Structure of Polyelectrolyte Solutions at a Charged Surface

Electrical double layer properties of spherical oxide nanoparticles

The accurate characterization of the electrical double layer properties of nanoparticles is of fundamental importance for optimizing their physicochemical properties for specific biotechnological and biomedical applications. In this article, we use classical solvation density functional theory and a surface complexation model to investigate the effects of the pH and the nanoparticle size on the structural and electrostatic properties of an electrolyte solution surrounding a spherical silica oxide nanoparticle. The formulation has been particularly useful for identifying dominant interactions governing the ionic driving force at a variety of pH levels and nanoparticle sizes. As a result of the energetic interplay displayed between electrostatic potential, ion-ion correlation and particle crowding effects on the nanoparticle surface titration, rich, non-trivial ion density profiles and mean electrostatic potential behavior have been found.

Ionic asymmetry and solvent excluded volume effects on spherical electric double layers: a density functional approach

In this article, we present a classical density functional theory for electrical double layers of spherical macroions that extends the capabilities of conventional approaches by accounting for electrostatic ion correlations, size asymmetry, and excluded volume effects. The approach is based on a recent approximation introduced by Hansen-Goos and Roth for the hard sphere excess free energy of inhomogeneous fluids [J. Chem. Phys. 124, 154506 (2006); Hansen-Goos and Roth, J. Phys.: Condens. Matter 18, 8413 (2006)]. It accounts for the proper and efficient description of the effects of ionic asymmetry and solvent excluded volume, especially at high ion concentrations and size asymmetry ratios including those observed in experimental studies. Additionally, we utilize a leading functional Taylor expansion approximation of the ion density profiles. In addition, we use the mean spherical approximation for multi-component charged hard sphere fluids to account for the electrostatic ion correlation effects. These approximations are implemented in our theoretical formulation into a suitable decomposition of the excess free energy which plays a key role in capturing the complex interplay between charge correlations and excluded volume effects. We perform Monte Carlo simulations in various scenarios to validate the proposed approach, obtaining a good compromise between accuracy and computational cost. We use the proposed computational approach to study the effects of ion size, ion size asymmetry, and solvent excluded volume on the ion profiles, integrated charge, mean electrostatic potential, and ionic coordination number around spherical macroions in various electrolyte mixtures. Our results show that both solvent hard sphere diameter and density play a dominant role in the distribution of ions around spherical macroions, mainly for experimental water molarity and size values where the counterion distribution is characterized by a tight binding to the macroion, similar to that predicted by the Stern model.

Nonrandom adsorption of polyelectrolyte chains on finite regularly charged surfaces

Adsorption phenomena are relevant in a wide variety of subjects, from biophysics to technological applications. Different aspects, such as molecular recognition, multilayer deposition, and dynamics of polymer adsorption have been addressed. The methodologies used range from analytical and numerical methods to molecular dynamics or Monte Carlo simulations. In this work, a coarse-grained model is used to explore the adsorption of charged backbones to oppositely charged regions of a surface. These regions encompass those small enough to prevent complete adsorption, but extend to surfaces sufficiently large to promote adsorption with minimal effect on the three-dimensional conformation in bulk. Apart from the different surface areas explored, variations on the surface charge density, polyelectrolyte chain length, and chain stiffness were also considered. The degree of compaction of the polyelectrolyte, on adsorption, is different from that found in the bulk. Also, results indicate an nonuniform adsorption pattern on regularly charged surfaces.

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

The structure of spherical electric double layers is studied using Monte Carlo simulation and density functional theory by considering solvent as the third component. In this molecular solvent model (MSM), ions and solvent molecules are considered as charged and neutral hard spheres, respectively, having equal diameter. The macroion is considered as an isolated hard sphere having uniform surface charge density surrounded by the electrolyte and the solvent. The theory is partially perturbative as the hard-sphere contribution to the one particle correlation function is evaluated using suitably averaged weighted density, and the ionic part is obtained through a second-order functional Taylor expansion around the bulk electrolyte. The Monte Carlo simulations have been performed in a canonical ensemble. The system is studied at varying concentrations of electrolytes, and the solvent molecules, at different valences of the electrolyte, at different macroion radii, and at varying surface charge densities. The theory is found to be in good agreement with the simulation results over a wide range of parametric conditions. The excluded volume effects due to the molecular nature of the solvent are shown to have much richer features in diffuse layer phenomena like layering and charge inversion.

Density functional theory for planar electric double layers: closing the gap between simple and polyelectrolytes

We report a nonlocal density functional theory (NLDFT) for polyelectrolyte solutions within the primitive model; i.e., the solvent is represented by a continuous dielectric medium, and the small ions and polyions by single and tangentially connected charged hard spheres, respectively. The excess Helmholtz energy functional is derived from a modified fundamental measure theory for hard-sphere repulsion, an extended first-order thermodynamic perturbation theory for chain connectivity, and a quadratic functional Taylor expansion for electrostatic correlations. With the direct and cavity correlation functions of the corresponding monomeric systems as inputs, the NLDFT predicts the segment-level microscopic structures and adsorption isotherms of polyelectrolytes at oppositely charged surfaces in good agreement with molecular simulations. In particular, it faithfully reproduces the layering structures of polyions, charge inversion, and overcharging that cannot be captured by alternative methods including the polyelectrolyte Poisson-Boltzmann equation and an earlier version of DFT. The NLDFT has also been used to investigate the influences of the small ion valence, polyion chain length, and size disparity between polyion segments and counterions on the microscopic structure, mean electrostatic potential, and overcharging in planar electric double layers containing polyelectrolytes.

