SAFT-P: A plaquette level perturbation for self-assembly in patchy colloids

Abstract

We introduce SAFT-P, a plaquette-level extension of Statistical Associating Fluid Theory for patchy particles. By treating local clusters as associating superparticles and contracting their free energy back to monomer densities, SAFT-P retains information about patch topology that is lost in conventional SAFT. Grand-canonical Monte Carlo simulations of binary and ternary mixtures show that SAFT-P captures topology-dependent critical points and coexistence curves and discriminates between particles with identical valence but different patch layouts. Beyond topology, incorporating plaquette-scale correlations also improves predictions in regimes where patch specific interactions are absent. Results indicate that resolving correlations at the plaquette scale provides an analytical route to model complex condensates and self-assembly with topology-sensitive local structure.

Figures (4)

• Figure 1: A schematic of a $2\times2$ plaquette and conversion of it into a superparticle. Internal bonds are in red and boundary edges in blue. Edge pairs in the same direction is converted to a single super-edge.
• Figure 2: Critical lines for stick-shaped (left) and L-shaped (right) particles as a function of directional and non-directional interaction strengths; insets depict the corresponding patch geometries.
• Figure 3: Components of the proposed isomeric mixture, From right to left: geometric isomer 1, geometric isomer 2, solvent
• Figure 4: Binodal of the isomeric mixture. Coexistence curve plotted as normalized temperature versus excess composition, where $\phi_1,\phi_2$ are the isomeric fractions in the two coexisting phases. Solid blue: theoretical binodal from plaquette coarse-grained free-energy / SAFT-P. Dashed orange: simulation binodal from Monte Carlo simulations on an $20\times20$ lattice