Effects of patch size and number within a simple model of patchy colloids

TL;DR

This study combines computer simulations and integral equation theory to analyze how patch size and number affect the phase behavior of patchy colloids, revealing critical points, crystallization limits, and structural transitions as coverage varies.

Contribution

It provides a comprehensive analysis of the two-patch Kern-Frenkel model, extending understanding of patchy colloids by exploring coverage effects on phase behavior and structure.

Findings

Integral equation theory accurately predicts phase behavior for high coverage.

Critical points shift to lower densities and temperatures as coverage decreases.

Crystallization is prevented below a certain patch coverage, leading to structural transitions.

Abstract

We report on a computer simulation and integral equation study of a simple model of patchy spheres, each of whose surfaces is decorated with two opposite attractive caps, as a function of the fraction $\chi$ of covered attractive surface. The simple model explored --- the two-patch Kern-Frenkel model --- interpolates between a square-well and a hard-sphere potential on changing the coverage $\chi$. We show that integral equation theory provides quantitative predictions in the entire explored region of temperatures and densities from the square-well limit $\chi = 1.0$ down to $\chi \approx 0.6$. For smaller $\chi$, good numerical convergence of the equations is achieved only at temperatures larger than the gas-liquid critical point, where however integral equation theory provides a complete description of the angular dependence. These results are contrasted with those for the one-patch case. We investigate the remaining region of coverage via numerical simulation and show how the gas-liquid critical point moves to smaller densities and temperatures on decreasing $\chi$. Below $\chi \approx 0.3$, crystallization prevents the possibility of observing the evolution of the line of critical points, providing the angular analog of the disappearance of the liquid as an equilibrium phase on decreasing the range for spherical potentials. Finally, we show that the stable ordered phase evolves on decreasing $\chi$ from a three-dimensional crystal of interconnected planes to a two-dimensional independent-planes structure to a one-dimensional fluid of chains when the one-bond-per-patch limit is eventually reached.