Self-Assembly of Patchy Particles into Polymer Chains: A Parameter-Free Comparison between Wertheim Theory and Monte Carlo Simulation

TL;DR

This study compares Wertheim theory and Monte Carlo simulations for a simple patchy particle model that self-assembles into polymer chains, showing excellent agreement without fitting parameters.

Contribution

It provides a parameter-free validation of Wertheim theory against simulations for particle self-assembly into chains, a first for this model.

Findings

Wertheim theory predictions match simulation data closely.

Thermodynamic properties of self-assembled chains are accurately described.

The model effectively captures equilibrium polymerization behavior.

Abstract

We numerically study a simple fluid composed of particles having a hard-core repulsion, complemented by two short-ranged attractive (sticky) spots at the particle poles, which provides a simple model for equilibrium polymerization of linear chains. The simplicity of the model allows for a close comparison, with no fitting parameters, between simulations and theoretical predictions based on the Wertheim perturbation theory, a unique framework for the analytic prediction of the properties of self-assembling particle systems in terms of molecular parameter and liquid state correlation functions. This theory has not been subjected to stringent tests against simulation data for ordering across the polymerization transition. We numerically determine many of the thermodynamic properties governing this basic form of self-assembly (energy per particle, order parameter or average fraction of particles in the associated state, average chain length, chain length distribution, average end-to-end distance of the chains, and the static structure factor) and find that predictions of the Wertheim theory accord remarkably well with the simulation results.