고분자 물성 (자료 3) 울산대학교 화학과 정 한 모

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”

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

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

for monodisperse : 1 (2) Weight average molecular weight: Mw 예) 분자량 10000; 60개, 100; 40개 60 x 10000 40 x 100 Mw = x 10000 + x 100 60 x 10000 +40 x 100 60 x 10000+40 x 100 = 0.993 x 10000 + 0.007 x 100 = 9935 ★ 분자량 10000인 분자의 중량분율이 0.993 : Mw가 의미 ★ 측정 : by light scattering ● Mw/Mn : polydispersity index for monodisperse : 1

a : 0.5∼1.0 ; function of solvent and polymer (3) Viscosity average molecular weight ∑ Nx Mxa+1 Mv = 1/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

Example 1 (p 56)

Example 2 (p 57)

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

(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

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

• 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 , 10-3 g/cm3 freezing point depression : 0.0002 ℃

• Osmotic pressure

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

(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

• 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

• 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

• 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 )

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

Example 3 (p 66)

● 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 = 0.137 and [ŋ] = 0.580 dL/g ∴ k’ = 0.408

(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)

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

● 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

● 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

- - - - - - ● 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

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?

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

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

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

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 ↓

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

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

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 = 0.4889 (J/cm3)1/2 = 0.4889 (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

- - - - - - - - 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

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

Groups ∑Ei (J/mol) ∑Fi ((J*cm3)1/2/mol) ∑Vi (cm3/mol) Example) M = 142.2 g/mol = 1.045 g/cm3 V = 136 cm3/mol Groups ∑Ei (J/mol) ∑Fi ((J*cm3)1/2/mol) ∑Vi (cm3/mol) 4-CH2- 4ⅹ4190 = 16760 4ⅹ272 = 1088 4ⅹ16.45 = 65.8 2-CH3 2ⅹ9640 = 19280 2ⅹ438 = 876 2ⅹ22.8 = 45.6 1 -5580 -190 4.75 1 13410 634 21.0 ∑Ei = 43870 ∑Fi = 2408J ∑Vi = 137.15 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

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)2 (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

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 + δh2 (7.8) EV V Ed EP Eh

• 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

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

n1 X1 n1 X1 + n2 X2 n1 1 n1 X1 + n2 X2 5. Flory – Huggins theory • Lattice model S S = -R ( n1 Ø1 + n2 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 = 80 n2 = 20 x1 = 1 x2 = 1 Fig 7.2 (b) n1 = 80 n2 = 1 x2 = 1 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

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

• The process of dissolution written in terms of the change in contacts ; [1,1] + [2,2] 2 [1,2] easily derived (other textbook) H = RT Ø2 n1 X1 (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

(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

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

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

• 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.

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.

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

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