G. N. Patey

The solution of the hypernetted‐chain approximation for fluids of nonspherical particles. A general method with application to dipolar hard spheres

In this paper we describe a general method for the numerical solution of the full hypernetted‐chain (HNC) theory for fluids characterized by angle‐dependent pair potentials. This method is also applicable to the closely related reference hypernetted‐chain (RHNC) approximation. The only formal restriction is that the pair potential and correlation functions must be expandable in a basis set of rotational invariants. We present explicit numerical solutions of the RHNC theory for dense dipolar hard sphere fluids and detailed comparisons are made with previous theories and computer simulation results. It is found that the full RHNC theory generally improves upon the previous reference linearized and quadratic HNC approximations. The values given by the RHNC theory for the static dielectric constants are smaller than those given by these earlier approximations and are in much better agreement with computer simulations.

On the molecular theory of aqueous electrolyte solutions. I. The solution of the RHNC approximation for models at finite concentration

This paper describes a theoretical study of the thermodynamic, dielectric, and structural properties of model aqueous electrolyte solutions. The model considered consists of hard sphere ions immersed in a hard polarizable dipole tetrahedral–quadrupole solvent with water‐like parameters. The calculations involve the solution of the reference hypernetted‐chain (RHNC) approximation for ion–solvent mixtures at finite concentration and some details of the general method are discussed. The influence of the molecular polarizability of the solvent particles is treated at the self‐consistent mean field (SCMF) level and, surprisingly, the mean dipole moment of the solvent is found to be nearly independent of the salt concentration. Numerical results are reported for model alkali halide solutions and other 1:1 electrolytes, and comparisons are made with experimental results at 25 °C. The agreement obtained between theory and experiment is variable depending upon the particular property and solution considered. In ad...

Fluids of polarizable hard spheres with dipoles and tetrahedral quadrupoles Integral equation results with application to liquid water

The mean spherical, linearized hypernetted chain and quadratic hypernetted chain approximations are solved for a fluid of hard spheres with embedded point dipoles and tetrahedral quadrupoles and this system is shown to be quite similar to the dipole-linear quadrupole case previously studied. However, tetrahedral quadrupoles have a larger influence upon the structural and thermodynamic properties and are slightly more effective in decreasing the dielectric constant from the purely dipolar value. Also we describe a simple self-consistent mean field theory which allows molecular polarizability to be taken into account. This approximation together with the integral equation methods is applied to a polarizable dipole-tetrahedral quadrupole fluid with water-like parameters. The dielectric constant of this system is found to be in good agreement with the experimental results for liquid water for temperatures ranging from 25°C to 300°C. The influence of molecular polarizability is shown to be very large. At 25°C ...

Electrical double layers. II. Monte Carlo and HNC studies of image effects

The effect of surface polarization (i.e., image forces) on the properties of electrical double layers is studied by means of Monte Carlo calculations on a primitive model electrolyte next to a planar charged surface bounding a semi‐infinite dielectric. Two cases are considered, that of a conducting material for which an ion is attracted by its own image and that of an insulator for which the self‐image force is repulsive. At low surface charge densities the image forces cause quite dramatic changes in the ionic densities near the wall; the effect on the electrostatic potential is small but increases with surface charge density. The modified Poisson–Boltzmann theory of Outhwaite is quite successful in describing the Monte Carlo results for the range of parameters studied. A screened self‐image model of image effects is also considered for which both Monte Carlo calculations and numerical solution of the HNC equation have been obtained.

The solution of the reference hypernetted-chain approximation for water-like models

In this paper we examine the dielectric and structural properties of hard polarizable multipolar models for liquid water. The theoretical results were obtained by solving the self-consistent mean field (SCMF) approximation together with the reference hypernetted-chain (RHNC) theory. The dielectric constants are in good agreement with experiment over a large range of temperatures and pressures. The rather poor agreement between the radial distribution functions determined for our water-like fluids at 25°C and those measured for liquid water is discussed.

