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2. Mol Wt Determination

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(1)

Chapter 3 Chapter 3

Molecular Weight Molecular Weight

1. Thermodynamics of Polymer Solution

2. Mol Wt Determination

(2)

1. Weight, shape, and size of polymers 1. Weight, shape, and size of polymers

monomer – oligomer – polymer

dimer, trimer, ---

telomer ~ oligomer from telomerization (popcorn polymerization) telechelic polymer ~ with functional group

macro(mono)mer ~ with polymerizable group [wrong definition p72]

pleistomer ~ mol wt > 1E7

usual range of mol wt of polymers

25000 ~ 1E6

mol wt of chain polymers are higher

molecular weight molecular size

LS (solution) and SANS (bulk) determine size.

conformation Æ shape

(3)

2. Solution 2. Solution

ΔG

m

= ΔH

m

– T ΔS

m

ΔSm > 0 always

ΔHm > 0 almost always

“like dissolves like”

ΔHm = 0 at best (when solute is the same to solvent) if not, ΔHm > 0

ΔHm < 0 only when specific interaction like H-bonding exists

For solution, ΔHm < T ΔSm

m for mixing

f for melting (fusion)

(4)

Solubility parameter Solubility parameter

ΔH

m

= V

m

[(ΔE

1

/V

1

)

½

– (ΔE

2

/V

2

)

½

]

2

v

1

v

2

= V

m

1

– δ

2

]

2

v

1

v

2

ΔE ~ cohesive energy ~ energy change for vaporization

ΔE = ΔHvap – PΔV ≈ ΔHvap – RT [J]

ΔE/V ~ cohesive energy density [J/cm3 = MPa]

δ ~ solubility parameter [MPa½]

[MPa½] = [(106 N/m2)½] = [(J/cm3)½] ≈ [(1/2)(cal/cm3)½]

1: solvent

2: solute

Table 3.1 & 3.2

(5)

Determination of δ

from ΔHvap data ~ for low mol wt, not for polymers with solvent of known δ

swelling ~ Fig 3.1 viscosity ~ Fig 3.2

group contribution calculation

δ = ρ ΣG / M ~ Table 3.3

G ~ group attraction constant example p79

ΔE = ΔEdispersion + ΔEpolar (+ ΔEHB) δ2 = δdispersion2 + δpolar2 (+ δHB2 )

(6)

For solution,

ΔHm < T ΔSm

without specific interaction

δ1 = δ2 at best Æ ΔHm = 0 Æ ΔGm < 0

Δδ < 20 MPa½ (?) ~ for solvent/solvent solution

Δδ < 2 MPa½ ~ a rough guide for solvent/polymer solution

ΔSm smaller

Δδ < 0.1 MPa½ ~ for polymer/polymer solution

semicrystalline polymers not soluble at RT

positive ΔHf Æ ΔHf + ΔHm > T ΔSm

(7)

3. Thermodynamics of polymer solution 3. Thermodynamics of polymer solution

Types of solutions

ideal soln ΔHm = 0, ΔSm = – k (N1 ln n1 + N2 ln n2) regular soln ΔHm ≠ 0, ΔSm = – k (N1 ln n1 + N2 ln n2) athermal soln ΔHm = 0, ΔSm ≠ – k (N1 ln n1 + N2 ln n2) real soln

ideal solution

ΔG1 = μ1 – μ1o = RT ln n1 ΔG2 = μ2 – μ2o = RT ln n2

ΔGm = (N1/NA)ΔG1 + (N2/NA)ΔG2

= kT (N1 ln n1 + N2 ln n2)

ΔHm = 0 Æ ΔSm = – k (N1 ln n1 + N2 ln n2)

Eqn (3.9) corrected n: mol fraction

N: number of molecules n1 = N1/(N1+N2)

Eqn (3.12)

(8)

Δ Δ S S

mm

from statistical thermodynamics from statistical thermodynamics

Lattice model

Filling N1 & N2 molecules in N1+N2 = N0 cells

volume of 1 ≈ volume of 2

Boltzmann relation, Sconfigurational = k ln Ω

Ω ~ number of (distinguishable) ways

Ω12 = (N1+N2)!/N1!N2! ΔSm = S12 – S1 – S2

= k ln Ω12 = k ln [(N1+N2)!/N1!N2!]

