of the two tangents

(blue lines) at the initial slope of the peak. It is assumed that the onset potential value corresponds to

the oxidation/reduction of the polymer chains with the largest conjugated π-system.

Figure 8: Typical CV of a polymer film (here, P3HT (poly(3-hexylthiophene), black curve) and potential depending conductance behaviour (red curve). In grey the overlapping of many different oxidation waves are schematically shown. The interception of the two tangents (blue lines) at the initial slope of the peak current corresponds to Eox

onset.

From the onset potential values of the oxidation and reduction, the HOMO and LUMO levels,

respectively, of the polymer can be calculated according to equations (2) and (3) (see, C. M. Cardona et

10

al. Electrochemical Considerations for Determining Absolute Frontier Orbital Energy Levels of Conjugated

Polymers for Solar Cell Applications, Adv. Mater., 2011, 23, 2367–2371):

[ ]

( )[ ]

The value 5.1 corresponds to the formal potential of Fc/Fc+ in the Fermi scale. From the HOMO and

LUMO level, the electrochemical band gap can be estimated according to eq. (4), which is a critical

quantity for polymer based organic photovoltaics.

| |

11

2. Experiment

Equipment and General Methods:

For all experiments a PGSTAT101 potentiostat from Metrohm and a gas-tight full glass three electrode

cell containing an ITO covered glass slide as working electrode, a Pt plate as counter electrode and a AgCl

covered Ag-wire acting as the reference electrode are used. All manipulations are carried out under

nitrogen atmosphere using standard Schlenk techniques. Solvents are pre-dried and should be handled

under nitrogen atmosphere.

Chemicals:

10 ml of a 0.1 M NBu4PF6/MeCN solution (NBu4PF6: M = 387.43 g/mol),

3,4-ethylenedioxythiophene (EDOT) (M = 142.18 g/mol ρ = 1.331 g/mL), CAUTION: EDOT is toxic!

pure acetonitrile, acetone

Electrodeposition:

Two electrochemical cells equipped with a reference electrode are filled with 10 ml of a 0.1 M

NBu4PF6/acetonitrile solution by means of a syringe under nitrogen atmosphere. The electrolyte solution

is deaerated by nitrogen bubbling for approximately 5 min. Then the monomer is added via a syringe

into one of the cells (c = 0.01 M). The working and counter electrode are carefully placed in the middle of

the cell (Note: the working electrode should be placed near the reference electrode to minimize the

effect of an uncompensated IR-drop, an error that is based on the resistance in the electrolyte solution).

- For the potentiodynamic electropolymerization of EDOT, potential cycles in a specified range and scan

rate are performed. The precise values are given by the supervisor and need to be noted for the later

evaluation of the data. The peak maximum in the forward scan of the first cycle corresponds to the

oxidation potential Eox of the monomer unit. After all cycles have been performed, the polymer covered

electrode is removed and washed gently with pure acetonitrile.

HOMO/LUMO determination:

For the voltammetric characterization of a polythiophene film, cyclic voltammetry in monomer-free

solution is applied. The cell prepared without monomer is used. The studied polymer film consists of

chemically synthesized Poly-(3-hexylthiophene) (P3HT) deposited on a gold electrode via spin coating.

For the determination of the onset potentials of the oxidation and reduction and thus the HOMO and

LUMO levels three cycles in a specified range and scan rate are performed. The precise values are given

12

by the supervisor and need to be noted for the later evaluation of the data. The first cycle is neglected to

avoid artefacts due to memory effects. The values for the onset potentials are extracted of the 2nd or 3rd

cycle.

Electrochromism:

The electrochromic-behavior of PEDOT shall be analyzed. PEDOT is blue in its neutral and transparent in

its oxidized state. Here, the time which is needed for the film to be totally switched from the one to the

other state shall be determined. For that purpose a positive and a negative potential is repeatedly

applied to the film and the current-time-slopes are recorded. As soon as the current stops flowing the

reaction in finished and the polymer film reaches the fully neutral or oxidized state. The optical

impression upon visual inspection (full conversion to the transparent state or not) should be noted.

After all electrochemical experiments have been performed the ferrocene standard is measured.

Therefore, a blank gold electrode is mounted in the cell and a small amount of ferrocene is added to the

electrolyte solution. For the determination of the formal potential of Fc/Fc+ the potential is cycled

between -0.1 to 0.7 V. For a consistent data set, at least three cycles (with stirring of the solution

between the single cycles) should be performed.

