Weighted Density Approach Research Articles

Size and charge correlations in spherical electric double layers: a case study with fully asymmetric mixed electrolytes within the solvent primitive model.

Size and charge correlations in spherical electric double layers are investigated through Monte Carlo simulations and density functional theory, through a solvent primitive model representation. A fully asymmetric mixed electrolyte is used for the small ions, whereas the solvent, apart from being a continuum dielectric, is also treated as an individual component. A partially perturbative density functional theory is adopted here, and for comparison, a standard canonical ensemble Monte Carlo simulation is used. The hard-sphere free energy is treated within a weighted density approach and the residual ionic contribution is estimated through perturbation around the uniform density. The results from both methods corroborate each other quantitatively over a wide range of physical parameters. The importance of structural correlations is envisaged through the size and charge asymmetry of the supporting electrolytes that includes the solvent as a component.

Effect of multivalent counterions on the spherical electric double layers with asymmetric mixed electrolytes: A systematic study by Monte Carlo simulations and density functional theory

The effect of multivalent counterions on the spherical electric double layers containing asymmetric electrolytes with size and charge asymmetry is studied using density functional theory and Monte Carlo simulations, in a systematic manner. A primitive model representation of the system is followed, where the macroion and small ions are represented as uniformly charged hard spheres of different size within a dielectric continuum as solvent. The theory approximates the hard-sphere contribution through a weighted density approach, whereas a functional expansion around the uniform fluid is used for the ionic part. The theory reproduces the simulation data quantitatively for a wide range of system parameters. The present study reflects the importance of size and charge correlations with inclusion of multivalent counterions as observed in spherical double layers.

Structure of Colloidal Solution with Size-Asymmetric Electrolytes: A Solvent Primitive Model Investigation

The structure of colloidal solution with size asymmetric electrolytes using a solvent primitive model representation is investigated using density functional theory and Monte Carlo simulation. The solvent is assumed to be an individual component apart from its behavior as a countinuum dielectric medium. The theory is partially perturbative with hard-sphere correlation being treated using a weighted density approach, whereas the residual ionic contribution is calculated through perturbation around the uniform density. A standard canonical ensemble Monte Carlo simulation method is also adopted here, for comparison. The theoretical results are in quantitative agreement with the simulation data for the entire range of parametric conditions. This study points to the importance of including the solvent as an individual component.

Structure of nonuniform four-component fluid mixtures: A systematic investigation through density functional theory and simulation

The static structure of four-component fluid mixtures is studied using a density functional approach and computer simulation. The input direct correlation function required in the simple weighted density approach is obtained analytically within the Percus–Yevick approximation. However, in the self-consistent density functional approach, the same is calculated numerically from the integral equation theory using a more consistent closure relation. The density profiles of the four-component hard sphere mixtures near a hard wall and around a large hard spherical solute as well as the radial distribution function of uniform system compare quite well with the computer simulation results over a wide variation of different parameters.

Structure of spherical electric double layers with fully asymmetric electrolytes: a systematic study by Monte Carlo simulations and density functional theory.

A systematic investigation of the spherical electric double layers with the electrolytes having size as well as charge asymmetry is carried out using density functional theory and Monte Carlo simulations. The system is considered within the primitive model, where the macroion is a structureless hard spherical colloid, the small ions as charged hard spheres of different size, and the solvent is represented as a dielectric continuum. The present theory approximates the hard sphere part of the one particle correlation function using a weighted density approach whereas a perturbation expansion around the uniform fluid is applied to evaluate the ionic contribution. The theory is in quantitative agreement with Monte Carlo simulation for the density and the mean electrostatic potential profiles over a wide range of electrolyte concentrations, surface charge densities, valence of small ions, and macroion sizes. The theory provides distinctive evidence of charge and size correlations within the electrode-electrolyte interface in spherical geometry.

The structure and properties of a simple model mixture of amphiphilic molecules and ions at a solid surface.

