Reference Interaction Site Model and Optimized Perturbation theories of colloidal dumbbells with increasing anisotropy

TL;DR

This study compares RISM and OPT theories in predicting the thermodynamic behavior of anisotropic colloidal dumbbells, showing that RISM aligns well with simulations except in high anisotropy regimes.

Contribution

It introduces a combined theoretical analysis of anisotropic colloidal dumbbells using RISM and OPT, providing benchmarks against simulations.

Findings

RISM accurately predicts coexistence curves except at high anisotropy.

Both theories show a linear critical temperature dependence on interaction strength.

Critical density predictions are less accurate as anisotropy increases.

Abstract

We investigate thermodynamic properties of anisotropic colloidal dumbbells in the frameworks provided by the Reference Interaction Site Model (RISM) theory and an Optimized Perturbation Theory (OPT), this latter based on a fourth-order high-temperature perturbative expansion of the free energy, recently generalized to molecular fluids. Our model is constituted by two identical tangent hard spheres surrounded by square-well attractions with same widths and progressively different depths. Gas-liquid coexistence curves are obtained by predicting pressures, free energies, and chemical potentials. In comparison with previous simulation results, RISM and OPT agree in reproducing the progressive reduction of the gas-liquid phase separation as the anisotropy of the interaction potential becomes more pronounced; in particular, the RISM theory provides reasonable predictions for all coexistence curves, bar the strong anisotropy regime, whereas OPT performs generally less well. Both theories predict a linear dependence of the critical temperature on the interaction strength, reproducing in this way the mean-field behavior observed in simulations; the critical density~--~that drastically drops as the anisotropy increases~--~turns to be less accurate. Our results appear as a robust benchmark for further theoretical studies, in support to the simulation approach, of self-assembly in model colloidal systems.