Rogers-Young Approximation Research Articles

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.

Transformation from Rogers-Young approximation to the density functional approach for nonuniform fluids: numerical recipe.

A numerical recipe is devised to extend the methodology [J. Chem. Phys. 112, 8079 (2000)] to nonhard-sphere nonuniform fluids where analytical expressions for the functional relationship of the bridge function as a function of indirect correlation function do not exist, the numerical recipe is also based on the universality of the free-energy density functional. As an example, the recipe is employed to calculate the density profile of a colloidal suspension near a single charged hard wall and the hard-sphere Yukawa fluid near a single hard wall and a single hard wall with an attractive tail, the agreement of the predictions of the theory with the simulation data is good. The difference of the present methodology from that of the weighted density approximation is discussed.

Theory of supercooled liquids and glasses for binary soft-sphere mixtures via a modified hypernetted-chain integral equation.

We discuss the equilibrium properties of highly supercooled binary soft-sphere fluids by a modified hypernetted-chain (MHNCS) equation proposed recently by us. The MHNCS approximation is made by a proper interpolation of the bridge functions of the Percus-Yevick hard-sphere model and the leading term of the elementary diagrams that were first successfully applied to classical one-component plasmas. The MHNCS approximation has been found to work well for one-component soft-sphere fluids above and below the freezing point. For a more crucial test, the MHNCS equation is extensively studied for the binary soft-sphere fluids. We have obtained numerical solutions of the MHNCS equation for a binary mixture of the 12th-inverse power potential with different core diameters. These results are compared with those of computer simulations and the Rogers-Young approximation. Below the freezing temperature, the solution of the MHNCS equation reproduces a splitting of the second peak of the pair distribution function (PDF) for various core size ratios, compatible with the computer simulations. Using the PDF thus obtained, thermodynamic and structural properties of the highly supercooled binary soft-sphere fluids are investigated.