1. 고분자 물성 (자료 3)
울산대학교 화학과
정 한 모

2. Chapter VI . Characterization of molecular Weight
1) 분자량과 기계적 성질
Dependence of mechanical strength on polymer molecular weight.
● 분자간 인력이 작은 polyethylene의 경우 : 수십∼수백만
● 분자간 인력이 큰 polyamide의 경우 : 수만
★ 분자량↑ ⇒ 가공성↓
“Compromise between processability and physical properties”

3. unimodal or bimodal 2) Polymer molecular weight is polydisperse :
Distribution of molecular weights in a typical polymer sample.
Weight fraction
Molecular weight

4. (1) Number average molecular weight: Mn
예) 분자량 10000; 60개, 100; 40개
Mn = x x 100 = 6040
측정 : from colligative properties,
- freezing point depression
- boiling point elevation
- vapor pressure lowering

5. for monodisperse : 1 (2) Weight average molecular weight: Mw
예) 분자량 10000; 60개, 100; 40개
60 x x 100
Mw = x x 100
60 x x x x 100
= x x = 9935
★ 분자량 10000인 분자의 중량분율이 : Mw가 의미
★ 측정 : by light scattering
● Mw/Mn : polydispersity index
for monodisperse : 1

6. a : 0.5∼1.0 ; function of solvent and polymer
(3) Viscosity average molecular weight
∑ Nx Mxa+1
Mv = /a
∑ Nx Mx
a : 0.5∼1.0 ; function of solvent and polymer
일반적으로 Mv ≅ Mw (within 10∼20%)
• Mv can be measured easily with cheap equipment :
Generally used for process control

7. Example 1 (p 56)

8. Example 2 (p 57)

9. Determination of molecular weight
1 ) General
(1) Absolute method : measured quantities are
theoretically related to the average molecular weight
• End group analysis : Mn
• Colligative property measurement : Mn
- freezing point depression
- boiling point elevation
- osmotic pressure
• Light scattering : Mw

10. (2) Relative method : relation must be established by
calibration with one of the absolute method
• Viscosity : Mv
• Gel permeation chromatography :
Mn , Mw ,and molecular weight distribution

11. 2 ) Absolute method
(1) End group analysis : Mn
• Should know the nature of end group
• Range : Mn < 10,000
Molecular weight ↑ end group ↓ sensitivity ↓
(2) Colligative property measurement : Mn
• The property that depends on the lowering of the
chemical potential of a solvent by the introduction
of a solute, regardless of their size and shape

13. • Freezing – point depression and boiling – point
elevation require precise measurements of very
small temperature differences.
These difficulties have prevented their widespread
application
(for example , Mn : 25,000 , g/cm3
freezing point depression : ℃

14. • Osmotic pressure

15. • • • • π C C Range : 50,000 < Mn < 1,000,000
low molecular weight π ↓ → precision ↓
polymer sneak

16. (2) Light scattering : Mw
• If polymer molecules are dissolved in a solvent,
the light scattered by the polymer far exceeds
that scattered by the solvent and is and absolute
measure of molecular weight.
• Range : 10,000 < Mw < 1,000,000
• Hard and tedious method
cylindrical sample container
Monochromic
light beam
Zimm plot at various
angle and concentration
Movable photocell

17. • Viscosity is increased sensitively by dissolved polymer
2 ) Relative method .
(1) Viscosity
• Viscosity is increased sensitively by dissolved polymer
• Inexpensive, rapid measurement
● Viscometer
• Ostwald : the same amount of liquid should
always be introduced
• Ubbelohde : independent of the solution in it

18. • Normally absolute viscosity , are not measured. Instead ;
● Solution viscosity terminology (p 64)
• Normally absolute viscosity , are
not measured. Instead ;
Quantity
Common unit
Common name
Recommended name η
Centipoise
Solution viscosity ηs
Solvent viscosity
ηr = η / ηs
Dimensionless
Relative viscosity
Viscosity ratio
ηsp = (η-ηs)/ηs = ηr - 1
Specific viscosity -
ηred = ηsp /c = ηr – 1/c
Deciliters/gram
Reduced viscosity
Viscosity number
ηinh = ln ηr /c
Inherent viscosity
Logarithmic viscosity number
[η] = lim ηred = lim ηinh
Intrinsic viscosity
Limiting viscosity number
C →0
C →0