13

3. Evaluation of experimental data

Give a detailed introduction in the principle of voltammetry and describe the setup with all components.

Why is the Ferrocen measurement necessary? Also, describe in detail the experimental procedure with

all parameters.

3.1 Polymerization

a) Determine the E1/2 of Fc/Fc+ of all measured cycles and build the average value out of this. For

evaluation of all your measured cyclic voltammograms substract E1/2 from the measured

potentials and plot all x-scales as E vs. Fc/Fc+.

b) Plot the I/E-curve of the potentiodynamic polymerization. Describe the curve and assign the

regions in the CV to processes happening. Draw and discuss in this context the mechanism of the

oxidative polymerization of EDOT.

3.2 Determination of the HOMO and LUMO levels

a) Estimate the onset potential values of the oxidation and reduction of P3HT according to the

protocol depicted in Figure 8. Give also an explanation why it’s not possible to determine E1/2 of

conducting polymers.

b) Calculate the HOMO and LUMO levels as well as the band gap according to equations (2)-(4).

3.3 Analysis of the electrochromic behavior of PEDOT

a) Describe the optical impression which was observed during the charging/ discharging cycles.

b) Plot the current-time curves obtained during the charging/discharging of the PEDOT film and

discuss in detail the influence of the switching times.

14

4. Questions

a) Only for chemistry students: Describe a chemical method for the synthesis of a polythiophene

polymer based on a transition metal complex catalyzed reaction (draw the reaction scheme in

which the structure of the monomer and the resulting polymer shall become clear as well as the

catalytic cycle!).

b) Draw the molecular structure of PEDOT:PSS (poly(3,4-ethylenedioxythiophene):

polystyrenesulfonate) in its quinoid stabilized form. In which form is the polystyrenesulfonate

present? Name at least two applications of this conducting polymer.

c) Describe a detailed buildup of a polymer electrochromic window.

d) P3HT is a common donor material in donor-acceptor based organic solar cells. The acceptor

material is often composed of a fullerene derivative (typically PCBM =[6,6]-Phenyl C61 butyric

acid methyl ester). Draw a sketch of a polymer based organic solar cell. Draw an energy diagram

containing the HOMO and LUMO levels of the donor and acceptor material.

Rheology

1 Introduction ................................................................................................................................ 2

2 Theoretical foundation .................................................................................................................. 2

2.1 Fundamental terms in rheology.............................................................................................. 2

2.2 Linear-viscoelastic behavior ................................................................................................. 4

2.3 Measuring technique ........................................................................................................... 7

2.3.1 Oscillation measurements ........................................................................................ 7

2.3.2 Rotational experiments ............................................................................................ 8

2.3.3 Tension experiment .............................................................................................. 10

2.3.4 Relaxation experiment ........................................................................................... 10

2.4 Borderline behavior of matter and rheological models .............................................................. 10

2.4.1 Elastic behavior ................................................................................................... 11

2.4.2 Plastic behavior .................................................................................................... 12

2.4.3 Viscous behavior .................................................................................................. 13

2.4.4 Viscoelastic behavior ............................................................................................ 14

2.4.5 Characterization by flow and viscosity curves ............................................................ 16

2.5 Time-dependent rheological behavior ................................................................................... 17

2.6 Rheometry (measuring technique) ........................................................................................ 18

3 Experimental ............................................................................................................................ 19

3.1 Conduction of rotational measurements ................................................................................. 19

3.2 Time-dependent change of viscosity ..................................................................................... 20

3.3 Oscillation measurements to determine the viscoelastic behavior ............................................... 20

4 Questions ................................................................................................................................. 21

5 Literature ................................................................................................................................. 21

- 2 -

1 Introduction

Rheology is the science which describes, explains, quantifies and applies the phenomena appearing

while bodies or liquids are deformed or while they flow. According to Ziabicki [1], the rheological

behavior is responsible for the drawability and thus of fundamental importance for the spinnability of

liquid systems. Further examples of applied rheology are found in various areas in natural science

and engineering. [2-7]

1. Colors and varnish (brushability, storage)

2. Polymer solutions and melts (polymer extrusion and spinning

3. Characterization of polymers (statement about molecular weights and molecular weight

distribution

4. Manufacture of high performance materials (ceramics)

5. Flow behavior of food (ketchup, convenience sauce)

6. Cosmetics and sanitary products (tooth paste, cream, shampoos)

7. Geo-rheology (simulation of volcanic flow)

8. Medicine (hemorheology)

9. Pharmaceutical products

10. Electronics

In the following paragraphs the basic principles of rheology, which are described in literature [1 –

20] are addressed.

