Interfacial Tension in Binary Polymer Blends and the Effects of Copolymers as Emulsifying Agents - Polymer Thermodynamics - page 240

the assumption of the random distribution of the copolymer chains in the bulk
copolymers. The fact that the theory was unable to describe the crossover regime
from a random distribution to the micelle formation was also discussed [ 70 ].
In another study, Noolandi and Hong [ 71 ] attempted to identify the relative
importance of the various contributions that affect the interfacial tension reduction
(as discussed earlier). The equations of their model were solved numerically in a
“computer experiment” and the various contributions to the free energy and the
interfacial tension were evaluated to determine their relative importance. The
results were also discussed in another publication [ 281 ]. For a symmetric diblock
copolymer, homopolymers of infinite molecular weight, and a symmetric solvent,
they found that the interfacial tension reduction,

Dg , with increasing copolymer
molecular weight and concentration arose mainly from the energetically preferred
orientation of the blocks at the interface into their respective compatible homo-
polymers. The main counterbalancing term in the expression for Dg was the entropy

loss of the copolymer that localizes at the interface. The loss of conformational or
“turning back” entropy of both copolymer and homopolymer chains at the interface
was shown to contribute little to

Dg .
Neglecting the loss of conformational entropy, Noolandi and Hong were able to
obtain an analytical expression for the interfacial tension reduction for infinite
homopolymer molecular weights, given by:

wf p
2 þ

d
b f c

1
N

1
N exp Nwf p =

Dg ¼ g g 0 ¼ 2 (96)

whereas the amount of copolymer at the interface is:

f c ð 0 Þ¼f c exp Nwf p = 2 (97)

where d is the full width at half height of the copolymer profile and b is the Kuhn
statistical segment length. Numerical calculations showed that d was almost
constant for varying copolymer molecular weight.

)isthe
copolymer volume fraction in the bulk homopolymer phases, which is very close
to the nominal amount of the block copolymer present because the material
segregated to the interface is negligible [ 71 ] compared to the total amount for a
large system;

f c ¼ f ( 1 ) ¼ f ( 1

f p is the
bulk volume fraction of polymer A or B (assumed equal), N is the degree of
polymerization of the symmetric copolymer, and, w is the Flory-Huggins interac-
tion parameter between A and B segments. It was assumed that the interaction
parameters between segments A and B and the solvent are w AS ¼ w BS ¼

f c (0) is the copolymer volume fraction at the interface.

0,
respectively. d is a parameter that was not determined by the simplified theory.
For Nwf p 1, ( 96 )reducesto:

d
b f c Nw

2 2

Dg ¼ g g 0 ¼ f

p =

8 Nwf p 1 (98)

;