Associative Percus-Yevick Approximation Research Articles

Analytic solution of two-density integral equations for sticky Janus dumbbells with arbitrary monomer diameters.

We study a pure fluid of heteronuclear sticky Janus dumbbells, considered to be the result of complete chemical association between unlike species in an initially equimolar mixture of hard spheres (species A) and sticky hard spheres (species B) with different diameters. The B spheres are particles whose attractive surface layer is infinitely thin. Wertheim's two-density integral equations are employed to describe the mixture of AB dumbbells together with unbound A and B monomers. After Baxter factorization, these equations are solved analytically within the associative Percus-Yevick approximation. The limit of complete association is taken at the end. The present paper extends to the more general, heteronuclear case of A and B species with size asymmetry a previous study by Wu and Chiew [J. Chem. Phys. 115, 6641 (2001)], which was restricted to dumbbells with equal monomer diameters. Furthermore, the solution for the Baxter factor correlation functions qij (αβ)(r) is determined here in a fully analytic way, since we have been able to find explicit analytic expressions for all the intervening parameters.

Theoretical and numerical investigations of inverse patchy colloids in the fluid phase.

We investigate the structural and thermodynamic properties of a new class of patchy colloids, referred to as inverse patchy colloids (IPCs) in their fluid phase via both theoretical methods and simulations. IPCs are nano- or micro- meter sized particles with differently charged surface regions. We extend conventional integral equation schemes to this particular class of systems: our approach is based on the so-called multi-density Ornstein-Zernike equation, supplemented with the associative Percus-Yevick approximation (APY). To validate the accuracy of our framework, we compare the obtained results with data extracted from NpT and NVT Monte Carlo simulations. In addition, other theoretical approaches are used to calculate the properties of the system: the reference hypernetted-chain (RHNC) method and the Barker-Henderson thermodynamic perturbation theory. Both APY and RHNC frameworks provide accurate predictions for the pair distribution functions: APY results are in slightly better agreement with MC data, in particular at lower temperatures where the RHNC solution does not converge.

The reference system for the highly asymmetric electrolyte solutions: The analytical treatment

A multicomponent model of dimerizing hard spheres is proposed for the description of association and clusterization in highly asymmetric electrolyte solutions. The special type of association between small and large spheres permits the larger spheres to be bond with many smaller spheres. General expressions for the Wertheim-Baxter factor correlation functions for this model are obtained in the Wertheim's associative Percus-Yevick approximation. Some numerical calculations illustrate the influence of association on the structural properties of the model.

Effective interaction between hard sphere colloidal particles in a polymerizing Yukawa solvent

The effective interaction between colloidal hard sphere particles in a Yukawa solvent that can polymerize with the formation of chains and rings is studied and compared with the corresponding results for colloidal hard sphere particles in a solvent of polymerizing hard spheres. The attractive nature of the polymerizing Yukawa solvent particles induces significant changes in the effective interactions between the colloid particles as compared to a polymerizing solvent of hard spheres that was investigated in previous studies. The results for the colloid–solvent mixture are obtained using the associative Percus–Yevick approximation for Wertheim’s Ornstein–Zernike integral equation; the colloidal species are taken at a nonvanishing but very small concentration throughout this article. We present the effects of the size ratio of colloid spheres to solvent spheres, the degree of polymerization, and the solvent density on the effective interactions between colloid and solvent particles. The intercolloidal potential of mean force (PMF) is found to be highly dependent on these parameters for Wertheim’s model. It is found that the correlations between colloid particles obtained using the Yukawa solvent model are longer ranged and more attractive than those found using the hard sphere solvent model. A greater depletion of the solvent density around the colloidal particles is also observed for the Yukawa solvent model as compared to the hard sphere model; an increased polymer chain length also enhances the depletion of the solvent density. The PMF is found to be oscillatory in structure. The oscillatory structure also depends upon the average polymer chain length, specifically, the oscillatory structure in the PMF is strongly diminished as the average polymer chain length increases. Additionally, as the average polymer length increases, the attraction at the colloid–colloid contact distance decreases.

