On the signs of fluorine spin coupling constants

From an exact expression for the free energy of a non-uniform fluid mixture a closure approximation for the inhomogeneous direct correlation functions is used to develop a theory of solvation forces in charged fluids based upon non-linear equations for the equilibrium ion number densities. In the limit of point ions, the expressions obtained reduce to those of the Poisson-Boltzmann theory of electrolytes. The numerical results obtained for a restricted primitive model electrolyte are compared with those of earlier work based on linear response theory and Poisson-Boltzmann theory with a simple Stern layer modification. At low electrolyte concentrations the agreement between all three theories is good. But at high electrolyte concentrations the Poisson-Boltzmann theory with a simple Stern layer correction fails to display the oscillations in the solvation force which characterize both the linear and non-linear theories.     

A two-dimensional model associating fluid with spherically symmetric intracore square-well shell. Integral equations and Monte Carlo simulation study

The structure and thermodynamics of a monolayer of an associating fluid in the framework of the primitive model of Cummings and Stell is studied by using a two-dimensional approximation. The model permits formation of dimer species for small values of the bonding length parameter, the formation of chains, if the bonding length is slightly larger, and also the vulcanization of species for bonding length values close to the diameter of particles. The structure and thermodynamics of the model that are of interest for statistical mechanics of surface chemical reactions, are studied by computer simulations in the canonical, grand canonical and isobaric ensembles and from the two-dimensional Ornstein—Zernike-like or Wertheim's Ornstein—Zernike integral equation. We have shown that the theory is satisfactory for the case of dimerization if the fluid density is low. For higher densities one must apply a correction for the cavity distribution functions to describe the fraction of unbonded species more adequately. For the case of chain formation the theory just resembles trends following from the simulation data. For the model with vulcanization of species we have obtained the fractions of differently bonded particles and have shown that chemical ordering of species is manifested in the antiphase oscillations of the pair distribution functions of species.     

Development of intermolecular potential models for electrolyte solutions using an electrolyte SAFT-VR Mie equation of state

ABSTRACT

We present a theoretical framework and parameterisation of intermolecular potentials for aqueous electrolyte solutions using the statistical associating fluid theory based on the Mie interaction potential (SAFT-VR Mie), coupled with the primitive, non-restricted mean-spherical approximation (MSA) for electrolytes. In common with other SAFT approaches, water is modelled as a spherical molecule with four off-centre association sites to represent the hydrogen-bonding interactions; the repulsive and dispersive interactions between the molecular cores are represented with a potential of the Mie (generalised Lennard-Jones) form. The ionic species are modelled as fully dissociated, and each ion is treated as spherical: Coulombic ion–ion interactions are included at the centre of a Mie core; the ion–water interactions are also modelled with a Mie potential without an explicit treatment of ion–dipole interaction. A Born contribution to the Helmholtz free energy of the system is included to account for the process of charging the ions in the aqueous dielectric medium. The parameterisation of the ion potential models is simplified by representing the ion–ion dispersive interaction energies with a modified version of the London theory for the unlike attractions. By combining the Shannon estimates of the size of the ionic species with the Born cavity size reported by Rashin and Honig, the parameterisation of the model is reduced to the determination of a single ion–solvent attractive interaction parameter. The resulting SAFT-VRE Mie parameter sets allow one to accurately reproduce the densities, vapour pressures, and osmotic coefficients for a broad variety of aqueous electrolyte solutions; the activity coefficients of the ions, which are not used in the parameterisation of the models, are also found to be in good agreement with the experimental data. The models are shown to be reliable beyond the molality range considered during parameter estimation. The inclusion of the Born free-energy contribution, together with appropriate estimates for the size of the ionic cavity, allows for accurate predictions of the Gibbs free energy of solvation of the ionic species considered. The solubility limits are also predicted for a number of salts; in cases where reliable reference data are available the predictions are in good agreement with experiment.     

