chapter 3 section 3.7

CONCLUSION

Simple solids with a short ranged attractive pair potential can exhibit phase separation in a expanded solid and a more dense solid. This isostructural first-order solid-solid transition is reminiscent of the liquid-vapor transition. The transition takes place between two phases of the same structure, the coexistence curve ends in a critical point and the location of the coexistence curves depends strongly on the interaction range. The simulations on the square-well model show that the solid-solid transition takes place both in two and three dimensions for potential well-widths 0.07. The analogy with liquid-vapor phase separation suggests that the solid-solid critical point should be of the 2D and 3D Ising universality class, although this still remains to be established. The critical density depends on the well-width and is well predicted by the uncorrelated cell-model. In contrast, the critical temperature hardly changes with . The critical temperature is finite for . This has been confirmed by direct simulations in this limit. Comparison of the adhesive sphere model theories with the simulations in the limit shows that the solid-solid transition already occurs for , where plays the role of temperature in the adhesive sphere model. This implies that at finite the only stable phases are the close-packed solid and a the infinite dilute gas. All other phases are, at best, meta-stable. This pathological behavior is thought to be a consequence of the monodispersity of the system. We expect that introducing a slight size polydispersity will cause the solid-solid transition to occur at finite .
The results for the solid-solid transition in Yukawa systems are comparable to those for the square-well model. The solid-solid transition occurs for 25, i.e. a potential well width narrower than 0.04. The major difference with the square-well results is that the critical temperature depends more strongly on .

An isostructural solid-solid transition, induced by the mechanism described above, will also occur in systems with repulsive ``square shoulder'' potentials. The critical temperatures are almost equal to that of the square well system, but the critical densities are significantly higher. Led by the theoretical work of Stell and Hemmer [52] and Kincaid, Stell and Goldmark [72] we have extrapolated the solid-solid binodals to T=0, where effectively two close packed solids are in coexistence.
An obvious question is whether the isostructural solid-solid phase transition due to short-ranged attraction, that we report here, can occur in real systems. We believe that such a transition can be observed in uncharged colloids with a short-ranged attraction. Such systems can be made, as we discussed in the previous chapters, by adding non-adsorbing polymer to a suspension of hard-sphere colloids (for a review, see e.g. ref. [8]). The polymers induce an effective attractive force between the colloidal spheres. The range of this attraction is directly related to the radius of gyration of the polymer. Hence, a colloidal crystal to which a polymer with a radius of gyration less than 7% of the radius of the colloidal spheres has been added, should exhibit the solid-solid phase behavior of the models discussed in this chapter.
However, introducing size polydispersity in the colloidal system will decrease the stability of the solid-solid transition. Our simulations show that for a colloidal dispersion with a polydispersity of more than 1% the solid-solid transition has become metastable with respect to the fluid-solid transition.

chapter 3 section 3.7