Vapor phase homogeneous nucleation and the thermodynamic properties of small clusters of argon atoms

Citation

McGinty, David Jackson (1972) Vapor phase homogeneous nucleation and the thermodynamic properties of small clusters of argon atoms. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/CSNR-SG47. https://resolver.caltech.edu/CaltechETD:etd-10142005-153958

Abstract

Two methods have been developed for calculating the thermodynamic properties of the small clusters of atoms believed important in the phenomenon of vapor phase homogeneous nucleation. Clusters of up to 100 argon atoms have been considered. The interactions among atoms are represented by the Lennard-Jones pairwise additive potential function and all degrees of freedom are explicitly included.

In the first method, the microcrystal model is used and the independent-cluster partition function is evaluated in the same way as one would evaluate that for a polyatomic molecule in the simplest approximation: the harmonic, rigid-rotator, and perfect-gas approximations are used to calculate the vibrational, rotational, and translational contributions to the partition function. The steady-state rate of formation of nuclei as a function of degree of supersaturation has been calculated and is found to have a behavior similar to that expected from the classical, "liquid-drop" model.

The importance of using several stable configurations of a cluster in calculating its properties from the microcrystal model is examined in detail. It is shown that the single-configuration approximation that has been used extensively in recent work can lead to serious errors. Methods for selecting configurations that will minimize these errors are suggested.

In the second method, molecular dynamics computer simulation calculations are used. In these calculations the classical equations of motion for the atoms in a cluster are numerically integrated to yield time records of the atomic position and velocity coordinates. Values of the independent-cluster thermodynamic functions are calculated from these coordinate data and are compared with those obtained from the microcrystal model. The comparison indicates surprising agreement for values of the Gibbs free energy of formation. The transition between "solid-like" and "fluid-like" diffusion in the clusters occurs gradually; no semblance of a phase transition is noted. The radial variation of density indicates that nearly all ther atoms of a cluster exist in the "surface" region; the radial distribution of potential energy indicates that the environment inside the clusters is quite different from that inside the bulk liquid or solid phases.

The largest error in the molecular dynamics results is statistical errror in the temperature. An expression for this error has been derived in terms of the kinetic-energy autocorrelation function. We have shown that this and other correlation functions can be computed from the molecular dynamics data very rapidly using a method based on the Fast Fourier Transform.

Finally, several very fundamental problems have been discovered in the classical, liquid-drop theory of nucleation. These problems a discussed in the context of a rigorous approach to nucleation theory that is based on the Frenkel-Band theory of noninteracting physical clusters.

Thesis Files