Chemistry Reference
In-Depth Information
1.0
0.8
0.6
γ/γ
∞
0.4
0.2
0.0
0.0
0.1
0.2
0.3
0.4
0.5
1/w
Fig. 15 Reduced interfacial tension
g
/
g
1
as a function of the inverse incompatibility l/
w
(
solid
line
). The
dashed line
is the asymptotic linear behavior (
86
) valid for large incompatibilities. Near
the critical point (l/
w
= 0.5), the
dotted line
represents the more exact solution of Joanny and
Leibler [
246
] (see Sect.
3.2.4
)
where
a
I
1
is the interfacial thickness of Helfand Tagami (
38
). The results are
expected to be valid for strongly incompatible systems where the interface is
smaller than the chain radii of gyration, whereas the analysis should not hold for
weakly incompatible systems where the interface becomes of the order of
R
G
or
larger.
Figure
15
shows the numerically calculated interfacial tension plotted as a
function of the inverse incompatibility 1/
w
, assumed to be the same for both
polymers. The asymptotic behavior of (
86
) is a good approximation for a wide
range of incompatibilities
w
>
5 (or l/
w
<
0.2). However, the increase in interfacial
tension with molecular weight is predicted to be weaker for smaller molecular
weights, in agreement with the experimental data of Anastasiadis [
20
].
Broseta also calculated the effect of molecular weight polydispersity on the
interfacial tension [
31
]. He considered a specific case of polydispersity where the
two polymer melts are binary mixtures with the same bimodal distribution of
molecular weights, with
r
1
being the length of the small chains,
r
2
the length of
the long chains (
r
1
<
r
2
), and
x
0
the volume fraction of monomers belonging to
small chains. Broseta analyzed the strong segregation regime, i.e., large values of
w
i
¼ wr
i
. The theory predicted a selective partitioning of the small chains to the
polymer polymer interface, which leads to a reduction of the interfacial tension.
The enrichment of the small chains to the interface decreases when the chain length
ratio
w
2
/
w
1
decreases to 1 and when both chain lengths simultaneously increase.
