Influence of size of solvent molecules on structural and thermodynamic properties of the electrode/electrolyte interface

The influence of size of solvent molecules on the structural and thermodynamic properties of the interface between the electrode and electrolyte, using the solvent primitive model, was studied by grand canonical Monte Carlo (GCMC) simulations. The computer simulation results are compared with those obtained from the modified Poisson–Boltzmann (MPB) theory. The ionic singlet distribution functions show that the solvent molecules of low diameter favour the counter ion adsorption on the electrode. With increasing diameter of the solvent molecules, the mean electrostatic potential increases, while the integral and differential capacitances decrease. The integral capacitance curves obtained by MPB theory are in qualitative agreement with those obtained by the GCMC simulation although the theoretical results are overestimated.     

The point ion modified Poisson–Boltzmann theory for a planar electric double layer with different permittivities for the electrode,inner layer and diffuse layer

The planar electric double layer is modelled by an electrode, inner layer and diffuse layer whose constant permittivities differ. A point ion modified Poisson–Boltzmann analysis is made of the model with the ions in the diffuse layer having a distance of closest approach to the electrode, which is greater than the inner layer thickness and mimics the ion radius of a primitive model electrolyte. Comparisons are made with existing Monte Carlo simulations for uncharged and charged electrodes. For 1:1 and 2:1 electrolytes with a charged electrode, the modified Poisson–Boltzmann theory successfully predicts the singlet ion normalised density functions and the mean electrostatic potential. With the uncharged electrode, the neglect of ion size is more critical and the theoretical predictions are now poor at the higher concentrations.     

Evidence for a second,local contact condition for a planar electric double layer containing size and valency asymmetric ions

A generalised form of a local contact condition for the charge profile in a primitive model planar double layer [Bhuiyan, Outhwaite, and Henderson, Mol. Phys. 107, 343 (2009)] at low electrode charge is examined for completely asymmetric, binary electrolytes. The cation and anion sizes are taken to be different from each other with the valencies being 2⁺:1^? or 1⁺:2^?, while the electrode surface charge density is varied from being negative through zero to being positive. Monte Carlo simulation data obtained for such double layer systems at varying ionic radius ratios and electrolyte concentrations suggest the generalised contact relation to be valid at low charge on the electrode.     

Contact value relations and density functional theory for the electrical double layer

The recently developed contact-corrected density functional theory is applied to an electric double layer containing a valence and size symmetric electrolyte. The restricted primitive model is used to describe the electrolyte, and a non-polarisable, smooth, planar, uniformly charged hard surface is used to model the electrode. Comparison with Monte Carlo simulation results for this system shows that the theory satisfies the first contact value relation in line with the premise of the approach. Additionally, the theory is found to satisfy the semi-empirical second contact value relation quite closely. This is a welcome result, since no reference is made to this second relation nor is the relation used in the theoretical development. The second contact relation is closely related to the anomalous positive temperature derivative of the double layer capacitance at low temperature, low ion concentration, and low electrode charge, and indeed, the contact-corrected density functional theory predicts this effect.     

Off-centre charge model of the planar electric double layer for asymmetric 2:1/1:2 valencies

ABSTRACT

Grand canonical Monte Carlo simulation results are reported for the structure and capacitance of a planar electric double layer containing off-centre charged rigid sphere cations and centrally charged rigid sphere anions. The ion species are assigned asymmetric valencies, +2:?1 and +1:?2, respectively, and set in a continuum dielectric medium (solvent) characterised by a single relative permittivity. An off-centre charged ion is obtained by displacing the ionic charge from the centre of the sphere towards its surface, and the physical double layer model is completed by placing the ionic system next to a uniformly charged, non-penetrable, non-polarizable planar electrode. Structural results such as electrode-ion singlet distribution functions, ionic charge density and orientation profiles are complemented by differential capacitance results at electrolyte concentrations of 0.2?mol/dm³ and 1?mol/dm³, respectively, and for various displacements of the cationic charge centre. The effect of asymmetry due to off-centre cations and valency asymmetry on the double layer properties is maximum for divalent counterions and when the cation charge is closest to the hard sphere surface.     