19. • For monodisperse : Mark – Houwink – Sakurada ( HHS) relation
● Mv vs [ ]
• For monodisperse : Mark – Houwink – Sakurada
( HHS) relation
• MHS constant : depends on polymer, solvent, T.
K : 0.5 ~ 5 x 10-4
a : 0.5 ~ 1.0
( a = 0.5 at θ temperature in θ solvent )

20. • For polydisperse
[ ] = K (Mv )a
Example 4 (p 66)
a = 0.72

21. Example 3 (p 66)

23. ● Huggins equation
The tedious process, where viscosity should be
measured at various concentrations, can be omitted
if the following equation is used
k’ turns out to be approximately equal to 0.4 for
a variety of polymer-solvent systems
k’’ = k’ – 0.5
In example 3;
ŋred vs c : slope = 0.137
k’[ŋ]2 = and [ŋ] = dL/g
∴ k’ = 0.408

24. (2) Size exclusion chromatography (SEC)
● Principle
sample
Small molecules visit every pore
The larger the molecule, the less time it spends
inside the gel
The largest emerge first
rigid porous gel
(highly crosslinked porous polystyrene
or porous glass)
gel permeation chromatography (GPC)

25. concentration detector
● Equipment
column : ⅜” diameter, 3~10 ft long
injection
part
0.5~3mL of
a 0.05~0.1%
solution
concentration detector
Pump : 1000~4000 psi
2~3 mL/min
on-line
intrinsic
viscosity
measurement
Solvent
reservoir
chart recorder
collector
flask
(Prep-GPC)
mutiangle light
scattering photometer
absolute molecular
weight
Amount of
polymer
eluted
elution volume
molecular weight

26. ● Data analysis relative to PS (or other polymer)
SEC is a relative method
It needs relation between M and v
Depends on polymer, solvent, T, flow rate, column
Molecular weight relative to monodisperse
PS ( anionically polymerized) is generally reported,
not the absolute value of the polymer

27. ● Universal calibration
The molecular weight relative to (PS) standards can
be converted to the absolute value of the polymer
[ŋ] M vs ν gives a single curve for a wide variety
of polymers
[ŋ] can be measured by on-line intrinsic viscosity
measurement
if not ;
[ŋ]0M0 = K Ma · M
log([ŋ]M) ν
[ŋ]0M0 = [ŋ]M at a ν
polymer A : standard polymer B
[ŋ]0M0
[ŋ]
M =
from Handbook

28. - - - - - - ● Calibration method using a single polydisperse sample
known Mn and Mw
The relation between log M and ν is linear, and
therefore it can be characterized by two
parameters ; a slope and an intercept
Adjust by computer program
Log M - - - - - -
Polymer B
Polymer A ν

29. Chapter Vll. Polymer Solubility and Solution 1. Introduction
Thermodynamics and statistics of polymer solutions
Not to cover the subject in detail
Concentrate on topics of practical interest
Try to indicate, at least qualitatively, their
fundamental bases
Three factors of general interest ;
What solvents will dissolve what polymers?
How do the interactions between polymer and solvent influence the properties of the solution?
To what applications do the interesting properties of polymer solutions lead?

30. 2. General rules for polymer solubility
1) Like dissolves like
Polar polymer in polar solvent
Non polar polymer in nonpolar solvent
2) Mw ↑ => rate of dissolution ↓
solubility ↓
Can be used in fractionation ; in in
MeOH
PS in
toluene
Higher molecular weight
fraction precipitate first

31. 3) Crosslinking ↑ => Solubility ↓
Crystallinity ↑ => Solubility ↓
Solubility increases when heated to near Tm PE
- no solvent at room temperature
- dissolves in hydrocarbons near 100 ℃

32. 4) The effect of T on solubility
Upper critical solution temperature (UCST)
Lower critical solution temperature (LCST)
Solvent-rich and polymer-rich phase
Tie line