2 Theory

2.1 Fundamental terms in rheology

To characterize the flow behavior of substances, they are subjected to defined forces and the

resulting deformations are described in detail in dependence of different parameters. Depending on

the direction of the affecting force, the relevant cases for rheometry are distinguished: elongation,

compression strain and shear strain. The effect occurring during the shear experiment of a liquid and

the associated fundamental terms in rheology can be explained with the aid of a two-plate-model

(Figure 1). In this model a liquid is located between two parallel plates of the area A. The upper plate

is moved relative to the lower static plate with a constant velocity. Thereby the power F needs to be

applied due to the internal friction. This shear strain causes a laminar flow of the velocity v which

linearly decreases from the moving to the static plate.

- 3 -

Fig.1: Two-plate-model. The resulting shear rate gradient is also called deformation velocity or shear velocity:

γγ==

=

=

dtd

dydx

dtd

dtdx

dyd

dydv

(1)

velocity gradient = shear rate

Deformation: αγ tan=≡dydx

[-] (2)

Deformation velocity: dtdγγ ≡ [1/s] (3)

When the force applied during the shearing experiment is related to the plate area A, the shear stress

τ is obtained, which is connected with the deformation velocity γ by the shear viscosity η.

Shear stress: γητ ⋅==AF

[Pa] (4)

Stationary shear viscosity: γτη

≡ [Pa·s] (5)

According to the dependence of the stationary shear viscosity on the shear rate, flow behavior can be

characterized as Newtonian, shear thinning and shear thickening (dilatant). Newtonian flow

behavior is present, when the viscosity is independent of the shear rate. If the viscosity decreases

with increasing shear rate, the behavior is called shear thinning, this is typical for polymer melts

- 4 -

and polymer solutions. When the viscosity increases with increasing shear rate the flow behavior is

referred to as shear thickening. Examples of viscosity curves are given in 2.4.5.

For a Newtonian liquid, a direct proportionality exists between shear stress and deformation rate,

whereas for an ideal Hook-type body a direct proportionality between shear stress and deformation is

present, i.e. Hook’s law is in force. The proportionality constant is the modulus of shear G:

Shear stress: γτ ⋅= G [Pa] (6) It should be noted, that also elastic systems exist which to not apply to Hook’s law (e. g. rubbery-

elastic materials). A general definition of elastic behavior is given in 2.4.1.

2.2 Linear-viscoelastic behavior

Many materials do not show exclusively viscous or elastic behavior but a combination of these

characteristics. This is referred to as viscoelastic behavior. The theory of linear viscoelasticity

describes the rheological phenomena of polymer solutions and melts, which is connected to the

preservation of the resting structure/state of the temporary network of entangled molecular chains.

The theory of non-linear viscoelasticity describes viscoelastic phenomena, which are connected with

depletion of the temporary network structure. The rheological material value functions for describing

linear viscoelasticity are determined with the aid of oscillatory experiments. Thereby, the latent state

of the sample is not disturbed, which permits to separately display viscous and elastic behavior. At a

deformation-controlled oscillatory measurement, the sample, which is located in a gap between two

plates, is loaded by a periodic deformation γ(t) and thereby a periodic strain τ(t) is induced, which

shows a displacement of phase δ relative to the preset deformation.

preset deformation resulting strain (response of the system)

}cos{0 t⋅⋅= ωγγ }cos{0 δωττ +⋅⋅= t ω radial frequency of the oscillation [rad/s] 𝜏0 strain amplitude [Pa] 𝛾0 deformation amplitude [-] Based on the displacement of phase δ, rheological behavior can be classified:

• elastic behavior: 0=δ

- 5 -

• viscous behavior: 2πδ =

• viscoelastic behavior: 20 πδ <<

Fig. 2: Course of strain and deformation during oscillatory measurements. To simplify rheological calculations, complex values are introduced. The transition to complex

values is performed by extending strain and deformation with the respective imaginary part. This

allows the transition from trigonometric functions to the complex e-function, thus simplifying

calculations considerably. The following rheological values are defined:

Complex shear strain:

)}(exp{})sin{}(cos{* 00 δωτδωδωττ +⋅⋅⋅=+⋅⋅++⋅≡ titit (7) Complex deformation:

}exp{})sin{}(cos{* 00 titit ⋅⋅⋅=⋅⋅+⋅≡ ωγωωγγ (8) Complex deformation velocity:

}exp{*)(* 0 tiidtd

⋅⋅⋅⋅⋅=≡ ωγωγγ (9)

Viscoelastic behavior can be described by the complex modulus G*, which is defined as the quotient

of complex strain and complex deformation.

