Gel and Glass Transitions in Short-Range Attractive Colloidal Systems - Food Colloids: Self-Assembly and Material Science - page 337

Figure 6 Static structure factor S(q) of the final configuration at representative packing
fractions
packing fraction, an indication that the typical length scale of the inhomo-
geneities is decreasing. At the same time the intensity of the peak decreases.
Once the packing fraction f ¼ 0.5 is reached, the static structure factor has no
sign of the low-q peak. At such a high packing fraction, the system is so dense
that the particles do not have time to diffuse and rearrange, and the homoge-
neous structure of the quenched liquid is retained. This re-enforces the idea
that the gel formed from the SRACS is a spatially inhomogeneous attractive
glass (in the MCT fashion 12 ), where the inhomogeneity is built by the phase
separation process. In this way, we have shown a clear connection between
the gel - as an arrested phase separation - and the attractive glass.
Before concluding this section, we discuss the pore distribution function P(r)
developed to quantify the porosity of heterogeneous materials, 39 and which has
also been used to provide a description of the gel structure obtained by
computer simulations. 40 This quantity is defined as the probability, P(r)dr,
that a randomly chosen point inside the pore volume lies between r and r +dr
from the pore surface; it is normalized to unity. In Figure 7, we plot the pore
distribution function for the initial and final configurations for three packing
fractions, f ¼ 0.1, 0.25, and 0.35. In the initial configurations the particles are
homogeneously distributed and the pore-size distribution function presents a
peak that reflects the typical inter-particle distance. In the final stage of
aggregation, however, the pore distribution decays to zero more slowly. Indeed
no peak is present but just a broad distribution of distances that get wider the
lower the density. For f ¼ 0.1, for example, P(r) is spread over more than three
diameters, indicating an extremely open structure. For the other two cases this
decay takes place on shorter length scale, indicating a more compact structure.
In the lower panel of Figure 7, we show the time evolution of the pore
distribution function for the case f ¼ 0.25. To relate the evolution of this