molecular weights, polymers, & polymer solutions (part i - chapter
TRANSCRIPT
Chemistry 5861 - Polymer Chemistry 1
Molecular Weights, Polymers, & Polymer Solutions (Part I - Chapter 2 in Stevens)1
I Number and Weight Average Molecular Weight - An Introduction
Importance of MW and MW Distribution A)
1)
a)
2)
a)
b)
3)
a)
b)
Optimum MW, MW Distribution, etc.
depends upon application via processing and performance tradeoffs
Typical MW values for commercial polymers
Vinyl polymers in the 105 and 106 range
Strongly H-bonding polymers in the 104 range
i)
i)
ii)
iii)
iv)
v)
vi)
e.g., 15,000 - 20,000 for Nylon
MW Determinations (many more details later in chapter)
We wish to determine both average values of MW and information about MW
distribution
Some Important Methods
Gel Permeation Chromatography, GPC
Light Scattering
Viscometry
Mass Spectroscopy
End Group Analysis (Chemical & Spectroscopic)
Colligative Properties (P-Chem Methods)
Boiling Point Elevation
Freezing Depression (Cryoscopy)
1 The graphics in these notes indicated by “Figure/Table/Equation/Etc., x.x in Stevens” are taken from our lecture text: “Polymer Chemistry: An Introduction - 3rd Edition” Malcolm P. Stevens (Oxford University Press, New York,
©2002, Dr. Allen D. Hunter, Youngstown State University Department of Chemistry
Chemistry 5861 - Polymer Chemistry 2
B)
Osmometry, etc.
Number Average Molecular Weight, Mn bar
1)
a)
2)
3)
a)
C)
This term is very sensitive to the total number of molecules in solution and hence is
especially sensitive to the low molecular weight monomers and oligomers
Determined by End Group Analysis and Colligative Properties
Mn bar = ΣNiMi / ΣNi
Example
9 moles of MW = 30,000 and 5 moles of MW = 50,000 ⇒ Mn bar ≈ 37,000
Weight Average Molecular Weight, Mw bar
1)
a)
2)
3)
a)
4)
This term is sensitive to the mass of the molecules in solution and hence is especially
sensitive to the very highest MW species present in the system
Determined by Light Scattering and Ultracentrifugation
Mw bar = ΣWiMi / ΣWi = ΣNiMi2 / Σ NiMi
Example
9 moles of MW = 30,000 and 5 moles of MW = 50,000 ⇒ Mw bar ≈ 40,000
Note:
a)
b)
c)
Mw bar ≥ Mn bar (Draw MW distribution chart)
Mw bar/Mn bar = Polydispersity Index
Mw bar/Mn bar = 1, Mw bar = Mn bar for a sample having a single MW
(Monodisperse)
1999).
©2002, Dr. Allen D. Hunter, Youngstown State University Department of Chemistry
Chemistry 5861 - Polymer Chemistry 3
d)
D)
Mw bar/Mn bar ≥ 1 is Polydisperse
General Molecular Weight Expression & Mz bar and Mv bar
1)
2)
a)
3)
a)
b)
II
M bar = ΣNiMi(a+1) / Σ NiMi
a
A Higher Order MW, called the Z average, is closely related to processing
characteristics ⇒ a = 2
Mz bar = ΣNiMi(2+1) / Σ NiMi
2 = ΣNiMi3) / Σ NiMi
2
A viscosity based MW, Mv bar, has 0 ≤ a ≤ 1 and closer to 1 (i.e., to Mw bar)
MV bar = ΣNiMi(1.x) / Σ NiMi
0.x
i)
ii)
i)
ii)
iii)
Where x is typically close to 1 and ∴ 1.x is typically close to 2
∴ MV bar = ΣNiMi(1.9) / Σ NiMi
0.9 in a typical case
Mz bar ≥ Mw bar ≥ Mv bar ≥ Mn bar
Polymer Solutions
Steps Dissolving a Discrete Molecule and a Polymer A)
1)
a)
2)
a)
Discrete Molecule Dissolution Steps for a Crystalline Sample
Polymer Dissolution Steps
solvent diffusion
solvation & swelling
⇒ Gel formation
network polymers stop at this stage, degree of swelling correlated with
crosslink density
©2002, Dr. Allen D. Hunter, Youngstown State University Department of Chemistry
Chemistry 5861 - Polymer Chemistry 4
b)
B)
True dissolution
i)
ii)
untangling of chains
very slow process and may not occur on timescale of real world
Thermodynamics of Polymer Dissolution
1)
a)
b)
2)
a)
b)
c)
3)
a)
b)
c)
4)
5)
C)
Choosing a Solvent for Polymers
Polymer Handbook!!!!! lists solvents and nonsolvents for common polymers
Rule of Thumb: Like dissolves Like
∆G = ∆H - T∆S
∆G must be negative for spontaneous (but not necessarily fast) dissolution
∆S will be positive because of greater mobility in solution
∴ need ∆H to be negative or at least not too positive
∆Hmix ∝ (δ1 - δ2)2
∆Hmix is the Enthalpy of mixing (dissolution)
δ1 is the Solubility Parameter of one component
δ2 is the Solubility Parameter of the other component
In practice, ∆H is seldom negative and we simply try to keep it from getting too
positive
∴ we see that we want the polymer and the solvent to have as similar of Solubility
Parameters as possible
Solubility Parameters, δ
1) The δ Parameters is related to the heat of vaporization of the sample