Chemical potential of electrolytes adsorbed in porous media with charged obstacles: application of the continuum replica methodology

A theoretical study is reported of a quenched-annealed system where both components were modelled as size symmetric +1: ?1 primitive model electrolytes. The partly quenched system was studied by using the replica Ornstein-Zernike (ROZ) integral equation theory in the hypernetted chain (HNC) approximation and grand canonical Monte Carlo (GCMC) simulations. The primary interest was the excess Gibbs free energy (logarithm of the mean activity coefficient) of the adsorbed electrolyte and an expression for this quantity, valid within the ROZ/HNC formalism, was derived. The effects of the concentration of matrix ions, pre-quenching conditions, and the electrolyte and solvent conditions (concentration, temperature, dielectric constant) on the structure and thermodynamics of the adsorbed electrolyte were examined. The numerical results indicated that the mean activity of the adsorbed electrolyte differs substantially from the corresponding quantity for the bulk electrolyte. The excess chemical potential depends strongly on the concentration of charged obstacles and matrix preparation, and also on the temperature and dielectric constant of the annealed electrolyte solution. Newly generated computer simulation results for the structural and thermodynamic parameters, obtained by the grand canonical Monte Carlo method, were used to assess the validity of the ROZ/HNC approximation. It was shown that the ROZ/HNC theory yields good agreement with the computer simulations.     

An association theory for the formation of ion oligomers and its application to 1-1 electrolytes

A theory for modelling electrolyte solutions which includes the formation of ion clusters of different size has been developed in the framework of the primitive model. In primitive models the solvent is described as a dielectric continuum and the solvent–solute interactions are neglected. For the dielectric constant the value of the pure solvent has been used. The ion cluster distribution is calculated from the mass action law. The association constants are related to integrals over the cluster distribution functions which are calculated with the Kirkwood superposition approximation from low density pair distribution functions. The ion clusters are defined by a certain distance which rules if two ions belong to the same cluster. This so-called Bjerrum distance is chosen according to fundamental investigations of the structure of ion cluster. All ion clusters are modelled as hard spheres. For the free ions and charged clusters the mean spherical approximation expression for the Coulomb interaction is added. The co-volumes of the ion clusters have been taken from the investigation of the ion cluster structures, and are consistent with the definition of an ion cluster chosen here.     

A self-consistent density-functional approach to the structure of electric double layer: charge-asymmetric electrolytes

A self-consistent density-functional approach has been employed to study the structure of an electric double layer formed from a charge-asymmetric (2:l) electrolyte within the restricted primitive model which corresponds to charged hard sphere ions and a continuum solvent. The particle correlation due to hard-core exclusions is evaluated by making use of the universality of the density functionals and the correlation function of the uniform hard sphere fluid obtained through the integral equation theory with an accurate closure relation whereas mean spherical approximation is employed for the electrical contribution. Numerical results on the diffuse layer potential drop, ionic density profile, and the mean electrostatic potential near the electrode surface at several surface charge densities are found to be in quantitative agreement with the available simulation data.     

Saturation and condensate fraction reduction of cold alpha matter

The ground state energy of ideal α  -matter at T=0$T=0$ is analyzed within the framework of variational theory of Bose quantum liquids. Calculations are done for three local α–α potentials with positive volume integrals and two-body correlation functions obtained from the Pandharipande–Bethe equation. The energy per particle of α matter is evaluated in the cluster expansion formalism up to four-body diagrams, and using the HNC/0 and HNC/4 approximation for a Bose liquid. At low densities the two methods predict similar EOS whereas at higher densities they are sensitively different, the HNC approximation providing saturation at lower density, bellow the saturation value of nuclear matter. Inclusion of higher-order terms in the cluster expansion of the condensate fraction is leading to a stronger depletion of the alpha condensate with the density compared to the two-body approximation prediction.     

Kinetic equation for the processes of local reorganization of molecular systems with charged species

A molecular dynamic theory based on the lattice-gas model for the local reorganization of multi-component systems containing charged species is considered. Expressions for the mono- and bimolecular stages of the elementary processes that describe chemical reactions and displacements and rotations of molecules in dense gases and liquids are derived, with consideration given to direct and indirect effects of the initiation of electron and proton transfer. The proposed kinetic equations describe small-scale restructuring of solutions containing components of different sizes under the influence of changes in the external parameters of the molecular system at the kinetic stage of evolution of the system. The theory retains the effects of direct spatial correlations in the distribution of all the components of the mixture with the help of pair distribution functions in the quasi-chemical approximation. The dynamics of the local reorganization of molecules includes the kinetic equations for the local densities and pair distribution functions. The equations derived are intended to describe liquid-phase reactions, ion charge exchange, mutual diffusion of components of different sizes in multicomponent solutions, extraction processes at liquid phase boundaries, and photochemical processes in condensed phases.     

