Gel and Glass Transitions in Short-Range Attractive Colloidal Systems - Food Colloids: Self-Assembly and Material Science - page 335

Figure 4 Snapshots of the final structure for three representative packing fractions. On
the left are three-dimensional representations. On the right are two-dimensional
slabs

between the fractal regime and the homogeneous regime, and it can be
extracted from the relation 37 :

1 = d f 3

f
n 0

x ¼ r 0 : ð 8 Þ

The quantity n 0 is obtained from the relation n ð r Þ¼ n 0 ð r = r 0 Þ d f by fitting the
numerical results and taking r 0 equal to the radius of the particles. The
integrated distribution functions for different packing fractions are shown in
Figure 5. For the most heterogeneous case ( f ¼ 0.1), there is a scaling regime
characterized by d f ¼ 2.2. From the relation in Equation (8), we obtain a
characteristic length scale x ¼ 6.9. This means that, if we consider the structure
of our aggregated systems only up to this length scale, the system is indeed