Asymmetric Binary Hard-sphere Mixtures Research Articles

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

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

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.

Influence of polydispersity on the critical parameters of an effective-potential model for asymmetric hard-sphere mixtures

We report a Monte Carlo simulation study of the properties of highly asymmetric binary hard-sphere mixtures. This system is treated within an effective fluid approximation in which the large particles interact through a depletion potential [R. Roth, Phys. Rev. E 62 5360 (2000)] designed to capture the effects of a virtual sea of small particles. We generalize this depletion potential to include the effects of explicit size dispersity in the large particles and consider the case in which the particle diameters are distributed according to a Schulz form having a degree of polydispersity 14%. The resulting alteration (with respect to the monodisperse limit) of the metastable fluid-fluid critical point parameters is determined for two values of the ratio of the diameters of the small and large particles: q(triple bond)sigma(s)/(-)sigma(b)=0.1 and q=0.05. We find that the inclusion of polydispersity moves the critical point to lower reservoir volume fractions of the small particles and high volume fractions of the large ones. The estimated critical point parameters are found to be in good agreement with those predicted by a generalized corresponding states argument which provides a link to the known critical adhesion parameter of the adhesive hard-sphere model. Finite-size scaling estimates of the cluster percolation line in the one phase fluid region indicate that inclusion of polydispersity moves the critical point deeper into the percolating regime. This suggests that phase separation is more likely to be preempted by dynamical arrest in polydisperse systems.

Freezing of Charge-Stabilized Colloidal Dispersions

The Rogers-Young approximation for the Ornstein-Zernike integral equation is combined with the Hansen-Verlet one-phase criterion for freezing to predict freezing of a hard core repulsive Yukawa model (HCRYM) fluid. Comparison of theoretical predictions with corresponding computer simulation data discloses the superiority of the Rogers-Young approximation over the hypernetted chain approximation and the rescaled mean spherical approximation for freezing. Then, the Rogers-Young approximation combined with the Hansen-Verlet one-phase criterion is employed for the freezing of many-component charge-stabilized colloidal dispersions, which consist of colloidal macroions, electrolyte small ions, and solvent molecules and are modeled as a single-component charged hard core macroion interacting through a screened Coulomb potential. The theoretically predicted freezing line with the macroion surface charge number being assumed as an adjustable parameter is in very good agreement with the corresponding experimental data. The reason why, by the empirical Hansen-Verlet structure function approach, the single-component coarse-grained effective potential is valid for the freezing description of the many-component charge-stabilized colloidal solutions but not valid for the case of asymmetric binary hard sphere mixtures is discussed.

True mixture versus effective one component fluid models of asymmetric binary hard sphere mixtures: a comparison by simulation

The pair distribution function of solute particles determined by simulation of true mixtures with diameter ratios of 5, 10 and 20 is compared with that obtained in their representation by effective one-component fluids with pairwise additive interactions. The pair distribution function near contact is found to be overestimated by the effective fluid approach, for all size ratios. In the domain of the phase diagram accessible to the simulation algorithm, the deviation is found to be moderate. Its consequences for the coexistence lines are discussed.

Triplet depletion forces from density functional optimization

A novel density functional theory optimization technique, based on Rosenfeld's “fundamental measure ” theory for hard-core particles and the use of an adaptive real-space grid, is developed to investigate highly asymmetric binary mixtures of hard spheres as models of bidisperse colloidal suspensions. The method is applied to the calculation of pair and triplet depletion forces between large colloids in a bath of much smaller colloidal particles. The computed pair forces are in generally good agreement with theoretical predictions and previous Monte Carlo work. The triplet forces, explicitly calculated for the first time, are an order of magnitude weaker than the much-studied pair interactions, and appear to be attractive.

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.

Stability of the AB crystal for asymmetric binary hard sphere mixtures

The thermodynamic stability of the AB (rocksalt) structure for binary mixtures of hard spheres is established by means of Monte Carlo and molecular dynamics simulations. Constant pressure and constant volume phase diagrams are presented for size ratios √2−1 and 0·45. A phase-separation molecular dynamics experiment is described, confirming the predictions of the phase diagram.

Stability of the AB crystal for asymmetric binary hard sphere mixtures

The thermodynamic stability of the AB (rocksalt) structure for binary mixtures of hard spheres is established by means of Monte Carlo and molecular dynamics simulations. Constant pressure and constant volume phase diagrams are presented for size ratios √2−1 and 0·45. A phase-separation molecular dynamics experiment is described, confirming the predictions of the phase diagram.

Binary hard-sphere mixtures: a comparison between computer simulation and experiment

The complex crystalline order, recently observed by Bartlett, P., Ottewill, R. H., and Pusey, P. N., 1992, Phys. Rev. Lett., 68, 3801, in asymmetric binary hard-sphere mixtures is discussed in detail. Experimental observation on phase separation in a complex fluid, a binary suspension of near hard-sphere colloids, are compared with phase diagrams obtained from computer simulations of an atomic hard-sphere liquid. Although there is in general a close degree of agreement between experiment and theory, a detailed comparison shows several unexpected differences. These differences are shown to reflect non-equilibrium effects, and possible reasons for their origin are evaluated.