Packing of ions near an electrolyte-electrode interface in the HNC/LMSA approximation to the RPM model

The standard HNC/MSA calculation of the ion distribution fails to describe the packing in a second layer seen in MC calculations. We describe an improved treatment which employs the particle-particle direct correlation function for non-neutral electrolyte compositions as found near the surface.     

Electric double layers with electrolyte mixtures: integral equations theories and simulations

A study of a planar electric double layer (EDL) in the presence of mixtures of electrolyte is presented. In particular, results from the Hyper-Netted-Chain/Mean-Spherical-Approximation (HNC/MSA) theory are compared with Monte Carlo (MC) simulations. In this way, the charge inversion induced by mixtures of multivalent and monovalent counterions is probed. Since overcharging phenomena in nature emerge under such conditions, the role of ion-ion correlations in the EDL appears as a crucial point in this kind of study. Unlike previous related works, a realistic hydrated ion size is used in the HNC/MSA calculations and simulations. In this way, a qualitative agreement between the results obtained from the theory and MC simulations is found. However, some discrepancies arise when the charge inversion is expected to be more noticeable, namely at high surface charges and/or elevated concentrations of multivalent electrolytes. Such differences are explained in terms of an overestimation of the charge inversion by the integral equation (IE) formalism.     

The electrical double layer for a fully asymmetric electrolyte around a spherical colloid: an integral equation study

The hypernetted chain/mean spherical approximation (HNC/MSA) integral equation for a totally asymmetric primitive model electrolyte around a spherical macroparticle is obtained and solved numerically in the case of size-asymmetric systems. The ensuing radial distribution functions show a very good agreement when compared to our Monte Carlo and molecular-dynamics simulations for spherical geometry and with respect to previous anisotropic reference HNC calculations in the planar limit. We report an analysis of the potential versus charge relationship, radial distribution functions, mean electrostatic potential, and cumulative reduced charge for representative examples of 1:1 and 2:2 salts with a size-asymmetry ratio of 2. Our results are collated with those of the modified Gouy-Chapman (MGC) and unequal radius modified Gouy-Chapman (URMGC) theories and with those of HNC/MSA in the restricted primitive model (RPM) to assess the importance of size-asymmetry effects. One of the most striking characteristics found is that, contrary to the general belief, away from the point of zero charge the properties of an asymmetric electrical double layer (EDL) are not those corresponding to a symmetric electrolyte with the size and charge of the counterion, i.e., counterions do not always dominate. This behavior suggests the existence of a new phenomenology in the EDL that genuinely belongs to a more realistic size-asymmetric model where steric correlations are taken into account consistently. Such novel features cannot be described by traditional mean-field theories such as MGC, URMGC, or even by enhanced formalisms, such as HNC/MSA, if they are based on the RPM.     

Statistical mechanical theories of the electric double layer

A comparison is made of present-day statistical mechanical theories of the diffuse part of the electric double layer in aqueous 1-1 electrolyte at a charged plane interface. These theories fall into three categories: (1) the modified Poisson-Boltzmann equation (MPB) based on the Kirkwood-Loeb charging of an ion; (2) the adaption to the electric double layer of the Bogoliubov-Born-Green-Yvon (BBGY) hierarchy of integral equations; (3) the use of the Ornstein-Zernike equation (OZ) for the direct correlation functions of the pair interfacial plane wall-molecular particle, as derived by Henderson, Abraham and Barker (HAB). The HAB-OZ equation is used in conjunction with the mean spherical approximation (MSA) or hypernetted chain approximation (HNC). All the theories make use of the primitive model of the bulk electrolyte, so that inhomogeneity of the dielectric permittivity next to the plane wall is neglected. Except perhaps for a variation of the BBGY theory, which uses a closure based on electrical neutrality, all the theories predict oscillatory behaviour in potential distribution as a function of distance at the higher electrolyte concentrations. The HAB-OZ model has the defect that electrostatic imaging is not consistent with the assumptions of central forces and pair-wise additivity of ionic interactions. It is found that the MPB provides the best overall agreement with Monte Carlo calculations.     

