Additive and non-additive hard sphere mixtures

Alternative Approaches to the Equilibrium Properties of Hard-Sphere Liquids

“…Nevertheless, the study of non-additive systems goes back fifty years [54][55][56] and is still a rapidly developing and challenging problem. As mentioned in the paper by Ballone et al [57], where the relevant references may be found, experimental work on alloys, aqueous electrolyte solutions, and molten salts suggests that hetero-coordination and homocoordination may be interpreted in terms of excluded volume effects due to non-additivity of the repulsive part of the intermolecular potential. In particular, positive non-additivity leads naturally to demixing in HS mixtures, so that some of the experimental findings of phase separation in the above mentioned (real) systems may be accounted for by using a model of a binary mixture of (positive) non-additive HS.…”

Depletion effects in binary hard-sphere fluids

“…For hard-sphere mixtures, the first successful integral equation was the famous Percus-Yevick equation [8]. However, more recent integral equations, such as the ones that result from the closures proposed by Rogers and Young (RY) [9] and by Ballone, Pastore, Galli and Gazzillo (BPGG) [10], have proven to provide a more accurate estimate of the pair structure of a hard-sphere fluid, in particular at high densities. Introducing the notation γ αβ (r) = h αβ (r) − c αβ (r), the PY, RY and BPGG closure relations take the forms…”

Molecular theory of partial molar volume and its applications to biomolecular systems

“…They found that the quantitative predictive capabilities of the RISM theory were improved by adopting the Martynov-Sarkisov (MaS) closure [82] or its generalization, the Ballone-Pastore-Galli-Gazzillo (BPGG) closure [83]. The bridge function for the latter is given by…”