Lutful Bari Bhuiyan

Polyelectrolyte solutions containing mixed valency ions in the cell model: A simulation and modified Poisson–Boltzmann study

Monte Carlo simulations of linear polyelectrolyte solutions containing mixed valency simple ions in the cylindrical cell model are reported. The equilibrium distributions of the simple ions and the osmotic pressure of the solution are calculated at various concentrations of the monomer units of the polyelectrolyte. Specifically, the following systems are studied—monovalent counterions with added 2:2 salt, divalent counterions with added 1:1 salt, and systems containing mono- and divalent counterions only, and mono- and trivalent counterions only. The simulation results are compared with the corresponding predictions from the Poisson–Boltzmann and modified Poisson–Boltzmann theories applied to the cell model. It is seen that upto moderate concentrations of the polyion, the modified Poisson–Boltzmann theory provides a very good description of the systems with deviations occurring at higher concentrations. The theory also reproduces the charge reversal observed in the simulations when strongly correlated cou...

Counterion layering at high surface charge in an electric double layer. Effect of local concentration approximation

Abstract A systematic study of the counterion layering phenomenon at high surface charge in a planar electric double layer is reported. Extensive canonical Monte Carlo simulations are performed on a 1:1 electrolyte to investigate the effect on layering due to a variation of electrode charge density, electrolyte concentration, and ionic size. For a 1 mol dm −3 salt at room temperature and ionic diameter 400 pm, the second layer begins to be formed at around a surface charge density of ∼0.4 C m −2 . It is seen that the variation of ionic size (at constant surface charge and salt concentration) leads to the most pronounced changes in the counterion layering. At an ionic diameter of 600 pm a third layer of counterions is observed. The simulations are extended to asymmetric valency 2:1 and 1:2 salts where layering effects are observed for monovalent counterions only. The calculated double layer capacitance is found to decrease in the presence of layering. A mean-field Poisson–Boltzmann equation coupled with a recently derived ionic exclusion volume term is found to predict this layering in qualitative agreement with the simulations. The use of a local concentration approximation improves the agreement in most cases.

Monte Carlo Simulation for the Double Layer Structure of an Ionic Liquid Using a Dimer Model: A Comparison with the Density Functional Theory

Theoretical difficulties in describing the structure and thermodynamics of an ionic liquid double layer are often associated with the nonspherical shapes of ionic particles and extremely strong electrostatic interactions. The recent density functional theory predictions for the electrochemical properties of the double layer formed by a model ionic liquid wherein each cation is represented by two touching hard spheres, one positively charged and the other neutral, and each anion by a negatively charged hard spherical particle, remain untested in this strong coupling regime. We report results from a Monte Carlo simulation of this system. Because for an ionic liquid the Bjerrum length is exceedingly large, it is difficult to perform simulations under conditions of strong electrostatic coupling used in the previous density functional theory study. Results are obtained for a somewhat smaller (but still large) Bjerrum length so that reliable simulation data can be generated for a useful test of the corresponding theoretical predictions. On the whole, the density profiles predicted by the theory are quite good in comparison with the simulation data. The strong oscillations of ionic density profiles and the local electrostatic potential predicted by this theory are confirmed by simulation, although for a small electrode charge and strong electrostatic coupling, the theory predicts the contact ionic densities to be noticeably different from the Monte Carlo results. The theoretical results for the more important electrostatic potential profile at contact are given with good accuracy.

Influence of electrode polarization on the capacitance of an electric double layer at and around zero surface charge

The influence of polarization of the electrode on the interfacial capacitance of a restricted primitive model planar double layer at and around zero surface charge is studied using a modified Poisson–Boltzmann theory for 1:1 electrolytes. The polarization, which occurs due to a dielectric discontinuity at the electrode–electrolyte interface, is treated by imagining fictitious image charges within the electrode, which mimic surface polarization charges. Specifically, the cases (i) when the electrode is a metallic conductor with infinite relative permittivity and (ii) when the electrode is a low relative permittivity insulator are investigated. The capacitance around zero surface charge is seen to undergo a gradual transition from having a camel-shaped form with a minimum at low electrolyte concentrations to having a maximum at higher concentrations consistent with the trends observed in earlier works in the absence of surface polarization. However, the transition envelope shifts to the lower concentration side relative to the no polarization situation for case (i), while it shifts to the higher concentration side for case (ii). The overall capacitance behaviour for both the situations indicates that the effect of the image interactions can be substantial, especially at low temperatures.

A modified Poisson–Boltzmann analysis of the capacitance behavior of the electric double layer at low temperatures

The modified Poisson-Boltzmann theory is used to analyze the anomalous behavior of the electric double layer capacitance for small surface charge at low temperatures and densities. Good agreement is found with simulation and recent density-functional theory results. Negative adsorption is also found in line with theory and simulation. An unsatisfactory feature is the relatively poor structure in this region due to the inherent approximations in the theory. This feature is unimportant in relation to the capacitance results but has implications when calculating adsorption properties.

Comparison of exclusion volume corrections to the Poisson-Boltzmann equation for inhomogeneous electrolytes.

