2008
Sep. 19, 2008
Molecular Weight & Polymer
Solutions
Chemical and Bioengineering
Konkuk University
Number average and weight average
moleculart weight
 몇몇 천연 고분자 (monodisperse):
all polymer molecules  같은 분자량
 합성 고분자 (polydisperse):
•
Polydisperse - a polymer that exists over a wide range of molecular
masses
•Characteristic of man-made polymers.
 고분자의 기계적 성질에 대한 분자량의 영향
매우 작은 분자량 ; poor mechanical property
매우 큰 분자량 ; too tough to process
최적 분자량; 105~106 for vinyl polymer
15,000~20,000 for polar functional group containing polymer (polyamide)
 분자량 결정 (Methods to determine molecular weight)
a. Absolute method :
mass spectrometry, colligative property
end group analysis, light scattering, ultracentrifugation
b. Relative method : solution viscosity
c. Fractionation method : GPC
Polymer
mass
3-1-1. 평균 분자량
A. number average molecular weight (
)
(colligative property and end group anaylsis)
B. weight average molecular weight (
)
(light scattering)
C. z average molecular weight (
)
(ultracentrifugation)
D. general equation of average molecular weight :
( a=0 ,
E.
>
>
a=1 ,
a=2 ,
)
3-1-2. Property of Molecular weight and
polymer
molecular weight determines the property: the attractive force between
molecular change
identity chemical structure : chain length, surface, attractive force rise
molecular weight increase  polymer property increase
Threshold molecular weight: the increase rate slow , differ depend on the
polymer type(structure)
Polyethylene(nonpolar polymer): low attractive force, high threshold
Polyamide (H-bond polymer): high attractive force, low threshold
 The effect of the average molecular weight
the concentration solution viscosity
Over the critical molecular weight suddenly rise
Entanglement molecular weight: Because of the bridging
phenomenon, the viscosity suddenly rise
Polydispersity index (PDI)
Measure of the distribution of molecular mass in a given
polymer sample.
The PDI calculated is the weight average molecular weight
divided by the number average molecular weight.
The PDI has a value always greater than 1,
But as the polymer chains approach uniform chain length, the
PDI approaches unity (1).
D. Polydispersity index : width of distribution
polydispersity index (PI) =
/
≥1
E. Example of molecular weight calculation
a. 9 moles, molecular weight (
5 moles, molecular weight (
) = 30,000
) = 50,000
b. 9 grams, molecular weight (
5 grams, molecular weight (
) = 30,000
) = 50,000
3-1-2. Polymer solution
A. Two-step process of polymer dissolution
first step : the solvent diffuses into polymer masses to make
a swollen polymer gel
second step : swollen polymer gel breaks up to solution
B. Thermodynamics of solubility : Gibb's free energy relationship
ΔG < 0 : spontaneously dissolve
T and ΔS are always positive for dissolving process
Conditions to be negative ΔG,
ΔH must be negative or smaller than TΔS
C. Solubility parameter : δ
ψ1, ψ2 = volume fraction
ΔE1/V1, ΔE2/V2 = cohesive energy densities (응집 에너지 밀도)
δ1, δ2 = solubility parameter
if
, then
D. Small's and Hoy's G parameter
a. Small(designated G derived from Heat of vaporization)
(d: density, M: molecular weight of unit)
ex) polystyrene :
b. Hoy(designated G based on vapor pressure measurement)
ex) polystyrene :
Group molar attraction constants
E. Hydrodynamic volume of polymer molecules in solution
a. polymer-polymer interaction
b. solvent-solvent interaction
c. polymer-solvent interaction
d. polymer structure (branched or not)
e. brownian motion
r = end-to-end distance
s = radius of gyration
Figure. Coil molecular shape
3-2.