We investigate microscopic structure, adsorption, and electric properties of a mixture that consists of amphiphilic molecules and charged hard spheres in contact with uncharged or charged solid surfaces. The amphiphilic molecules are modeled as spheres composed of attractive and repulsive parts. The electrolyte component of the mixture is considered in the framework of the restricted primitive model (RPM). The system is studied using a density functional theory that combines fundamental measure theory for hard sphere mixtures, weighted density approach for inhomogeneous charged hard spheres, and a mean-field approximation to describe anisotropic interactions. Our principal focus is in exploring the effects brought by the presence of ions on the distribution of amphiphilic particles at the wall, as well as the effects of amphiphilic molecules on the electric double layer formed at solid surface. In particular, we have found that under certain thermodynamic conditions a long-range translational and orientational order can develop. The presence of amphiphiles produces changes of the shape of the differential capacitance from symmetric or non-symmetric bell-like to camel-like. Moreover, for some systems the value of the potential of the zero charge is non-zero, in contrast to the RPM at a charged surface.

Fourier space approach to the classical density functional theory for multi-Yukawa and square-well fluids

We present a Fourier space density functional approach for hard particles with attractive interactions, which is based on a previously developed two-dimensional approach [S. Hlushak, W. Rżysko, and S. Sokołowski, J. Chem. Phys. 131, 094904 (2009)] for hard-sphere chains. The interactions are incorporated by means of a three-dimensional Fourier image of the direct correlation function that is obtained from the first-order mean-spherical approximation. In order to improve the computational efficiency, we make extensive use of fast Fourier transforms for calculating density convolution integrals. A two-dimensional implementation of the new density functional approach, based on the expansion of the functional around the bulk fluid density, is used to study structure and adsorption of two model fluids in narrow cylindrical pores. We also investigate two methods that improve the accuracy of the theory as compared to the conventional DFT approach, which expands the free energy functional around the bulk fluid density: One a variant of the reference fluid density functional theory used by Gillespie et al. [Phys. Rev. E 68, 031503 (2003)], and the second a weighted density approach with energy route thermodynamics. Results from these two methods are compared to the conventional approach and also to the results of Monte Carlo simulations. We find that the method of Gillespie et al. and the weighted density approach with energy route thermodynamics yield significant improvement over the conventional approach.

Structure of Colloidal Solution in Presence of Mixed Electrolytes: A Solvent Restricted Primitive Model Study

The structure of colloidal solution in presence of mixed electrolytes is studied using Monte Carlo simulation and density functional theory, based on a four-component model of the spherical double layer. In this model the ions and solvent molecules are treated as charged and neutral hard spheres, respectively, having equal diameter, and in addition the mixture of mono- and multivalent co-ions are also considered. The macroion is considered as a uniformly charged hard sphere surrounded by the electrolyte and the solvent. The density functional theory is based on a partially perturbative scheme, where the electrical part is calculated through perturbation with respect to uniform density and the hard sphere contribution is approximated using a weighted density approach. The theory is found to be in quantitative agreement with the Monte Carlo simulation results, for singlet density as well as the mean electrostatic potential profiles. The system is studied over a wide range of parametric conditions, viz. with different ionic valences as well as size, at varying electrolyte concentration ratio of mono- and multivalent co-ions of mixed electrolytes, at different surface charge densities, and radius of the macroion. The present work reflects that even a simple primitive model for the solvent is able to manipulate the hard-sphere and electrostatic correlations of the diffuse double layer in the ionic density as well as mean electrostatic potential profiles.

Effect of Ionic Size on the Structure of Cylindrical Electric Double Layers: A Systematic Study by Monte Carlo Simulations and Density Functional Theory

