Spring 2008
Chap 5. Characterization of MW
Unlike small molecules, polymers are typically a mixture of differently sized
molecules. Only an average molecular weight can be defined.
In case of Low
MW,
MolecularWt. M 
W
totalsample wt

N number of molesin sample
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Spring 2008
Measurements of average molecular weight (M.W.)
Number average molecular weight, Mn
Considers the number of molecules of each size, Mi, in the sample.

Wtotal x - mer sample
W
Mn 


N
t ot al# of molesin sample x - mer
w
x 1

n
x 1
x


n M
x 1

x
n
x
x 1
x

n 
  x 
x 1  N 
x
nx
: molefract ionx - mer
N
Weight Average Molecular Weight, Mw
The weight average, Mw, considers the mass of molecules of each size within the
sample.
Mw 

t ot alwt of samples
t ot alwt of x - mer samples
w M
w
x
x
x

w1M1 w2 M 2
w 

     x M x 
W
 wx  wx
n M
n M
x
x
x
x
wx
: wt fract ionof x - mer in sample
W
Hanyang Univ.
Spring 2008
Viscosity average Molecular Weight, Mη
Average determined by viscosity measurements. Closer to Mw than Mn
Z-average Molecular Weight, Mz
Average determined by centrifuge.
Svedverg eqn. => M = N0m = SRT/D(1-Vρρs)
 Polydispersity : Polydispersity = Mw/ Mn
Mw
> 1 Polydisperse
Mn
Mw
= 1 Monodisperse
Mn
RELATED LINK:
For further details,
CLICK the following link.
http://www.pslc.ws/mactest/weight.htm
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Spring 2008
Influence of Increasing Molar Mass on Properties
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Spring 2008
Influence of Molecular Weight on Mechanical Properties
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Spring 2008
Methods of Molecular Weight Determination
 Number Average Molecular Weight
End-group analysis
determine the number of end-groups in a sample of known mass
Colligative Properties
most commonly osmotic pressure, but includes boiling point elevation and
freezing point depression
 Weight Average Molecular Weight
Light scattering
translate the distribution of scattered light intensity created by a dissolved
polymer sample into an absolute measure of weight-average MW
 Viscosity Average Molecular Weight
Viscometry
the viscosity of an infinitely dilute polymer solution relative to the solvent
relates to molecular dimension and weight.
 Molecular Weight Distribution
Gel permeation chromatography
fractionation on the basis of chain aggregate dimension in solution
 Z-average Molecular Weight
Centrifuge
average determined by centrifuge
Hanyang Univ.
Spring 2008
Determination of Molecular Weight
Weight Average Molecular Weight
Light scattering
• Large particles in solution/suspension scatter light.
• Responsible for phenomena such as refraction, Tyndall effect.
• Extent of scattering is a function of the size and shape of the particles.
• Consequently yields information about Mw.
Measuring Light scattering
• Ar or He/Ne laser source
• Photometer/goniometer measures
light intensity at various angles (θ)
Hanyang Univ.
Spring 2008
Determination of Molecular Weight
Viscosity Average Molecular Weight
Viscometry
• The concentration dependence is
observed to follow this functional
dependence:
s p
c
  k c  k c
2
2
y-intercept
k = Huggins constant
k=2 for rigid uncharged spheres
k=0.35 for flexible polymers
• Neglect higher order term in c.
• Plot of hsp/c vs c will yield [h] as yintercept.
Hanyang Univ.
Spring 2008
  KM
a
• K and a are empirical
parameters characteristic of
a polymer and a solvent
- a=0.5 for a well-coiled polymer
in a poor solvent
- a=1.7 for rigid rod-like polymer
Virtual Experiment
Case Western Reserve Univ.
Polymer and Liquid Crystals
Viscosity Measurements
Click the next homepage, experiment part
http://plc.cwru.edu/tutorial/enhanced/lab/visco/visco
.htm
If you have the trouble viewing this site,
See this page
http://plc.cwru.edu/tutorial/enhanced/software.html
http://www.macromedia.com/shockwave/download/t
riggerpages_mmcom/default.html
Hanyang Univ.
Spring 2008
Determination of Molecular Weight
Molecular Weight Distribution
Gel permeation chromatography
•Solvent flow carries molecules from left to right; big ones come out first
while small ones get caught in the pores.
•It is thought that particle volume controls the order of elution.
•But what about shape?
For further details
Surfing to the internet
Size Exclusion Principle
CLICK the following link,
http://www.pslc.ws/mactest/sec.htm
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Spring 2008
Simple GPC
c
log10M
c
DRI
Ve
column
reservoir
c
degas
pump
injector
log10M
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Spring 2008
Chap 6. Polymer Solubility and Solutions
Three factors are of general interest
1. What Solvents will dissolve what polymer?
2. How does the polymer-solvent interaction influence the solution
properties/
3. To what applications do the interesting properties of polymer solutions
lead?
General rules foe polymer solubility
1. Like dissolve like; Polar polymers- polar solvents Nonpolar polymernonpolar solvent. ex) PVA in water, PS in toluene
2. Solubility will decrease with increasing molecular weight at const. temp.
3. Crystallinity decreases solubility.
4. Crosslinking eliminates solubility.
5. The rate of solubility increases with short branches, allowing the solvent
molecules to penetrate more easily.
6. The rate of solubility decreases with longer branches, because the
entanglement makes it harder for individual molecules to separate.
Hanyang Univ.
Spring 2008
Thermodynamics Basics
ΔGm=ΔHm-TΔSm < 0
Where, ΔGm = the change in Gibbs free energy in the process
ΔHm = the change in enthalpy in the process
ΔSm = the change in entropy in the process
Only if ΔGm is negative will the solution process be feasible.
DGmix < 0
A
AB solution
B
+
Immicible
DGmix > 0
A positive ΔH  solvent and polymer “prefer their own company”, the pure
materials are in a lower energy state.
A negative ΔH  the solution is in the lower energy state, specific interactions
are formed between the solvents and polymer molecules.
[Ref : H.Tompa; polymer solutions, Butterworths,London, 1956,chapter 7]
Hanyang Univ.
Spring 2008
Solubility Parameter
The solubility parameter is defined as:
δ
 x1v1δ1  x2 v2δ2
solvent m ixture
x1v1  x2 v2
(cal/cm3soln)
1, 2 : vol. frac.
1 : polymer solubility parameter.
2 : solvent solubility parameter.
 = (CED)1/2 = (Ev/v)1/2 = (cal/cm3)1/2
Ev/v : molar vol. of liq.
rule of thumb
1  2  0.5 for solubility.
x:m ole fraction , v:m olar volum e
Fig. Determination of

