Gel and Glass Transitions in Short-Range Attractive Colloidal Systems - Food Colloids: Self-Assembly and Material Science - page 333

process starts to set in. This slows down significantly once a number of bonds
of the order of 6 (U/N 3) per particle is reached. Two different types of

behaviour can be distinguished. At very low density ( f o 0.05) the energy
continues to drop and does not seem to reach any stationary value in the
simulation time window. For f 4 0.05, however, the time dependence of the
energy abruptly stops and the system does not show signs of further evolution.
This can be seen as indicating that an arrested structure has formed, consistent
with growing evidence, numerical 24,32-35 and experimental, 22 that the gel state
results from an arrested phase separation when the phase separation dynamics
generates regions of local density sufficiently large to undergo an attractive
glass transition. If the system were to be quenched to a higher temperature, but
one still below the critical point, the system would present a drift in the energy,
indicating that the separation process does not arrest during the simulated
time. 23
We report also in Figure 3 the BD results. Despite the different microscopic
dynamics, the time dependence of the energy shows a similar trend, and the
value of the energy at which the system stops for different densities is indeed
very similar to the ND case. Comparing in more detail the two simulations, one
notices that the Brownian aggregation dynamics is smoother compared to the
Newtonian one. The reason for this difference in behaviour is probably the fact
that the ND momentum conservation law requires many-body interactions for
cluster aggregation. Indeed, two-body interactions between a pair of monomers
cannot produce a bounded dimer state; at least three particles have to interact
to bond. Once this happens small clusters start to appear in the system and
consequently the aggregation speeds up significantly. As shown in the inset of

E

Figure 3 Evolution of the potential energy per particle, U/N, in Newtonian dynamics
(above) and Brownian dynamics (below) as a function of time for different
packing fractions above the percolation threshold. The inset shows the energy of
the final structure versus packing fraction f