A computer simulation study of racemic mixtures

A simple model for a chiral molecule is proposed. The model consists of a central atom bonded to four different atoms in tetrahedral coordination. Two different potentials were used to describe the pair potentials between atoms: the hard sphere potential and the Lennard-Jones potential. For both the hard sphere and the Lennard-Jones chiral models, computer simulations have been performed for the pure enantiomers and also for the racemic mixture. The racemic mixture consisted of an equimolar mixture of the two optically active enantiomers. It is found that the equations of state are the same, within statistical uncertainty, for the pure enantiomer fluid and for the racemic mixture. Only at high pressures does the racemic mixture seem to have a higher density, for a given pressure, than the pure enantiomer. Concering the structure, no difference is found in the site-site correlation functions between like and unlike molecules in the racemic mixture either at low or at high densities. However, small differences are found for the site-site correlations of the pure enantiomer and those of the racemic mixtures. In the Lennard-Jones model, similar conclusions are drawn. The extension of Wertheim's first-order perturbation theory, denoted bonded hard sphere theory (ARCHER, A. L., and JACKSON, G., 1991, Molec. Phys., 73, 881; AMOS, M. D., and JACKSON, G., 1992, J. chem. Phys., 96, 4604), successfully reproduces the simulation results for the hard chiral model. Virial coefficients of the hard chiral model up to the fourth have also been evaluated. Again, no differences are found between virial coefficients of the pure fluid and of the racemic mixture. All the results of this work illustrate the quasi-ideal behaviour of racemic mixtures in the fluid phase.     

Effect of ionic size on the structure of spherical double layers: a Monte Carlo simulation and density functional theory study

The effect of ionic size on the diffuse layer characteristics of a spherical double layer is studied using Monte Carlo simulation and density functional theory within the restricted primitive model. The macroion is modelled as an impenetrable charged hard sphere carrying a uniform surface charge density, surrounded by the small ions represented as charged hard spheres and the solvent is taken as a dielectric continuum. The density functional theory uses a partially perturbative scheme, where the hard sphere contribution to the one particle correlation function is evaluated using weighted density approximation and the ionic interactions are calculated using a second-order functional Taylor expansion with respect to a bulk electrolyte. The Monte Carlo simulations have been performed in the canonical ensemble. The detailed comparison is made in terms of zeta potentials for a wide range of physical conditions including different ionic diameters. The zeta potentials show a maximum or a minimum with respect to the polyion surface charge density for a divalent counterion. The ionic distribution profiles show considerable variations with the concentration of the electrolyte, the valency of the ions constituting the electrolyte, and the ionic size. This model study shows clear manipulations of ionic size and charge correlations in dictating the overall structure of the diffuse layer.     

Integral equation theory of a one dimensional hard-ellipse fluid between hard walls

Density functional theory is used to study the structure of a one dimensional fluid model of hard-ellipse molecules with their axes freely rotating in a plane, confined between hard walls. A simple Hypernetted chain (HNC) approximation is used for the density functional of the fluid and the integral equation for the density is obtained from the grand potential. The only required input is the direct correlation function of the one dimensional hard-ellipse fluid. For this model, the pressure, sum rule and the density at the walls are obtained. The Percus Yevick (PY), for lower density, and HNC, for higher density, integral equations are also solved to obtain the direct correlation function of hard-ellipse model introduced here. We obtain the average density at the wall as well as the radial density profile. We compare these with Monte Carlo simulations of the same model and find reasonable agreement.     

Fluids with highly directional attractive forces. IV. Equilibrium polymerization

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.Supported by the NSF under grant No. CHE-82-11236.     

Phase separation in strongly coupled binary ionic mixtures at zero temperature

The ground-state energy of strongly coupled binary ionic mixtures is evaluated by solving the hypernetted-chain (HNC) equations for the pair distribution functions. The point ions are immersed in a rigid and uniform neutralizing background of relativistic electrons. We have calculated the equation of state and the pair structure of these binary fluids for three concentrations and over a rather extensive range of densities. The miscibility essentially depends on the statistics of the species and on the coupling. We show that the phase separation is very sensitive to the choice of the wave function used to describe the mixture.     

The point ion modified Poisson–Boltzmann theory for a planar electric double layer with different permittivities for the electrode,inner layer and diffuse layer

The planar electric double layer is modelled by an electrode, inner layer and diffuse layer whose constant permittivities differ. A point ion modified Poisson–Boltzmann analysis is made of the model with the ions in the diffuse layer having a distance of closest approach to the electrode, which is greater than the inner layer thickness and mimics the ion radius of a primitive model electrolyte. Comparisons are made with existing Monte Carlo simulations for uncharged and charged electrodes. For 1:1 and 2:1 electrolytes with a charged electrode, the modified Poisson–Boltzmann theory successfully predicts the singlet ion normalised density functions and the mean electrostatic potential. With the uncharged electrode, the neglect of ion size is more critical and the theoretical predictions are now poor at the higher concentrations.     

