6. polymer characterization 1 new clean short tepe

Part III: Polymer Characterization

- Chapter 6: Characterization of Molecular Weight

- Chapter 7: Polymer Solubility and Solution

- Chapter 8: Phase Transition in Polymer

Chapter 6: Characterization of Molecular Weight

• Average molecular weight– : number-average molecular weight– : weight- average molecular weight– xn: no. avg. degree of polymerization

– xw: wt. avg. degree of polymerization

– Mo: Mw of monomer (or repeating unit)– PI, MWD: polydispersity index = Nw M/M

wMnM

Mw, Mn calculations

Mn = first moment = C(M)M dM C(M) dM

Mw = 2nd moment = C(M)M2 dM C(M)M dM

Definition of Mw, Mn

nM = First Moment =

dMMc

MdMMc

)(

)(

wM = Second Moment =

dMMc

dMMMc

)(

)( 2

In integral form

In discrete summation form

ni = mole fraction = i

i

NN wi = weight fraction = i

i

WW =

ii

ii

MnMn

11 ii wn

i

iii

iiiiw

i

ii

i

iii

i i

iiiin

N

MNMnMwM

N

W

N

MN

NMN

MnM

2

2

)(

11 ii wn

ii

i

2ii

2iiiiw

i

ii

i

iii

i i

iiiin

MN

MNMnMwM

N

W

N

MN)

NMN

(MnM

Ex1. Measurements on two monodisperse fractions of a linear polymer, A and B, yield molecular weights of 100 000 and 400 000, respectively. Mixture 1 is prepared from one part by weight of A and two parts by weight of B. Mixture 2 contains two parts by weight of A and one of B.

Determine the weight- and number-average molecular weights of mixtures 1 and 2

Solution. For mixture 1

555

5555100.2

105.0101104105.010101

NiNiMi

nM

555 10310432101

31Mi)

WWi(wM

5101100000

1 AN

5105.0400000

2 BN

For mixture 2

51025.0400000

1 BN

5102100000

2 AN 5

55

5555

1033.11025.0102

1041025.010102

nM

555 10210431101

32

wM

Ex2. Two polydisperse samples are mixed in equal weights. Sample A has M n = 100 000 and Mw = 200 000. Sample B has Mn = 200 000 and Mw = 400 000. What are Mn and Mw of the mixture ?

Solution. First, let’s derive general expressions for calculating the averages of mixtures:

i

i

Ni

Wi

NWnM

Where the subscript i refers to various polydisperse components of the mixture.Now, for a given component,

niMWiNi

i

i

niMWi

WimixturenM

/)(

i

i iixx

xx

Wi

Mw

WMw

wM

i

ixxx

W

MwwiM

wiM

WiWi

W

WMmixturewM

iii

i

iiwi

)(

Where ( ) is the weight fraction of component i in the mixture. In this case,

Let WA =1 g and WB = 1 g. Then

WiWi /

133000102/110/1

11// 55

nBBnAA

BA

MWMWWW

nM

WBBA

BWA

BA

A MWW

WM

WWW

wM

30000010421102

21 55

Note that even though the polydispersity index of each component of the mixture is 2.0, the PI of the mixture is greater, 2.25.

Determination of average molecular weight• 2 catagories

(a) Absolute methods:

(b) Relative methods:

-Measured quantities are theoretically related to MW

-Measured quantities are related to MW-but need calibration with one of the absolute methods

Ex. Endgroup analysis (Mn) Colligative property measurement (Mn) Light scattering (Mw) Ultracentrifuge (Mw)

Ex. Solution viscosity (Mv) Size-Exclusion Chromatography (MWD)

(a) Absolute methods:-Measured quantities are theoretically related to MW

A1. Endgroup analysis (Mn)

A2. Colligative property measurement (Mn)

A3. Light scattering (Mw)

A.4 Ultracentrifuge (Mw)

(b) Relative methods:

-Measured quantities are related to MW-but need calibration with one of the absolute methods

Ex.1 Solution viscosity (Mv)

Ex.2 Size-Exclusion Chromatography (MWD)

Solution viscosity (Mv)

Vis=a+bt

t = travel timea,b = constants

r = relative viscosity

SP = - S = - 1 = r – 1 S

S

Solution viscosity = (S , T, polymer conc., no. of entanglements, M )

- measure using Ostwald type Viscometer

Ublelohde typeDefinition: = solution viscosity

s = solvent viscosity

Specific viscosity SP

Get quantitative MW

show effect of [ ] = lim (/S) – 1 ขึ้นกับ coil dimensionSingle polymer c0 Ccoil to viscosity

= lim red

c0

Reduced viscosity (normalized for conc.)

C

C

red = SP = (/S) – 1

get rid of entanglement effect by reducing viscosity to zero conc.

Intrinsic viscosity

[] MW of polymer in soln

polymer – solvent system fix solvent, temp.

temp.

Huggin’s equation for r < 2 or (solution < 2solvent)

red = = [] + k′[]2c (Huggin’s equation)

where k′ is ~ 0.4 (for a variety of polymer – solvent system)

Advantage if [] is known can obtain relationship of red and conc.

Equivalent form of Huggin’s equation

inh = = [] + k” []2c

where inh = inherent viscosity

k” = k’ – 0.5

csp

cln r

][

Ref: S.L. Rosen,JohnWiley & Sons 1993

Vis conc.1 0.12 0.5

(alternative definition of intrinsic viscosity)[] =

Relationship of [] vs. M

[for monodisperse sample of a certain MW]

เรยีกวา่ Mark-Houwink-Sakurada (MHS) relation

[]x = K(Mx)a (0.5<a<1)

K, a Look up inpolymer handbook at a specific temp.

inhc 0 c 0lim lim

sln( / )C

a/1

xx

)a1(xx

a/1

xx

xxa

x

a/1

xa

xa/1

v MnMn

MnMnM

WWM

K][M

โดย 0.5 < a < 1, Mn<< Mv < Mw


[]x = K(Mx)a

Ex. Mv (viscosity average molecular weight)

• Example 1: PMMA, calculate Mv for mixture 1 and 2 in acetone at 30

oC and compare with Mn and Mw (From experiment: a = 0.72)

Mixture 1:

Mixture 2:

000,300M000,200M:tocompare

000,28810x43210x1

31M

Ww

M

wn

72.0/172.0572.05a/1

ax

xv

000,200M000,133M:tocompare

000,18710x43110x1

32M

Ww

M

wn

72.0/172.0572.05a/1

ax

xv

Ex1. Measurements on two monodisperse fractions of a linear polymer, A and B, yield molecular weights of 100 000 and 400 000, respectively. Mixture 1 is prepared from one part by weight of A and two parts by weight of B. Mixture 2 contains two parts by weight of A and one of B.

•Example 1: PMMA, calculate Mv for mixture 1 and 2 in

acetone at 30 oC and compare with Mn and Mw (From

experiment: a = 0.72)

Solution viscosity terminology


Size-Exclusion Chromatography (MWD)(or Gel Permeation Chomatography (GPC))

- หา Molecular weight + MWD รวดเรว็

“gel” – a cross linked polymer that is swollen by solvent

Porous particle (gel)

Last but Not Least!

Unimodal = 1 peakBimodal =2 peak

big molecule smallest come out last

“column”

large molecules come out first

small molecule

large molecules small moleculescome out first come out last

(go through interstices of the substrate pores)

Most common detector : differential refractometer (measure refractive index difference)

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