Ë Sterling’s approximation, ln x! = x ln x – x

ΔSm = k [(N1+N2) ln (N1+N2) – (N1+N2) – N1 ln N1 + ---

= – k (N1 ln n1 + N2 ln n2)

Fig 3.3(a)

S1 = k ln Ω1 = k ln (N1!/N1!) = 0 = S2

(9)

Δ Δ S S

mm

of polymer of polymer soln soln from stat thermo from stat thermo

developed by Flory & Huggins

polymer soln = mixture of solvent/polymer

volume of 1 << volume of 2 (by x)

A polymer molecule with x mers (repeat units) takes x cells.

volume of 1 mer ≈ volume of 1 solvent molecule

Filling N1 solvents & N2 polymers in N1+ xN2 = N0 cells

ΔSm = S12 – S1 – S2 = k ln [Ω121Ω2]

Number of ways to fill the (i+1)th chain in N0 cells νi+1 = (N0-xi) z(1-fi) (z-1)(1-fi) --- (z-1)(1-fi)

1st 2nd 3rd xth segment (mer) z ~ coordination number (# of nearest neighbor) fi ~ probability of a site not available ≈ xi/N0

Fig 3.3(c)

(10)

(cont’d)

νi+1 = (N0-xi) z(1-fi) (z-1)(1-fi) --- (z-1)(1-fi)

= (N0–xi) z (z–1)x-2 [1–(xi/N0)]x-1

= (N0–xi) (z–1)x-1 [(N0xi)/N0]x-1

= (N0–xi)x [(z–1)/N0]x-1

= {(N0–xi)!/[N0–x(i+1)]!} [(z–1)/N0]x-1

(N0-xi)! / [N0-x(i+1)]! =

(N0-xi)(N0-xi-1)(N0-xi-2)----(3)(2)(1) (N0-xi-x)(N0-xi-x-1)---(3)(2)(1)

= (N0-xi)(N0-xi-1)----(N0-xi-x+1)

(11)

ΔSm = S12 – S1 – S2 = k ln [Ω121Ω2]

Ω12 ~ # of ways to fill N1+N2 molecules in N0 cells

= (1/N2!) Π νi+1 (from i = 0 to N2-1) (x 1)

= (1/N2!) {[N0!/(N0–x)!][(N0–x)!/(N0–2x)!] --- [(N0–(N2–1)x)!/(N0–N2x)!]} [(z–1)/N0]N2(x-1)

= (1/N2!) [N0!/(N0–N2x)!] [(z–1)/N0]N2(x-1)

= [N0!/ N1!N2!] [(z–1)/N0]N2(x-1) << [N0!/ N1!N2!]

Ω1 ~ # of ways to fill N1 solvent molecules in N1 cells = 1 Ω2 ~ # of ways to fill N2 polymer molecules in xN2 cells

~ xN2 mers in xN2 cells ~ Ω2 = 1? No

= (1/N2!) [(xN2)!/(xN2–N2x)!] [(z–1)/xN2]N2(x-1)

= [(xN2)!/N2!] [(z–1)/xN2]N2(x-1)

(12)

Allcock p412

Sc = ΔSdis + ΔSm = (a) + (b)

ΔSdis for disorientation ~ equiv to S2 2) ~ Ω with N1 = 0 ΔSm = Sc – ΔSdis

ΔSm ΔSdis

S = 0 S = Sc = S12

(13)

(con’t)

ΔSm = k ln [Ω122]

= k ln {[N0!/N1!xN2!] [xN2/N0]N2(x-1)}

Ë Sterling’s approximation, ln x! = x ln x – x

= k {– N1 ln [N1/N0] – N2 ln [xN2/N0]}

= – k [N1 ln v1 + N2 ln v2]

xÇ (mol wt Ç) Æ N2 È Æ ΔSmÈ

for polymer/polymer soln, ΔSm even smaller (N1 & N2 È)

Flory-Huggins theory

volume fraction instead of mole fraction

Eqn (3.16) v ~ volume fraction

Eqn (3.19)

(14)

ΔSm = – k [N1 ln v1 + N2 ln v2]

xÇ (mol wt Ç) Æ ΔSmÈ

for polymer/polymer soln, ΔSm even smaller

Examples (for the same v1 = v2 = .5)

case 1: N1=10000, N2=10000, x1 = x2 = 1

ΔSm = – k [10000 ln .5 + 10000 ln .5] = – 20000 k ln .5 case 2: N1=10000, N2=100, x2 = 100; ΔSm = – 10100 k ln .5 case 3: N1=10000, N2=10, x2 = 1000; ΔSm = – 10010 k ln .5 case 4: N1=10, N2=10, x1 = x2 = 1000; ΔSm = – 20 k ln .5

more examples p85

(15)