- 6 -

Complex modulus:

'''}exp{***

0

0 GiGiG ⋅+=⋅⋅=≡ δγτ

γτ

(10)

Here, G’ is the storage modulus and G’’ is the loss modulus. The storage modulus represents the

degree of elastic behavior, i.e. the energy, which is reversibly stored by restoring forces. The loss

modulus represents the amount of viscous behavior, i.e. the energy which irreversibly dissipated due

to viscous flow. For G’ and G’’ applies:

Storage modulus: δγτ cos'

0

0 ⋅=G [Pa] (11)

Loss modulus: δγτ sin''

0

0 ⋅=G [Pa] (12)

The ratio of loss and storage modulus is the dissipation factor 𝑡𝑎𝑛(𝛿):

Dissipation factor: '"tan

GG

≡δ [-] (13)

The dissipation factor is used to estimate, whether the viscous or elastic behavior is dominating. The

following classification is used:

• tan δ < 1: elastic behavior dominates

• tan δ > 1: viscous behavior dominates

Based on equation (10), it accounts for the absolute value of the complex modulus:

0

022 '''*γτ

=+= GGG [Pa] (14)

The absolute value of the complex modulus corresponds to the ratio of stress amplitude and

deformation amplitude.

The viscoelastic behavior may also be described with help of the complex viscosity η*, which is

defined as the quotient of complex sheer stress τ* and complex deformation velocity *γ .

Complex viscosity:

- 7 -

'''*}exp{***

0

0 ηηω

δγω

τγτη ⋅−=

⋅=⋅⋅

⋅⋅=≡ i

iGi

i (15)

η’ is a measure for the viscose behavior, η’’ describes the elastic behavior.

For η’ and η’’ accounts:

ωδ

ωγτη 'cos''0

0 G=⋅

⋅= [Pa∙s] (16)

ωδ

ωγτη ''sin'0

0 G=⋅

⋅= [Pa∙s] (17)

It results for the absolute value of complex viscosity:

0

0

0

022

22 ''''''*γτ

ωγτ

ωηηη

=

⋅=

+=+=

GG [Pa∙s]

(18) Accordingly, the absolute value of complex viscosity corresponds to the ratio of stress amplitude and

deformation rate amplitude.

2.3 Measuring technique

2.3.1 Oscillation measurements

Oscillation measurements are used to study the linear-viscoelastic behavior. In the rheometers used,

the sample is located in a gap between an upper plate or cone and a lower plate. This setup is also

called plate-plate or cone-plate geometry. (In the following sections, measuring geometries will be

further explained.) In principle, both geometries are suitable for oscillation measurements.

2.3.1.1 Amplitude sweep (= strain sweep and stress sweep)

During the amplitude test, the frequency is held constant and the amplitude of the deformation signal

or the strain signal is varied, depending on whether the following frequency measurement is

supposed to be conducted by deformation control or by strain control. If the amplitude is not too

high, the rheological material value functions (i.e. G‘(ω) and G‘‘(ω)) do not show any dependence

on the amplitude. This measurement range is called region of linear viscoelasticity. In this range, the

idle state of the sample is not disturbed. Starting from a specific amplitude value, the rheological

material functions G‘(ω) and G‘‘(ω) decrease with increasing amplitude. In this range the laws of

- 8 -

non-linear viscoelasticity are applicable; the idle state of the sample is disturbed. For solutions and

melts of polymers a disentanglement of entangled (verhakt) molecular chains occurs.

2.3.1.2 Frequency sweep

Within the frequency test, the radial frequency ω is varied, whereas the deformation amplitude γ0 is

held constant in case of deformation-controlled oscillation experiments and the strain amplitude τ0 is

held constant for strain-controlled experiments. Concerning an optimum in signal to noise ratio, the

highest possible deformation or strain amplitude is chosen from the rheograms of the previously

performed amplitude tests, which is just in the linear viscoelastic area. Usually, storage modulus

𝐺′(𝜔), loss modulus 𝐺′′(𝜔) and the absolute value of complex viscosity Iη*I are measured and

drawn against radial frequency ω in a double logarithmic reference frame, because the rheological

material value functions change with radial frequency over several orders of magnitude.

