Phase behavior and percolation in mixed patchy colloids

Patchy colloids can be modeled as hard spheres with directional conical association sites. A variety of physical phenomena have been discovered in the patchy colloid system due to its short range and directional interactions. In this work, we combined a cluster distribution theory with generalized Flory and Stockmayer percolation theory to investigate the interplay between phase behavior and percolation for a binary patchy colloid system. The binary patchy colloid system consists of solute molecules with spherically symmetric bonding sites and solvents with two singly bondable sites. Wertheim's first order thermodynamic perturbation theory (TPT1) has been widely applied to the patchy colloids system and it has been combined with percolation theory to study the percolation threshold. However, due to assumptions behind TPT1, it will lose accuracy for a system in which particles have multiple association sites or multiply bondable sites. A recently proposed cluster distribution theory accurately models association at sites that can form multiple bonds. In this work, we investigate the comparison among cluster distribution theory, TPT1, and Monte Carlo simulation for the bonding states of this binary system in which cluster distribution theory shows excellent agreement with Monte Carlo simulation, while TPT1 has a large deviation with the simulation. Cluster distribution theory was further combined with the Flory and Stockmayer percolation theory to investigate the interplay between phase behavior and percolation threshold. We found that the reduced density and the relative bonding strength of solvent-solvent association and solute-solvent association are key factors for the phase behavior and percolation. Percolation can form at low density and low temperature in the vapor phase of this binary system, where the star-like molecules with 12 long branches formed.