Comparisons are made of exclusion volume corrections to the Poisson-Boltzmann equation for the electric double layer next to a charged electrode. The exclusion volume terms treated are based mainly on (i) Langmuir type theories and (ii) the Bogoliubov-Born-Green-Yvon integral equations. The Langmuir type theories are modified to incorporate a distance of closest approach to the charged surface for comparison purposes. The theories are applied to the spherical electric double layer around a large macroion and the planar electric double layer. At high surface charge steric effects dominate when the Langmuir theories predict saturation in the counterion profile at and near contact, while the Bogoliubov-Born-Green-Yvon based theories predict layering in the same profile.

Numerical solution of a modified Poisson-Boltzmann equation for 1 : 2 and 2 : 1 electrolytes in the diffuse layer

A modified Poisson-Boltzmann (MPB) equation for an unsymmetrically charged electrolyte in the diffuse part of the electric double layer at a plane charged wall is solved numerically using a quasi-linearization procedure. Computations are carried out for 1 : 2 and 2 : 1 restricted primitive model electrolytes with no imaging and for a metallic wall and the results compared with the classical Gouy-Chapman-Stern theory. Except for negligible surface charge, the system with a divalent counter ion is the most sensitive to any change in its physical parameters. In general the MPB mean electrostatic potential, in contrast to the Gouy-Chapman-Stern potential, is not a monotonic decreasing function. The asymptotic behaviour of the MPB equation implies charge oscillations above a critical electrolyte concentration (≳0·23 M) while below this concentration imaging or surface charge-ion interactions can produce a charge inversion. Charge separation is found for no surface charge with a metallic wall. The point ion lim...

Understanding polyelectrolyte solutions: Macroion condensation with emphasis on the presence of neutral co-solutes

The multi-faceted applications of polyelectrolyte solution systems to a kaleidoscope of technological and biological processes make the understanding of these systems important and of interest. The highly relevant issue of instabilities that may occur in a polyelectrolyte solution and the ensuing macroion condensation constitute the premise of this review. An abundance of experimental and numerical simulation results in recent years provide evidence that a net electrostatic attractive force may exist between macroions and may lead to a phase separation. Specifically, in this review, three different types of instability involving macroions of spherical geometry are discussed. (i) The instability arising out of strong Coulomb correlations between counterions in the solution; this is most likely to occur in solutions containing multivalent counterions and/or in the presence of solvents of low relative permittivity. (ii) The instability caused by the macroion surface-charge fluctuations; the resultant charge correlations may induce an effective attraction between the weakly charged macroions. (iii) The instability due to the combined effect of electrostatic and crowding interactions when an inert co-solute is added to the solution. A sufficient increase in the concentration of the neutral species leads to a gradual change in the nature of the interaction between two macroions, from being repulsive to less repulsive and ultimately attractive. The structural features and thermodynamics in these complex systems are shaped by the collective and often competing effects of the species.

Influence of anisotropic ion shape on structure and capacitance of an electric double layer: a Monte Carlo and density functional study.

The effect of anisotropic ion shapes on the structure and the differential capacitance of an electric double layer in the electrolyte solution regime is studied using the density functional theory and Monte Carlo simulations. The double layer is modelled by a uniformly charged, non-polarizable planar electrode next to an electrolyte where the cation is a dimer consisting of two tangentially touching rigid spheres one of which is positively charged while the other is neutral, the anion is a negatively charged rigid sphere, and the solvent is a dielectric continuum. Numerical results are reported for monovalent electrolytes at room temperature for a series of electrolyte concentrations and varying electrode surface charge densities. Asymmetry in ionic shape leads to more structure near the electrode when its charge is opposite to that of the non-spherical ions. Overall, the theoretically predicted density and mean electrostatic profiles reproduce the corresponding simulation results to a very good degree. The asymmetry of the ion shape also yields asymmetry in the differential capacitance curve plotted as a function of the electrode charge density. The differential capacity evolves from being distorted bactrian camel-shaped (a minimum flanked by a maximum on either side) at low electrolyte concentrations to being bell-like (a single broad maximum) at higher concentrations. The theoretical capacitance results again agree well with the simulations.

The tail effect on the shape of an electrical double layer differential capacitance curve.

The differential capacitance curve for the double layer formed by an electrolyte dissolved in a solvent is commonly believed to be parabolic-like with a minimum at low electrolyte charge concentration and low electrode surface charge density, and independent of electrolyte concentration at high electrolyte concentrations and high electrode charge and would be, in the absence of solvent effects, featureless at these latter conditions. This is the prediction of the popular Gouy-Chapman-Stern theory. In contrast, for an ionic liquid this curve can have a single or a double hump (or a bell or camel shape). Fedorov et al. [Electrochem. Commun. 12, 296 (2010)]10.1016/j.elecom.2009.12.019 have related these humps, particularly the double hump, to the neutral tails of ions in many ionic liquids. Evidence presented here shows, however, that such humps are general features of the differential capacitance of a double layer, whether it be formed by ions with or without a neutral tail. The presence of a double or single hump results from the magnitude of the electrolyte charge concentration. For both spherical ions or non-spherical ions consisting of charged heads and neutral tails, the shape of the differential capacitance transforms continuously from a double hump to a single hump as the electrolyte concentration is increased.