Δ Δ H H

mm

of polymer of polymer soln soln

regular solution

ΔHm ≠ 0, ΔSm = – k (N1 ln n1 + N2 ln n2) ΔHm = N1 z n2 Δw

Δw ~ energy change per contact = w12 – [(w11+w22)/2]

for polymer solution

ΔHm = k T N1 v2 χ

χ ~ Flory-Huggins interaction parameter [dimensionless]

kTχ ~ interaction energy (solvent in soln – in pure solvent)

χ È Æ ΔHm È Æ solvent power Ç

ΔHm = Vm 1 δ2]2 v1v2 ~ k T N1 v2 χ Æ χ = β1 + (V1/RT) [δ1 δ2]2

β1 ~ entropic 0

χ = χ1 = χ12 Eqn (3.21)

Table 3.4 Eqn (3.28)

1---1

1---2 2---2

See Young pp143-144

(16)

Δ Δ G G

mm

~ Flory ~ Flory - - Huggins Huggins Eqn Eqn

ΔG

m

= ΔH

m

– T ΔS

m

= kT [N

1

ln v

1

+ N

2

ln v

2

+ χN

1

v

2

]

useful for predicting miscibility (solubility) drawbacks

no volume change self-intersection

for concentrated solutions only (high v2) χ is not purely enthalpic

example calculation p85

Eqn (3.22)

See Young p145

(17)

Partial molar free energy of mixing for solvent Partial molar free energy of mixing for solvent

ΔG

1

= ∂ΔG

m

/∂m

1

from Flory-Huggins eqn

ΔGm = kT [N1 ln v1 + N2 ln v2 + χN1v2]

Ë N1 = NAm1, v1 = m1/(m1+xm2), v2 = xm2/(m1+xm2), kNA = R

ΔG1 = RT [ln (1 – v2) + (1 – 1/x)v2 + χv22]

other form of Flory-Huggins eqn

ΔG

1

= μ

1

– μ

1o

= RT ln a

1

= RT ln n

1

γ

1

ΔG

1

= μ

1

– μ

1o

= (μ

1

–μ

1o

)

ideal

+ (μ

1

–μ

1o

)

xs

¾ ideal: (μ1–μ1o)ideal = RT ln n1

¾ excess: (μ1–μ1o)xs = RT ln γ1

m: # of moles

Eqn (3.23)

a: activity

γ: activity coeff.

n: mol fraction

Eqn (A) Sup 2 Young p145-149

(18)

Thermo of

Thermo of dilute dilute polymer polymer soln soln

dilute polymer soln

polymer chains separated by solvent FH theory does not hold

In FH theory, chains are placed randomly

Modification ~ Flory-Krigbaum theory

for dil polym soln

n2 = v2/x

É v2 = xN2/(N1+xN2) ≈ xN2/N1 (N1 >> xN2) É n2 = N2/(N1+N2) ≈ N2/N1 (N1 >> N2)

ln v1 = ln (1 – v2) = – v2 – v22/2 – v23/3 – --- ln n = ln (1 – n ) = – n – n 2/2 – n 3/3 – ---

(19)

from Eqn (3.23)

ΔG1 = μ1–μ1o = RT [– v2 – v22/2 + v2 + v2/x + χv22]

= –RT(v2/x) + RT(χ – ½)v22 Eqn (3.23-1)

from Eqn (A)

ΔG1 = μ1–μ1o = RT ln n1 + (μ1–μ1o)xs

= –RT(v2/x) + (μ1–μ1o)xs By Flory-Krigbaum

ΔG1xs = (μ1–μ1o)xs = ΔHxs – T ΔSxs

= RTκ v22 – T Rψ v22 = RT(κ – ψ) v22 ΔG1xs = RTψ [(θ/T) – 1] v22 = RT (χ – ½) v22

When T = θ, χ = ½ Æ ΔG1xs = 0 Æ ΔG1= ΔG1ideal

θ-condition (Flory condition) ~ becomes ideal solution

When T > θ, χ < ½ Æ ΔG1xs < 0 Æ soluble

κ = ψθ/T

Table 3.4

χ = ½ for ideal

(20)

Chapter 3 Chapter 3

Molecular Weight Molecular Weight

1. Thermodynamics of Polymer Solution

2. Mol Wt Determination

(21)

4. Mol wt and mol wt distribution 4. Mol wt and mol wt distribution

mol wt distribution

xi ~ number (mol) of i = Ni i ~ molecule having Mi

wi ~ weight (amount) of i = NiMi

Usually xi and wi are fractions xi = Ni/ΣNi , wi = NiMi/ΣNiMi Not in this textbook

