Chemistry Reference
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although the fractal dimension remains at d
f
¼
2, the pre-factor a increases with
increasing ionic strength and decreasing pH. The most turbid gels that could be
studied had an average correlation length of
1 mm.
Assuming that the system can be modelled as an ensemble of close-packed
monodisperse blobs of size R
a
and molar mass M
a
, then the following equation
relates the protein concentration to R
a
and M
a
:
C
E
3M
a
/(4N
A
p
R
a
).
B
(6)
Utilizing the relationship between M
a
and R
a
, it follows that we have R
a
p a
1.5
C
1
and M
a
p a
3
C
2
for d
f
¼
2. This result is compatible with the concen-
tration dependence of M
a
and R
a
for b-LG at 100 mM NaCl.
28
However, the
strong increase of M
a
at a given protein concentration with increasing ionic
strength cannot be explained by the weak increase of a. We conclude that the
gels become increasingly heterogeneous; i.e., the concentration fluctuations are
characterized by a range of correlation lengths. In terms of the blob picture, the
gels consist of an ensemble of blobs with a size distribution that increases with
decreasing electrostatic repulsion. The values of R
a
and M
a
determined by
scattering techniques represent the z-average radius and the weight-average
molar mass of the blobs, and therefore the largest blobs have a strong weight. If
the size distribution of the concentration fluctuations varies, then R
a
and M
a
are no longer simply related to the protein concentration through the fractal
dimension. Similar observations have been made for gels formed by small clay
particles (Laponite) at different NaCl concentrations:
51
at a fixed concentra-
tion, the correlation length strongly increased with increasing ionic strength,
while the local structure remained the same.
When the length-scale of the heterogeneity approaches 1 mm, it can be
observed using CSLM,
29,43,50,52
as illustrated in Figure 12. The gels appear to
consist of aggregated micrometre-sized particles. For this reason turbid glob-
ular protein gels are often called as particle gels or particulate gels. Typically,
TEM and (particularly) SEM show a network of partly fused and roughly
spherical particles with diameters of the order of 1 mm
16,53-55
(Figure 13).
Figure 12 CSLM image of a
b
-LG gel formed at C
¼
50 g L
1
,pH
¼
7, and 0.2 M
NaCl.
50
The total width of the image is 160
m
m
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