Fluids with competing interactions: II. Validating a free energy model for equilibrium cluster size

TL;DR

This paper validates a semi-empirical free energy model predicting equilibrium cluster sizes in fluids with competing short-range attraction and long-range repulsion, using extensive computer simulations.

Contribution

It extends and improves a classical free energy-based model by incorporating size-dependent interface energy penalties, validated against extensive simulation data.

Findings

Model accurately predicts cluster sizes between 6 and 60 monomers.

Identifies a superlinear scaling regime for intracluster bonding.

Provides a framework for understanding self-limiting aggregation in complex fluids.

Abstract

Using computer simulations, we validate a simple free energy model that can be analytically solved to predict the equilibrium size of self-limiting clusters of particles in the fluid state governed by a combination of short-range attractive and long-range repulsive pair potentials. The model is a semi-empirical adaptation and extension of the canonical free energy-based result due to Groenewold and Kegel [J. Phys. Chem. B, 105 (2001)], where we use new computer simulation data to systematically improve the cluster-size scalings with respect to the strengths of the competing interactions driving aggregation. We find that one can adapt a classical nucleation like theory for small energetically-frustrated aggregates provided one appropriately accounts for a size-dependent, microscopic energy penalty of interface formation, which requires new scaling arguments. This framework is verified in part by considering the extensive scaling of intracluster bonding, where we uncover a superlinear scaling regime distinct from (and located between) the known regimes for small and large aggregates. We validate our model based on comparisons against approximately 100 different simulated systems comprising compact spherical aggregates with characteristic (terminal) sizes between six and sixty monomers, which correspond to wide ranges in experimentally-controllable parameters.