Chemistry Reference
In-Depth Information
f
GG
, can be given [
189 192
] in terms of the molecu-
lar constants of the individual phases, including polarizabilities, ionization poten-
tials, dipole moments, and molar volumes. The utility of the approach is limited by
the lack of information about those molecular parameters for most polymer sys-
tems. Another difficulty arises from the fact that a
The interaction parameter,
10% error in
f
GG
will result in
a
50% error in calculating
g
, because for polymers the surface tensions are very
similar. Thus, the
f
GG
between
some polymer pairs have been calculated from the measured interfacial and surface
tensions [
193
,
194
], and are found to be in the range 0.8 1.0. Empirically, it has
been shown [
194
] that:
f
GG
values must be accurately known. Values of
@f
GG
@
T
¼
0
(22)
An alternative treatment [
153
,
195
] is based upon (
18
), where the work of
adhesion is calculated using the theory of fractional polarity. Intermolecular
energies are assumed to consist of additive nonpolar (i.e., dispersive) and polar
components. Thus, the work of adhesion and the pure-component surface tensions
can be separated into their dispersive (superscript d) and the polar (superscript p)
components, such that:
p
i
d
s
i
¼ s
i
þ s
(23)
and:
W
a
þ
W
a
W
a
¼
(24)
The various polar interactions (including dipole energy, induction energy, and
hydrogen bonding) are combined into one polar term.
Relationships between (
23
) and (
24
) have been obtained for two limiting cases.
For low energy surfaces, characteristic of most polymer systems, the harmonic-
mean approximation is valid for both the dispersive and the polar terms. This,
combined with (
18
) gives:
p
1
s
p
2
4
s
1
s
2
4
s
g ¼ s
1
þ s
2
2
(25)
p
1
þ s
p
2
s
1
þ s
s
which has been found to give good results for polymers. Equation (
25
)can
berewrittenintermsof(
21
); the interaction parameter
f
GG
is then given
by [
195
]:
2
x
1
x
2
g
1
x
1
þ
2
x
1
x
2
g
1
x
1
þ
f
GG
¼
g
2
x
2
þ
(26)
g
2
x
2