Hypernetted‐chain closure with bridge diagrams. Asymmetric hard sphere mixtures

Methods of calculating the first two terms in the density expansion of the bridge function are given. The closure to the Ornstein–Zernike equation is now exact to two orders in density beyond the hypernetted‐chain or Percus–Yevick approximations. The bridge function is resummed as a Pade approximant, and the results for hard spheres are relatively accurate over the whole density regime. The closure is shown to yield physically reasonable results for highly asymmetric mixtures. Infinitely dilute hard sphere solutes with diameters up to 30 times that of the hard‐sphere solvent are also considered. The Derjaguin approximation for rescaling the force between spheres to the interaction free energy between planes is examined and found to give the dominant curvature correction.

Cavitation of a Lennard-Jones fluid between hard walls, and the possible relevance to the attraction measured between hydrophobic surfaces

A Lennard‐Jones fluid confined between two planar hard walls is simulated using grand canonical Monte Carlo, and capillary evaporation is found for liquid subcritical bulk states. General methods are given for simulating a metastable fluid beyond coexistence. For the systems studied, the liquid and the gas phases coexist in equilibrium at a separation of ∼5 diam, the spinodal cavitation separation is at ∼4 diam, and the spinodal condensation separation is at ≳15 diam. The interaction pressure between the walls is found to be attractive and increases rapidly as the spinodal separation is approached. On the equilibrium liquid branch, the net pressure still appears significantly larger than the van der Waals attraction at separations of ∼10 diam. A simple analytic theory is given, which relates the force to the approach of the separation‐induced phase transition. It is suggested that this is the microscopic origin of the measured attractions between hydrophobic surfaces in water.

Molecular solvent model for an electrical double layer: Reference hypernetted‐chain (RHNC) results for solvent structure at a charged surface

We report results of solving the full reference hypernetted‐chain (RHNC) theory for a large, multiply charged macroion at infinite dilution in a solvent of hard spheres with point dipole and quadrupole moments chosen to represent liquid water. We obtain results for the restructuring of this model solvent next to the macroion surface for a range of surface charges and macroion sizes up to 30 solvent diameters. Although we are unable to solve the theory for larger particles, when this largest macroion is neutral we find a solvent orientational structure in the surface layer that is in good qualitative agreement with computer simulation results for water‐like models at a planar surface. Our RHNC calculations show that this surface structure proves surprisingly resistant to the effect of surface charges as high as 17.5 μC/cm2, apparently because even such strong fields cannot compete with the still stronger intermolecular forces of water‐like models. There is, nevertheless, strong oscillatory behavior in both...

The thermodynamic properties of electrolyte solutions: Some formal results

The Kirkwood–Buff approach is used to obtain exact determinate expressions for the thermodynamic properties of electrolyte solutions. The solvent is treated at a molecular level and the thermodynamic functions are expressed in terms of ion–ion, ion–solvent, and solvent–solvent correlation functions. The equations obtained are particularly useful when used in conjunction with integral equation theories. The low concentration limiting behavior of the microscopic expressions is examined and it is shown that the Debye–Huckel limiting law for the activity coefficient can be readily extracted from the molecular theory. Also the partial molecular volume of the salt is considered in some detail and microscopic relationships are given for the infinite dilution value.

The solution of the hypernetted-chain and Percus-Yevick approximations for fluids of hard nonspherical particles. Results for hard ellipsoids of revolution

In this paper we describe a general approach which allows the hypernetted chain (HNC) and Percus–Yevick (PY) integral equation theories to be solved numerically for fluids of hard nonspherical particles. Explicit results are given for fluids of hard ellipsoids of revolution and comparisons are made with recent Monte Carlo calculations. It is found that for dense systems of highly anisotropic ellipsoids the HNC and PY closures give significantly different results. The HNC theory is superior predicting the existance of a nematic phase in qualitative agreement with computer simulations. The PY approximation strongly and erroneously suggests that the isotropic phase is stable throughout the liquid regime.