Ni xi

Mi

Mi wi

NiMi

(22)

mol wt averages mol wt averages

number-average mol wt

(수평균 분자량)

weight-average mol wt

(중량평균 분자량)

z-average mol wt

viscosity-average mol wt

(점도평균 분자량)

= total weight/total number

~ weight of 1 molecule

a dep on solvent & temp

Mn, Mw, Mz are absolute mol wts.

z+1-average mol wt, etc

Eqn (3.31-34)

(23)

mol wt distribution (MWD) mol wt distribution (MWD)

Mol wt of polymers almost always has a distribution.

polydisperse (다분산성) ↔ monodisperse (단분산성) polydispersity index (PDI) = Mw/Mn

other indexes; Mz/Mw, Mz+1/Mz

Most probable distribution (Flory(-Schultz) distribution)

Mn/Mw/Mz = 1/2/3 ideal, not probable practically Mw/Mn > 2 p86 wrong!

Fig 3.4

(24)

mol wt & properties mol wt & properties

mol wt independent properties

density, refractive index, solubility, stability, etc dep on repeat unit (chemical) structure

M

n

dependent properties

thermal and mechanical properties

Tg, Tm, strength, modulus, etc

dep on segmental motion, chain-end concentration

Tg = Tg – A/Mn Tg

(25)

mol wt & properties (2) mol wt & properties (2)

M

w

dependent properties

(melt) viscosity

dep on whole chain motion

MWD dependent properties

shear-rate sensitivity of viscosity dep more on larger molecules

log η

log Mw

(26)

5. Determination of

5. Determination of M M

nn

end-group analyses

step polymers

HOOC---COOH H2N---NH2 HO---OH titration or spectroscopic methods

chain polymers

RMMMM--- (R=initiator fragment) spectroscopic methods

accurate but limited

(27)

Colligative property measurements

colligative (collective) property ~ property that depends only on the number of molecules

osmotic pressure, boiling point, freezing point, etc counting number & measuring weight Æ Mn

ΔG1 = μ1 – μ1o = RT ln a1 = RT ln γ1n1 For dilute polymer solution (c2 Æ 0)

Ë solvent behaves ideally, a1 ≈ n1

μ1 – μ1o = RT ln n1 = RT ln (1–n2)

= –RT[n2 + n22/2 + n23/3 + ---]

a: activity

γ: activity coeff.

n: mol fraction c: wt conc’n

(28)

n2 = N2/(N1+N2) ≈ N2/N1 = (N2/NA)/(N1/NA)

= m2/m1 = (m2/L)/(m1/L)

= (c2/M2)/(1/V10) [(g/L)/(g/mol)]/[(1/(L/mol)]

= (c2V10)/M2

μ1 – μ1o = –RT[n2 + n22/2 + n23/3 + ----]

= –RTV10[(1/M2)c2 + (V10/2M22)c22 + (V102/3M23)c23 --]

–(μ1 – μ1o)/V10 = RT [(1/M2) c2 + A2 c22 + A3 c23 + ----]

virial equation

A2 ~ 2nd virial coeff, A3 ~ 3rd virial coeff

for dilute polymer soln, c2 Æ 0

[CP/c] = RT/M

colligative property (CP)

CP/c

A2 RT/Mn

c: wt conc’n m: # of moles V10: molar vol M: mol wt

(29)

ebulliometry (bp elevation)

ΔTb/c = Ke [(1/Mn) + A2 c + A3 c2 + ----]

Ke calibrated with known mol wt

limited by precision of temperature measurement

useful only for Mn < 30000 not used these days

cryoscopy (fp depression)

ΔTf/c = Kc [(1/Mn) + A2 c + A3 c2 + ----]

Kc calibrated with known mol wt

limited by precision of temperature measurement

useful only for Mn < 30000 not used these days

Eqn (3.35)

Eqn (3.36)

(30)

membrane osmometry

static or dynamic method

useful for 30000 < Mn < 10E6

diffusion of solute

h Æ ρgh = π ~ osmotic pressure

μ1(1,P) = μ1(n1,P+π)

μ10(P) = μ10(P) + ∫PP+π V10dP + RT ln a1 πV10 = RTV10 [(1/Mn)c + A2 c2 + A3 c3 ----]

π/c = RT [(1/Mn) + A2 c + A3 c2 + ----]

Eqn (3.41)

(31)

Determination without extrapolation?

