Determining Bulk Equilibrium Constants for Cluster Formation from Constant NVT Ensemble Simulations at Small N

Understanding the behavior of systems that display self-assembly or phase nucleation requires calculation of free energies of reversibly associated clusters as a function of number of monomers in the cluster. The law of mass action provides the connection between these free energies and the equilibrium distribution of cluster sizes in a large system via the equilibrium constant for association of monomers into clusters. Direct application of the law of mass action to find these free energies or association constants is only valid for sufficiently large systems, which may be inconvenient to simulate explicitly. This report gives a brief review of some established strategies to find cluster free energies, then highlights a recently developed approach to correlate equilibrium cluster size distributions in small systems with the size-dependent equilibrium constants that can be applied in the bulk. A demonstration of the ability of this approach to predict size distributions of Lennard-Jones clusters in small-system NVT simulations is presented.