Ion-ion Correlation Functions Research Articles

Ion correlation forces between uncharged dielectric walls

The interaction pressure between two uncharged planar walls immersed in various electrolyte solutions containing mono- and/or divalent ions is investigated. The solution is treated as a primitive model electrolyte, and the wall surfaces constitute dielectric discontinuities. Ionic image charge and ion-wall dispersion interactions are included. The interaction parameters are appropriate for hydrocarbon (polystyrene)/water interfaces, and the electrolyte concentrations considered lie between 0.250M and 1.00M. The anisotropic hypernetted chain method is used to self-consistently calculate the ion density profiles and the ion-ion correlation functions in the inhomogeneous electrolyte. Thereby, the effects of image charge interactions and dispersion interactions on the pressure and the electrolyte structure are included in a fully consistent manner. The explicit consideration of correlations between the ions in the presence of image charges ensures that the screening of the zero-frequency van der Waals interaction is taken into account. Of special interest are the effects of asymmetries between anions and cations with respect to valency and/or dispersion interaction with the walls. Such asymmetries create an electric double layer in the electrolyte outside each electroneutral surface. This causes the wall-wall interaction for large surface separations to be similar to the interaction between charged surfaces. For intermediate separations, around 1-2 nm, a substantial repulsive peak appears in the ionic pressure. In some cases the repulsion is larger than the van der Waals attraction between the walls, which implies that there is a repulsive barrier in the total pressure despite that the surfaces are uncharged. The strongest repulsion is found for 2:1 electrolytes where the monovalent anions interact strongly with the walls via dispersion forces. In general, ion-wall dispersion forces acting on ions of lower valency have a much greater effect than equally strong dispersion forces acting on ions of higher valency. This is mainly due to the more strongly repulsive image charge forces on ions of higher valency that counteract the attractive dispersion forces. Effects of confinement on the ion-ion correlations also contribute to this difference. For all electrolytes the interaction pressure from the ions is attractive for small surface separations. The main cause is a depletion of ions between the walls from the self-image repulsion and confinement effects. For totally symmetric electrolytes the attractive pressure extends to large separations in most cases.

Neutrino scattering in heterogeneous supernova plasmas

Neutrinos in core-collapse supernovae are likely trapped by neutrino-nucleus elastic scattering. Using molecular dynamics simulations, we calculate neutrino mean free paths and ion-ion correlation functions for heterogeneous plasmas. Mean free paths are systematically shorter in plasmas containing a mixture of ions compared to a plasma composed of a single ion species. This is because neutrinos can scatter from concentration fluctuations. The dynamical response function of a heterogeneous plasma is found to have an extra peak at low energies describing the diffusion of concentration fluctuations. Our exact molecular dynamics results for the static structure factor reduce to the Debye-H\"uckel approximation, but only in the limit of very low momentum transfers.

Ion-ion correlations in electric double layers from Monte Carlo simulations and integral equation calculations

The anisotropic ion-ion correlation function g(R 1, R 2), where R 1 and R 2 are the coordinates of ions 1 and 2, is calculated for double layer systems composed of counterions between two charged, planar walls. The primitive model of the electrolyte is used. The Widom formula for the excess chemical potential is applied in the neighbourhood of a confined particle in the double layer to obtain g(R 1, R 2) from Monte Carlo (MC) simulations. The pair correlations are also calculated in the anisotropic RHNC approximation, where the reference hypernetted chain (RHNC) closure is applied at the pair (ion-ion) level and where the anisotropic bridge function is taken from an inhomogeneous reference system composed of a hard sphere fluid with the same density profile as the double-layer system. The results of the MC simulations and RHNC calculations are generally in very good agreement with each other. This demonstrates the fact that the anisotropic RHNC approximation is a very accurate method for calculating the v...

Ion-ion correlations in electric double layers from Monte Carlo simulations and integral equation calculations

The anisotropic ion-ion correlation function g(R 1, R 2), where R 1 and R 2 are the coordinates of ions 1 and 2, is calculated for double layer systems composed of counterions between two charged, planar walls. The primitive model of the electrolyte is used. The Widom formula for the excess chemical potential is applied in the neighbourhood of a confined particle in the double layer to obtain g(R 1, R 2) from Monte Carlo (MC) simulations. The pair correlations are also calculated in the anisotropic RHNC approximation, where the reference hypernetted chain (RHNC) closure is applied at the pair (ion-ion) level and where the anisotropic bridge function is taken from an inhomogeneous reference system composed of a hard sphere fluid with the same density profile as the double-layer system. The results of the MC simulations and RHNC calculations are generally in very good agreement with each other. This demonstrates the fact that the anisotropic RHNC approximation is a very accurate method for calculating the various double-layer properties. It also follows that the Widom technique is a very versatile tool in simulation studies of double-layer systems. To obtain 15 points for the pair correlation function by simulation takes about 60 times longer than to obtain 200 000 points by anisotropic RHNC calculations (the latter takes a few minutes on an IBM RS-6000/590 workstation).