(polymer ) by swelling
Uncrosslinked
polymer
Swelling
H  E = 12(1  2
)2
Likely
crosslinked
polymer
Surfing to the internet
For further details,
Click next homepage.
http://palimpsest.stanford.edu/byaut
h/burke/solpar/
Polymer
solvent
:
solubility parameter
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Spring 2008
Lattice model of solubility
(a) Low-molecular-weight solute
(b) polymeric solute.
Filled circles : Solute
Open circles : Solvent
Boltzman’s law
S = klnP = -R[n1lnx1 + n2lnx2]
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Spring 2008
Hansen’s 3-D Solubility Parameter
internal energy on vaporization
E v Eh E d Ep




v
v
v
v
 2  p2   d2  h2
Ev = Eh + Ed + Ep
dP
H
 Ei 
where i  

 v 
1
2
The cohesive energy, δ 2 , is divided into three
parts:
1)
Dispersion forces (δd )
2)
Polar forces ( δp )
3)
Hydrogen bonding ( δH )
Hanyang Univ.
Spring 2008
Hansen’s 3-D Solubility Parameter
SOLVENT

d

P

H

Chloroform
8.8
1.5
2.8
9.36
THF
8.2
2.8
3.9
9.50
MEK
7.77
4.4
2.5
9.27
m-cresol
8.8
2.5
6.3
11.1
Methanol
7.4
6.0
10.9
14.5
Toluene
8.82
0.7
1.0
8.91
H2O
6.0
15.3
16.7
23.5
PS
8.6
3.0
2.0
9.33
Styrene
9.09
0.49
2.0
9.32
Hanyang Univ.
Spring 2008
Properties of dilute solutions
-Good solvent : Solubility parameter closely matches that of the polymer.
The secondary forces between polymer segments and solvent
molecules are strong, and the polymer molecules are strong, and the
polymer molecules will assume a spread-out conformation in solution.
-Poor solvent : the attractive forces between the segments of the polymer chain are
greater than those between the chain segments and the solvent.
Ex) polystyrene (δ = 9.0 ~ 9.3 )
Chloroform (δ = 9.2 )
Then non-solvent is added , methanol( δ = 14.5 ),the mixed solvent(Chloroform +
methanol)
becomes too”poor” to sustain solution, and the polymer precipitates out.
When ΔG = 0 and ΔH = TΔS (θ condition)
Hanyang Univ.
Spring 2008
Chap 7. Transitions in Polymers
Glass Transition
PMMA, PS  hard, rigid glassy plastics at RT when heated to 125C, become rubbery
Polybutadiene
Polyethylacrylate
Polyisoprene
rubbery at RT, when cooled in Liq. N2
become rigid and glassy, shatters when break
• At low temperatures, all amorphous polymers are stiff and glassy, sometimes
called as the Vitreous State, especially for inorganic polymers.
• On Warming, polymers soften in a characteristic temperature range known as the
glass-rubber transition region.
• The glass transition temperature (Tg), is the temperature at which the amorphous
phase of the polymer is converted between rubbery and glassy states.
• Tg constitutes the most important mechanical property for all polymers. In fact,
upon synthesis of a new polymer, the glass transition temperature is among the
first properties measured.
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Spring 2008
Molecular Motions in an Amorphous Polymer
•Amorphous regions of the material begin
to exhibit long-range, cooperative
segmental motion
•Molecular motion available to polymer
chains below their Tg are restricted
primarily to vibrational modes.
•Above Tg there is sufficient thermal
energy for the chains, through cooperative
