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 = NiMi / Ni
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 = WiMi / Wi = NiMi2 / 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 = NiMi(a+1) / NiMia
A Higher Order MW, called the Z average, is closely related to processing
characteristics a = 2
Mz bar = NiMi(2+1) / NiMi2 = NiMi3) / NiMi2
A viscosity based MW, Mv bar, has 0 a 1 and closer to 1 (i.e., to Mw bar)
MV bar = NiMi(1.x) / NiMi0.x
i)
ii)
i)
ii)
iii)
Where x is typically close to 1 and 1.x is typically close to 2
MV bar = NiMi(1.9) / NiMi0.9 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 - TS
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 (1 - 2)2
Hmix is the Enthalpy of mixing (dissolution)
1 is the Solubility Parameter of one component
2 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,
1) The 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 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
= d G / 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,
= 1 is the value for the non-expanded polymer in the ideal statistical coil
having the smallest possible size
as 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 ()
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
[] = Intrinsic Viscosity (i.e., the viscosity in an Ideal Solution)
Mark- Houwink-Sakurada Equation
[] = 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 concentra