33. nonpolar material such as hexane ↑ Polar material such as water ↓
Example 1 (p 84)
n ↑ => Absorption of
nonpolar material such as hexane ↑
Polar material such as water ↓

34. 3. Thermodynamic of polymer solubility
polymer + solvent => solution
ΔG = ΔH - TΔS
ΔS :
positive
not so large as in the mixture of low molecular
weight materials
Mw ↑ => ΔS ↓ => solubility ↓ ΔH
generally positive except when there is
strong interaction such as hydrogen band

35. ΔEv : Molar change in internal energy on vaporization (cal/mol)
4. Solubility parameter
1) Cohesive energy density (CED) and solubility parameter
CED = (cal/cm3)
ΔEv : Molar change in internal energy on
vaporization (cal/mol)
Vl : Molar volume (cm3/mol)
A measure of the strength of secondary bonds
Evaluated by measuring the vapor pressure P as
a function of absolute temperature T :
Clausius-Clapeyron equation
ΔEv = ΔHv – Δ(PV) = ΔHv-RT for 1 mol
ΔEv Vl

36. 1 (cal/cm3)1/2 = 1 Hildebrand = 0.4889 (J/cm3)1/2 = 0.4889 (MPa)1/2
Solubility parameter
δ = (CED)1/2 (cal/cm3)1/2
1 (cal/cm3)1/2 = 1 Hildebrand = (J/cm3)1/2
= (MPa)1/2
Example) n-heptane
ΔHv = 8700 cal/mol
ρ = 0.68 g/cm3
M=100 g/mol
δ = =
= 7.4 (cal/cm3)1/2
methyl ethyl ketone : 9.3 H
water : 23.4 H M ρ
=> V = =147cm3/mol

37. - - - - - - - - 2) Solubility parameter of solvent mixture
δmix = = Σ Øi δi
3) Solubility parameter of polymer
Polymer solubility parameters are determined by
soaking lightly crosslinked samples in a series of
solvents of known solubility parameter.
The value of the solvent at which maximum swelling
is observed is taken as the solubility parameter of the
polymer
Σ yi viδi
Σ yi vi
volume fraction
mole fraction
molar volume
dissolve - -
uncrosslinked polymer - - - - - -
Swelling
lightly crosslinked polymer
Solubility parameter of solvent

38. 4) Group contribution method
Theoretical calculation of polymer physical properties,
such as solubility parameter
from Ecoh , V data of each group or
from F (molar attraction constant), V data of each
group

41. Groups ∑Ei (J/mol) ∑Fi ((J*cm3)1/2/mol) ∑Vi (cm3/mol)
Example) M = g/mol
= g/cm3
V = 136 cm3/mol
Groups ∑Ei (J/mol) ∑Fi ((J*cm3)1/2/mol) ∑Vi (cm3/mol)
4-CH ⅹ4190 = ⅹ272 = ⅹ16.45 = 65.8
2-CH ⅹ9640 = ⅹ438 = ⅹ22.8 = 45.6
∑Ei = ∑Fi = 2408J ∑Vi =
δ = ( )1/2 = ( )1/2 = 17.9 (J/cm3)1/2
δ = = = 17.7 (J/cm3)1/2
43780 J/mol
136 cm3/mol
2408 (J∙cm3)1/2/mol

42. 5) Hdissolution can be estimated from solubility
parameter ( the case where solute and solvent
do not form specific interaction like hydrogen
bond; Regular solution)
H E = Ø1Ø2 (δ1 - δ2) (7.2)
• Generally, in order to be dissolved ; rule of thumb
lδ1 – δ2l < 1 (cal/cm3)1/2
-based on visual observation of 0.5g polymer
in 5 cm3 of solvent at room temperature
• Too complex a phenomenon to be
described quantitatively with a single
parameter
• If there is a specific interaction, it
can be dissolved even when lδ1 - δ2l is
higher than 1. ~ =
If there is
no volume change in mixing
Volume fraction

