On the application of Flory–Huggins and integral equation theories to asymmetric hard sphere mixtures

General theory of asymmetric steric interactions in electrostatic double layers

We study the mean-field Poisson-Boltzmann equation in the context of dense ionic liquids where steric effects become important. We generalise lattice gas theory by introducing a Flory-Huggins entropy for ions of differing volumes and then compare the effective free energy density to other existing lattice gas approximations, not based on the Flory-Huggins Ansatz. Within the methodology presented we also invoke more realistic equations of state, such as the Carnahan-Starling approximation, that are not based on the lattice gas approximation and lead to thermodynamic functions and properties that differ strongly from the lattice gas case. We solve the Carnahan-Starling model in the high density limit, and demonstrate a slow, power-law convergence at high potentials. We elucidate how equivalent convex free energy functions can be constructed that describe steric effects in a manner which is more convenient for numerical minimisation.

Virial Coefficients and Demixing of Athermal Nonadditive Mixtures

We compute the fourth virial coefficient of a binary nonadditive, hard-sphere mixture over a wide range of deviations from diameter additivity and size ratios. Hinging on this knowledge, we build up a y expansion (Barboy, B.; Gelbart, W. N. J. Chem. Phys. 1979, 71, 3053) in order to trace the fluid-fluid coexistence lines, which we then compare with the available Gibbs-ensemble Monte Carlo data and with the estimates obtained through two refined integral-equation theories of the fluid state. We find that in a regime of moderately negative nonadditivity and largely asymmetric diameters, relevant to the modeling of sterically and electrostatically stabilized colloidal mixtures, the fluid-fluid critical point is unstable with respect to crystallization.

Thermodynamic Stability of Fluid−Fluid Phase Separation in Binary Athermal Mixtures: The Role of Nonadditivity

We studied the thermodynamic stability of fluid-fluid phase separation in binary nonadditive mixtures of hard-spheres for moderate size ratios. We are interested in elucidating the role played by small amounts of nonadditivity in determining the stability of fluid-fluid phase separation with respect to the fluid-solid phase transition. The demixing curves are built in the framework of the modified-hypernetted chain and of the Rogers-Young integral equation theories through the calculation of the Gibbs free energy. We also evaluated fluid-fluid phase equilibria within a first-order thermodynamic perturbation theory applied to an effective one-component potential obtained by integrating out the degrees of freedom of the small spheres. A qualitative agreement emerges between the two different approaches. We also addressed the determination of the freezing line by applying the first-order thermodynamic perturbation theory to the effective interaction between large spheres. Our results suggest that for intermediate size ratios a modest amount of nonadditivity, smaller than earlier thought, can be sufficient to drive the fluid-fluid critical point into the thermodinamically stable region of the phase diagram. These findings could be significant for rare-gas mixtures in extreme pressure and temperature conditions, where nonadditivity is expected to be rather small.

Self-consistent molecular field theory for packing in classical liquids

Building on a quasichemical formulation of solution theory, this paper proposes a self-consistent molecular field theory for packing problems in classical liquids, and tests the theoretical predictions for the excess chemical potential of the hard sphere fluid. Results are given for the self-consistent molecular fields obtained, and for the probabilities of occupancy of a molecular observation volume. For this system, the excess chemical potential predicted is nearly as accurate as the most accurate prior theories, specifically the scaled particle (Percus-Yevick compressibility) theory. A compact formula is obtained to throw light on the variation of the chemical potential with the radius of a distinguished hard sphere solute in general solvents. It is argued that the present approach is particularly simple, permits a natural description of possibilities for multiphasic behavior of the solution, and should provide a basis for a molecular-scale description of more complex solutions.