Simple density functional approach to adsorption of biomolecules on solid surfaces

A simple density functional approach for modeling the adsorption of biomolecules is considered. The model comprises a three-component mixture consisting of spherical and differently charged ions and chain molecules. Spherical ions can form associative bonds with selected segments of a chain. To enable the formation of bonds between chain segments and spherical ions, the statistical associating fluid theory is applied. The present theory is used to study the structure of adsorbed layers, the excess adsorption isotherms, and the capacitance of the double layer.

Effect of attractions on the structure of polymer solutions confined between surfaces: A density functional approach

A density functional theory is presented to study the effect of attractions on the structure of polymer solutions confined between surfaces. The polymer molecules have been modeled as a pearl necklace of freely jointed hard spheres and the solvent as hard spheres, both having Yukawa-type attractions and the mixture being confined between attractive Yukawa-type surfaces. The present theory treats the ideal gas free energy functional exactly and uses weighted density approximation for the hard chain and hard sphere contributions to the excess free energy functional. The attractive interactions are calculated using the direct correlation function obtained from the polymer reference interaction site model theory along with the mean spherical approximation closure. The theoretical predictions on the density profiles of the polymer and the solvent molecules are found to agree quite well with the Monte Carlo simulation results for varying densities, chain lengths, wall separations, and different sets of interaction potentials.

Density functional theory for polyelectrolytes near oppositely charged surfaces

We report a nonlocal density functional theory of polyelectrolyte solutions that faithfully accounts for both short- and long-range correlations neglected in a typical mean-field method. It is shown that for systems with strong electrostatic interactions, the long-range correlations are subdued by direct Coulomb attractions, thereby manifesting strong local excluded-volume effects. The theory has also been used to describe the influence of the polyion chain length and small ion valence on charge inversion due to the adsorption of polyelectrolytes at an oppositely charged surface.

Density-functional theory for fluid mixtures of charged chain particles and spherical counterions in contact with charged hard wall: Adsorption, double layer capacitance, and the point of zero charge

We consider a density-functional theory to describe nonuniform fluids composed of chain molecules, containing a charged segment each, and spherical counterions. The chain molecules are modeled as freely jointed chains of hard spheres, the counterions are oppositely charged spheres of the same diameter as all segments of chain molecules. The theory is applied to study the structure of adsorbed layers, the excess adsorption isotherms, the capacitance of the double layer, and the potential of the zero charge. We show that all electric properties are strongly dependent on the length of the chain molecules. Moreover, these properties are also dependent on the position of the charged segment in the chain.

Effect of attractive interactions on the structure of polymer melts confined between surfaces: A density-functional approach

A density-functional theory is presented to study the structure of polymers, having attractive interactions, confined between attractive surfaces. The theory treats the ideal-gas free-energy functional exactly and uses weighted density approximation for the hard-chain contribution to the excess free-energy functional. The bulk interactions of freely jointed hard spheres are obtained from generalized Flory equation of state and the attractive interactions are calculated using the direct correlation function obtained from the polymer reference interaction site model theory along with the mean spherical approximation closure. The theoretical predictions are found to be in quite good agreement with the Monte Carlo simulation results for varying densities, chain lengths, and different interaction potentials. The results confirm important implications of using different approximations for the hard-sphere and attractive interactions.

Density functional theory of adsorption of mixtures of charged chain particles and spherical counterions

We propose a microscopic density functional theory to describe nonuniform ionic fluids composed of chain molecules with charged "heads" and spherical counterions. The chain molecules are modeled as freely jointed chains of hard spheres, the counterions are oppositely charged spheres of the same diameter as all segments of chain molecules. The theory is based on the approach of Yu and Wu [J. Chem. Phys. 117, 2368 (2002)] of adsorption of chain molecules and on theory of adsorption of electrolytes [O. Pizio, A. Patrykiejew, and S. Sokolowski, J. Chem. Phys. 121, 11957 (2004)]. As an application of the proposed formalism we investigate the structure and adsorption of fluids containing segments of different length in a slitlike pore.

Influence of the diffuse layer overcharging or undercharging on the stability of charged interfaces: a restricted grand canonical Monte Carlo study

We have applied a restricted grand canonical Monte Carlo procedure to describe, in the framework of the primitive model, the counterion exchange mechanism between diffuse layers of counterions surrounding segregated charged lamellae. The net charge transfer between the dense and dilute domains is shown to vary as a function of the valence of the neutralizing counterions: undercharging of the dense interlayer is detected in the presence of monovalent counterions and overcharging with divalent counterions. Furthermore, no net reduction of the swelling pressure is detected for monovalent counterions, while a large enhancement of the net interlamellar attraction is found for charged lamellae neutralized by divalent counterions.