2.3.1.3 Time sweep

Time sweep is carried out at constant amplitude γ0 or τ0, respectively and constant angular velocity.

The time-dependent behavior of the rheological material value functions is observed. Thus, changes

in the material properties over time can be recorded by using rheology. One example is the

thickening process in the manufacture of gels or the stability of polymer solutions against gelling.

2.3.1.4 Temperature sweep

A temperature ramp at constant angular frequency and deformation is applied. The temperature

dependent measurement is illustrated by a semi-logarithmic plot of storage and loss modulus as a

function of temperature. With the aid of a temperature sweep, for example, glass transition

temperature and crystallization temperature of polymers can be determined. This technique is often

called dynamic mechanical thermal analysis (DMTA).

2.3.2 Rotational experiments

Rotational experiments offer another possibility to either preset strain or deformation rate. In a

strain-controlled experiment, the resulting deformation rate is received as the answer of the system,

in deformation-controlled experiments, respectively, the resulting strain is obtained. Rotational

experiments are usually conducted with cone/plate geometry, because with this measuring system,

the deformation rate is independent of the distance r to the middle of the plate and thus constant.

- 9 -

Exclusively rotational experiments are performed to record flow curves (plot of 𝜏 against �̇� ) or

viscosity curves (plot of η against �̇�).

- 10 -

2.3.3 Tension experiment

This experiment is a rotational experiment in which the time-dependent behavior of rheological

quantities is recorded. Here, a constant deformation rate is preset and the resulting strain signal is

measured as a function of time. In the ideal case of the experiment, the angular frequency escalates

from the idle state to a constant value. Viscoelastic liquids exhibit a delayed increase in shear stress.

If the measured time-dependent shear stress is correlated to the preset constant deformation rate, the

time-dependent (transient) viscosity η+(t) is obtained:

γτ

η

)()( tt ≡+

[Pa·s] (19)

In the case of viscoelastic fluids the transient viscosity approximates a boundary value with

progressing measurement time. This boundary value is called stationary (= time-independent) shear

viscosity η:

)(),(lim γηγη =+

∞→

tt

[Pa·s] (20)

2.3.4 Relaxation experiment

In the relaxation experiment, the sample is stressed by an escalating deformation γo and the resulting

strain signal τ(t), which decreases with time, is measured. Due to its elastic restoring force a strain is

produced by the preset deformation. A relaxation process within the sample takes place by viscous

flow and the generated strain diminishes. If the strain signal is correlated with the preset

deformation, the nonlinear-viscoelastic relaxation modulus is obtained, with is dependent of time and

the existent deformation:

Relaxation modulus: 0

0)(),(

γτγ ttG ≡ [Pa]

τ(t): strain [Pa] γo: deformation [-]

2.4 Borderline behavior of matter and rheological models

In rheometry material-specific dependencies of the above mentioned interactions of applied shear

stress and resulting shear deformation are obtained. Thereby, the material’s behavior is distinguished

by the following properties: viscous, elastic, viscoelastic and plastic behavior. These behaviors of

material are sketched in Figure 3. All liquids can be described with the aid of viscosity.

- 11 -

Fig. 3: Boundary behavior of matter: (1) elastic (steel), (2) plastic (modelling clay), (3) viscous (water), (4) viscoelastic (silicone rubber).

2.4.1 Elastic behavior

Upon application of strain, which is held constant over a certain period of time, an elastic material

experiences a deformation, which is constant over time, too (Figure 4). In case a strain is applied as a

step function, the resulting deformation shows the same escalating behavior. Solids with this

behavior are defined elastic. If there is an additional directly proportional ratio between applied

strain and the resulting deformation, the solid is called Hookean solids, i.e. Hook’s law is applicable

(see section 2.1, eq. 6). Note that also elastic solids exist, that do not follow Hook’s law, i.e. strain

and deformation are not linearly connected to each other (e. g., materials for which the law of rubber-

elasticity is applicable).

Fig. 4: Definition of elasticity in general: applied strain as a step function and resulting deformation

of escalating behavior.