Electric double-layer properties calculated in the anisotropic reference hypernetted chain approximation

Double-layer interactions and ion density profiles are calculated in the anisotropic reference hypernetted chain (RHNC) approximation, which uses the RHNC approximation for the anisotropic ion-ion correlation functions in the double layer. The ion-ion bridge functions are taken from a hard sphere reference system with the same density profiles as the full system. Excellent agreement with simulation results is obtained even at high concentrations and surface charges. If the bridge functions are neglected (i.e. the anisotropic hypernetted chain (HNC) approximation is used) only qualitative agreement with simulation is obtained in regimes where the local ion density is high and the contributions from ion-ion correlations at short range are very important. Otherwise, both the anisotropic HNC and RHNC approximations give equally good results for the systems investigated. Some methodological questions for the RHNC calculations are discussed.

Computer simulation of aqueous Na-Cl electrolytes

The equilibrium structure of aqueous Na-Cl electrolytes in the concentration regime between 1 and 5 mol l-1 is studied by means of a molecular dynamics computer simulation using interaction-site descriptions of water and the ionic components. The electrostatic interactions are treated both with the newly developed charged-clouds scheme and with Ewald summation. In the case of a 5 mol l-1 electrolyte, the results for pair correlations obtained by the two methods are in excellent agreement. However, the charged-clouds technique is much faster than Ewald summation and makes simulations at lower salt concentrations feasible. It is found that both ion-water and ion-ion correlation functions depend only weakly on the ionic concentration. Sodium and chloride ions exhibit only a negligible tendency to form contact pairs. In particular, no chloride ion pairs in contact are observed.

Computer simulations do not support Cl-Cl pairing in aqueous NaCl solution

Ion-ion correlation functions of a 5M NaCl-SPC water model were calculated by molecular dynamics and Monte Carlo simulations. No paired anions were found in contradiction with the extended reference-interaction-site model theory predicting Cl-Cl pairs for the same model. In order to check for a possible water model dependence the transferable interacting point sites model was also considered. Calculations for a 5 M solution using molecular dynamics and for a single chloride pair in water using constrained molecular dynamics again did not show the formation of anion pairs in contact.

The structure and electronic density distribution in the liquid alkali metals

We present ab initio calculations for the electronic density distribution, and electron-ion and ion-ion correlation functions for the liquid alkali metals at conditions near the melting point. Our calculations are based on the use of the neutral pseudoatom method to derive the interionic pair potential and on the variational modified hypernetted chain integral equation theory of liquids. The resulting theory is free of adjustable parameters, using the atomic numbers as the only input data. The interionic pair potentials obtained follow the expected trends, whereas the theoretical structural functions show a good agreement with experiment.

Thomas-Fermi model for dense plasmas.

The average degree of ionization for a dense plasma is calculated with the aid of a newly established atomic model based on the Thomas-Fermi (TF) method. This new model is characterized by the following features: (i) the bound electrons and free electrons are treated separately, (ii) a physically reasonable definition of the bound electrons is given, (iii) the system is described as a strongly coupled plasma of free electrons and TF ions, (iv) the source density in the Poisson equation is determined by the electron-ion and ion-ion correlation functions, and (v) the degree of ionization is calculated through the minimization of the total free energy. Results from the first and second approximations are presented, corresponding to models of increasing sophistication for the ion-ion correlation function. A comparison of these results with the results from earlier TF calculations and with the results from the Saha equation is also provided.

Inconsistent dielectric behaviour of proposed hamiltonian models for ionic solutions

Analytical results are shown to imply that proposed interaction site hamiltonian models for ionic solutions lead to inconsistent values for the dielectric constant of the pure solvent compared to that implied by the asymptotic behaviour of ion-ion correlation functions in that solvent. The result follows from the flexibility permitted in choosing coulombic parameters, and it is shown that important qualitative errors can result if such models are used directly in an accurate theory.

Correlation Funktions of a System with Different Temperatures of the Particle Components

We consider a plasma consisting of particle components with different temperatures. The components are uniformly distributed in the configuration space and MAXWELLIAN in the velocity space. Pair correlations are assumed to be small and higher order correlations negligible. It is shown from the BBGKY-hierarchy that the influence of the electrons on the ion kinetics can be taken into account by treating the ions as dressed particles. The hierarchy for these dressed particles provides the ion-ion correlation function. The electron-ion pair correlation is calculated from the POISSON equation using the ion-ion correlation and relating the electron-ion pair distribution to the average potential. By the same procedure we derive the electron-electron correlation making use of the electron-ion correlation. The results are compared with those of other authors.