长直组合矩形柱面电容传感器电容的研究

通过求解电势的拉普拉斯方程，讨论长直组合矩形柱面电容器中的电势、电荷和电容。     

带缝的长直圆柱面电容传感器电容的讨论

通过求解带缝的长直圆柱面电容器中的电势的拉普拉斯方程,讨论该电容器的电容计算公式。     

Zeta potential of colloidal particle in solvent primitive model electrolyte solution: a density functional theory study

A systematic study of zeta potential for a spherical double layer (SDL) around a colloidal particle in electrolyte solutions, is performed using density functional theory and Monte Carlo simulation. The usual recipe under the solvent primitive model is employed to model the system, where macroion, counterions, and coions are represented by charged hard spheres of uniform charge density and the presence of solvent is taken into account by modelling it as neutral hard spheres. All the components of the system are embedded in a dielectric continuum in order to consider the electrostatic effect of the solvent. The density functional theory employs a suitable weighted density approximation to calculate the hard-sphere contribution, whereas the residual electrostatic interactions are calculated as a small perturbation around the uniform fluid. The zeta potential profiles of a SDL in the presence of a number of electrolytes have been calculated and are found to be considerably influenced in the presence of solvent with an increase in the concentration of the electrolyte. The theory successfully predicts the maxima and sign reversal of the zeta potential profiles at high macroion surface charge density and in the presence of multivalent counterions, as obtained from the Monte Carlo simulation.     

A simulation study of the e~+/e~- sensitivity of a low resistive phosphate glass electrode in a RPC using GEANT MC

The resistivity of conventional glass is quite high and is unacceptable in a high rate environment. Low resistive glass-electrodes could be a solution for this problem. The present study reports the e+/e-simulation results of an RPC detector made from low resistive phosphate glass electrodes. The detailed geometrical configuration of the content materials which are the essential components of the glass of the RPC detector have been created with the GEANT4 simulation code. Two different types of particle sources, i.e. for e+/e-, have been located on the detectors surface to evaluate the performance of the phosphate glass RPC. Both of the particles have been simulated as a function of their respective energies in the range of 0.1 MeV – 1.0 GeV. The present simulation work has shown that the resistive electrode plays an important role for the particle production in the RPC configuration.     

A simulation study of the e~+/e~- sensitivity of a low resistive phosphate glass electrode in a RPC using GEANT MC

The resistivity of conventional glass is quite high and is unacceptable in a high rate environment. Low resistive glass-electrodes could be a solution for this problem. The present study reports the e+/e-simulation results of an RPC detector made from low resistive phosphate glass electrodes. The detailed geometrical configuration of the content materials which are the essential components of the glass of the RPC detector have been created with the GEANT4 simulation code. Two different types of particle sou...     

Two-dimensional modeling of optical transmission on the surface of a lenticular array for autostereoscopic displays

In this study, we suggest a customized model describing optical phenomena at the surface of a lenticular array for autostereoscopic displays in a mathematical form and analyzed the optical characteristics of lenticular array for the first time. We checked the validity of our mathematical model by examining and comparing our result with conventional lens theory. Monte Carlo simulations were performed to obtain the angular distribution of light from each sub-pixel corresponding to each views under actual design conditions. From the results, we think the optical model is very useful for designing optical parameters of autostereoscopic displays.     

Comparison of the Monte Carlo estimation of surface electrostatic potential at the hematite (0 0 0 1)/electrolyte interface with the experiment

The Monte Carlo simulations of the surface electrostatic potential are presented for the hematite (0 0 0 1) crystal plane. According to the ab initio calculations, the Fe-terminated (0 0 0 1) plane contains only one type of surface groups. The charge of this surface group is predicted using quantum population analyses, and the result is very close to this of the 1-pK model assumption. The surface topology and topography were constructed using the relaxed crystal plane structure. The Monte Carlo simulations for the reduced (including only hydrogen ions) and the extended (containing also electrolyte) models give the linear non-Nernstian pH-profile of surface potential. The simulation results are in agreement with the experimental measurements carried out by Kallay et al. [N. Kallay, Z. Dojnovi?, A. Cop, J. Colloid Interface Sci. 286 (2005) 610-614.] in the point of zero charge vicinity. This suggests that in this pH-region the surface properties are basically governed by the H⁺ ions uptake/release and the electrolyte ions complexations. The discrepancy for strongly acidic and basic regions suggests that some additional processes take place in the single-crystal electrode measurement, which results in the non-linear ψ₀=f(pH) profile.     