(1) (2) (3) (4)

t0

t

t t0

γ

t t1

response input

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The behavior of a Hookean solid is described by a spring for which Hook’s law is applicable.

Fig. 5: Spring as the mechanical model for elastic behavior.

2.4.2 Plastic behavior

Plastic behavior is characterized by a flow behavior with an existing flow limit. The flow limit is the

strain value under which no or only elastic deformation occurs. Above this limit a permanent

deformation appears. Plastic behavior is illustrated with the Saint Venant body. This mechanical

model consists of a slider, which only moves if the applied force overcomes the resistance of static

friction.

Fig. 6: Shearing of a plastic body as a consequence of strain; for deformation a certain shear stress is

necessary, then, shear stress is constant.

Fig. 7: Saint Venant body as a mechanical model for plastic behavior.

τ

γ

τ0

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2.4.3 Viscous behavior

Viscous behavior is found for ideal liquids, the so-called Newtonian liquids. For the definition of the

stationary shear viscosity η the previously described two plate model can be used, for which a

laminar flow is induced in the liquid between two plates as a consequence of the applied shear.

Because of the inner friction of the liquid, the layers only move partially against each other.

Assuming that a laminar flow is present, a velocity gradient is formed in the liquid between the two

plates. As described in section 2.1, for Newtonian liquids, there is a direct proportionality between

shear stress and shear rate, where the constant value is called shear viscosity.

Fig. 8: Applied strain as a step function and resulting deformation for Newtonian liquids. The viscous flow behavior of a Newtonian liquid is described by the mechanical model of an

attenuator. At a constant affecting shear force, force and piston speed are proportional. The piston

immediately stops at the position where it was, when the force effect is finished. Therefore the

deformation of the liquid fully persists even when the force is relieved.

Fig. 9: Attenuator as a mechanical model for viscous flow behavior.

t0

input

τ

tt0 t1t1

γ

tt1

response

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2.4.4 Viscoelastic behavior

As described in section 2.2 many materials do not show exclusively viscous or elastic behavior, but a

combination of both properties. Depending on the type of strain that is applied to the material, the

respective components of viscoelastic flow behavior appear more or less pronounced. Rheological

material value functions used for describing viscoelastic flow behavior are given in section 2.2.

Viscoelastic behavior can be described by mechanical models where spring and attenuator are

combined. For describing the behavior of viscoelastic liquids (polymer melts or concentrated

polymer solutions) one or several Maxwell elements are used. A Maxwell element is a series of

connected springs and attenuators. If a force is applied in form of a step function, the result is a

spontaneous deflection (elastic behavior). Then, the effect of the attenuator appears (viscous

behavior). The initial position is not reached again. This model describes the ideal behavior of

viscoelastic liquids.

Fig. 10: Applied strain as a step function and resulting deformation for a simple Maxwell element.

Fig. 11: Maxwell element as a simple mechanical model for viscoelastic liquids.

For many viscoelastic liquids this model does not describe the flow behavior adequately enough.

Only by parallel connection of several Maxwell elements viscoelastic liquids can be described with

satisfactory accuracy. This approach is called generalized Maxwell model.

τ

t t0 t1

γ

t t1 t0

spring

attenuator regression of the spring

input

response

- 15 -

Fig. 12: Generalized Maxwell model for improved description of the behavior of viscoelastic liquids.

For viscoelastic solids, the viscoelastic behavior is described by the Kelvin Voigt model. Within this

model, spring and attenuator are connected in parallel. The deformation occurs as long as the

straining force is acting with constant intensity. Both components can only be deformed at the same

time and to the same degree, because they are connected by a fixed frame. The spring cannot be

deformed in the same spontaneous way as it would if it was a single spring with liberty of action,

because it is retarded by the attenuator. As a result of the strain period, deformation behavior is

observed as a curved, time-dependent e-function in the γ(t)-graph having deformation values rising

to a certain maximum value. Accordingly, the spring tends to move back to its initial state when the

force is released. This energy effects that both components reach their initial positions. However, this

happens after a certain time. Due to the presence of the attenuator, this is a time-delayed process, too.

Fig. 13: Strain input as a step function and resulting deformation for the Kelvin Voigt model.

input

τ

t t0 t1

γ

t t1 t0

response

- 16 -

Fig. 14: Kelvin Voigt model as a simple mechanical model for viscoelastic solids.