43. 6) Hansen’s there-dimensional solubility parameter
• EV may be considered as the sum of
three individual contributions ; dispersion force,
dipole interaction, hydrogen bond
EV = Ed + EP + Eh =
δ2 = δd2 + δP2 + δh (7.8) EV V Ed EP Eh

44. • A polymer is characterized by values of
δd, δp, δh, and R.
• It has been found on a purely empirical
basis that if δd is plotted on a scale twice
the size as that used for δp and δh, all
solvents that will dissolve that polymer fall
within a sphere of radius R surrounding
the point (δd, δp, δh) for the polymer

45. Example 2 (p 90)
• In order to be dissolved, the contribution of each
term should be similar

46. n1 X1 n1 X1 + n2 X2 n1 1 n1 X1 + n2 X2 5. Flory – Huggins theory
• Lattice model S
S = -R ( n Ø1 + n Ø2 ) (7.10)
Ø1 = (7.10a)
Ø2 = (7.10b)
• For solvent, normally X1=1
For polymer, X2 is normally Xn (number average degree of
polymerization)
Fig 7.2 (a) n1 = n2 = 20
x1 = x2 = 1
Fig 7.2 (b) n1 = n2 = 1
x2 = x2 = 20
Volume fraction (instead of mole faction)
moles of solute
moles of solvent
n1 X1 + n2 X2
n1 X1
n1 X1 + n2 X2
n1 1
number of segment in the species

47. Example 3 (p 91~92)
Xps = = 962
Xppo = = 833

49. • The process of dissolution written in
terms of the change in contacts ;
[1,1] + [2,2] [1,2]
easily derived (other textbook)
H = RT Ø2 n1 X (7.11)
when n1 moles of solvent (with X1) and
n2 moles of polymer (with X2) is mixed
: Flory – Huggins interaction parameter
The energy change (in units of RT) that
occurs when a mole of solvent molecules
is removed from the pure solvent and is
immersed in an infinite amount of pure
polymer

50. (n1X1 + n2 X2) • v • Ø1Ø2 (δ1-δ2)2 = RT Ø2 n1 X1
• H = (7.2) = (7.11)
(n1X1 + n2 X2) • v • Ø1Ø2 (δ1-δ2)2 = RT Ø2 n1 X1
total lattice number
(mol)
each lattice volume
(cm3/mol)
normally 100 cm3/mol
(7.2)
(cal/cm3)
= • • Ø1 = 1 Ø1
• Empirically ;
• For dissolution ; ~
0.34 +
≤ 0.5

51. ● Flory – Huggins theory cannot explain
LCST.
Advanced theories
• UNIQUAC
• UNIFAC

52. 6. Properties of dilute solutions
1) Conformation in solvent
• Entanglements between molecules starts when ;
Berry number Be = [ ]C > 1
• Normally this equation is satisfied
when concentration is more than several %
• Conformation of polymer in solvent

53. • Multi-viscosity motor oil (oil + polymer)
viscosity of solution
viscosity of solvent
Volume fraction of polymer sphere
• Good solvent↑⇒ Ø↑⇒ ↑ •
• Multi-viscosity motor oil (oil + polymer)
T ↑ ⇒ oil viscosity ↓ ⇒ constant viscosity
polymer Ø ↑ by the compensation of
two phenomena
• Paint formulation ;
polymer + Good solvent with high b.p.
poor solvent with low b.p.
Poor solvent gives low viscosity when applied,
however it vaporize first, then viscosity increases
by good solvent. So, the polymer solution does not
flow easily after application.

54. 2) Plasticizer
• Miscible low molecular weight material
• Soften the plastic
• PVC
• dioctyphthalate (DOP)
• Migration can be reduced by
higher molecular weight plasticizer
or polymeric plasticizer such as poly(caprolactone)
• Mal-odor in new car
• A cause of endocrine disruptor (환경호르몬)
• Reduction of inflammability by DOP can be
compensated when chlorinated wax or
tricresyl phosphate is used as a plasticizer instead.

55. ● Lubricant
• Not mixed homogeneously but lies
at the interface between polymer melt
and manufacturing machine
Flowbility ↑
Processbility ↑

56. 감사 합니다