Analysis of molecular aggregation equilibria using random mixing statistics.

Aggregation processes in both the gas phase and aqueous solutions are analyzed by comparing aggregate size distributions obtained from molecular dynamics simulations with analytical predictions pertaining to a nonaggregating random mixture. The latter predictions are obtained by using the binomial distribution to predict the statistical properties of a uniformly mixed solution containing molecules of the same size and concentration as those in the solution of interest. Simulations are performed on systems containing neopentane dissolved in either methane, aqueous methanol, or aqueous NaI solutions. Comparisons of the theoretical and simulation results are used to both classify and quantify the influence of intermolecular interactions on such aggregation processes, including the equilibrium constants and thermodynamic functions pertaining to the partitioning of molecules between the bulk and first coordination shell of neopentane. Although the present results are primarily intended to describe and illustrate the random mixing analysis strategy, they also imply that neopentane has a greater tendency to aggregate with methane in the dense gas phase than with either methanol or iodide ions in aqueous solutions.