Demixing transition, structure, and depletion forces in binary mixtures of hard-spheres: The role of bridge functions

Abstract

Asymmetric binary mixtures of hard-spheres exhibit several interesting thermodynamic phenomena, such as multiple kinds of glassy states. When the degrees of freedom of the small spheres are integrated out from the description, their effects are incorporated into an effective pair interaction between large spheres known as the depletion potential. The latter has been widely used to study both the phase behavior and dynamic arrest of the big particles. Depletion forces can be accounted for by a contraction of the description in the multicomponent Ornstein-Zernike equation [R. Castañeda-Priego, A. Rodríguez-López, and J. M. Méndez-Alcaraz, Phys. Rev. E 73, 051404 (2006)]. Within this theoretical scheme, an approximation for the difference between the effective and bare bridge functions is needed. In the limit of infinite dilution, this difference is irrelevant and the typical Asakura-Osawa depletion potential is recovered. At higher particle concentrations, however, this difference becomes important, especially where the shell of first neighbors is formed, and, as shown here, cannot be simply neglected. In this work, we use a variant of the Verlet expression for the bridge functions to highlight their importance in the calculation of the depletion potential at high densities and close to the spinodal decomposition. We demonstrate that the modified Verlet closure predicts demixing in binary mixtures of hard spheres for different size ratios and compare its predictions with both liquid state and density functional theories, computer simulations, and experiments. We also show that it provides accurate correlation functions even near the thermodynamic instability; this is explicitly corroborated with results of molecular dynamics simulations of the whole mixture. Particularly, our findings point toward a possible universal behavior of the depletion potential around the spinodal line.

Note: Depletion potentials in non-additive asymmetric binary mixtures of hard-spheres

“…However, we have demonstrated that for this type of systems a variant of the Verlet closure, proposed by Kinoshita, 2 allowed us to accurately determine all the structural functions needed to evaluate the effective pair potential between big spheres. 1 In this note, we show that our formalism for the effective interactions can also be applied to non-additive mixtures. For a binary mixture we then have three different parameters characterizing the hard-sphere interactions: σ 11 , σ 12 (=σ 21 ), and σ 22 , where σ 11 ≥ σ 22 .…”

“…Based on the contraction of the description, developed within the framework of integral equations theory, we have recently shown that the depletion potential among big particles, u eff 11 (r), in an additive asymmetric binary mixture of hard-spheres can be calculated at all particle concentrations. 1 In fact, it is possible to evaluate the effective potential near the theoretically predicted demixing transition provided the difference between the effective and bare bridge functions of the observable species (in this case the big spheres) is explicitly known. There is not established universal bridge function for additive binary mixtures of hard-spheres.…”

“…(2) is the difference between the bare and the effective bridge functions. 1 Then, according to Eq. (2) all the details of the effective potential are fully contained in the correlation functions.…”

“…1 Effective potentials represent a reduced description of many-body systems, since the explicit incorporation of all the degrees of freedom in any theoretical framework is an impossible task. Based on the contraction of the description, developed within the framework of integral equations theory, we have recently shown that the depletion potential among big particles, u eff 11 (r), in an additive asymmetric binary mixture of hard-spheres can be calculated at all particle concentrations.…”

“…To assess the accurateness of the m-Verlet approximation, we have systematically compared its predictions with an event-driven molecular dynamics (MD) algorithm, 1 where the non-additivity is introduced according to Eq. (1).…”