Polymer Physics

11.2 Enhanced Phase Separation in the Blends Containing

Crystallizable Polymers

Crystallization is often component-selective in a multi-component system, causing
the same effect of component segregation as phase separation. Therefore, when
liquid-liquid phase separation happens at a temperature higher than the melting
point, molecular driving forces for crystallization are naturally a part of molecular
driving forces for phase separation, as expressed in (10.12). Assuming a binary
blend of two polymers with the same chain lengths ofr, the numbers of polymer
molecules are separatelyN 1 andN 2 , and the total volumeN¼rN 1 þrN 2. Again,
assuming only polymers labeled with 2 can crystallize, similar with the solution
system described in (10.8), the partition function of polymer blends is given by

Z¼

N

N 1

N 1

N

N 2

N 2

q

2

N 1 þN 2

zcðN^1 þN^2 Þðr^2 ÞeðN^1 þN^2 Þðr^1 ÞzpN^2 ðr^1 ÞzmN^2 r (11.1)

where

zc¼ 1 þðq 2 Þexp 

Ec

kT



;

zp¼exp 

q 2

2

1 

2 N 2 ðr 1 Þ

qN



EP

kT



;

zm¼exp 

N 1 r

N

ðq 2 ÞB

kT



:

Similarly, for the change of mixing free energy, one can get the formula
consistent with Flory-Huggins equation as

DFm

NkT

¼

f 1

r

lnf 1 þ

f 2

r

lnf 2

þf 1 f 2 ðÞq 2

B

kT

þ 1 

2

q



1 

1

r

 2

EP

kT

"

(11.2)

One can see from (11.2), the Flory-Huggins parameter w includes both
contributions from the mixing energy and the parallel packing energy. When the
chain lengths of both components are very large, the contribution of mixing entropy
in the mixing free energy will be very small. Furthermore, if the chemical structures
of two components are similar, such as the isotactic and atactic sequences of
polypropylene chains, their mixing interactionsBwill be minimal. We know that
in the blends of these different stereochemical compositions, isotactic

226 11 Interplay Between Phase Separation and Polymer Crystallization