section 3.1
In this chapter, we consider what happens in colloidal systems with a very short ranged attraction, where the liquid-vapor transition is absent. We show that these systems may exhibit a type of solid-solid transition that is in many ways reminiscent of the liquid-vapor transition: in particular,
As a first approximation, we use the square well potential to model
short-ranged interactions in colloids.
This model, although simple, should provide an adequate description of a wide
class of uncharged colloidal particles with short-ranged attraction.
The square well model has been the subject of many theoretical and
simulation studies [43,44]. In particular, the molecular
dynamics studies of Young and Alder [44] on the phase diagram
of a long ranged square well system already show the possibility of
a solid-solid phase transition. However, as the authors of
ref [44] correctly point out, the latter transition is an
artifact of the square well model and is not expected to occur in any
real system. As we shall show below, the occurrence of the
solid-solid transition in systems with short ranged potentials is not
sensitive to the precise form of the potential and is therefore more
likely to be experimentally observable.
Additional evidence for the insensitivity of the solid-solid
transition to the precise shape of the intermolecular potential comes
from recent theoretical work by Tejero et al. [45] and by
Rascon et al. [46].
These authors predict the existence of a solid-solid transition in different models of particles with a short-ranged attractive potential.
An interesting question that we address in the present study is
whether or not the solid-solid transition exists in other dimensions
than three. It is well known that systems with a short-ranged
attraction cannot exhibit a phase transition in one dimension, but the
solid-solid phase separation could occur in two-dimensional colloidal
systems. Our simulations show that this is indeed the case.
The existence of the transition in two dimension has consequences for
the issue of stability of the hexatic phase [47,48,49]. Bladon and
Frenkel [50] showed that a hexatic stable phase region can occur in the
vicinity of the 2D solid-solid critical point.
The simulations results also indicate that the critical temperature of
the solid-solid transition remains finite in the limit of infinitely
narrow well-width. We study this limit by simulation of a lattice
model and compare the results of the lattice model with that of the
well-known adhesive sphere model introduced by Baxter [51].
In section 3.2, we present our simulation results on the square-well
model for both two and three dimensions, followed by the discussion
on the infinitely narrow well-width limit.
In section 3.3, we discuss the application of a simple uncorrelated
cell model to the square-well system. These calculations provide
considerable insight in the mechanism of the phase transition.
To verify that the solid-solid transition is not an artifact of the
square-well model we
also performed extensive simulations on hard-core systems with an
attractive Yukawa potential. The latter model is thought to provide a
fairly realistic description of the effective colloid-colloid
interaction in mixtures of uncharged colloids and non-adsorbing
polymer [7,9,10].
The results of the Yukawa simulations are presented in section 3.4.
Solid-solid transitions can also occur for repulsive potentials
[52]. In section 3.5 we discuss the
simulations we performed on a repulsive ``square shoulder''
potential. Finally, because most colloidal dispersions exhibit a
certain amount of size-polydispersity, we explore the influence of polydispersity on the
solid-solid transition in section 3.6.
section 3.1