Classical fluids

Abstract: Recent theoretical work on the microscopic structure and surface tension of the liquid-vapour interface of simple (argon-like) fluids is critically reviewed. In particular, the form of pairwise intermolecular correlations in the liquid surface and the capillary wave treatment of the interface are examined in some detail. It is argued that conventional capillary wave theory, which leads to divergences in the width of the density profile, is unsatisfactory for describing all the equilibrium aspects of the interface. The density functional formalism which has been developed to study the liquid-vapour interface can also be profitably applied to other problems in the statistical mechanics of non-uniform fluids; here a new generalization of the ‘linear’ theory of spinodal decomposition is formulated and by considering a ‘nearly uniform’ fluid, some useful results for the long-wavelength behaviour of the liquid structure factor of various monatomic liquids are obtained. Some other topics of current inte...

Abstract: A new formulation of statistical thermodynamics is derived for classical fluids of molecules that tend to associate into dimers and possibly highers-mers due to highly directional attraction. A breakup of the pair potential into repulsive and highly directionally attractive parts is introduced into the expansion of the logarithm of the grand partition function in fugacity graphs. The bonding by the directional attraction is used to classify the graphs and to introduce a topological reduction which results in the replacement of the fugacity by two variables: singlet densityρ and monomer densityρ 0. Results for the thermodynamic functions as functionals ofρ andρ 0 are given in the form of graph sums. Pair correlations are analyzed in terms of a new matrix analog of the direct correlation function. It is shown that the low-density limit is treated exactly, while major difficulties arise when the Mayer expansion, which employs onlyp, is used. The intricate resummations required for the Mayer expansion are illustrated for the case where dimers are the only association products.

Abstract: The optimized cluster expansion methods developed in the first article of this series (I) are generalized to apply to molecular fluids. These methods make use of summations of ring and chain cluster diagrams. The summations are performed explicitly for certain classes of molecular models. The molecules in these classes contain several ``interaction sites,'' and the total interaction between two molecules is a sum of site‐site potentials that depend on the scalar distances between sites on the two molecules. The principal results of this work are computationally simple techniques for calculating the thermo‐dynamic properties and pair correlation functions of molecular fluids in which the intermolecular interactions are highly angular dependent. The techniques should be reliable since they arise from the same approximations that have been shown to be very accurate when applied to simple fluids.