Chemistry Reference
In-Depth Information
10
3
G(
)
10
2
overlap model
10
1
Princen model
G
o
10
0
10
-1
0.65
0.7
0.75
0.8
0.85
0.9
0.95
volume fraction, ϕ
Figure 6.27
A plot of the high-frequency shear modulus G(N) and the static modulus
G(0) versus volume fraction. The points are the experimental data, the
solid lines represent the models.
where j
e
is the volume fraction of the drop and the stabilising shell. If n
m
is the
number of molecules per droplet and every molecule is elastically effective, a
reasonable assumption with liquid-crystalline order then the number of effec-
tive chains per unit volume is simply calculated. It is given by the number of
interactions per unit volume multiplied by n
m
:
3j
c
4pa
c
r
e
¼
n
m
C
a
ð
6
:
132
Þ
Here, j
c
is the volume fraction of the core and a
c
its radius. This equation has
not been widely tested owing to a paucity of data. Thorough characterisation
allows all the terms to be determined except j
m
and f
L
. The packing fraction
can be found by extrapolation to zero concentration of a plot of the high-
frequency shear modulus as a function of volume fraction since this corre-
sponds to the volume fraction before the chains come into contact. The
functionality of the link can be used as an adjustable parameter. For the
system here a good fit is found with f
L
¼
8/3 as shown in Figure 6.27.
A universal model for the viscoelastic response of HIPEs is unlikely to be
satisfactory without the inclusion of the interfacial film effects. For example,
Pons and coworkers
42
has suggested for systems stabilised by nonionic surfac-
tants that the Princen equation for G(0) can be used to describe the high-
frequency shear modulus rather than the static modulus. The difference