The effective interaction between colloidal hard sphere particles in a polymerizing solvent. Application of Wertheim's theory of association

The effective interaction between colloidal particles in a solvent of hard spheres, which can polymerize with the formation of chains and rings, is studied. Polymerization results in changes of the effective interaction between the colloid particles, compared with the effective interaction for unpolymerized solvents that has been extensively studied in previous publications. To describe the mixture, we use the associative Percus-Yevick approximation for Wertheim's Ornstein-Zernike integral equation. Both the infinite dilution and the nonvanishing concentration limits for the colloid species are considered. It is shown that, in the model of Wertheim for polymerization, the intercolloidal potential of mean force (PMF) depends primarily on the solvent density and to a lesser extent on the degree of polymerization. A depletion of the solvent density around the colloid particles is observed. If the solvent consists of longer chains, compared with hard spheres, the correlations between the colloid particles are of longer range. The oscillations of the PMF depend upon the average chain length but not so strongly as in the model with chains having a fixed number of beads; this is probably due to the flexibility of the chain conformations in Wertheim's model. We also study the effect of the size ratio of the colloid spheres and the solvent monomers. We observe that the polymer hypernetted chain closure is difficult to apply to the systems under study. This closure shares difficulties, especially near the critical point, that are well known in the study of the phase diagram of fluids with both repulsive and attractive interactions. For large colloidal particles, the mixed closure of Henderson is useful.

Solution of the Percus-Yevick approximation for an n-component mixture of associating hard spheres in the multidensity formalism

The analytical solution of Wertheim's associative Percus-Yevick approximation for an M-component mixture of associating hard spheres in the multidensity formalism is analysed. The general expressions for the Wertheim-Baxter factor correlation functions, partial structure factors and thermodynamic quantities are obtained.

Chemical equilibrium in a solution of a dimerizing fluid in a hard sphere solvent. Associative Percus-Yevick approximation

The dimerization of hard spheres in a hard sphere solvent is studied. Earlier, Cummings and Stell examined this system using the usual Ornstein-Zernike formalism and found that the law of mass action is not satisfied. Here we apply the theory of Wertheim for association and the associative Percus-Yevick closure. Many of our results are qualitatively similar to those of Cummings and Stell. The association constant increases with the reactant density. We find that the reaction equilibria can be controlled by varying solvent density, but to a much lower extent than predicted from the usual Percus-Yevick approximation.

Solvation Force for an Associative Fluid in a Slit-like Pore

The solvation force for an associating fluid inside a slit-like pore is studied by using a singlet theory of inhomogeneous fluids. A one-component system of hard spheres with an embedded sticky attractive site located inside their hard cores is chosen as a model of the bulk fluid. The bulk fluid is considered in the framework of Wertheim's theory of association. Two models permitting dimerization and characterized by different bond lengths are investigated. It is shown that the associative Percus–Yevick approximation in conjunction with the singlet theory of inhomogeneous fluids provide a quilitatively correct description of the solvation force dependence on the pore width for low and intermediate densities. For a fluid of short dimers the applicability of the theory is restricted to low densities. An increase of the degree of dimerization leads to an overall decrease of the value of the solvation force. Its dependence on the pore width is qualitatively similar for low and high degrees of dimerization. For high degrees of dimerization the curves possess cusps for the pore width equal to the bonding length. For an increasing density the oscillations of the solvation force are observed. Their decay with an increasing pore width depend on the degree of association. However, in a whole range of the degree of association, the distance between the first maxima is approximately equal to the hard-sphere diameter.

Solution of the associative Percus-Yevick approximation for the multicomponent mixture of dimerizing hard spheres with surface adhesion

An analytical solution of the two-density Ornstein-Zernike equation closed by the associative Percus-Yevick approximation for the multicomponent mixture of dimerizing adhesive hard spheres (DAHS) is obtained in closed form. This is the generalization of the previous solution for the one-component DAHS model, which has been proposed for the description of protein effect on the properties of reverse micelles. Although the solution is illustrated by its application to the structure of the two-component model, it can be easily utilized for the arbitrary number of components.

Solution of the associative Percus—Yevick approximation for the n-component mixture of dimerizing hard spheres

An analytical solution of Wertheim's associative Percus-Yevick (APY) approximation for the n-component mixture of dimertizing hard spheres is presented. The solution is illustrated by the numerical results obtained for the two-component mixture with associative interaction only between particles of a different sort. In the limiting case of complete dimerization the results of the APY approximation are in good agreement with the predictions of the Monte Carlo simulation performed for the corresponding system of heteronuclear hard dumbbells. In this limit the present solution can be used as a simple analytical approach in the description of the system of heteronuclear hard dumbbells and their mixtures.