2.4.5 Characterization by flow and viscosity curves

In the following graphs flow and viscosity curves are summarized, which are used to characterize the

rheological behavior of fluid media.

Fig. 15: Flow curves for the description of rheological behavior.

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Fig. 16: Viscosity curves for the description of rheological behavior. For a shear thinning substance, viscosity is dependent on the extent of shear strain. With increasing

strain, the flow curve exhibits a negative slope, viscosity decreases, respectively. In the consequence

of shearing, a structural change is induced, which results in the decrease of viscosity. For the filled

systems, the arrangement of the particles is in favor of the lowest possible flow resistance. Thereby,

the arrangement significantly relies on the underlying structure of the deformed material.

Fig. 17: Effect of shearing on the structure of shear thinning materials.

2.5 Time-dependent rheological behavior

To study the time-dependency of structure disassembly and assembly, experiments are conducted

during which the deformation rate is preset as a step function and viscosity is measured in

dependence of time. By such measurements it is possible to distinguish between thixotropic

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(structure disassembly) and rheopectic (structure amplification) behavior, whereat these notations

may only be used in case of fully reversible and isothermally occurring processes. If the disassembly

of structure is irreversible, the behavior is denoted non-thixotropic. These time-dependent

deformation phenomena are defined as follows:

Thixotropy:

Thixotropy describes the disassembly of a structure at constant shear strain and complete reassembly

of the structure after a certain period of time. This disassembly/reassembly cycle is a completely

reversible process. Well-known examples for materials with thixotropic behavior are, e.g.,

dispersions like paste, creams, ketchup, lacquer, etc.

Non-thixotropic behavior:

If the reassembly of structure is incomplete or not happening even after a long period of recovery,

the shear strain induces a permanent change in the structure. This effect is sometimes called “unreal”

or “incomplete” thixotropy. A very prominent example for this effect is mixing up yoghurt. After

mixing, the yoghurt is flowing much more than before, even after a long relaxation period.

Rheopecty:

Rheopecty means an increase in structural strength during shear strain, i.e. assembly of structure

during constant shearing and complete disassembly after relaxation. This assembly/disassembly

cycle is a completely reversible process.

2.6 Rheometry (measuring technique)

For conducting rheological studies, rotational rheometers of different geometries can be used. Each

measuring geometry is used for a different value of viscosity. The most common geometries are:

Plate-plate-geometry:

A plate-plate meassuring system consists of two even plates. Ususally the upper plate is the rotor and

thus the movable part of the meassuring geometry (“measuring plate”) und the lower plate is fixed on

the rheometer stand. The geometry is determined by the plate’s radius R. A disadvantage of this

geometry is, that even at a constant rotational speed, the deformation speed – viewed over the entire

plate gap – is not constant but depends on the distance r to the middle of the plate. That is, a radius-

dependent shear rate distribution exists. These non-uniform, non-constant shear conditions are seen

as a disadvantage for scientifically working rheologists, especially when performing exclusively

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rotational experiments. These experiments should be conducted with cone-plate geometry for the

above mentioned reasons. However, this disadvantage is of low relevance when determining

rheological material value constants of linear viscoelasticity (that is G’, G’’ and Iη*I), for this reason,

the plate-plate geometry is often used for performing oscillation measurements, especially when the

sample is analyzed at different temperatures or, if the sample is filled with particles (e. g., filled

polymer melts or dispersions with relatively large particles). Plate-plate geometry allows for larger

gap positions, thus, phenomena which negatively affect the measured values, like thermal expansion

of the measuring tools or friction effects due to incorporated particles in filled systems could be

minimized.

Cone-plate geometry:

A cone-plate measuring system consists of a round measurement body with a slightly tilted, slightly

cone-shaped surface and a plate. Usually, the cone is the rotor and hence, the upper, moveable part of

the measuring geometry and the lower plate is unmovably fixed on the rheometer stand. The

dimensions of the conical surface are determined by the cone’s radius R and the cone angle α. A

major advantage of the cone-plate geometry is that with this measurement system, the deformation

rate is independent of the distance r to the middle of the plate. Because of this relationship, cone-

plate geometry is especially recommended for performing rotational experiments.

Coaxial cylinder geometry:

Coaxial cylinder measuring systems consist of a measurement body (inner cylinder) and a measuring

cup (outer cylinder). Coaxial means that both cylindrical components are located along one identical

rotationally symmetric axis when the system is in working position. These measuring systems are

especially used for studying low viscous liquids. According to the operating mode, two system types

are distinguished. In the Couette system, the outer cylinder is rotating whereas in the Searle system,

it is the inner cylinder.

