Chemistry Reference
In-Depth Information
where
N
A
is the number of segments of component A and
N
B
is the number of
segments of component B. The above equation shows the indices of the variables
and parameters to indicate that it refers to a polymer blend. For such systems, the
definition of a segment is not as evident as for polymer solutions, where the solvent
usually fixes its volume. Sometimes the monomeric unit of one of the components
is chosen to specify a segment, but in most cases it is arbitrarily defined as 100 mL
per mole of segments, a choice that eases the comparison of the degrees of
incompatibility for different polymer pairs.
In the case of polymer solutions, only one component of the binary mixtures
suffers from the restrictions of chain connectivity, namely the macromolecules,
whereas the solvent can spread out over the entire volume of the system. With
polymer blends this limitations of chain connectivity applies to both components. In
other words: Polymer A can form isolated coils consisting of one macromolecule A
and containing segments of many macromolecules B and vice versa. This means
that we need to apply the concept of microphase equilibria twice [
27
] and require
two intramolecular interaction parameters to characterize polymer blends, instead
of the one l in case of polymer solutions.
The conditions for the establishment of microphase equilibria in the case of
polymer blends [
27
], analogous to (
17
) for polymer solutions, yields two para-
meters. One, called
a
, quantifies the restrictions of the segments of a given polymer
B to mix with the infinite surplus of A segments surrounding its isolated coil
(microphase equilibrium for component A) and an analogous parameter
b
, referring
to the restrictions of the segments of a given polymer A to mix with the infinite
surplus of B segments. The following relations hold true for
a
and
b
:
1
2
N
A
þ
1
N
B
F
o
;
B
a
¼
(47)
and:
1
2
N
B
þ
1
N
A
F
o
;
A
b
¼
(48)
where the F values are volume fractions of segments in isolated coils, by analogy to
those introduced in (
17
).
For the calculation of phase diagrams by means of the minimization of the Gibbs
energy of the systems [
19
], we need to translate the information of (
47
) and (
48
),
based on the chemical potentials of the components, into the effects of chain
connectivity as manifested in the integral interaction parameter
g
. This expression
reads [
27
]:
a
AB
2
a
b
3
þ
þ
b
a
3
'
B
g
AB
¼
Þ
z
AB
(49)
ð
1
n
AB
Þ
ð
1
n
AB
'
B
