Richard K. Bowles

Free energy surface of ST2 water near the liquid-liquid phase transition

We carry out umbrella sampling Monte Carlo simulations to evaluate the free energy surface of the ST2 model of water as a function of two order parameters, the density and a bond-orientational order parameter. We approximate the long-range electrostatic interactions of the ST2 model using the reaction-field method. We focus on state points in the vicinity of the liquid-liquid critical point proposed for this model in earlier work. At temperatures below the predicted critical temperature we find two basins in the free energy surface, both of which have liquid-like bond orientational order, but differing in density. The pressure and temperature dependence of the shape of the free energy surface is consistent with the assignment of these two basins to the distinct low density and high density liquid phases previously predicted to occur in ST2 water.

Phase transitions in systems small enough to be clusters

We analyze peculiarities of phase transitions in small systems. We focus on the formation of a tiny liquid drop in a small N, V, T system, and develop an “extended modified liquid drop” model, which incorporates the effect of the fluctuations relevant for small systems. We compare the predictions for the p−v isotherms and the density profiles with the results of Monte-Carlo simulations of a Lennard-Jones system, and Density Functional Theory.

A MOLECULAR THEORY OF THE HOMOGENEOUS NUCLEATION RATE. I. FORMULATION AND FUNDAMENTAL ISSUES

A molecular theory of the rate of homogeneous vapor phase nucleation is formulated. The ultimate goal is a theory that contains no ad hoc assumptions or arbitrary parameters having magnitudes that must be assigned in an ad hoc manner. The centerpiece of the theory is a defined cluster denoted as the n/v-Stillinger cluster, a hybrid that combines the original Stillinger cluster and the more recent n/v cluster. The Stillinger component assures that redundancy is avoided in the characterization of the cluster and the n/v component makes the Monte Carlo simulation of the free energy of the cluster relatively simple, and also allows dynamics to weight the importance of a cluster to the nucleation rate process. In the companion paper (paper II), dealing with the application of the theory to argon vapor, it is shown that the avoidance of redundancy is of primary importance to the non ad hoc nature of the theory. The theory provides a standard against which subtle inconsistencies in earlier theories, both molecul...

A molecular theory of the homogeneous nucleation rate. II. Application to argon vapor

The molecular theory of the homogeneous nucleation rate based on the n/v-Stillinger cluster, and developed in the preceding paper (paper I), is applied to the condensation of supersaturated argon vapor, in a preliminary calculation of the rate of nucleation for a single set of conditions (temperature=85 K, pressure=2500 Torr). Free energies are obtained by means of Monte Carlo simulation. Upper and lower bounds differing by only two orders of magnitude are obtained. Since the best current measurements of vapor phase nucleation rates are accurate to within about a single order of magnitude, this result is considered promising. The direction of future work to improve the accuracy of the predicted rate is clear, and considerable improvement should be possible. These directions are discussed in the paper. Also, the essentially non ad hoc nature of the n/v-Stillinger cluster is demonstrated by the appearance of a range of connectivity distances (in a predicted location) within which the calculated nucleation r...

A theorem for inhomogeneous systems: The generalization of the nucleation theorem

We show that the validity of the nucleation theorem transcends the phenomenon of nucleation and extends to all equilibrium systems containing local nonuniform density distributions stabilized by external fields, and that it remains valid down to the molecular level. This result is tested by the application of exact theory at the molecular level and is shown to be valid in all the cases for which we have been able to complete such an exact analysis. These cases include cavities and clusters in hard rod fluids, as well as the molecular excesses associated with the “atmospheres” of molecules in single and multicomponent fluids. We show that, at the molecular level, the theorem can be associated with the compressibility equation of state and, at the macroscopic level, with the Gibbs adsorption equation. It is thus a relation of great power and should be useful in many contexts.

Simulative determination of kinetic coefficients for nucleation rates

Nucleation kinetics can be formulated generally and rigorously as a set of master equations that govern the time evolution of the cluster distribution that underlies the observable rate process. However, this general formulation is only useful if the magnitudes of the coefficients that describe the loss and gain (evaporation and condensation) of molecules by a cluster are quantitatively known. Moreover, these coefficients can refer to multiple losses and gains of molecules (several molecules in a single step). In order to measure these coefficients accurately and efficiently, we have devised a molecular dynamics (MD) simulation that follows the development and equilibration of a single cluster in a small container (volume) that involves only a small number of molecules (in our case 216). There is evidence that such a system can provide a reliable picture of the behavior of a cluster in a larger system. This approach has been applied to supersaturated argon vapor at 85 K. In particular, we have been able t...

A molecular based derivation of the nucleation theorem

We show that, for condensation in an almost ideal vapor, the nucleation theorem is essentially a consequence of the law of mass action. The usual form of the theorem, with the effects of the translational degrees of freedom of the cluster included, is then derived using statistical mechanics and molecular theory, but only under the assumptions that the cluster excludes a volume to the surrounding vapor and that the vapor is ideal. The form of the result obtained via molecular theory is such that it appears unlikely (but not impossible) that the theorem remains valid for cases when the vapor is nonideal. This suggests that further work is necessary before the theorem can be regarded as established. We also consider the effects of the presence of a carrier gas.

Some fundamental statistical mechanical relations concerning physical clusters of interest to nucleation theory

A number of statistical mechanical formulas, important to the theory of nucleation, have been used, recently and in the past, in both molecular and phenomenological theories of nucleation without a full description (and possibly without a full understanding) of their fundamental meanings. These formulas have involved the numbers of physical clusters, the reversible work of formation of such clusters, and the distinct roles of translational and internal cluster degrees of freedom. In this paper we perform careful molecular level analyses of some of these formulas in an effort to establish their fundamental bases.

Nonclassical Nucleation in a Solid-Solid Transition of Confined Hard Spheres

A solid-solid phase transition of colloidal hard spheres confined between two planar hard walls is studied using a combination of molecular dynamics and Monte Carlo simulation. The transition from a solid consisting of five crystalline layers with square symmetry (5□) to a solid consisting of four layers with triangular symmetry (4△) is shown to occur through a nonclassical nucleation mechanism that involves the initial formation of a precritical liquid cluster, within which the cluster of the stable 4△ phase grows. Free-energy calculations show that the transition occurs in one step, crossing a single free-energy barrier, and that the critical nucleus consists of a small 4△ solid cluster wetted by a metastable liquid. In addition, the liquid cluster and the solid cluster are shown to grow at the planar hard walls. We also find that the critical nucleus size increases with supersaturation, which is at odds with classical nucleation theory. The △-solid-like cluster is shown to contain both face-centered-cubic and hexagonal-close-packed ordered particles.

Crystal nucleation in a supercooled liquid with glassy dynamics.

In simulations of supercooled, high-density liquid silica we study a range of temperature T in which we find both crystal nucleation as well as the characteristic dynamics of a glass forming liquid, including a breakdown of the Stokes-Einstein relation. We find that the liquid cannot be observed below a homogeneous nucleation limit (HNL) at which the liquid crystallizes faster than it can equilibrate. We show that the HNL would occur at lower T, and perhaps not at all, if the Stokes-Einstein relation were obeyed, and hence that glassy dynamics plays a central role in setting a crystallization limit on the liquid state in this case. We also explore the relation of the HNL to the Kauzmann temperature, and test for spinodal-like effects near the HNL.