# 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:**A novel method is suggested to analytically solve a nonlinear Poisson–Boltzmann (NLPB) equation. The method consists chiefly of reducing the NLPB equation to linear PB equation in several segments by approximating a free term of the NLPB equation by piecewise linear functions, and then, solving analytically the linear PB equation in each segment. Superiority of the method is illustrated by applying the method to solve the NLPB equation describing a colloid sphere immersed in an arbitrary valence and mixed electrolyte solution; extensive test indicates that the resulting analytical expressions for both the electrical potential distribution Ψ (r) and surface charge density/surface potential relationship (σ/Ψ 0) are characterized with two properties that mathematical structures are much simpler than those previously reported and application scope can be arbitrarily wide by adjusting the linear interpolation range. Finally, it is noted that the method is “universal” in that its applications are not limited to the NLPB equation.Colloid and Polymer Science 04/2012; 291(4). DOI:10.1007/s00396-012-2805-9 · 2.41 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**Monte Carlo simulations of a planar negatively charged dielectric interface in contact with a mixture of 1:1 and 3:1 electrolytes are carried out using the unrestricted primitive model under more realistic hydrated ion sizes. Two typical surface charge densities are chosen to represent the systems from the weak to strong coupling regimes. Our goal is to determine the dependence of the degree of charge inversion on increasing concentration of both mono- and trivalent salts and to provide a systematic study on this peculiar effect between short-range and electrostatic correlations. The numerical results show that addition of monovalent salt diminishes the condensation of trivalent counterions due to either the favorable solvation energy or the available space constraints. As the concentration of trivalent salt increases, on the other hand, the inclusion of the ionic size and size asymmetry results in a damped oscillatory charge inversion at low enough surface charge and another counterintuitive surface charge amplification. It is proposed that both of the anomalous events in the weak coupling regime are thought to be entropic in origin which is completely different from the electrostatic driven charge inversion in the strong coupling regime. In addition, the electrostatic images arising from the dielectric mismatch lead to a decaying depletion effect on the structure of double layer with growing salt concentration in the case of low charged interface but have no effect at high surface charge values. The microscopic information obtained here points to the need for a more quantitative theoretical treatment in describing the charge inversion phenomenon of real colloidal systems.The Journal of Chemical Physics 08/2010; 133(6):064704. DOI:10.1063/1.3469795 · 3.12 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**In this work, a Monte-Carlo algorithm in the constant-voltage ensemble for the calculation of 3d charge concentrations at charged surfaces functionalized with biomolecules is presented. The motivation for this work is the theoretical understanding of biofunctionalized surfaces in nanowire field-effect biosensors (BioFETs). This work provides the simulation capability for the boundary layer that is crucial in the detection mechanism of these sensors; slight changes in the charge concentration in the boundary layer upon binding of analyte molecules modulate the conductance of nanowire transducers. The simulation of biofunctionalized surfaces poses special requirements on the Monte-Carlo simulations and these are addressed by the algorithm. The constant-voltage ensemble enables us to include the right boundary conditions; the dna strands can be rotated with respect to the surface; and several molecules can be placed in a single simulation box to achieve good statistics in the case of low ionic concentrations relevant in experiments. Simulation results are presented for the leading example of surfaces functionalized with pna and with single- and double-stranded dna in a sodium-chloride electrolyte. These quantitative results make it possible to quantify the screening of the biomolecule charge due to the counter-ions around the biomolecules and the electrical double layer. The resulting concentration profiles show a three-layer structure and non-trivial interactions between the electric double layer and the counter-ions. The numerical results are also important as a reference for the development of simpler screening models.Nanoscale 02/2011; 3(4):1608-17. DOI:10.1039/c0nr00791a · 6.74 Impact Factor