The effect of ionic size on the diffuse layer characteristics of a cylindrical electric double layer is studied using density functional theory and Monte Carlo simulations for the restricted primitive model and solvent primitive model. The double layer is comprised of an infinitely long, rigid, impenetrable charged cylinder also referred to as the polyion, located at the center of a cylindrical cell containing the electrolyte, which is composed of charged hard spheres and the solvent molecules as neutral hard spheres (in the case of the solvent primitive model). The diameters of all the hard spheres are taken to be the same. The theory is based on a partially perturbative scheme, where perturbation is used to approximate the ionic interactions and the hard sphere contribution is treated within the weighted density approach. The Monte Carlo simulations are performed in the canonical ensemble. The zeta potential profiles as a function of the polyion surface charge density are presented for cylindrical double layers at different ionic concentrations, ionic valences, and different hard sphere (ionic and the solvent) diameters of 2, 3, and 4 Å. The theory agrees quite well with the simulation results for a wide range of system parametric conditions and is capable of showing the maximum and minimum in the zeta potential value for systems having divalent counterions. The steric effects due to the presence of solvent molecules play a major role in characterizing the zeta potential and the ionic density profiles. A noticeable change in the concavity of the zeta potential plots with increasing particle size at very low concentrations of monovalent electrolytes is suggestive of the occurrence of infinite differential capacitance for such systems.

Three component model of cylindrical electric double layers containing mixed electrolytes: A systematic study by Monte Carlo simulations and density functional theory

The structure of electric double layer around a hard rigid impenetrable cylindrical polyion is studied using density functional theory as well as Monte Carlo simulations. The three component model, presented here, is an extension of solvent primitive model where the solvent molecules are treated as the neutral hard spheres, counterions and coions as the charged hard spheres, all of equal diameters, and in addition the mixture of mono- and multivalent counterions are also considered. The theory is partially perturbative where the hard sphere interactions are treated within the weighted density approach and the corresponding ionic interactions have been evaluated through second-order functional Taylor expansion with respect to the bulk electrolyte. The theoretical predictions in terms of the density profiles and the mean electrostatic potential profiles are found to be in good agreement with the simulation results. The presence of neutral hard spheres incorporate the effects of exclude volume interactions (ionic size correlations) while the mixture of mono- and multivalent counterions enhance the ionic charge correlation effects. Thus, this model study shows clear manipulations of ionic size and charge correlations in dictating the ionic density profiles as well as mean electrostatic potential profiles of the diffuse layer. The behavior of diffused double layer has been characterized at varying ionic concentrations, at different concentration ratios of mono- and multivalent counterions of mixed electrolytes, at different diameters of hard spheres, and at varying polyion surface charge density.

Molecular solvent model of cylindrical electric double layers: A systematic study by Monte Carlo simulations and density functional theory

We present the Monte Carlo simulation and density functional study of structure of cylindrical double layers considering solvent as the third component. We have chosen molecular solvent model, where ions and solvent molecules are considered as charged and neutral hard spheres, respectively, having equal diameter. The polyionic cylinder is modeled as an infinite, rigid, and impenetrable charged hard cylinder surrounded by the electrolyte and the solvent spheres. The theory is partially perturbative where the hard-sphere interactions are treated within the weighted density approach, the corresponding ionic interactions have been evaluated through second-order functional Taylor expansion with respect to the bulk electrolyte. The Monte Carlo simulations have been performed in canonical ensemble. The system is studied at varying concentrations of electrolyte ions and the solvent molecules, at different valences of the electrolyte, at different sizes of hard spheres, and at varying surface charge density. The theory and the simulation results are found to be in good agreement at different parametric conditions. The hard-sphere exclusion effects due to molecular nature of the solvent are shown to have special implications in characterizing diffuse layer phenomena such as layering and charge inversion.

Weighted density functional theory of the solvophobic effect

We are interested in the spatial density of a molecular fluid in the presence of a solute of arbitrary size and shape. The density functional is written as the sum of a F0[rho(r)] that effectively describes small deviations around the uniform density, plus an energy density part that is responsible for formation of liquid-vapor interface. Using the weighted density approach, we require the density functional to match with several observed properties of the fluid such as equation of state and surface tension. We also show that weighting functions for calculating the weighted density can be obtained from experimental data. Using these elements, we construct a spatial density functional theory of water and apply it to obtain densities and solvation energies of a hard-sphere solute with encouraging results.