On the Use of a H2–O2 Gas Target in Muonic Hydrogen Atom Hyperfine Splitting Experiments

We propose a substantial improvement of the experimental method for the measurement of the hyperfine splitting of the ground state of muonic hydrogen described in earlier papers [1,2]. By further developing the idea to use the diffusion of the muon hydrogen atoms as a signature of laser-induced hyperfine transitions, we suggest a technique based on the energy dependence of the rate of muon transfer to oxygen in the thermal region, and demonstrate its efficiency and significant practical advantages. This revised version was published online in July 2006 with corrections to the Cover Date.     

Effect of ionic size on the structure of spherical double layers: a Monte Carlo simulation and density functional theory study

The effect of ionic size on the diffuse layer characteristics of a spherical double layer is studied using Monte Carlo simulation and density functional theory within the restricted primitive model. The macroion is modelled as an impenetrable charged hard sphere carrying a uniform surface charge density, surrounded by the small ions represented as charged hard spheres and the solvent is taken as a dielectric continuum. The density functional theory uses a partially perturbative scheme, where the hard sphere contribution to the one particle correlation function is evaluated using weighted density approximation and the ionic interactions are calculated using a second-order functional Taylor expansion with respect to a bulk electrolyte. The Monte Carlo simulations have been performed in the canonical ensemble. The detailed comparison is made in terms of zeta potentials for a wide range of physical conditions including different ionic diameters. The zeta potentials show a maximum or a minimum with respect to the polyion surface charge density for a divalent counterion. The ionic distribution profiles show considerable variations with the concentration of the electrolyte, the valency of the ions constituting the electrolyte, and the ionic size. This model study shows clear manipulations of ionic size and charge correlations in dictating the overall structure of the diffuse layer.     

Monte Carlo simulation of many-arm star polymers in two-dimensional good solvents in the bulk and at a surface

A Monte Carlo technique is proposed for the simulation of statistical properties of many-arm star polymers on lattices. In this vectorizing algorithm, the length of each arml is increased by one, step by step, from a starting configuration withl=1 orl=2 which is generated directly. This procedure is carried out for a large sample (e.g., 100,000 configurations). As an application, we have studied self-avoiding stars on the square lattice with arm lengths up tol _max=125 and up tof=20 arms, both in the bulk and in the geometry where the center of the star is adsorbed on a repulsive surface. The total number of configurations, which behaves asNl ^{G–1 fl} , where=2.6386 is the usual effective coordination number for self-avoiding walks on the square lattice, is analyzed, and the resulting exponents G=(f) and _s (f) for the bulk and surface geometries are found to be compatible with predictions of Duplantier and Saleur based on conformai invariance methods. We also obtain distribution functions for the monomer density and the distance of the end of an arm from its center. The results are consistent with a scaling theory developed by us.     

Structure of rutile TiO2 (1 1 0) in water and 1 molal Rb at pH 12: Inter-relationship among surface charge, interfacial hydration structure, and substrate structural displacements

The rutile (1 1 0)-aqueous solution interface structure was measured in deionized water (DIW) and 1 molal (m) RbCl + RbOH solution (pH 12) at 25 °C with the X-ray crystal truncation rod method. The rutile surface in both solutions consists of a stoichiometric (1 × 1) surface unit mesh with the surface terminated by bridging oxygen (BO) and terminal oxygen (TO) sites, with a mixture of water molecules and hydroxyl groups (OH⁻) occupying the TO sites. An additional hydration layer is observed above the TO site, with three distinct water adsorption sites each having well-defined vertical and lateral locations. Rb⁺ specifically adsorbs at the tetradentate site between the TO and BO sites, replacing one of the adsorbed water molecules at the interface. There is no further ordered water structure observed above the hydration layer. Structural displacements of atoms at the oxide surface are sensitive to the solution composition. Ti atom displacements from their bulk lattice positions, as large as 0.05 Å at the rutile (1 1 0)-DIW interface, decay in magnitude into the crystal with significant relaxations that are observable down to the fourth Ti-layer below the surface. A systematic outward shift was observed for Ti atom locations below the BO rows, while a systematic inward displacement was found for Ti atoms below the TO rows. The Ti displacements were mostly reduced in contact with the RbCl solution at pH 12, with no statistically significant relaxations in the fourth layer Ti atoms. The distance between the surface 5-fold Ti atoms and the oxygen atoms of the TO site is 2.13 ± 0.03 Å in DIW and 2.05 ± 0.03 Å in the Rb⁺ solution, suggesting molecular adsorption of water at the TO site to the rutile (1 1 0) surface in DIW, while at pH 12, adsorption at the TO site is primarily in the form of an adsorbed hydroxyl group.