©2002, Dr. Allen D. Hunter, Youngstown State University Department of Chemistry
Chemistry 5861 - Polymer Chemistry 5
2)
3)
a)
4)
a)
For small molecules these can be measured experimentally
∴ the δ Parameters of solvents are tabulated
multiple parameter expressions can also be used for more precision
For conventional polymers these can be estimated using tables
Group Molar Attraction Constants
b)
c)
D)
Table 2.1 in Stevens
δ = d ΣG / M
i)
ii)
iii)
G = the individual Group Molar Attraction Constants of each structural
fragment
d = density
M = molecular weight
Hydrodynamic Volume in Solution
1)
2)
The apparent size of the polymer in solution
Reflects both the polymer chain itself and the solvating molecules in inner and outer
spheres
3)
4)
a)
b)
Figure 2.1 in Stevens
Hydrodynamic Volume is related to an
Expansion Factor, α
α = 1 is the value for the “non-expanded” polymer in the “ideal” statistical coil
having the smallest possible size
as α increases, so does the Hydrodynamic Volume of the sample
©2002, Dr. Allen D. Hunter, Youngstown State University Department of Chemistry
Chemistry 5861 - Polymer Chemistry 6
E) The Theta State (θ)
1)
2)
3)
4)
F)
Solubility varies with temperature and the nature of the solvent
∴ there will be a minimal dissolution temperature call the Theta Temperature and at
that point the solvent is said to be the Theta Solvent
The Theta State at this point is the one in which the last of the polymer is about to
precipitate
Compilations of Theta Temperatures & Solvents are available in the literature
Intrinsic Viscosity & Molecular Weight
1)
2)
a)
b)
c)
III
[η] = Intrinsic Viscosity (i.e., the viscosity in an “Ideal Solution”)
Mark- Houwink-Sakurada Equation
[η] = K (Mv bar)a
K and a are characteristic of the particular solvent/polymer combination (more
later)
Mv bar = the Viscosity Average Molecular Weight
Measurement of Number Average Molecular Weight
A) General Considerations
1)
a)
Ideal Instrument
Gives full information on the molecular weight distributions for sample
i)
ii)
Reliable for all species in sample from monomers to crosslinked polymers
From this MW distribution can be extracted mathematically for the
various types of MW averages (Mw bar, Mn bar, Mv bar, etc.)
©2002, Dr. Allen D. Hunter, Youngstown State University Department of Chemistry
Chemistry 5861 - Polymer Chemistry 7
iii)
iv)
i)
i)
ii)
iii)
i)
i)
Highly sensitive so can use small & very dilute samples
Data quality
b)
c)
2)
a)
b)
c)
d)
e)
f)
B)
highly accurate
highly precise
Requires no calibration
Neither at the start of each run nor for different types of samples
Cost and convenience
low cost to buy and maintain
highly reliable/robust
easy to operate
Real Instruments
Most methods give only averages
exceptions are: GPC, Light Scattering, & MS
Most methods’ results vary depending on the structure of the sample
∴ need to calibrate each sample and/or know some structural information
such as branching
Most methods have limited sensitivities and/or linear ranges
Most methods require expensive instrumentation
There can be substantial disagreements between the results of different techniques
However, many methods are improving in these areas rapidly
End-Group Analysis
1) Basic principles
©2002, Dr. Allen D. Hunter, Youngstown State University Department of Chemistry
Chemistry 5861 - Polymer Chemistry 8
a)
b)
c)
2)
a)
b)
c)
3)
a)
b)
c)
The structures of the end groups must be different from that of the bulk repeating
units (e.g., CH3 vs. CH2 in an ideal polyethylene)
∴ If you detect the concentration of the end group and know the total amount of
sample present you can calculate the average MW, Mn bar
i)
ii)
i)
ii)
iii)
i)
i)
ii)
need to have either a perfectly linear polymer (i.e., two end groups per
chain) or need to know information about the amount of branching
∴ the Mn bar values that come out for “linear” polymers must typically be
considered an upper bound since there may be some branching
Detection of concentrations of end groups
Spectroscopy - IR, NMR, UV-Vis
Elemental Analysis
Radioactive or Isotopic labels
Strengths
The requisite instruments are in any department
can be quite quick
Sometimes this information comes out “free” during polymer structural studies
Weaknesses
does not give MW distribution information
need to know information about the structure
identity and number of end groups in each polymer molecule
