Binary nucleation of sulfuric acid-water: Monte Carlo simulation

We have developed a classical mechanical model for the ${\mathrm{H}}_{\mathrm{2}}{\mathrm{SO}}_{\mathrm{4}}{\mathrm{/H}}_{\mathrm{2}}\mathrm{O}$ binary system. Monte Carlo simulation was performed in a mixed ensemble, in which the number of sulfuric acid molecules is fixed while that of water molecules is allowed to fluctuate. Simulation in this ensemble is computationally efficient compared to conventional canonical simulation, both in sampling very different configurations of clusters relevant in nucleation and in evaluating the free energy of cluster formation. The simulation yields molecular level information, such as the shape of the clusters and the dissociation behavior of the acid molecule in the cluster. Our results indicate that the clusters are highly nonspherical as a result of the anisotropic intermolecular interactions and that a cluster with a given number of acid molecules has several very different conformations, which are close in free energy and hence equally relevant in nucleation. The dissociation behavior of ${\mathrm{H}}_{\mathrm{2}}{\mathrm{SO}}_4$ in a cluster differs markedly from that in bulk solution and depends sensitively on the assumed value of the free energy $f_{\mathrm{hb}}$ of the dissociation reaction ${\mathrm{H}}_{\mathrm{2}}{\mathrm{SO}}_{\mathrm{4}}{\mathrm{+H}}_{\mathrm{2}}{\mathrm{O\to HSO}}_{\mathrm{4}}^{\mathrm{-}}{\mathrm{\cdot H}}_{\mathrm{3}}{\mathrm{O}}^{\mathrm{+}}\mathrm{.}$ In a small cluster, no dissociation is observed. As the cluster size becomes larger, the probability of having an ${\mathrm{HSO}}_{\mathrm{4}}^{\mathrm{-}}{\mathrm{\cdot H}}_{\mathrm{3}}{\mathrm{O}}^{+}$ ion pair increases. However, in clusters relevant in nucleation, the resulting ion pairs remain in contact; about 240 water molecules are required to observe behavior that resembles that in bulk solution. If a larger value of $f_{\mathrm{hb}}$ is assumed to reflect its uncertainty, the probability of dissociation becomes negligible. A reversible work surface obtained for a condition typical of vapor to liquid nucleation suggests that the rate-limiting step of new particle formation is a binary collision of two hydrated sulfuric acid molecules. The ion pairs formed by dissociation play a key role in stabilizing the resulting cluster. The reversible work surface is sensitive to the assumed value of $f_{\mathrm{hb}},$ thus pointing to the need for an accurate estimate of the quantity either by ab initio calculations or experiments.