Accounting for Finite-Number Effects on Cluster Size Distributions in Simulations of Equilibrium Aggregation.

An approach is given to analyze aggregate size distributions obtained from simulations of a fixed number N of monomers undergoing reversible self-assembly. Equilibrium distributions are derived from size-dependent equilibrium association constants by appropriately weighted sums over all partitions of N monomers into aggregates. Conversely, equilibrium association constants can be obtained from an iterative fit to a finite-N equilibrium distribution. Model data for a micelle-forming system are used to show how results from simulations containing few micelles can yield infinite-N limiting distributions. A strategy is also suggested to exploit small-N effects on aggregate size distributions to enhance sampling of critical clusters in determination of nucleation free energy functions.