Number
Measurement
Average
Molecular
Weight-
3-2-1. End-group Analysis
A. Molecular weight limitation up to 50,000
B. End-group must have detectable species
a. vinyl polymer : -CH=CH2
b. ester polymer : -COOH, -OH
c. amide and urethane polymer : -NH2, -NCO
d. radioactive isotopes or UV, IR, NMR detectable functional group
e. MW of linear polymer
C.
n / end-group moles per 1 g (n=number of end-group)
COOH: 염기로 페놀프탈레인 end point 까지 적정
OH: acetylation 후 적정
D. Requirement for end group analysis
1. The method cannot be applied to branched polymers
2. In a linear polymer there are twice as many end of the chain and groups as
polymer molecules
3. If having different end group, the number of detected end group is average MW
4. End group analysis could be applied for polymerization mechanism identified
E. High solution viscosity, low solubility, steric hindrance :
Mn = 5,000 ~ 10,000
Ex. A 0.5 g sample of an unsaturated polyester resin was reacted with excess
acetic anhydride. Titration of the reaction mixture with 0.0102 M KOH
required 8.17 ml to reach the end point. What is the number average
molecular weight?
불포화 polyester 0.5 g이 과량의 acetic anhydride와 반응 시킨 후, 반응 혼합물을
0.0102 M KOH로 적정하니 8.17 ml의 KOH가 소모됨. Polyester의 수평균
분자량은?
Ex.
What is the DP of a sample of polyester prepared from 4-hydroxybenzoic
acid if the acid number, determined with standard KOH solution, is 11.2?
기본 단위가 (CH4O2)이고, 하나의 carboxyl 그룹을 말단기로 갖는 polymer의 경우,
표준 KOH 용액으로 부터 조사된 acid number가 11이라면 이때의 DP는?
(Acid number: mg KOH/g polymer)
KOH: 56.1g/mol
3-2-2. The measure of colligative property
 용액의 총괄적 성질 (colligative property)
Colligative properties are properties of solutions that depend on the number
of particles in a given volume of solvent and not on the mass of the
particles.
the freezing point depression, the boiling point elevation, the steam
pressure depression, the osmotic pressure
 The mole number of polymer  average molecular weight
This equation show that the concentration equation of solvent was the chemcal
potential difference between the solution of solvent and pure solvent
수평균 분자량 측정
(1) Boiling-point elevation (Ebulliometry)
A2 : second virial coefficient
: boiling point elevation
: the latent heats of vaporization
C : the concentration in grams per cubic centimeter
R : gas constant
limitation of
: below 30,000
(2) Freezing-point depression (Cryoscopy)
: freezing-point depression,
T : freezing point
: the latent heats of fusion
(3) 분리막 삼투압법 (Membrane Osmometry)
According to van't Hoff equation
용매와 용액의 높이차 (cm)
p=rg h
limitation of
: 50,000~2,000,000
The major error arises from low-MW
species diffusing through the
membrane.
i. Static Osmometer
ii. Dynamic Osmometer
(4) 증기상 삼투압법 (Vapor Pressure Osmometry)
 Raoult의 법칙: 이상용액에서 각 성분의 분압은 몰분율에 비례
The equilibrium state:
Solvent pressure of both sides equal, the
Temperature differ
 Gap of temperature  The steam pressure
drop
평형상태:
양쪽 방울 용매 증기압 동일
온도 상이
 온도차  증기압 강하 정도
 Raoult의 법칙: 이상용액에서
각 성분의 분압은 몰분율에 비례
Raoult’s law: the vapor pressure of an
ideal solution is dependent on the
vapor pressure of each chemical
component and the mole fraction of
the component present in the
solution
Vapor Pressure Osmometry
The measuring vapor pressure difference of solvent and solution drops.
λ : the heat of vaporization per gram of solvent
m : molality
limitation of
: below 30,000
Calibration curve is needed to obtain MW of polymer sample
Standard material : Benzil
Mw 30,000 over: the separation osmotic
pressure method
Mw 30,000 under: steam osmotic pressure
method
The average
molecular weight
(5) Mass Spectrometry
A. Conventional mass spectrometer for low molecular-weight compound
energy of electron beam : 8 -13 electron volts(eV)
The each polymer’s molecular
ionization
 the condensation phase-> gas
phase tranformation
 TOF (time-of-flight) MS: the
molecular ion mass measure
개개의 고분자 분자를 이온화
 응축상에서 기체상으로 변환
 TOF (time-of-flight) MS에서
분자이온질량 측정
B. Modified mass spectrometer for synthetic polymer
a. matrix-assisted laser desorption ionization mass spectrometry
(MALDI-MS)
b. matrix-assisted laser desorption ionization time-of-flight
(MALDI-TOF)
c. soft ionization
sampling: polymers are imbedded by UV laser absorbable organic
compound containing Na and K.
d.
