Phase diagram of highly asymmetric binary hard-sphere mixtures

We study the phase behavior and structure of highly asymmetric binary hard- sphere mixtures. By first integrating out the degrees of freedom of the sma ll spheres in the partition function we derive a formal expression for the effective Hamiltonian of the large spheres. Then using an explicit pairwise (depletion) potential approximation to this effective Hamiltonian in compu ter simulations, we determine fluid-solid coexistence for size ratios q = 0 .033, 0.05, 0.1, 0.2, and 1.0. The resulting two-phase region becomes very broad in packing fractions of the large spheres as q becomes very small. We find a stable, isostructural solid-solid transition for q less than or equ al to 0.05 and a fluid-fluid transition for q less than or equal to 0.10. H owever, the latter remains metastable with respect to the fluid-solid trans ition for all size ratios Mie investigate. In the limit q-->0 the phase dia gram mimics that of the sticky-sphere system. As expected,the radial distri bution function g(r) and the structure factor S(k) of the effective one-com ponent system show no sharp signature of the onset of the freezing transiti on and we find that at most points on the fluid-solid boundary the value of S(k) at its first peak is much lower than the value given by the Hansen-Ve rlet freezing criterion. Direct simulations of the true binary mixture of h ard spheres were performed for q greater than or equal to 0.05 in order to test the predictions from the effective Hamiltonian. For those packing frac tions of the small spheres where direct simulations are possible, we find r emarkably good agreement between the phase boundaries calculated from the t wo approaches-even up to the symmetric Limit q = 1 and for very high packin gs of the large spheres, where the solid-solid transition occurs. Tn both l imits one might expect that an approximation which neglects higher-body ter ms should fail, but our. results support the notion that the main features of the phase equilibria of asymmetric binary hard-sphere mixtures are accou nted for by the effective pairwise depletion potential description. We also compare our results with those of other theoretical treatments and experim ents on colloidal hard-sphere mixtures. [S1063-651X(99)07805-8].