rotational motion about the backbone
bonds, to flow under an applied stress.
Tg
•The presence of this large-scale segmental
motion (20–50 atoms moving in concert)
above Tg produces an increase in the free
volume of the polymer.
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Spring 2008
Differential Thermal Analysis (DTA)
Principal components of the experiment include:
• an oven for the controlled heating of the samples
• separate temperature sensing transducers for both the analysis and reference samples
DTA Design
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Spring 2008
Differential Scanning Calorimeter (DSC)
Two samples, each heated independently. Temperature difference is monitored.
Control heat flow into analysis sample (adjusting heater power) to keep the
temperature difference ∆T = 0. This is a null experiment with feedback.
Tg
Tc
Surfing to the internet
For further details, Click next
homepage.
http://www.pslc.ws/mactest/dsc.htm
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Tm
Spring 2008
DTA & DSC Images and Sample data
DTA
DTA sample data
DSC sample data
Hanyang Univ.
Spring 2008
Main factor of Tg
1.Free volume of the polymer vf.
Free volume vf = v vs
v: specific volume of polymer mass
vs: volume of solidly packed molecules
WLF Eq.
vf
 a  b(T - T g)
vf  vs
a  0.025
b  0.00048
2. Attractive forces between molecules.  Tg
Hanyang Univ.
Spring 2008
3. Internal mobility of chains (= freedom to rotate about bond)
Example (1)

Tg
Eo
Silicone
7.3
-120
~0
PE
7.9
-85
3.3
PTFE
6.2
>20
4.7
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Spring 2008
4. Stiffness of the materials
Young’s Modulus E may be written as:
σ = Eε
σ = Tensile stress; ε = Tensile strain
Young’s modulus is a fundamental
measure of the stiffness of the material.
The higher its value, the more resistant
the material is to being stretched.
Unit of E: dynes/cm2 (10 dynes/cm2 = 1 Pascal)
5. Chain Length.
Tg  Tg  
c
x
for
x  500 Tg  Tg 
Hanyang Univ.
Spring 2008
Tg of Copolymer
w
w
1
 1  2
T g T g1 T g2
w : wt. fractionof monomersin copolymer
T : Kelvin temperature
1, 2 : polymer 1 and 2
Surfing to the internet
For further details about Tg,
Click next homepage.
http://www.pslc.ws/mactest/tg.htm
&
http://plc.cwru.edu/tutorial/enhanced/files/polymers/therm/therm.htm
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Spring 2008
Tg Comparision
Nylon n Tm  TS water cont
Example (2)
Tm (C)
 (g/cm3)
TS (psi)
Water cont (%)
Nylon 6
216
1.14
12,000
1.7
Nylon 11
185
1.04
8,000
0.3
Nylon 12
177
1.02
7,500
0.25
PE
135
0.97
5,500
Nil.
Example (3)
O
PU
O C
O
NH ( CH2 )
n
PA NH C
x
Tm
Purea NH CO NH
Tm
Tm
H-bonding Hm
PU : O (Swivel)  flexibility
Extra NH in polyurea  more extensive H-bond. Hm
Hanyang Univ.
Spring 2008
Example (4)
300 C , PET rapidly cooled to
RT
rigid and transparent
heated to 100 C maintained at
that temp
and becomes translucent
then cooled down to RT again
 now, it is translucent rather
than transparent.
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Spring 2008
Influence of Copolymerization on Properties
•Homogeneous, amorphous
•Amorphous and glassy, rigid
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