,
are calculated by using mass spectra.
e. The price of this mass is much more than conventional mass.
f. Up to
= 400,000 for monodisperse polymers.
MS Analysis of p-Aminobenzyl Amine Conversion Product
CH2
NH2
NO2
CH2NH2
NH2
PrnD
CH2NH2
CH2NO2
NO2
NH2
2D SDS-PAGE and MALDI-TOF Mass Analysis
Peptides identical to PrnD
MALDI-TOF MS
Spot expected
to be PrnD
• MS fingerprinting
• MS sequencing
1. 1329.656:
QPTLVTAER
2. 1710.910:
AFYRGWVDRVASER
3. 2021.235:
AVVMDRHCSHLGANLAD
2
1
3
 pQE 80L-PrnD is expressed in E. coli
MALDI-TOF Mass Analysis
Poly(methyl methacrylate): 수평균 분자량 6,400
3-3. Measurement of Weight Average Molecular Weight
3-3-1. Light Scattering
A. The intensity of scattered light or turbidity(τ) is depend on following factors
a. size, b. concentration, c. polarizability, d. refractive index, e. angle
f. solvent and solute interaction
g. wavelength of the incident light
: concentration
: refractive index of the solvent
λ : wavelength of the incident light
: Avogadro's number
: specific refractive increment
: function of the angle,θ
Zimm plot(after Bruno Zimm): double extrapolation of conc. and angle to zero
B. Light source
High pressure mercury lamp and laser light
C. Limitation of molecular weight(
) : 104~107
The light scattering of the particle
(a) When the scattering
particle was small
(a) When the scattering
particle was large
3-3-2. Ultracentrifugation
A. This technique is used
a. for protein (생체 고분자) rather than synthetic polymers
b. for determination of synthetic polymer’s
B. Principles: under the centrifugal field, size of molecules are
distributed perpendicularly axis of rotation
Distribution process: sedimentation
침강 속도: 분자량에 비례
침강평형방법, 침강속도방법
Sedimentation(침강 속도): proportion of molecular weight
침강평형방법, 침강속도방법
3-4. Viscosity: the method of relative molecular weight from the
assumption of the molecular size
1) 5% polymer solution: too sticky to flow
low molecular weight solution: easy flow
2) Viscosity: resistance of flow
long chain molecule: large friction
3-4-1. Viscosity & Molecular weight
IUPAC suggested the terminology of solution viscosities as following.
Relative viscosity :
: solution viscosity
: solvent viscosity
: flow time of solution
: flow time of solvent
Specific viscosity :
Reduced viscosity :
Inherent viscosity :
Intrinsic viscosity :
3-4. 점도법
3-4-2. 점도평균 분자량:
상대적 분자량
Mark-Houwink-Sakurada (MHS) equation
(K, a : viscosity-Molecular weight constant)
 Condition: Unperturbed state
a = 0.5
is closer to
than
3-5. Measuring Molecular Weight Distribution
3-5-1. Fractionation of Molecular weight
 Fractional Solution
Soxhlet-type extraction by using mixed solvent
Reverse GPC: from low MW fraction to high MW fraction
Inert beads are coated by polymer sample
 Fractional Precipitation
Dilute polymer solution is precipitated by variable non-solvent mixture
Precipitate is decanted or filtered
Reverse fractional solution: from high MW fraction to low MW fraction
 Thin-layer Chromatography (TLC)
Alumina- or silica gel coated plate
Low cost and simplicity
Preliminary screening or monitoring polymerization processes
3-5-2. Gel Permeation Chromatography(GPC)
A. GPC or SEC (size exclusion chromatography)
a. GPC method is a modified column chromatography
b. Packing material: Poly(styrene-co-divinylbezene), glass or silica bead
swollen and porous surface
c. Detector: RI, UV, IR detector, light scattering detector
d. Pumping and fraction collector system for elution
e. By using standard (monodisperse polystyrene), we can obtain
,
Schematic diagram of GPC separation
Schematic representaion of a GPC system