6. polymer characterization 1 new clean short tepe
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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
Ref: S.L. Rosen,JohnWiley & Sons 1993
[]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
Ref: S.L. Rosen,JohnWiley & Sons 1993
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)
Ref: S.L. Rosen,JohnWiley & Sons 1993
Ref: S.L. Rosen,JohnWiley & Sons 1993
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