πV10 = RTV10 [(1/Mn)c+A2 c2+ --] = –RT ln a1 = –(μ1–μ1o) μ1–μ1o = –RT(v2/x) + RT(χ – ½)v22

π = RT(v2/xV10) + RT(χ – ½)v22/V10

Ë v2 ≈ xN2/N1, V = (N1/NA)V10, Mn = ΣNiMi/ΣNi = M2/(N2/NA) Ë c2 = M2/V = MnN2/NAV, ρ2 = V2/Mn, x = V2/V1

π/c = RT(1/Mn) + RT (χ – ½)(1/V1ρ22) c

= RT [1/Mn + A2 c]

At θ-condition, χ = ½ , A2 = 0

no conc’n dependence

determination at 1 conc’n ~ need no extrapolation hard to do ~ not a good solvent (ppt)

Eqn (3.23-1) dil soln

Eqn (3.26)

Fig 3.5

(32)

vapor phase (pressure) osmometry (VPO)

P10 –P1 = ΔP

~ vapor pressure drop due to solute

ΔP Æ ΔT Æ Δr

Δr/c = KVPO[(1/Mn) + A2 c ----]

KVPO calibrated with known mol wt at the same temp, drop size, time

Useful for Mn < 30000

small signal (Δr)

(33)

6. Determination of M 6. Determination of M

ww

light scattering (LS)

Light scattered by fluctuation in

refractive index (n) Å concentration Å mol wt

Hc/Rθ = 1/Mw + 2 A2c + 3 A3c2 + ---

H = 2π2n02(dn/dc)2/NAλ4

Why Mw? intensity ∝ (amplitude)2 ∝ (mass)2

[Hc/Rθ]cÆ0 = 1/Mw for small molecules, not for polymers

r θ I0

λ

iθ

iθ/I0 = f (dn/dc, M, λ, n0) Rayleigh ratio, Rθ = (iθ/I0)r2

Eqn (3.43)

(34)

for large molecules (D > λ/20)

Hc/Rθ = 1/(MwP(θ)) + 2 A2c + ---

P(θ) = scattering (form) factor = Rθ/R0 1/P(θ) = 1 + (8π2/9λ2)<r2>sin2(θ/2)

= 1 + (16π2/3λ2)<Rg2>sin2(θ/2)

r = end-to-end distance Rg = radius of gyration

<r2>0 = 6 <Rg2>0

Hc/Rθ = 1/Mw + (16π2/3λ2Mw)<Rg2>sin2(θ/2) + 2 A2c + ---

[Hc/Rθ]θ=0 = 1/Mw + 2 A2c + ---

[Hc/Rθ]c=0 = 1/Mw + (16π2/3λ2Mw)<Rg2>sin2(θ/2)

r

Rg

Eqn (3.50), Fig 3.10(c)(d)

i30 ≠ i45

Eqn (3.51), Fig 3.10(a)(b) Eqn (3.61)

(35)

7. MW of common polymers 7. MW of common polymers

MW of commercial polymers

step polymers: 20000 – 40000

chain polymers: 20000 – 1000000 MWD

Flory-Schultz distribution: PDI = 2

when ideal

Poisson distribution: PDI = 1

anionic living polymerization

In most polymerizations: PDI > 2

Table 3.9

PDI(chain polymers) > PDI(step polymers)

(36)

8. Determination of

8. Determination of M M

vv

dilute solution viscometry (DSV)

viscosity Å size mol wt measures molecular size, not weight

not an absolute method, but a relative method

viscosity, η

η = η0 (1 + ωv2) Einstein eqn

ω = 2.5 for sphere v2 ∝ size of solute

η/η0 – 1 = 2.5 N2Ve/V

ηrel – 1 = ηsp = 2.5 cNAVe/M (g/L)(1/mol)(L)/(g/mol)

[η /c] = 2.5 N V /M = [η] ‘intrinsic viscosity’

η0: solvent only

v2: vol fraction of solute V: vol of soln

Ve: vol of equiv. sphere c: wt conc’n

M: mol wt

for η’s, see handout p92 Fig 3.13

Fig 3.12

shape

(37)

[η] Æ mol wt

Ve = (4/3)πRe3 = (4/3)πH3Rg3 ∝ (4/3)πH3(M/M0)3/2

É Re = HRg, Rg ∝ (M/M0)½ at θ-condition

[η]θ = 2.5 NAVe/M ∝ (10πNAH3/3M03/2)M½ [η]θ = Kθ M0.5 at θ-condition

in good solvent, Rg = α Rgθ

[η] = α3 [η]θ = α3 Kθ M0.5 = λ3 Kθ M(0.5+3Δ) = K Ma

É α = λ MΔ

[η] = K Mva ‘Mark-Houwink-Sakurada (MHS) eqn’

