Frank P. Buff

Spherical Interface. II. Molecular Theory

The statistical mechanical theory of plane and spherical interfaces is developed on the basis of the virial theorem and the Gibbsian mechanical and thermodynamic definitions of surface tension. The expressions for the relevant thermodynamic functions in terms of molecular variables are employed in a discussion of the curvature dependence of surface tension which leads to an asymptotic expansion of the grand partition function in terms of the geometrical parameters that characterize the interface and thus provide a criterion for the range of validity of macroscopic concepts.

The Spherical Interface. I. Thermodynamics

An extension of the Gibbs thermodynamic theory of spherical interfaces leads to generalized forms for the Kelvin relation and the Gibbs adsorption equation. Quantities of physical interest are calculated in terms of the particular dividing surface making the superficial density of matter vanish, frequently more convenient than the surface of tension. An expression is proposed for the work required to form a droplet which is not in equilibrium with the surrounding vapor.

Surface Tension of Ionic Solutions

As an illustration of the molecular theory of surface regions, the singlet and pair distribution functions are evaluated for very dilute ionic solutions. When they are substituted into the statistical mechanical formulas for surface tension, expressions are obtained for the increase in surface tension over that of the pure solvent. The results of the theory are in better agreement with experiment than the earlier calculation of Onsager and Samaras, which was based on integration of the Gibbs adsorption equation. Finally, the distribution function approach is simply related to Mayers recent virial coefficient theory for strong electrolyte solutions.

Curved Fluid Interfaces. II. The Generalized Neumann Formula

Following an analysis of the phenomenological concept of surface stress, the confluence properties of three fluid phases are examined from the molecular point of view. The detailed theory leads to a generalization of the Neumann surface tension triangle, which provides a boundary condition for the Laplace equations describing the surfaces of a fluid lens. It is found that the classical equation must be supplemented by a thermodynamic length parameter which, however, does not contribute to the Archimedean equilibrium of the lens. As in the preceding investigation, the first‐order correction terms of the theory again provide criteria for the breakdown of thermodynamic concepts.

Some Considerations of Unimolecular Rate Theory

It is the purpose of this paper to examine the pressure dependence of the rate constant k of unimolecular decompositions within the framework of the generalized Lindemann mechanism. For trace amounts of reactive polyatomic molecules possessing very small equilibrium fractions of reactive states, the observed k may be identified with the lowest eigenvalue of the relaxation spectrum. After an examination of the Kassel and Slater microscopic decomposition frequencies (m.d.f.s), this approach is applied to the strong collision mechanism which is a common feature of both theories. Finally, the lowest eigenvalue is calculated for the inefficient stepwise activation mechanism in combination with the simple Kassel m.d.f. The pressure dependence of k on a reduced basis is found to be relatively insensitive to the details of the activation mechanism employed. The effect of less efficient processes in the intermolecular energy transfer and of anharmonicities in the intramolecular energy transfer tend to broaden the...

Small Perturbations in Solution Theory

A general perturbation theory is developed for the solution properties of systems with comparable intermolecular interactions. By employing our earlier general statistical mechanical theory of solutions as a starting point, the dominant contribution to the excess chemical potential is developed rigorously to first and second orders in the perturbation parameters. The very small first‐order terms are in agreement with those originally found by Longuet‐Higgins and the second‐order results may be exhibited in alternative forms. One of these, with use of a physically plausible approximation for the solute‐solvent radial distribution function, evaluated in the pure solvent, leads to formulas identical with those of the Prigogine‐Scott two‐fluid model. Alternatively, this distribution function may be expressed exactly in terms of the pair and triplet correlation function of the solvent. Numerical calculations on the latter, based on liquid argon as reference fluid, provide additional support for the successful ...

Electrostatics of Diffuse Anisotropic Interfaces. I. Planar Layer Model

In problems involving the electrostatic potential due to charges in the presence of a diffuse interface, for simplicity it is assumed that the interface is an abrupt one. We have investigated the effects of relaxing this assumption. By a procedure related to the method of invariant imbedding, we have formulated, within the regime of macroscopic continuum theory, the calculation of the electrostatic potential for a charge in the presence of an anisotropic diffuse layer. For distances far from the interface, the leading term in the image potential is the same as that for an abrupt interface, but referred to an origin which is determined by the components of the dielectric tensor. The next term arising from an induced quadrupole moment is negligible in representative cases. Close to the interface, divergences in the image potential can only be avoided if the values and first derviatives of the dielectric parameter are continuous. These results are illustrated by model dielectric profiles for the diffuse laye...

Curved Fluid Interfaces. III. The Dependence of the Free Energy on Parameters of External Force

The parameter of external force dependence of the free energy Ω appearing in the grand partition function is first illustrated on the basis of ideal gas models. In order to obtain a corresponding asymptotic estimate of Ω for real fluids in the presence of external fields, our earlier hydrostatic results are transcribed into thermodynamic terms. The resulting expression for Ω is shown to yield work elements in agreement with the detailed theory and, furthermore, when Ω is subjected to an appropriate variational principle the earlier relations describing the surfaces are obtained. These asymptotic formulas demonstrate that for macroscopic applications the classical equations are completely valid. Since these equations determine the spatial distribution of fluids, their connection with Duhems theorem is described.

Computer simulation of the photodissociation and recombination of iodine in gaseous krypton using a droplet model

Computer simulations of the photodissociation of an I2 molecule that is physically clustered with Kr atoms are performed. Geminate recombination is observed on the excited A state potential of the iodine atoms, in contrast to previous work. A grand ensemble formulation of the process is developed in which cluster probabilities of the initial configurations are evaluated by Monte Carlo and particle insertion techniques. It is followed by molecular dynamics simulations on the system when the I2 molecule is excited. Excellent agreement with experiment is obtained for the density dependence of the quantum yield of recombination. Analysis of the trajectories reveals that the time evolution of recombinations is approximately exponential, whereas that for escapes reveals a fast immediate component followed by a tail at intermediate times which exhibits approximately exponential decay.

Phase instability and the direct correlation function integral equation

Extensive searches for the equilibrium liquid–solid coexistence line have been based on the identification of this line with the bifurcation points in integral equations such as the lowest order Kirkwood lambda coupling equation, the lowest order Born and Green equation, and a similar relation between the direct correlation function and the singlet density. In applications where these integral equations should be identical, different results have been found. The difference is explained by noting that additional, implicit approximations have always been introduced. A new formulation free of such approximations is given, and it is shown that the general condition for bifurcation to occur is simply expressed in terms of the direct correlation function and has a simple physical interpretation: An approximation free search for bifurcation points will identify points of liquid instability and not points of liquid–solid coexistence.