Charge reversal in real colloids: Experiments, theory and simulations

In the last years, the inclusion of ionic short-range correlations in the study of colloidal stability has led to significant disagreements with the predictions obtained from classical treatments. An example of these discrepancies is the occurrence of charge reversal of charged particles. In order to shed light on this issue, the charge reversal of latex particles in the presence of asymmetric electrolytes has been investigated through Monte Carlo (MC) simulations. In particular, experimental results concerning electrophoretic mobility reversals and the Hyper-Netted-Chain/Mean-Spherical-Approximation (HNC/MSA) predictions have been compared with simulations in which two alternative methods for evaluating energies have been applied. A realistic hydrated ion size is used in the HNC/MSA calculations and simulations. In this way, the existence of a reversal in the electrophoretic mobility due to ion size correlations and without requiring specific counterion adsorption is probed. Moreover, the simulations appears as a useful tool for explaining those results in which the HNC/MSA does not reproduce the experimental trends.     

Dynamics of electrical double layer formation at a charged solid surface

A theoretical study of the dynamics of electrical double layer formation near a charged solid surface is presented. A microscopic expression for the time dependent inhomogeneous charge density of an ionic solution next to a newly charged surface is derived by using linear response theory and molecular hydrodynamics. The presence of interionic correlations is included through ionic structure factors. The rate of electrical double layer formation is found to depend rather strongly on ion concentration and on the dielectric constant of the medium. It is also found that the formation of double layer becomes slower with increase in distance from the charged surface.     

An integral equation theory for inhomogeneous molecular fluids: the reference interaction site model approach

An integral equation theory which is applicable to inhomogeneous molecular liquids is proposed. The "inhomogeneous reference interaction site model (RISM)" equation derived here is a natural extension of the RISM equation to inhomogeneous systems. This theory makes it possible to calculate the pair correlation function between two molecules which are located at different density regions. We also propose approximations concerning the closure relation and the intramolecular susceptibility of inhomogeneous molecular liquids. As a preliminary application of the theory, the hydration structure around an ion is investigated. Lithium, sodium, and potassium cations are chosen as the solute. Using the Percus trick, the local density of solvent around an ion is expressed in terms of the solute-solvent pair correlation function calculated from the RISM theory. We then analyze the hydration structure around an ion through the triplet correlation function which is defined with the inhomogeneous pair correlation function and the local density of the solvent. The results of the triplet correlation functions for cations indicate that the thermal fluctuation of the hydration shell is closely related to the size of the solute ion. The triplet correlation function from the present theory is also compared with that from the Kirkwood superposition approximation, which substitutes the inhomogeneous pair correlation by the homogeneous one. For the lithium ion, the behavior of the triplet correlation functions from the present theory shows marked differences from the one calculated within the Kirkwood approximation.     

Electrokinetic properties of monovalent electrolytes confined in charged nanopores: Effect of geometry and ionic short-range correlations

The electrokinetic properties (such as capillary conductance, electroviscosity, and the streaming potential) are obtained for a restricted primitive model electrolyte confined in a slitlike nanopore made up of two infinite parallel plates and in a cylindrical cavity of infinite extension. The hypernetted chain/mean spherical approximation (HNC/MSA) is used to obtain the equilibrium ionic concentration profiles inside the pores, which in turn are used to calculate the electrokinetic properties via linear hydrodynamic equations. Our results are compared with those obtained via the classical Poisson–Boltzmann (PB) theory. Important quantitative and qualitative effects, attributed to geometry and to the proper consideration of short-range correlations by HNC/MSA, are discussed.     

