Canonical free-energy barrier of particle and polymer cluster formation

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.