limited to relatively low MW for sensitivity reasons
5,000 - 10,000 is typical MW range
Can be high with some detections types
©2002, Dr. Allen D. Hunter, Youngstown State University Department of Chemistry
Chemistry 5861 - Polymer Chemistry 9
C)
radioactive labeling of end groups
fluorescent labeling of end groups
Colligative Properties - Membrane Osmometry
1) Figures 2.2, 2.3, & 2.4 in Stevens
2)
a)
b)
c)
3)
a)
4)
a)
b)
Basic principles
molecules dissolved in solvents change the structure of the solution
solvent molecules want to diffuse into the solution with the highest solute
concentration (in terms of moles)
Figure 2.3 in Stevens
Strengths
quick
Weaknesses
does not give MW distribution information
range of 50,000 to 2,000,000 limited by low molecular weight species present and
sensitivity, respectively
©2002, Dr. Allen D. Hunter, Youngstown State University Department of Chemistry
Chemistry 5861 - Polymer Chemistry 10
D) Colligative Properties - Vapor Pressure Osmometry
1)
a)
b)
2)
a)
b)
c)
3)
a)
b)
E)
Basic principles
Diagram
Same physical chemistry principles as membrane osmometry except that the
solvent molecules move through gas phase instead of membrane
Strengths
quick
not hurt by low MW species as is membrane Osmometry
home-made systems can be very inexpensive
Weaknesses
does not give MW distribution information
while can be used up to MW of 40,000 is more typically used for MW below
25,000
Colligative Properties - Cryoscopy & Ebulliometry
1)
a)
2)
a)
3)
a)
b)
Basic principles
changes in solution structures upon dissolution decrease mp and increase bp
Strengths
can be quick and inexpensive
Weaknesses
does not give MW distribution information
mostly limited to MW below 20,000
©2002, Dr. Allen D. Hunter, Youngstown State University Department of Chemistry
Chemistry 5861 - Polymer Chemistry 11
IV Measurement of Weight Average Molecular Weight
A) Light Scattering
1)
a)
Basic Principles - Static and Dynamic
Instrumentation
i)
ii)
iii)
i)
ii)
iii)
iv)
Figures 2.7 in Stevens
Moving detector
Multiple Solid State Detectors
b)
c)
each polymer molecule in solution (and its associated solvent molecules) has a
different refractive index than neat solvent
∴ they behave as tiny lenses and scatter light
scan detector over a range of angles or use multiple detectors
measure scattered intensity as a function of angle and concentration
Use “Zimm” plot to extrapolate to infinite dilution and to zero degrees
Figure 2.6 in Stevens
d)
2)
a)
b)
c)
3)
a)
Brownian motion effects and dynamic
light scattering
Strengths
an absolute method that does not need
calibration
can give shape information as well as MW information
quite sensitive and easy to couple to an LC
Weaknesses
cost!
©2002, Dr. Allen D. Hunter, Youngstown State University Department of Chemistry
Chemistry 5861 - Polymer Chemistry 12
B) Ultracentrifugation
1)
a)
b)
c)
2)
a)
3)
a)
b)
c)
d)
V
Basic Principles
each polymer molecule in solution (and its associated solvent molecules) has a
different density than neat solvent
∴ if one has a density gradient in the solution (ultracentrifuge generates this from
the salt solution) the polymers will settle to their optimum levels
measure sedimentation height/velocity
Strengths
excellent for polymers having a variety of specific MWs, e.g., proteins
Weaknesses
does not give MW distribution information
costly if don’t have an ultracentrifuge for other reasons
time consuming
not as useful with true “bell curve” MW distributions
Viscometry
A) Viscosity Measurement
1)
2)
a)
Table 2.2 in Stevens
Basic Principles
Math & Mark-Houwink-Sakurada Equation
[α] = K (Mv bar)a i)
©2002, Dr. Allen D. Hunter, Youngstown State University Department of Chemistry
Chemistry 5861 - Polymer Chemistry 13
ii)
iii)
i)
ii)
iii)
i)
i)
ii)
i)
K and a are characteristic of the particular solvent/polymer combination
(more later)
Mv bar = the Viscosity Average Molecular Weight
b)
c)
d)
Measurement of [η]
Make up 5-6 solutions at different
concentrations of the same sample and
of pure solvent
measure the time it takes each of
them to flow through the viscometer
extrapolate to viscosity at zero concentration which gives the intrinsic
viscosity
Measurement of [η] K and a
Plot the [η] values against the MW values from another technique and get
K and a from the intercept and slope
MW determination for a polymer of known structure
Look up K and a in the Polymer
