1. Chap 6. 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

2. Measurements of average molecular weight (M.W.)
Number average M.W. (Mn): Total weight of all chains divided by # of chains
Weight average M.W. (Mw): Weighted average. Always larger than Mn
Viscosity average M.W. (Mv): Average determined by viscosity measurements. Closer to Mw than Mn
Weight Average Molecular Weight
Mw: Since most of the polymer mass is in the heavier fractions, this gives the average molecular weight of the most abundant polymer fraction by mass.

3. Number average molecular weight Mn

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High MW sensitive
Low MW sensitive
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5. Determination of Molecular Weight
Absolute Method
End-group Analysis
Colligative Property Measurements
Relative Method
Viscosity Measurements
The concentration dependence is observed to follow this functional dependence:
Neglect higher order term in c.
Plot of hsp/c vs c will yield [h] as y-intercept.
y-intercept
k = Huggins constant
k=2 for rigid uncharged spheres
k=0.35 for flexible polymers

6. Determination of Molecular Weight
Virtual Experiment
Case Western Reserve Univ. Polymer and Liquid Crystals
Viscosity Measurements
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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

7. Molecular Weight Distribution

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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?
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Size Exclusion Principle

9. Simple GPC c log10M log10M c Ve c log10M DRI degas pump injector
It is all smoke and mirrors to the physical chemist, but darned if it doesn’t work!
Then again, if I have to be a plumber, shouldn’t I be paid more?
degas
pump
injector

10. Chap 7. 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 polymer-nonpolar 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.

11. Thermodynamics of polymer solubility
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 AB solution
Immicible
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
DGmix < 0
DGmix > 0 A B

12. For Small Molecules No = N1 + N2 Ω = No! / N1!·N2! S = klnΩ
Smix = -R[n1lnx1 + n2lnx2]
Two-dimensional lattice representation of a solution

13. Vi+1 = (No-xi) · Z(1-fi) · (Z-1)(1-fi) · (Z-1)(1-fi)···
For Macromolecules
No = N1 + xN2
Vi+1 = (No-xi) · Z(1-fi) · (Z-1)(1-fi) · (Z-1)(1-fi)···
1st
segment
2nd
3rd
4th
Vi+1 = (No-xi)Z(Z-1)x-2(1-fi)x-1
Ω = 1 / N2! (∏ vi) = 1 / N2! (∏ vi+1) N2
i=1
N2-1
i=0
∆Smix = -k(N1 ln N1/N1 +xN2) +
(N2ln xN2/N1+XN2)
∆Smix = -R(n1lnØ1 + n2lnØ2)
Two-dimensional lattice representation of a polymer molecule in solution

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Solubility Parameter
The solubility parameter is defined as:
H  E = 12(1  2)2 (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.
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15. Hansen’s 3-D Solubility Parameter
internal energy on vaporization
Ev = Eh + Ed + Ep
The cohesive energy, δ 2 , is divided into three parts:
dispersion forces (δd )
2) polar forces ( δp )
3) hydrogen bonding ( δH )

16. 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)

17. Chap 8. Transitions in Polymers
Glass Transition
PMMA, PS  hard, rigid glassy plastics at RT when heated to 125C, become rubbery
Polybutadiene
Polyethylacrylate rubbery at RT, when cooled in Liq. N2
Polyisoprene 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.

18. 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.
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.

19. 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

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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.
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21. DTA & DSC Images and Sample data
DSC sample data
DTA sample data

22. Main factor of Tg Free volume of the polymer vf.
Free volume vf = v vs
v: specific volume of polymer mass
vs: volume of solidly packed molecules
* Pressure가 높아지면 vf가 작아짐. Tg
2. Attractive forces between molrcules.  Tg

23.  Tg Eo Silicone 7.3 -120 ~ 0 PE 7.9 -85 3.3 PTFE 6.2 >20 4.7
3. Internal mobility of chains (= freedom to rotate about bond)  Tg Eo
Silicone
7.3
-120
~ 0 PE
7.9
-85
3.3
PTFE
6.2
>20
4.7

24. 4. Stiffness of the materials Young’s Modulus E may be written as:
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.

25. Surfing to the internet For further details about Tg,
Tg of Copolymer
T : Kelvin temperature
1, 2 : polymer 1 and 2
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&

26. Example 4) Nylon n Tm  TS water cont

27. Example 5)
H-bonding Hm
PU : O (Swivel)  flexibility
Extra NH in polyurea  more extensive H-bond. Hm

28. Example 6)
 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.

29. Influence of Copolymerization on Properties
 homogeneous, amorphous
 amorphous and glassy, rigid