Phase diagrams of binary mixtures of patchy colloids with distinct numbers of patches: The network fluid regime

TL;DR

This paper investigates how the difference in patch number (functionality) between two types of patchy colloids influences their phase behavior, revealing conditions for phase separation, miscibility, and changes in phase diagram topology.

Contribution

It introduces a theoretical framework combining Wertheim's perturbation theory and Flory-Stockmayer's theory to analyze the phase diagrams of binary patchy colloid mixtures with varying functionalities.

Findings

Functionality difference controls phase separation and miscibility.

Phase diagram topology changes from type I to V when $f_A^{(1)}>2$.

Complete miscibility occurs when $f_A^{(2)}-f_A^{(1)}=1$, with closed gaps for larger differences.

Abstract

We calculate the network fluid regime and phase diagrams of binary mixtures of patchy colloids, using Wertheim's first order perturbation theory and a generalization of Flory-Stockmayer's theory of polymerization. The colloids are modelled as hard spheres with the same diameter and surface patches of the same type, $A$. The only difference between species is the number of their patches -or functionality-, $f_A^{(1)}$ and $f_A^{(2)}$ (with $f_A^{(2)}>f_A^{(1)}$). We have found that the difference in functionality is the key factor controlling the behaviour of the mixture in the network (percolated) fluid regime. In particular, when $f_A^{(2)}\ge2f_A^{(1)}$ the entropy of bonding drives the phase separation of two network fluids which is absent in other mixtures. This changes drastically the critical properties of the system and drives a change in the topology of the phase diagram (from type I to type V) when $f_A^{(1)}>2$. The difference in functionality also determines the miscibility at high (osmotic) pressures. If $f_A^{(2)}-f_A^{(1)}=1$ the mixture is completely miscible at high pressures, while closed miscibility gaps at pressures above the highest critical pressure of the pure fluids are present if $f_A^{(2)}-f_A^{(1)}>1$. We argue that this phase behaviour is driven by a competition between the entropy of mixing and the entropy of bonding, as the latter dominates in the network fluid regime.