Handbook
e)
Table 2.3 in Stevens
Use the [η] values to calculate Mv bar
directly
Bootstrapping for a new polymer
make 3 or more samples of your polymer having different average MWs
measure the viscosities of each of these
©2002, Dr. Allen D. Hunter, Youngstown State University Department of Chemistry
Chemistry 5861 - Polymer Chemistry 14
ii)
iii)
iv)
v)
vi)
vii)
viii)
go to Polymer Handbook or your own research and find K and a values for
the most closely related polymer
3)
a)
b)
4)
a)
b)
these are a 1st guess/estimate of those for your polymer
use these K and a values and the experimental [η] values to give a 1st
estimate of the MW values for your polymer
use these 1st estimate MW values and the experimental [η] values to
calculate new K and a values
use these new K and a values and the experimental [η] values to get a
better estimate of the MW values
use these 2nd estimate MW values and the experimental [η] values to
calculate new K and a values
use these new K and a values and the experimental [η] values to get a
better estimate of the MW values
continue until these results converge
Strengths
very quick and reliable
no expensive equipment required
Weaknesses
does not give MW distribution information
need good values for K and a
©2002, Dr. Allen D. Hunter, Youngstown State University Department of Chemistry
Chemistry 5861 - Polymer Chemistry 15
VI Molecular Weight Distribution
A) Gel Permeation Chromatography, GPC
1) Basic Principles
a)
b)
c)
Figure 2.9 in Stevens
this is a type of liquid chromatography
(also called size exclusion
chromatography)
one uses a different type of column for separation
i)
ii)
iii)
iv)
v)
i)
ii)
NOT affinity but rather via the residence time in different sized pores of
the packing material
the beads are made from styrene and divinyl benzene copolymer where the
exact conditions and the nature of the template molecules allows the vendors
to make packing beads of controllable diameters
High MW samples come through
first (they don’t fit in the pores)
Low MW samples come through
last
Figure 2.10 in Stevens
d)
e)
The Chromatogram is a graph of intensity vs. time
Calibration curve
Figure 2.12 in Stevens
this needs to be calibrated wrt.
©2002, Dr. Allen D. Hunter, Youngstown State University Department of Chemistry
Chemistry 5861 - Polymer Chemistry 16
standards to put MW on bottom axis
f)
typically monodisperse polystyrene or poly(vinyl alcohol)
iii)
iv)
v)
i)
ii)
iii)
iv)
want a perfectly linear calibration chart for MW from 0 to 100,000,000
however, it curves up at high MW because all of the large polymers are
excluded from the pores and ∴ come strait through
also, it curves down at low MW because to all of the small molecules the
pores are equally oversized
need to do a calibration curve for each polymer/solvent combination
Gives Polystyrene (or Poly(vinyl alcohol)) Equivalent MWs
Universal calibration
Figure 2.11 in Stevens
log([η]M) is plotted with time on the x
axis
All or almost all polymers then fit on
the same curve as the intrinsic viscosity
acts as a “fudge factor”
Gives Polystyrene (or Poly(vinyl
alcohol)) Equivalent MWs
2)
a)
3)
a)
b)
Strengths
gives a full molecular weight distribution
Weaknesses
costs
need to calibrate
©2002, Dr. Allen D. Hunter, Youngstown State University Department of Chemistry
Chemistry 5861 - Polymer Chemistry 17
c)
B)
∴ use an online absolute detector such as a light scattering detector
Mass Spectrometry
1)
a)
b)
c)
Basic Principles
sample volatilization
i)
ii)
iii)
iv)
v)
i)
ii)
iii)
i)
Field Desorption, FD
Fast Atom Bombardment, FAB
Laser Desorption, LD
Matrix Assisted Laser Desorption, MALDI
Electrospray, ESI
ion separation by mass
Ion Traps / Ion Cyclotron Resonance, IT/ICR
Quadrupole, Q
Time of Flight, TOF
Combinations of different components,
e.g., MALDI-TOF
Figure 2.5 in Stevens
d)
2)
a)
b)
c)
3)
Rapidly improving due to proteomics/genomics research
Strengths
One often has the equipment for other purposes
Can give MW distributions, especially when coupled to an LC
Can give structural information
Weaknesses
©2002, Dr. Allen D. Hunter, Youngstown State University Department of Chemistry
Chemistry 5861 - Polymer Chemistry 18
©2002, Dr. Allen D. Hunter, Youngstown State University Department of Chemistry
a)
b)
C)
cost
time to optimize conditions
Fractional Solution & Fractional Precipitation
1)
2)
3)
Basic Principles
Strengths
Weaknesses