液——液界面双电层统计力学处理

应用巨正则系综统计法处理液／液界面（ＩＴＩＥＳ）双电层体系。根据ＭＶＮ模型,假定溶液中离子可穿入界面内层（定向溶剂分子层）,由体系（内层）巨正则配分函数导出内层微分电容（Ｃ１）统计表达式,拟合计算Ｃ１随该层表面电荷密度（σｍ）变化关系。理论同时表明,Ｃ１与σｍ涨落存在确定关系     

Effect of charge density gradient on characteristics of electric double layer for salt melts

The equilibrium conditions are analyzed for a spatially inhomogeneous ionic liquid using the density functional theory with allowance made for the second order gradient corrections. Solutions for the distribution of potential and charge density in the electric double layer at the ionic liquid/vapor interface are obtained using a parameterized total density profile normal to the surface. It is shown that taking into account the effects of the charge density gradient in the theory results in the appearance of damped oscillations of the charge density near the surface, while the double layer localized on the surface is reduced.     

Mechanisms behind concentration profiles illustrated by charge and concentration distributions around ions in double layers

The mechanisms behind the behaviour of concentration and charge density profiles in diffuse electric double layers are investigated quantitatively for 1:1 and 2:2 electrolytes. This is done by analysing various contributions to the mean force that acts on each ion. The forces are obtained from the calculated ionic charge and concentration distributions around individual ions at various positions in the double layer. These distributions are presented graphically which allows an immediate visual illustration of the mechanisms in action. Some features studied are charge inversion in double layers for divalent aqueous electrolytes, overcompensation of surface charge due to large amounts of physisorbed counterions, ion size effects in the double layer structure and various mechanisms that cause deviations from the predictions of the Poisson–Boltzmann approximation. A major objective of the paper is to present the results in a visual form and explain aspects of modern double layer theory in a simple manner.     

Ab initio theoretical study of temperature and density dependence of molecular and thermodynamic properties of water in the entire fluid region: autoionization processes

The temperature and density dependence of the molecular and thermodynamic properties of water is investigated theoretically by means of the ab initio electronic structure theory combined with the reference interaction site model method, so-called RISM-SCF. We consider the autoionization process (H2O + H2O right harpoon over left harpoon H3O+ + OH-) by regarding H2O, H3O+, and OH- as "solute" molecules in an aqueous solution and evaluate molecular geometry, electronic structure, solvation structure, and the ionic product of water (pKw) of these species as functions of thermodynamic conditions. In our previous paper, we calculated these properties by using essentially the same method in a wide range of density values (0.6-1.4 g/cm3). However, the calculation was limited at rather higher density (>0.6 g/cm3) due to the difficulty of convergence, which is inherent to the hypernetted-chain (HNC) closure. The problem is overcome in this study by employing the Kovalenko-Hirata (KH) closure which hybridizes the HNC and the mean-spherical approximation (MSA). Here, we present the results for the thermodynamic range of densities from 0.025 to 1.0 g/cm3 and for temperatures from 300 to 800 K including the supercritical point.     

The electric double layer capacitance for a hard sphere ion-dipole electrolyte in the mean field approximation

The electric double layer capacitance for a hard sphere ion-dipole system in the neighbourhood of a plane charged wall is calculated in the mean field approximation. To order ka the capacitance predicts the same structural features as the MSA capacitance.     

Remarks on the correlation function implied by the Bjerrum theory of ion pairing

The Friedman theory of correlation functions implied by the Bjerrum theory is generalized by taking into account additional terms and by improving the basic expression for the free energy. By combining the mean spherical approximation (MSA) and the mass action law (MAL) good agreement with HNC and MC data is reached.     

Vapor pressure measurements on nonaqueous electrolyte solutions. Part 6. Some remarks on integral equations

Various combinations of the hypernetted chain (HNC) equation with the mean spherical approximation (MSA) and the Percus-Yevick (PY) equation are compared both for a well-known aqueous 2-2 electrolyte model solution and for real acetonitrile solutions. Belloni's self-consistency test shows that classical HNC calculations yield the best compressibility data for the two systems despite an apparently unrealistic g₊₊ maximum in the case of the aqueous solution. Effective concentration-dependent potentials making use of the dependence of the solution permittivity on electrolyte concentration are used for HNC calculations of osmotic coefficients for methanol solutions.     

