Chemistry Reference
In-Depth Information
K
L
;
Y
r
L
3
k
¼
(55)
The only information required for model calculations concerning the incompatibil-
ity of linear and branched polymers on the basis of (
54
) concerns b, the degree
of branching of the nonlinear component, k (i.e., the viscosity molecular weight
relationship for the linear polymer under theta conditions) and the polymer density,
plus Z
¼
z
AB
/b, the conformational response of the system normalized to b
[cf. (
53
)].
2.1.3 Mixed Solvents
For the modeling of ternary systems(the topic of the next section), the applicabil-
ity of (
26
) to mixtures of low molecular weight liquids would be very helpful,
because of the possibility to describe all subsystems by means of the same
relation. First experiments [
29
], presented in Sect.
4
, show that this is indeed
possible. This means that (
26
) remains physically meaningful upon the reduction
of the number of segments down to values that are typical for low molecular
weight compounds. With respect to l one must, however, keep in mind that this
parameter loses its original molecular meaning.
2.2 Ternary Systems
The segment molar Gibbs energy of mixing for three component (indices
i
,
j
, and
k
)
with
N
i
,
N
j
, and
N
k
segments, respectively, as formulated on the basis of the Flory
Huggins theory reads in its general form:
'
i
þ
'
j
N
j
D
RT
¼
'
i
G
'
j
þ
'
k
N
k
ln
ln
ln
'
k
þ
g
ij
'
i
'
j
þ
g
ik
'
i
'
k
þ
g
jk
'
j
'
k
N
i
þ
t
ijk
'
i
'
j
'
k
(56)
The first three terms stand for the combinatorial part of the Gibbs energy, the next
three terms represent the residual contributions stemming from binary interactions,
and the last term accounts for ternary contacts.
The double-indexed
g
parameters are for binary interaction parameters. The first
line of the above relation represents the combinatorial part, and the second line the
residual part of the reduced segment molar Gibbs energy of mixing. This relation
also contains a ternary interaction parameter
t
ijk
that accounts for the expectation
that the interaction between two components of the ternary mixture may change in
the presence of a third component.
