Gel and Glass Transitions in Short-Range Attractive Colloidal Systems - Food Colloids: Self-Assembly and Material Science - page 336

Figure 5 Log-log plot of integrated radial distribution function n(r) for representative
packing fractions. The inferred fractal dimension d f for the various regimes is
indicated, and also the characteristic length scale x for f ¼ 0.1

fractal. As expected, for r Z x , the system exhibits a non-fractal uniform
structure. Moving to higher packing fractions we could not find any sign of a
fractal structure. Hence it appears that a gel with some fractal structure can be
obtained only for a density close to the percolation threshold. When the system
is denser, the percolating structure is thicker and compact.
So far we have shown that no fractal structure emerges on increasing the
density of the arrested phase separated structure, but we still have to consider
whether the system is more homogeneous. To do this we study the static
structure factor along the isotherm T f ¼ 0.05. The static structure factor is
defined as

;

S q ð t f Þ¼ r ð q ; t f Þ r ð q ; t f Þ

ð 9 Þ

where the density variable is defined as

r ð q ; t f Þ¼ X
k ¼ 1 ; N

exp ð i ! !

k ð t f ÞÞ

p N ; ð 10 Þ

and the time t f is the final time of the simulation. The structure factor has been
studied in ageing in the arrested phase separation regime 23 and also at high
density, i.e., in the glass. 38 When the system presents strong inhomogeneities on
a length scale larger than the particle diameter, a peak in S(q) emerges at small
q. In our case this is due to spinodal decomposition. For f ¼ 0.1, there is low-q
peak that strongly indicates an open structure as also seen from the snapshots
of the configuration in Figure 6. The peak moves to higher q on increasing the