The structural properties of a two-Yukawa fluid: Simulation and analytical results

Standard Monte Carlo simulations are carried out to assess the accuracy of theoretical predictions for the structural properties of a model fluid interacting through a hard-core two-Yukawa potential composed of a short-range attractive well next to a hard repulsive core, followed by a smooth, long-range repulsive tail. Theoretical calculations are performed in the framework provided by the Ornstein-Zernike equation, solved either analytically with the mean spherical approximation (MSA) or iteratively with the hypernetted-chain (HNC) closure. Our analysis shows that both theories are generally accurate in a thermodynamic region corresponding to a dense vapor phase around the critical point. For a suitable choice of potential parameters, namely, when the attractive well is deep and/or large enough, the static structure factor displays a secondary low-Q peak. In this case HNC predictions closely follow the simulation results, whereas MSA results progressively worsen the more pronounced this low-Q peak is. We discuss the appearance of such a peak, also experimentally observed in colloidal suspensions and protein solutions, in terms of the formation of equilibrium clusters in the homogeneous fluid.     

Density functional approach to thermodynamics of self-assembly

A local density functional approximation for predicting the surface crystallization of a thermodynamically small system under gravity is described and tested. Using the model of the classical soft-sphere fluid, the state parameters for such systems are identified. A generalized phase diagram based upon the scaling variables is obtained; systems with the same reduced-state parameters exhibit identical profiles of thermodynamic properties such as density, pressure, and intrinsic chemical potential, measured in the direction of the applied field. The point-thermodynamic approximation of Rowlinson and the local density approximation of the density functional formalism are found to be remarkably accurate. A configurational temperature is defined and shown to agree with the corresponding kinetic temperature for inhomogeneous systems at equilibrium. The structural profiles at the crystal-fluid interface are indicative of a mesolayer of lower density crystal, not seen in the field-free isobaric crystal-liquid interface.     

Electrochemistry,ion adsorption and dynamics in the double layer: a study of NaCl(aq) on graphite

Graphite and related sp² carbons are ubiquitous electrode materials with particular promise for use in e.g., energy storage and desalination devices, but very little is known about the properties of the carbon–electrolyte double layer at technologically relevant concentrations. Here, the (electrified) graphite–NaCl(aq) interface was examined using constant chemical potential molecular dynamics (CμMD) simulations; this approach avoids ion depletion (due to surface adsorption) and maintains a constant concentration, electroneutral bulk solution beyond the surface. Specific Na⁺ adsorption at the graphite basal surface causes charging of the interface in the absence of an applied potential. At moderate bulk concentrations, this leads to accumulation of counter-ions in a diffuse layer to balance the effective surface charge, consistent with established models of the electrical double layer. Beyond ∼0.6 M, however, a combination of over-screening and ion crowding in the double layer results in alternating compact layers of charge density perpendicular to the interface. The transition to this regime is marked by an increasing double layer size and anomalous negative shifts to the potential of zero charge with incremental changes to the bulk concentration. Our observations are supported by changes to the position of the differential capacitance minimum measured by electrochemical impedance spectroscopy, and are explained in terms of the screening behaviour and asymmetric ion adsorption. Furthermore, a striking level of agreement between the differential capacitance from solution evaluated in simulations and measured in experiments allows us to critically assess electrochemical capacitance measurements which have previously been considered to report simply on the density of states of the graphite material at the potential of zero charge. Our work shows that the solution side of the double layer provides the more dominant contribution to the overall measured capacitance. Finally, ion crowding at the highest concentrations (beyond ∼5 M) leads to the formation of liquid-like NaCl clusters confined to highly non-ideal regions of the double layer, where ion diffusion is up to five times slower than in the bulk. The implications of changes to the speciation of ions on reactive events in the double layer are discussed.

CμMD reveals multi-layer electrolyte screening in the double layer beyond 0.6 M, which affects ion activities, speciation and mobility; asymmetric charge screening explains concentration dependent changes to electrochemical properties.