Cluster Free Energies from Simple Simulations of Small Numbers of Aggregants: Nucleation of Liquid MTBE from Vapor and Aqueous Phases

Abstract

We introduce a global fitting analysis method to obtain free energies of association of noncovalent molecular clusters using equilibrated cluster size distributions from unbiased constant-temperature molecular dynamics (MD) simulations. Because the systems simulated are small enough that the law of mass action does not describe the aggregation statistics, the method relies on iteratively determining a set of cluster free energies that, using appropriately weighted sums over all possible partitions of N monomers into clusters, produces the best-fit size distribution. The quality of these fits can be used as an objective measure of self-consistency to optimize the cutoff distance that determines how clusters are defined. To showcase the method, we have simulated a united-atom model of methyl tert-butyl ether (MTBE) in the vapor phase and in explicit water solution over a range of system sizes (up to 95 MTBE in the vapor phase and 60 MTBE in the aqueous phase) and concentrations at 273 K. The resulting size-dependent cluster free energy functions follow a form derived from classical nucleation theory (CNT) quite well over the full range of cluster sizes, although deviations are more pronounced for small cluster sizes. The CNT fit to cluster free energies yielded surface tensions that were in both cases lower than those for the simulated planar interfaces. We use a simple model to derive a condition for minimizing non-ideal effects on cluster size distributions and show that the cutoff distance that yields the best global fit is consistent with this condition.

Simulations of NaCl Aggregation from Solution: Solvent Determines Topography of Free Energy Landscape

“…Our previous report of MTBE cluster formation discussed how nonideal contributions to cluster free energies from excluded volume effects might be finessed with an appropriate choice of cluster cut‐off, through which a change in free volume associated with monomer association or dissociation is balanced by changes in attractive interactions between monomers. Varying cut‐offs did not, however, improve the systematic nonideal effects revealed in the present aqueous NaCl systems.…”

“…S1) and thus it was not possible to identify a cutoff that minimized the error of the global fit as was done in Ref. []. An example of how the cutoff distance influences the best‐fit free energy curve is given in Supporting Information Figure S1; in this example the variation over a range of cutoff distances 0.32–0.39 nm is <1 k B T .…”

“…At these smaller system sizes, the formation and breaking of larger clusters significantly alters the concentration of other cluster sizes in the system and the law of mass action no longer serves as a good model to calculate the equilibrium association constants. Our previous work on methyl t‐butyl ether (MTBE) cluster formation shows that the deviation from the real association constants increase as cluster size increases . A number of approaches have been used to account for this depletion effect in simulations of nucleation at fixed number of particles .…”

“…Our previous work on methyl t-butyl ether (MTBE) cluster formation shows that the deviation from the real association constants increase as cluster size increases. [35] A number of approaches have been used to account for this depletion effect in simulations of nucleation at fixed number of particles. [27,[36][37][38] Here, we apply the recently developed partition enabled analysis of cluster histograms (PEACH) method, which avoids this problem as it accounts for the discrete nature of state partitions explicitly.…”

Re‐weighted random series path integral simulations of molecular clusters: Applications to lithium solvated by a mixed Stockmayer cluster

“…Clusters are gas phase nano‐sized aggregates of matter, they are vitally important for technological advances, and can serve as model systems to untangle and simplify the investigation of otherwise intractable problems at the fundamental level using a combination of theoretical and experimental methods. The contributions along these two lines are so numerous that it would be impossible to provide a meaningful comprehensive review of the literature within the confines of a research article. One fundamental issue that can be addressed theoretically and experimentally using clusters is the determination of the nuclear quantum effects on the dynamics and thermodynamics of microsolvation.…”