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...

The nature of the liquid-vapour interface and other topics in the statistical mechanics of non-uniform, classical fluids

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.

Fluids with highly directional attractive forces. I. Statistical thermodynamics

The formalism of statistical thermodynamics developed in the preceding paper is used as a basis for deriving tractable approximations. The system treated is one where repulsion and highly directional attraction due to a single molecular site combine to allow the formation of dimers, but no highers-mers. We derive thermodynamic perturbation theory, using the system interacting with only the repulsive potential as a reference system. Two distinct integral equations for the pair correlation are derived. The first one treats both parts of the interaction approximately; the other one employs the repulsive reference system used in perturbation theory. We show that each of these integral equations permits the calculation of an important thermodynamic function directly from the solution at a single state of density and temperature. In the first case this applies to a pressure consistent with the compressibility relation, in the second to the excess Helmholtz free energy over the reference system.

Fluids with highly directional attractive forces. II. Thermodynamic perturbation theory and integral equations

We investigate approximation methods for systems of molecules interacting by core repulsion and highly directional attraction due to several attraction sites. The force model chosen imitates a chemical bond by providing for bond saturation when binding occurs. The dense fluid is an equilibrium mixture ofs-mers with mutual repulsion. We use a previously derived reformulation of statistical thermodynamics, in which the particle species are monomeric units with a specified set of attraction sites bonded. Thermodynamic perturbation theory (TPT) and integral equations of two types are derived. The use of TPT is illustrated by explicit calculation for a molecular model with two attraction sites, capable of forming chain and ring polymers. Successes and defects of TPT are discussed. The integral equations for pair correlations between particles of specified bonding include calculation of self-consistent densities of species. Methods of calculating thermodynamic properties from the solutions of integral equations are given.

Fluids with highly directional attractive forces. IV. Equilibrium polymerization

The thermodynamic properties and phase behavior of water in confined regions can vary significantly from that observed in the bulk. This is particularly true for systems in which the confinement is on the molecular-length scale. In this study, we use molecular dynamics simulations and a powerful solvent analysis technique based on inhomogenous solvation theory to investigate the properties of water molecules that solvate the confined regions of protein active sites. Our simulations and analysis indicate that the solvation of protein active sites that are characterized by hydrophobic enclosure and correlated hydrogen bonds induce atypical entropic and enthalpic penalties of hydration. These penalties apparently stabilize the protein-ligand complex with respect to the independently solvated ligand and protein, which leads to enhanced binding affinities. Our analysis elucidates several challenging cases, including the super affinity of the streptavidin-biotin system.

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Motifs for molecular recognition exploiting hydrophobic enclosure in protein–ligand binding

A classical system enclosed in a finite volume and affected by external forces is treated in a general way. The main results are partly applicable to solids as well as to fluids. Exact integral equations are found for the one- and two-particle distribution frnctions. Some thermodynamic functions are expressed in terms of these distribution functions. It is shown that there exist variational principles, which require that the grand partition function is at a maximum with respect to the variations in the one- and twoparticle distribntion functions. Variational principles are found also for the Helruholtz free energy. It is suggested that Mayer's theory of condensation may give the end point of the metastable gaseous state. It is pointed out that a hyper-netted chain approximation has a meaning in solids as well as in fluids. (auth)

A New Approach to the Theory of Classical Fluids. III: General Treatment of Classical Systems

An exact integral equation is found for the pair distribution function. The integral equation is of somewhat different nature from the usual ones known in the theory of classical fluids, in the point that it involves an infinite series. The Helmholtz free energy is expressed as a series expansion which may be more rapidly convergent than the usual one. It is shown that the integral equation can be derived also by means of a variational principle from the expression for the free energy. It is pointed out that the theory of classical fluids may be constructed with the knowledge of the pair distribution function alone, even if a form of the pair interaction potential is not known.

A New Approach to the Theory of Classical Fluids. I

It is shown that the radial distribution function of fluid can be derived from the expression for the free energy in the form of a “functional derivative” with respect to the pair interaction potential. Three examples are treated on the line of the theory: (1) the simple chain approximation of classical fluid, (2) the second quantization and (3) the lowest state of the spinless bosons derived by Bogolyubov and Zubarev. A procedure, which differs from the usual one, is given in the derivation of the expressions by which the pressure and the internal energy are expressed in terms of the radial distribution function.

Kazuo Hiroike

Papers

A New Approach to the Theory of Classical Fluids. III: General Treatment of Classical Systems

A New Approach to the Theory of Classical Fluids. I

Radial Distribution Function of Fluids, III

A New Approach to the Theory of Classical Fluids. II Multicomponent Systems

Integral Equation for Pair Distribution Function