David W. Oxtoby

Homogeneous nucleation: theory and experiment

Recent theoretical and experimental advances in the study of homogeneous nucleation are reviewed, with emphasis placed on phase transitions involving single-component liquids (condensation, cavitation, and crystallization from the melt). Extensions of classical nucleation theory are described and compared with new experiments that now directly measure nucleation rates. Novel methods of statistical mechanics, including density-functional theory and computer simulations, are presented. The recent rapid evolution of this field has opened up many new questions for further research.

Nonclassical nucleation theory for the gas–liquid transition

We use density functional methods to develop a new nonclassical theory for the homogeneous nucleation of the gas to liquid phase transition. The extent of agreement between our results and the classical prediction of Becker, Doring, and Zeldovich is strongly dependent on the range of the attractive potential which we employ. We show that our predictions are consistent with experimental data using cloud chambers, and we suggest several directions in which experimentalists might look in order to find nonclassical effects. In particular, we suggest that cavitation (gas bubble formation in a liquid subjected to tensile stress) should nucleate at a significantly greater rate than that predicted by classical theory.

Theory of the time development of the stokes shift in polar media

Abstract We present a theory for the time evolution of the Stokes shift of a polar molecule in a polar solvent. The time-dependent solute—solvent interaction is calculated in a continuum model by replacing the surrounding solvent by a frequency-dependent dielectric continuum. An expression for the time dependence of the fluorescence maximum is derived. This expression can be considered a direct generalization of the well-known Ooshika—Lippert—Mataga equation to the time domain. We also present an approximate expression for the wavelength dependence of the dynamics of the Stokes shift, and find it to be consistent with recent experimental results. We have investigated the effect of polarizability of the solute molecule and found that for many molecules this effect is not negligible.

A molecular theory for the solid–liquid interface

We present an order parameter theory of the solid–liquid interface which uses structural information about the uniform liquid phase. The order parameters are the coefficients of a Fourier expansion of the nonuniform density in terms of reciprocal lattice vectors characteristic of the uniform solid phase. The theory provides explicit formulas for the interfacial density profile and the surface free energy. Connection is made with recent theories of freezing and of the liquid–vapor interface. Two special cases of particular interest are considered: the flat interface, for which numerical simulations have been attempted, and the spherical ball, which is important in theories of liquid–solid nucleation.

NUCLEATION: Measurements, Theory, and Atmospheric Applications

New experiments have succeeded in measuring actual rates of nucleation and are revealing the shortcomings of classical nucleation theory, which assumes that the molecular-scale regions of the new phase may be treated using bulk thermodynamics and planar surface free energies. In response to these developments, new theories have been developed that incorporate information about molecular interactions in a more realistic fashion. This article reviews recent experimental and theoretical advances in the study of nucleation of liquids from the vapor and of crystals from the melt, with particular emphasis on phenomena that relate to particle formation in the atmosphere.

A general relation between the nucleation work and the size of the nucleus in multicomponent nucleation

We prove a general theorem that relates the variation of the work of formation of the critical nucleus with chemical potential and the size and composition of the critical nucleus. Applications are made to multicomponent nucleation and to both isothermal and nonisothermal phase transformations. We show that the excess number of molecules and the excess entropy of the critical nucleus are thus accessible to experimental determination with the help of data for the dependence of the nucleation rate on supersaturation. The results derived do not rely on classical nucleation approximations and thus apply down to the smallest nuclei of a few molecules only.

Theory of electronic relaxation in solution in the absence of an activation barrier

We present a theory which describes the effects of viscosity on those electronic relaxation processes in solution in which the intramolecular potential surface does not present a barrier to the motion leading to the decay of the initially formed excited state. We model the reactive motion as the motion of a solute particle on the excited state potential surface with a position dependent sink which gives rise to the decay of the excited state population. Three different types of sinks are considered: (A) a pinhole sink at the minimum of the potential surface; this models the situation when the molecule decays to ground state as soon as it reaches the potential minimum; (B) a Gaussian sink with probability of decay maximum at the potential minimum; (C) a Lorentzian sink with maximum decay at the potential minimum. For case (A) an explicit analytic solution is obtained for the decay rate, but for cases (B) and (C) we obtained the decay rate numerically. Model (A) predicts nonexponential decay at all viscosit...

Gas–liquid nucleation in Lennard‐Jones fluids

We have applied a nonclassical density functional theory of nucleation to the gas–liquid and liquid–gas transitions of a Lennard‐Jones fluid. For the liquid‐to‐gas transition (cavitation) deviations from classical theory are extremely large: 15 orders of magnitude in rates. For the gas‐to‐liquid transition (condensation) the deviations are smaller in magnitude but still systematic. Our nonclassical theory agrees with classical theory in its prediction of the dependence of nucleation rates on supersaturation, but it differs in its prediction of temperature dependence. Good agreement is found between our theory and experiments on condensation nucleation of nonane.

A molecular dynamics simulation of dephasing in liquid nitrogen

We relate the dephasing of molecular vibrations in liquids to certain correlation functions involving only the translational and rotational degrees of freedom; these correlation functions are then determined through a classical molecular dynamics simulation of rigid, nonvibrating molecules. Using a Lennard‐Jones atom–atom potential for N2 (liq) near its boiling point, we calculate a dephasing time of 62 psec, in good agreement with picosecond pulse and isotropic Raman linewidth measurements. The importance and characterisic time scales of different dephasing mechanisms are studied, and the significant effect of vibrational anharmonicity is demonstrated.

Hydrodynamic theory for vibrational dephasing in liquids

A hydrodynamic model is presented for the dephasing of molecular vibrations in liquids; the effects of vibrational anharmonicity are included. Agreement with coherent picosecond pulse experiments and isotropic Raman line shape data is good for lower viscosity liquids, and the qualitative temperature and density dependence of the dephasing rate is predicted correctly. The final result shows a surprising formal similarity to the isolated binary collision model developed previously.