Gel and Glass Transitions in Short-Range Attractive Colloidal Systems - Food Colloids: Self-Assembly and Material Science - page 329

Figure 1 The general phase diagram for the short-range attractive colloidal system
(SRACS)

this article we discuss results for the SRACS most especially connected to gel
formation, a phenomenon ubiquitous in nature, but still far from understood.
We always keep open the connection to the glass transition that is present on
the high-density side of the phase diagram. Recent results tend to interpret the
gel transition in the SRACS as an arrested phase separation where the tendency
of the system to form an inhomogeneous structure is frozen in by the tendency of
the particle to stick together. 22,23 We shall discuss how the possibility to reach a
percolating arrested structure from the one-component fluid (i.e., without any
phase separation) seems ruled out by the computer simulations. 24

22.2 The Gel Transition: Arrested Phase Separation
Within the framework that treats colloidal particles as atoms with a tuneable
interaction, the model we shall discuss is a system of hard spheres interacting
via a square-well potential. We simulate a 1:1 binary mixture of 2000 spherical
particles with a size ratio of d 1 /d 2 ¼ 1.2 which effectively suppresses crystalli-
zation. The interaction potential is defined by

<

1; r o d ij ;

u ij ðÞ ¼ u 0 ; d ij o r o d ij þ D ij ; ð 1 Þ

:

0 ; r4d ij þ D ij ;

where d ij ¼ (d i + d j )/2, with d i being the hard-core diameter of the particle of
component i ( ¼ 1,2) and D ij representing the range of the attraction. We
shall measure the range of the attraction by the non-dimensional variable
e ¼ D ij /(d ij + D ij ) with e ¼ 0.005. This chosen e value is arbitrary, but it is
representative of all square-well potentials with interaction range smaller than a
few percent as far as the thermodynamic and equilibrium properties are
concerned. 24,25 For the chosen potential the critical temperature is T c ¼ 0.20.