Structure of binary hard-sphere mixtures near a hard wall: A simple weighted-density-functional approach

The structure of binary hard-sphere mixtures near a hard wall is studied using a density functional theory. The formalism is based on a simple weighted density approach for the one-particle correlation functions of the nonuniform system, and requires as input only the one- and two-particle direct correlation functions of the corresponding uniform system. The approach is designed in a way, where the weight function is decoupled from the weighted density. Numerical results on the density profiles are shown to compare well with available simulation data.

Density Functional Theory for the Distribution of Small Ions around Polyions

A density functional theory is presented for the distribution of charged hard spheres (model for salt) around an infinite, rigid, and impenetrable charged cylinder (model for DNA or tobacco mosaic virus). The theory is based on a weighted density approach where the hard-sphere contribution to the one-particle correlation function is evaluated nonperturbatively using a position dependent effective density, and the ionic part is obtained through a second-order functional Taylor expansion around a uniform fluid. The theory is in good agreement with Monte Carlo simulations for the density distribution of monovalent, divalent, and mixed salts. For axial charge densities corresponding to DNA, the hypernetted chain integral equation theory is not as accurate as the density functional theory, but both liquid state approaches are superior to the Poisson−Boltzmann theory. For higher axial charge densities the density functional theory predicts interesting charge inversion effects that are absent in the nonlinear Po...

Colloidal dispersion confined in a planar slit: A density functional approach

We present a simple density functional approach for the prediction of the local density profile of a colloidal suspension confined in a charged planar slit. Both the interparticle and wall–particle interactions are modeled to be of screened Coulomb type. The short range part of the interparticle correlation is treated through a nonperturbative weighted density approach, while the long range contribution is treated perturbatively in terms of the density inhomogeneity. The input correlation functions for the bulk fluid are obtained through the rescaled mean spherical approximation. The calculated density profiles are shown on an average to compare well with results from computer simulation.

Density functional theory of ordering in charge-stabilized colloidal dispersions.

We employ a simple density functional approach to predict the phase diagram of charge-stabilized colloidal dispersions consisting of bcc, fcc, and liquid phases. The systems are modeled to consist of charged hard sphere macroions interacting through a screened Coulomb potential for which the rescaled mean spherical approximation is used for the direct correlation function. The three-body effect is found to play a significant role and is incorporated here through a simple parametrization of the corresponding correlation function in a perturbative approach and also alternatively using a suitable version of the nonperturbative modified weighted density approach. The calculated phase diagrams for two different colloidal systems are shown to be in excellent agreement with the corresponding experimental results.

A nonlocal density functional theory of electric double layer: Symmetric electrolytes

The density functional theory of inhomogeneous classical neutral fluids is extended to study the structure of electric double layer using the restricted primitive model as well as the nonprimitive three-component molecular solvent model. The formalism is based on a weighted density approach where the hard-sphere contributions to the excess free energy density and the one-particle correlation function are evaluated nonperturbatively using a position-dependent effective density while the corresponding ionic part is obtained through a second-order functional Taylor expansion around this effective density. The calculated results for the density profiles of the ions and the mean electrostatic potential are in good agreement with the available simulation results for the continuum solvent primitive model. The corresponding results for the nonprimitive molecular solvent model provide insight into the layering effect due to hard-sphere exclusion and the charge inversion phenomena.

Weighted-density-functional theory of solvation forces in liquids.

The weighted-density-functional theory developed by us recently [Phys. Rev. E 47, 4088 (1993)] for inhomogeneous ionic fluids is employed to calculate the solvation forces between two planar charged surfaces with an electrolyte solution confined between them. The restricted primitive model corresponding to charged hard-sphere ions with continuum solvent as well as the molecular solvent model with charged and neutral hard spheres representing the ions and the solvent, respectively, are used to represent the constituents of the electric double layer formed near each of the two charged hard walls. The forces on the walls are evaluated from the density distributions of the ions (and the solvent) obtained from the proposed fully nonperturbative weighted density approach using position-dependent effective densities. Neutral liquids and their mixtures are also studied as special cases. The calculated solvation forces as well as the density distributions are shown to compare quite well with available computer simulation results. A rigorous first-principles calculation of the interaction energies between colloidal particles through this approach is thus shown to be possible.