Canonical free-energy barrier of particle and polymer cluster formation

TL;DR

This paper introduces a shape-free method to determine free-energy barriers in particle and polymer cluster formation, enabling finite-size scaling analysis without defining cluster boundaries.

Contribution

It presents a novel shape-free approach for calculating free-energy barriers in cluster formation, applicable to both particles and polymers, validated through simulations.

Findings

Agreement with theoretical predictions for particle droplet formation

Extension of the method to polymer solutions

Analogy between polymer cluster formation and particle condensation

Abstract

A common approach to study nucleation rates is the estimation of free-energy barriers. This usually requires knowledge about the shape of the forming droplet, a task that becomes notoriously difficult in macromolecular setups starting with a proper definition of the cluster boundary. Here, we demonstrate a shape-free determination of the free energy for temperature-driven cluster formation in particle as well as polymer systems. Combined with rigorous results on equilibrium droplet formation, this allows for a well-defined finite-size scaling analysis of the effective interfacial free energy at fixed density. We first verify the theoretical predictions for the formation of a liquid droplet in a supersaturated particle gas by generalized-ensemble Monte Carlo simulations of a Lennard-Jones system. Going one step further, we then generalize this approach to cluster formation in a dilute polymer solution. Our results suggest an analogy with particle condensation, when the macromolecules are interpreted as extended particles.