3 Experimental

All experiments are conducted with a cone-system (Ø=50 mm, cone-plate-geometry). Temperature

control of the plate is conducted by a Peltier element. Unless stated otherwise, all experiments are

carried out at a temperature of T = 25 °C.

3.1 Conduction of rotational measurements

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The following samples should be classified according to their characteristic flow behavior. The

respective flow phenomena and the underlying structure are to be discussed based on the measured

flow and viscosity curves.

Sample 1: Honey

Shear rate: �̇� = 10-1 to 103 1𝑠

Sample 2: 14 wt.-% PVP-solution (H2O) (Mw = 1,300,000 g/mol)

Temperature: T = 20°C

Shear rate: �̇� = 100 to 103 1𝑠

Sample 3: starch/H2O suspension (50 wt.-%)

Shear rate: �̇� = 10-1 to 102 1𝑠

3.2 Time-dependent change of viscosity

Time-dependent measurements at predetermined deformation rates are performed and the

characteristic evolution of the viscosity function depending on time is discussed. The observed effect

is to be discussed with regard to the underlying effects.

Sample 4: Ketchup Measuring program: From t = 0 to 3 s: γ = 0.1 1

𝑠

From t = 3 to 6 s: γ = 100 1𝑠

From t = 6 to 250 s: γ = 0.1 1𝑠

3.3 Oscillation measurements to determine the viscoelastic behavior

Two oscillation experiments are preformed and the measured curves are discussed. The highest

possible deformation amplitude is chosen from the viscoelastic region and used as a constant

parameter (default value) for the following frequency test.

3.3.1 Oscillation measurement by varying the deformation amplitude at a constant angular

frequency (amplitude test)

Sample 5: 20 wt.-% PVP-solution (H2O) (Mw = 360,000 g/mol)

- 21 -

Temperature: T = 20°C

Measuring program: angular frequency: ω = 10 rad/s

Deformation amplitude from 𝛾𝑜 = 1 % to 1000 %

Illustration of G’, G’’ and |𝜂∗| as a function of the deformation amplitude 𝛾𝑜 and choice of the

deformation amplitude from the measured curves for the subsequent oscillation measurement (from

linear viscoelastic to non-linear viscoelastic behavior).

3.3.2 Oscillation measurement by varying the angular frequency

Temperature: T = 20°C

Measuring program: Use of the deformation amplitude determined in 3.3.1 as a default

Angular frequency from ω = 100 to 0.1 rad/s

Illustration of G’, G’’ and |𝜂∗| as a function of angular frequency. Explain the rheological behavior

based on the depicted curves (viscosity, viscoelasticity and elasticity). Describe the structural events

at the transition between the borderline cases.

4 Questions

1. Term other applied examples for the determination of materials’ viscosity.

2. Sketch the most important flow and viscosity diagrams.

3. Describe the advantages and disadvantages of plate/plate and cone/plate geometry.

5 Literature

1. M. Dragoni, A. Tallarico, J. Volcanol. Geoth. Res. (1994), 59, 241

2. G. Miyamoto, S. Sasaki, Computers & Geosciences (1996), 23, 283

3. G. B. Thurston, Biophys. J. (1972), 12, 1205

4. W.P. Cox, E.H. Merz: J. Polym. Sci. (1958), 28, 619

5. G. Böhme, M. Stenger: Chem. Eng. Technol. (1988), 11, 199

6. G. V. Vinogradov, A. Y. Malkin, Y. G. Yanovsky, E. A. Dzyura V. F. Schumsky, V. G.

Kulichikhin: Rheol. Acta 8 (1969), 490-496

7. G. V. Vinogradov, N. V. Prozorovskaya: Rheol. Acta 3 (1964)

8. G. V. Vinogradov, A. Y. Malkin: J. Polym. Sci. A: Polym. Chem. (1964), 2, 2357

9. H. M. Laun: Progr. Coll. Pol. Sci. (1987), 75, 111

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10. H. M. Laun: Rheol. Acta (1978), 17, 1

11. J. D. Ferry: Viscoelastic properties of polymers, John Wiley & Sons, Inc. (1970)

12. L. E. Nielsen: Polymer Rheology, Marcel Dekker, Inc., New York – Basel (1977)