An application of classical thermodynamics to solid-fluid equilibrium in hard sphere mixtures

Calculation of the interfacial free energy of a binary hard-sphere fluid at a planar hard wall

Using molecular-dynamics simulation and Gibbs-Cahn Integration, we calculate the interfacial free energy γ of a binary hard-sphere fluid mixture at a structureless, planar hard wall. The calculation is performed as a function of packing fraction (density) for several values of the diameter ratio α = σ2∕σ1, where σ1 and σ2 are the diameters of the two particle types in the mixture. Our results are compared to those obtained from the bulk version of the White Bear Mark II (WBII) classical density-functional theory, which is a modification of the Fundamental-Measure Theory of Rosenfeld. The WBII bulk theory is shown to be in very good agreement with the simulation results, with significant deviation only at the very highest packing fractions.

A study of the phase behavior of a simple model of chiral molecules and enantiomeric mixtures

We present a study of the solid-fluid and solid-solid phase equilibrium for molecular models representative of chiral molecules and enantiomeric mixtures. The models consist of four hard sphere interaction sites of different diameters in a tetrahedral arrangement with the fifth hard sphere interaction site at the center of the tetrahedron. The volumetric properties and free energies of the pure enantiomers and binary mixtures were calculated in both fluid and solid phases using isobaric Monte Carlo simulations. The models exhibit essentially ideal solution behavior in the fluid phase with little chiral discrimination. In the solid phase the effects of chirality are much greater. Solid-fluid phase behavior involving the pure enantiomer solids and also racemic compounds was calculated. The calculations indicate that, depending on the relative sizes of the hard sphere interaction sites, packing effects alone can be sufficient to stabilize a racemic compound with respect to the pure enantiomer solids.

Solid–fluid and solid–solid phase equilibrium in a model of n-alkane mixtures

Solid-fluid and solid-solid phase equilibrium for binary mixtures of hard sphere chains modeling n-hexane, n-heptane, and n-octane has been calculated using Monte Carlo computer simulations. Thermodynamic integration was used to calculate the Gibbs free energy and chemical potentials in the solid and fluid phases from pure component reference values. A multiple stage free energy perturbation method was used to calculate the composition derivative of the Gibbs free energy. Equation of state and free energy data for the fluid phase indicate ideal solution behavior. Nonideality is much more significant in the solid phase with only partial solubility of shorter chains in the longer chains and essentially no solubility at the other end of the composition range. The miscibility decreases with increasing chain length difference between the components. For the model of n-hexane/n-octane mixtures solid--solid phase separation has been observed directly in some of the simulations, with the components segregating between the layers of the solid structure. The behavior is similar to that seen in some binary n-alkane mixtures with longer chain lengths but comparable chain length ratios between the components. Such phase separation, although indicated thermodynamically, is not seen directly in the simulations of the n-heptane/n-octane mixture due to the difference in the pure component crystal structures.

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 small 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 computer 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< or =0.05 and a fluid-fluid transition for q< or =0.10. However, the latter remains metastable with respect to the fluid-solid transition for all size ratios we investigate. In the limit q-->0 the phase diagram mimics that of the sticky-sphere system. As expected, the radial distribution function g(r) and the structure factor S(k) of the effective one-component system show no sharp signature of the onset of the freezing transition 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-Verlet freezing criterion. Direct simulations of the true binary mixture of hard spheres were performed for q > or =0.05 in order to test the predictions from the effective Hamiltonian. For those packing fractions of the small spheres where direct simulations are possible, we find remarkably good agreement between the phase boundaries calculated from the two approaches-even up to the symmetric limit q=1 and for very high packings of the large spheres, where the solid-solid transition occurs. In both limits one might expect that an approximation which neglects higher-body terms should fail, but our results support the notion that the main features of the phase equilibria of asymmetric binary hard-sphere mixtures are accounted for by the effective pairwise depletion potential description. We also compare our results with those of other theoretical treatments and experiments on colloidal hard-sphere mixtures.