Sine-Gordon Theory for the Equation of State of Classical Hard-Core Coulomb Systems. III. Loopwise Expansion

We present an exact field theoretical representation of an ionic solution made of charged hard spheres. The action of the field theory is obtained by performing a Hubbard–Stratonovich transform of the configurational Boltzmann factor. It is shown that the Stillinger–Lovett sum rules are satisfied if and only if all the field correlation functions are short range functions. The mean field, Gaussian and two-loops approximations of the theory are derived and discussed. The mean field approximation for the free energy constitutes an exact lower bound for the exact free energy, while the mean field pressure is an exact upper bound. The one-loop order approximation is shown to be identical with the random phase approximation of the theory of liquids. Finally, at the two-loop order and in the pecular case of the restricted primitive model, one recovers results obtained in the framework of the mode expansion theory.     

Numerical solution of a modified Poisson-Boltzmann equation for 1 : 2 and 2 : 1 electrolytes in the diffuse layer

A modified Poisson-Boltzmann (MPB) equation for an unsymmetrically charged electrolyte in the diffuse part of the electric double layer at a plane charged wall is solved numerically using a quasi-linearization procedure. Computations are carried out for 1 : 2 and 2 : 1 restricted primitive model electrolytes with no imaging and for a metallic wall and the results compared with the classical Gouy-Chapman-Stern theory. Except for negligible surface charge, the system with a divalent counter ion is the most sensitive to any change in its physical parameters. In general the MPB mean electrostatic potential, in contrast to the Gouy-Chapman-Stern potential, is not a monotonic decreasing function. The asymptotic behaviour of the MPB equation implies charge oscillations above a critical electrolyte concentration (?0·23 M) while below this concentration imaging or surface charge-ion interactions can produce a charge inversion. Charge separation is found for no surface charge with a metallic wall. The point ion limit is briefly considered.     

Solution of the mean spherical approximation for hard ions and dipoles of arbitrary size

The general solution of the mean spherical approximation (MSA) for an arbitrary mixture of hard spherical ions and dipoles, in which the ions can be of different size, is found. This solution is given in terms of three parameters that are calculated by solving an algebraic equation. Two of these parameters are scaling parameters required to satisfy the general symmetry of the pair correlation functions, and are similar to the one introduced in the solution of the MSA for an ionic mixture in earlier work. For equal size and low ionic concentration, we get a rather explicit solution of the MSA, which is formally similar to the Waisman-Lebowitz solution of the restricted primitive model, but with a concentration-dependent dielectric constant.Supported in part through NSF grant 77-04597.     

Effects of polydispersity in quenched-annealed fluids: An integral equation approach

An extension of the replica Ornstein-Zernike (ROZ) equations for partly quenched polydisperse systems is presented. Explicit calculations have been performed for a monodisperse hard sphere fluid confined by a polydisperse hard sphere disordered matrix by using Percus-Yevick and hypernetted chain (HNC) approximations. The chemical potential of adsorbed fluid species has been evaluated. A numerical solution of the ROZ equations makes use of the orthonormal polynomials with the weight function corresponding to the distribution function of the diameters of matrix species. We have also compared the results of theoretical predictions with Monte Carlo simulation in a canonical ensemble. The result of this comparison suggests that the HNC approximation performs slightly better in predicting the structural properties of the system.     

Zeta potential of colloidal particle in solvent primitive model electrolyte solution: a density functional theory study

A systematic study of zeta potential for a spherical double layer (SDL) around a colloidal particle in electrolyte solutions, is performed using density functional theory and Monte Carlo simulation. The usual recipe under the solvent primitive model is employed to model the system, where macroion, counterions, and coions are represented by charged hard spheres of uniform charge density and the presence of solvent is taken into account by modelling it as neutral hard spheres. All the components of the system are embedded in a dielectric continuum in order to consider the electrostatic effect of the solvent. The density functional theory employs a suitable weighted density approximation to calculate the hard-sphere contribution, whereas the residual electrostatic interactions are calculated as a small perturbation around the uniform fluid. The zeta potential profiles of a SDL in the presence of a number of electrolytes have been calculated and are found to be considerably influenced in the presence of solvent with an increase in the concentration of the electrolyte. The theory successfully predicts the maxima and sign reversal of the zeta potential profiles at high macroion surface charge density and in the presence of multivalent counterions, as obtained from the Monte Carlo simulation.