Mv~ viscosity-average mol wt a ≥ 0.5

(38)

M

v

~ viscosity-average mol wt

ηsp = Σ(ηsp)i ~ Ni moles of Mi mol wt

= Σ ci [η]i = Σ (NiMi) (KMia) = K ΣNiMi1+a [η] = [ηsp/c]cÆ0 = K ΣNiMi1+a/ΣNiMi = K Mva Mv = [ΣNiMi1+a/ΣNiMi]1/a

0.8 ≥ a ≥ 0.5

0.5 at θ-condition

when a = 1, Mv = Mw when a = –1, Mv = Mn Mv close to Mw

(39)

DSV experiment

capillary viscometer Å Poiseulli eqn, Q = V/t = πr4P/8ηL η ∝ t Æ η/η0 = t/t0

Procedure

measure t0, t1, t2 --- at c0, c1, c2 --- (0 ~ solvent) [η] = [ηred]cÆ0 = [ηsp/c]cÆ0 = [(ηrel – 1)/c]cÆ0

= [(η/η0 – 1)/c]cÆ0 = [(t/t0 – 1)/c]cÆ0 or [η] = [ηinh]cÆ0 = [ln ηrel/c]cÆ0

= [ln (η/η0)/c]cÆ0 = [ln (t/t0)/c]cÆ0 [η] = K Mva

K, a from handbook at the same temp and solvent

Cautions: temp control < 0.2 K t0 > 100 s (laminar)

c < 1 g/dL (Newtonian)

Table 3.10 Fig 3.14

(40)

9. Gel Permeation Chromatography (GPC) 9. Gel Permeation Chromatography (GPC)

size exclusion chromatography

separation by size using porous gel substrate Larger molecules elute earlier.

Instrumentation

injector – column(s) – detector

A chromatogram

Fig 3.16-18

VR: retention volume VR = tR x flow rate

VR ~ size Æ mol wt (Mi) Hi ~ amount Æ NiMi

Needs calibration

(41)

Universal calibration

With the same instrument, column, and solvent, the same VR represents the same hydrodynamic volume.

[η] M = [2.5 NA V] = K Mva+1

Many polymers fall on the same curve on the [η]M – VR plot ~ universal calibration curve

Procedure of an experiment

1. From the chromatogram, read VRi and Hi

(column 1 and 2).

2. Run the same experiment with polystyrene standards.

Fig 3.23

(42)

2 (cont’d) PS standard anionically polymerized with known mol wt

3. Draw a calibration curve (Mi vs VRi) for PS.

4. Read Mi (PS) for each VRi (column 1 , sample).

(43)

5. M (PS) Æ M (sample)

[η]PSMPS = [η]sampleMsample

KPSMPSa(PS)+1 = KsampleMsamplea(sample)+1

6. Ni = Hi / Mi (column 2 / column 3) 7. Calculate Mn, Mw, MWD.

Are Mn and Mw obtained absolute? No.

from handbook

from calibration curve column 3

(44)

10. Mass spectrometry 10. Mass spectrometry

MS determines mol wt

by detecting molecular ion, M+ in vapor phase

ionization of polymers in gas phase?

MALDI-TOF technique

soft ionization

choice of the matrix critical for not-too-high mol wt

useful for (highly) branched polymers

(45)

11. Conclusions 11. Conclusions

At theta condition (solvent/temp)

A2 = 0, χ = ½

Rg is the same to that of the bulk polymer

infinite mol wt fraction just precipitate (poor/good)

Absolute and relative methods

Table 3.15

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The 24hr proteinuria level were increased in kidney with cyclosporine-A group but significantly decreased in iNOS inhibitor and green tea polyphenol group..

Results: In this research, in the group with fibromyalgia patients group, systemic lupus erythematosus patients group and without systemic autoimmune

1. Free radical initiator abstract a hydrogen from polymer chains 2. Through chain transfer of propagating chain with polymer chain 3. Polymer mixtures are mechanically

Methyl group controls the regiochemistry because methyl Methyl group controls the regiochemistry, because methyl group is a strong activating

Going from a set of functional group building blocks to potential molecular starting materials can generate very large potential molecular starting materials can generate

 Although van der Waals equation is still less accurate at high