Analytic solution of the multidensity Ornstein-Zernike equation for hard-sphere fluid with tetrahedral quadrupolar-like surface adhesion

TL;DR

This work addresses the challenge of describing hard-sphere fluids with anisotropic, tetrahedral-like surface adhesion by developing a multidensity Ornstein–Zernike framework with an associative Percus–Yevick closure. The authors derive an analytic solution using the invariant expansion method and Baxter factorization, enabling calculation of structural and thermodynamic properties. A key finding is that, while low stickiness yields agreement with single-density approaches, increasing stickiness requires the multidensity description as the single-density theory can lose convergence. The results highlight the importance of multidensity treatments for strongly associating anisotropic fluids and set the stage for future simulations and model extensions including additional dipolar features.

Abstract

We develop a multidensity formulation of the Ornstein-Zernike equation with Percus-Yevick closure for hard spheres with anisotropic surface adhesion of tetrahedral quadrupolar-like symmetry. An analytical solution is obtained using the invariant expansion method combined with Baxter's factorization technique. Structural properties are evaluated using both the multidensity theory and the previously proposed single-density molecular OZ approach. At low stickiness, the two theories yield nearly identical predictions, while increasing stickiness leads to growing discrepancies and eventual loss of convergence of the single-density approach. These results highlight the importance of multidensity descriptions for strongly associating anisotropic fluids.

Figures (3)

• Figure 1: Fractions of $i-$times bonded particles $x_i$: $x_0$ (black lines), $x_1$ (brown lines), $x_2$ (blue lines), $x_3$ (green lines) and $x_4$ (red lines) at $\tau=0.5$ (solid lines) and $\tau=0.04$ (dashed lines).
• Figure 2: The radial distribution function $g^{000}_{00}(r)$ and projections $h^{22l}_{22}(r)$ for $\tau=0.5$ (left column of panels), $\tau=0.1$ (middle column of panels) and $\tau=0.04$ (right column of panels). Here $\rho=0.4$ (red lines), $\rho=0.8$ (black lines), solid lines represent results of the present mult-idensity theory and dashed lines represent results of the single-density theory cummings1986analytic.
• Figure 3: The radial distribution function $g^{000}_{00}(r)$ and projections $h^{22l}_{22}(r)$ for $\tau=0.5$ (left column of panels), $\tau=0.1$ (middle column of panels) and $\tau=0.04$ (right column of panels). Here $\rho=0.4$ (red lines), $\rho=0.8$ (black lines), solid lines represent results of the present mult-idensity theory and dashed lines represent results of the single-density theory cummings1986analytic.