Three component model of cylindrical electric double layers containing mixed electrolytes: A systematic study by Monte Carlo simulations and density functional theory.
ABSTRACT 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.
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ABSTRACT: 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.The Journal of Chemical Physics 05/2014; 140(20):204510. · 3.12 Impact Factor
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ABSTRACT: For the first time, the classical density functional theory (DFT) is numerically solved in three- and two-dimensional spaces for a two sphere model of electrostatic interactions between two spherical nanoscale colloids immersed in a primitive model electrolyte solution. Two scientific anomalies are found that (i) contrary to what is often asserted that presence of multivalent counter ion is necessary to induce a like-charge attraction (LCA), univalent counter ion also induces the LCA only if bulk electrolyte concentration and colloid surface charge are high enough, and (ii) although the LCA in general becomes stronger with the bulk electrolyte concentration, adverse effects unexpectedly occur if the colloid surface charge quantity rises sufficiently. In addition, effects of counter ion and co-ion diameters in eliciting the LCA are first investigated and several novel phenomena such as monotonic and non-monotonic dependence of the LCA well depth on the counter ion diameter in different colloid surface charge zones are confirmed. Based these findings, a hydrogen bonding style mechanism is suggested and surprisingly, by appealing to fairly common-sense concepts such as bond energy, bond length, number of hydrogen bonds formed, and counter ion single-layer saturation adsorption capacity, self-consistently explains origin of the LCA between two spherical nanoscale particles, and all phenomena previously reported and observed in this study.AIP Advances 03/2013; 3(3). · 1.59 Impact Factor
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ABSTRACT: Electric double-layer capacitors are a family of electrochemical energy storage devices that offer a number of advantages, such as high power density and long cyclability. In recent years, research and development of electric double-layer capacitor technology has been growing rapidly, in response to the increasing demand for energy storage devices from emerging industries, such as hybrid and electric vehicles, renewable energy, and smart grid management. The past few years have witnessed a number of significant research breakthroughs in terms of novel electrodes, new electrolytes, and fabrication of devices, thanks to the discovery of innovative materials (e.g. graphene, carbide-derived carbon, and templated carbon) and the availability of advanced experimental and computational tools. However, some experimental observations could not be clearly understood and interpreted due to limitations of traditional theories, some of which were developed more than one hundred years ago. This has led to significant research efforts in computational simulation and modelling, aimed at developing new theories, or improving the existing ones to help interpret experimental results. This review article provides a summary of research progress in molecular modelling of the physical phenomena taking place in electric double-layer capacitors. An introduction to electric double-layer capacitors and their applications, alongside a brief description of electric double layer theories, is presented first. Second, molecular modelling of ion behaviours of various electrolytes interacting with electrodes under different conditions is reviewed. Finally, key conclusions and outlooks are given. Simulations on comparing electric double-layer structure at planar and porous electrode surfaces under equilibrium conditions have revealed significant structural differences between the two electrode types, and porous electrodes have been shown to store charge more efficiently. Accurate electrolyte and electrode models which account for polarisation effects are critical for future simulations which will consider more complex electrode geometries, particularly for the study of dynamics of electrolyte transport, where the exclusion of electrode polarisation leads to significant artefacts.Physical Chemistry Chemical Physics 03/2014; · 4.20 Impact Factor