Isamu Kusaka

Binary nucleation of sulfuric acid-water: Monte Carlo simulation

We have developed a classical mechanical model for the H2SO4/H2O 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 H2SO4 in a cluster differs markedly from that in bulk solution and depends sensitively on the assumed value of the free energy f(hb) of the dissociation reaction H2SO4+H2O-HSO4-. H3O+. In a small cluster, no dissociation is observed. As the cluster size becomes larger, the probability of having an HSO4-. H3O+ 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(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(hb), thus pointing to the need for an accurate estimate of the quantity either by ab initio calculations or experiments.

Direct evaluation of the equilibrium distribution of physical clusters by a grand canonical Monte Carlo simulation

A new approach to cluster simulation is developed in the context of nucleation theory. This approach is free of any arbitrariness involved in the definition of a cluster. Instead, it preferentially and automatically generates the physical clusters, defined as the density fluctuations that lead to nucleation, and determines their equilibrium distribution in a single simulation, thereby completely bypassing the computationally expensive free energy evaluation that is necessary in a conventional approach. The validity of the method is demonstrated for a single component system using a model potential for water under several values of supersaturation.

Thermodynamic formulas of liquid phase nucleation from vapor in multicomponent systems

Interfacial thermodynamics is extended to noncritical liquid clusters in vapor for multicomponent systems so as to clarify the uncertainty over whether or not size and composition dependence of interfacial tension must be taken into account in taking the extremity condition of the reversible work of forming a noncritical cluster to derive the size and the composition of a critical nucleus. It is found that the differential of interfacial tension does not arise in the extremity condition due to the Gibbs–Duhem relation derived for a system of a noncritical cluster and the vapor which is in equilibrium under an additional constraint to maintain the number of molecules contained in a cluster.

Identifying physical clusters in vapor phase nucleation

We present a new approach to cluster simulation as a step toward a molecular theory of vapor phase nucleation. This approach does not involve a cluster criterion which is commonly introduced to determine whether a given molecule in the system belongs to the vapor or to a cluster for any instantaneous configuration of molecules. Instead, the stochastic evolution of the metastable vapor phase was explored in a grand canonical Monte Carlo (MC) simulation aided by the umbrella sampling technique. The physical clusters, i.e., density fluctuations, that lead to nucleation emerge naturally as we attain a coarse-grained description of this stochastic process by introducing proper order parameters, in particular the molecular content and the potential energy of the system suitably chosen in the vapor. Our method also allows an efficient evaluation of the free energy of cluster formation as a function of these order parameters. The method was applied to a Lennard-Jones fluid at temperatures above the bulk melting p...

Ion‐induced nucleation: A density functional approach

Density functional theory is applied to ion‐induced nucleation of dipolar molecules. The predicted reversible work shows a sign preference, resulting in a difference in the nucleation rate by a factor of 10–102, for realistic values of model parameters. The sign effect is found to decrease systematically as the supersaturation is increased. The asymmetry of a molecule is shown to be directly responsible for the sign preference in ion‐induced nucleation.

Ion-induced nucleation. II. Polarizable multipolar molecules

Density functional theory is applied to ion‐induced nucleation of polarizable multipolar molecules. The asymmetric nature of the ion–molecule interaction is shown to cause the sign preference in ion‐induced nucleation. When the ion–molecule interaction is weak, the observed sign preference is consistent with that of the bare ion–molecule interaction potential and decreases with increasing supersaturation. However, as the ion–molecule interaction becomes stronger, the sign preference in the reversible work exhibits some nontrivial behavior. For molecular parameters applicable for CS2 and CH4, the predicted values of the reversible work of nucleation depend on the sign of the ion charge, yielding a difference in the nucleation rate by factors of 10 to 102 and 10 to 105, respectively.

Evaluating free energy, enthalpy, and entropy of protonated water clusters by a grand canonical Monte Carlo simulation

We report the results of a Monte Carlo simulation of ion clusters using the polarizable model potentials for hydronium ion and a water molecule proposed by Kozack and Jordan [J. Chem. Phys. 96, 3120 (1992); 96, 3131 (1992)]. The grand canonical Monte Carlo simulation aided by the umbrella sampling technique allows us to evaluate very efficiently the equilibrium distribution of ion clusters of various sizes. Thermochemical data of interest, such as the standard free energy, enthalpy, and entropy of protonated water clusters follow immediately from this distribution.

On the scaling behavior of the free energetics of nucleation

We study free energetics of nucleation of simple fluids using density functional theory to assess the validity of recently proposed scaling relations, which point to the existence of a common scaling function that spans across fluid phase nucleation of various materials at different values of the temperature. While particular functional forms found in the literature are of moderate success in capturing the quantitative behavior of the model systems we studied, i.e., square-well potential and truncated and shifted Lennard-Jones potential, some of the essential ingredients of the scaling propositions are found to hold quite well. For example, the free energetics of vapor phase condensation can be described by a single scaling function depending only weakly on the temperature and the details of the model potentials. The same holds for bubble nucleation.

Identifying physical clusters in bubble nucleation

We present a new approach to molecular simulation of bubble nucleation. Our approach does not involve any ad hoc criteria to define a bubble for a given instantaneous configuration of molecules. Instead, we explore the stochastic evolution of a system chosen as a small part of the liquid phase by means of an isothermal–isobaric Monte Carlo simulation aided by the umbrella sampling technique. The physical clusters relevant to nucleation, bubbles in the present case, emerge naturally as we attain a coarse-grained description of this stochastic process by introducing proper order parameters, i.e., the volume and the interaction potential of the system. Thus, the concept of cluster commonly employed to describe vapor to liquid nucleation is generalized naturally for the case of bubble nucleation. The method is applied to Lennard-Jones fluids to evaluate the free energy of bubble formation under a moderate negative pressure. The interaction potential plays a similar role to that in vapor to liquid nucleation i...

On the direct evaluation of the equilibrium distribution of clusters by simulation

An expression is derived that relates the average population of a particular type of cluster in a metastable vapor phase of volume Vtot to the probability, estimated by simulation, of finding this cluster in a system of volumeV taken insideVtot , where V!Vtot . Correct treatment of the translational free energy of the cluster is crucial for this purpose. We show that the problem reduces to one of devising the proper boundary condition for the simulation. We then verify the result obtained previously for a low vapor density limit @J. Chem. Phys. 108, 3416~1998!#. The difficulty implicit in our recent calculation@J. Chem. Phys. 110, 5249~1999!#, in which the approach in the former was generalized to higher vapor densities, is shown to be resolved by a method already suggested in that paper. ©1999 American Institute of Physics. @S0021-9606 ~99!50944-6#