Teresa S. Ree

Significant Structure Theory of Surface Tension

The approximation is made that the dividing surface between a liquid and its vapor phase is a monomolecular layer, in which a molecule has a free volume larger than for an interior molecule and a potential energy less than for the latter. By introducing the approximation into the significant structure theory of liquids, a partition function fN is derived which involves the terms belonging to the surface as well as to the bulk liquid. The surface tension is calculated by γ = (∂A/∂Ω)N,V,T, where A is the Helmholtz free energy which equals —kTlnfN, Ω is the surface area, N the total number of molecules in the system, V the volume of the liquid, and T the absolute temperature. The surface tensions of nonpolar substances at various temperatures are calculated with good results. Our theory is compared with other theories, and it is found that the present theory most satisfactorily predicts the surface tensions at various temperatures.

Activated Complexes of Fast Bimolecular Reactions

The specific rates of radical association and ion‐molecule reactions (e.g., CH3+CH3→C2H6, H2++H2→H3++H, etc.) were calculated with the use of the absolute reaction‐rate theory and were compared with the observed values. Except for some special reactions, the observed rates agree with the theoretical values with a transmission coefficient, 1 to 1/10.The over‐all entropy change of the backward reactions ΔSb were calculated by the usual statistical thermodynamical method, and also the activation entropy of the backward reactions, ΔSb‡, were calculated. The two quantities agree fairly well.From these results it was concluded that the activated complexes of the fast reactions have loose structures such that the reactant molecules (radicals or ions) rotate freely with the restriction that they cannot move independently in the translational degrees of freedom.

Significant‐Structure Theory and Cell Theory for Two‐Dimensional Liquids of Hard Disks

The significant‐structure theory of liquids is applied to describe a two‐dimensional liquid of hard disks. The results are in quite good agreement with the molecular‐dynamics calculations. However, the virial expansion of the equation of state is in only fair agreement with the machine calculations. Cell theory is also applied to the two‐dimensional liquid; it is found that although the agreement with the molecular‐dynamics data is poor in the liquid range, the cell theory shows good agreement in the solid region.

Recent developments in the significant structure theory of liquids

Abstract As the important structures in explaining the properties of liquids, the significant structure theory picks out three structures, the solid-like structure, the configurational degeneracy associated with a solid-like molecule, and the gas-like structure. In conjunction with these cardinal concepts, it also follows from the model that the portion of the solid-like part is V s V and another portion ( 1− V s V ) is the gas-like part where V and V s are the molar volumes of the liquid and of the solid, respectively. Using this model, the partition function of liquid is formulated, and the thermodynamic properties are calculated with good agreement with experiment. The significant structure theory is applicable for calculating transport properties, such as viscosity, the diffusion coefficient and the thermal conductivity, with good results. It is also applicable for deriving the adsorption isotherms of rare gases on graphite by assuming that the adsorbate forms a two dimensional liquid. Further tests of the significant structure theory are made by applying it to the systems of hard spheres and hard disc, and by comparing the calculated thermodynamic properties with the results of computer calculations by the Monte Carlo or molecular dynamics method. The agreement is excellent. The significant structure theory is also applicable to liquid mixtures, for example, the binary mixtures of Ar and N 2 , Ar and O 2 , and O 2 and N 2 . The calculated excess-properties such as the heat content. Gibbs free energy and molar volume agree satisfactorily with experiment.