PPT Slide
Such a repulsive interaction in the potential of mean force of two colloidal spheres is qualitatively similar to the oscillating force between the solid surfaces that confine a thin layer of liquid [7].
A simple lattice model of binary hard-core mixture was constructed in 1992 by Daan Frenkel and Ard A. Loius [8]. By transforming to a grand-canonical ensemble they were able to map this mixture onto a one-component lattice gas with attractive nearest-neighbour interactions. This model, in turn, can be mapped onto Ising-like model for which the phase behaviour is known. This gives the exact proof for the existence of a first-order entropy-driven demixing transition for the simple lattice model for hard-core mixture.
Some theoretical models [9] as well as experimental data [10] indicate that a fluid-fluid demixing transition might be preempted by the coexistence between a fluid and an amorphous or crystalline solid of a very different composition. Ordinary simulation work is severely hampered by ergodicity problems [11], some recent advances are due to cluster algorithms [12]. The question whether osmotic depletion alone may lead to fluid-fluid phase separation, has not received a final answer.
Another, quite different mechanism, is non-additivity of the hard-sphere diameters, i.e., if sa and sb denote the range of interaction between particles of the same type, and sab (sba) the range of the repulsion between particles of different species, then
sab =1/2 (sa +sb ) * (1+a)
where a is called the non-additivity parameter.
Hard sphere is an idealized model to describe real particles with strong repulsive interactions and there is no reason, a priori, why the effective diameters associated with different species should be strictly additive. For example, colloid-polymer mixtures have to be modeled as non-additive hard spheres, since the interaction between polymers is usually quite weak.
When a < 0 particles 'A' and 'B' "like" each other and mixing is favored. In contrast, when a > 0, which is the case of polymer-colloid mixtures, particles 'A' and 'B' "prefer" not to mix and separation can occur.