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.     

Impurity effects on ionic-liquid-based supercapacitors

Small amounts of an impurity may affect the key properties of an ionic liquid and such effects can be dramatically amplified when the electrolyte is under confinement. Here the classical density functional theory is employed to investigate the impurity effects on the microscopic structure and the performance of ionic-liquid-based electrical double-layer capacitors, also known as supercapacitors. Using a primitive model for ionic species, we study the effects of an impurity on the double layer structure and the integral capacitance of a room temperature ionic liquid in model electrode pores and find that an impurity strongly binding to the surface of a porous electrode can significantly alter the electric double layer structure and dampen the oscillatory dependence of the capacitance with the pore size of the electrode. Meanwhile, a strong affinity of the impurity with the ionic species affects the dependence of the integral capacitance on the pore size. Up to 30% increase in the integral capacitance can be achieved even at a very low impurity bulk concentration. By comparing with an ionic liquid mixture containing modified ionic species, we find that the cooperative effect of the bounded impurities is mainly responsible for the significant enhancement of the supercapacitor performance.     

A self-consistent density-functional approach to the structure of electric double layer: charge-asymmetric electrolytes

A self-consistent density-functional approach has been employed to study the structure of an electric double layer formed from a charge-asymmetric (2:l) electrolyte within the restricted primitive model which corresponds to charged hard sphere ions and a continuum solvent. The particle correlation due to hard-core exclusions is evaluated by making use of the universality of the density functionals and the correlation function of the uniform hard sphere fluid obtained through the integral equation theory with an accurate closure relation whereas mean spherical approximation is employed for the electrical contribution. Numerical results on the diffuse layer potential drop, ionic density profile, and the mean electrostatic potential near the electrode surface at several surface charge densities are found to be in quantitative agreement with the available simulation data.     

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.     

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.     

不同N掺杂构型石墨烯的量子电容研究

超级电容器是一种利用界面双电层储能或在电极材料表面及近表面发生快速可逆氧化还原反应而储能的装置, 其特点是功率密度高、循环寿命长. 制备出兼有高能量密度的电极材料是当前超级电容器研究的重点. 以提高电容储能为目标, 通过掺杂N原子来调制石墨烯的电子结构, 使用基于密度泛函理论的第一原理计算了不同N掺杂构型石墨烯的态密度和能带结构, 拟合出了石墨烯的量子电容, 分析了量子电容储能提升的原因.     

On the low temperature anomalies in the properties of the electrochemical interface. A non-local free-energy density functional approach

The restricted primitive model has proved to be a useful system to describe the behaviour of electrical double layers. In this model, ions are represented by charged hard spheres of equal diameter and the solvent is represented by a uniform dielectric constant. Classical Gouy-Chapman's theory, and its modification by Stern, always predicts a monotonically decreasing capacitance for this system when the fluid's temperature is increased. Similar results are given by the mean spherical approximation. These predictions are in qualitative agreement with experiment for dissolved electrolytes, but disagree with molten salt experiments where capacitance increases with temperature. Additionally, recent Monte Carlo (MC) simulations for this model show that at very low temperatures, the capacitance of the interface, near its point of zero charge, increases with increasing temperature for both diluted and highly concentrated salts. In this work we apply a particular model of a non-local free-energy density functional theory to study the capacitance of the electrical interface. In our calculations we considered symmetrical 1:1 systems for both diluted electrolytes and highly concentrated salts at very low electrode surface charge. Density functional theory agrees very well with MC results for capacitance at high temperature, but fails to predict a positive slope for this property at low temperatures. Comparison of theoretical density profiles with MC results allows the exploration of possible causes of failure.     

Contact condition for the density profiles in spherical and cylindrical double layers

Exact sum rules involving the contact values of the density profiles and bulk osmotic pressure in spherical and cylindrical electric double layers are formulated. When the radius of curvature in these systems tends to infinity, the contact conditions reduce to the well-known contact condition in planar double layer due to Henderson, Blum, and Lebowitz (1979). However, unlike the latter relation, the contact conditions in the non-planar geometries are non-local, and require for their implementation full knowledge of the electrode–ion singlet distribution functions.     

On the interfacial capacitance of an electrolyte at a metallic electrode around zero surface charge

The behaviour of the capacitance of a planar double layer containing a restricted primitive model electrolyte (equi-sized rigid ions moving in a continuum dielectric) at and around zero surface charge is examined for a polarizable electrode with particular emphasis on a metallic surface. Capacitance results are reported for symmetric valency (1:1) salts encompassing a range of concentrations and temperatures covering both electrolyte solution and ionic liquid regimes. Although the modified Poisson–Boltzmann theory is principally employed, at higher concentrations the theoretical calculations have been supplemented by Monte Carlo simulations. Capacitance anomaly, that is, increase of capacitance with temperature at low temperatures, is seen to occur when the electrode is an insulator with a low dielectric constant or when it is unpolarized. No capacitance anomaly is, however, seen for a metallic electrode with an infinite dielectric constant and in this situation the capacitance increases (a) dramatically at low temperatures (strong coupling) at a given concentration, and (b) as concentration increases at a given temperature. These capacitance trends are consistent with earlier works in the presence or absence of surface polarization and, in particular, the results for a conducting electrode at ionic liquid concentrations are consistent with that recently reported by Loth et al. [Phys. Rev. E, 82, 056102 (2010)]. Overall the theoretical predictions are qualitative to semi-quantitative with the simulations.     

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.     

迁移率对单层有机发光器件中电场与载流子分布的影响

有机发光器件的宏观特性与有机层中的电场和载流子浓度分布密切相关。建立的有机电致发光器件模型是由两个金属电极中间夹一层有机发光薄膜材料组成的单层器件,金属与有机发光层之间为欧姆接触。模型以载流子运动的扩散-漂移理论为基础,利用数值方法研究了有机发光层中双极载流子注入时的电势、电场、载流子浓度和复合密度分布。分析结果表明:当两种载流子的迁移率相同时,电场强度、载流子浓度、复合密度的分布呈对称形式。而当电子和空穴的迁移率μn和μp相差比较大时,高迁移率的载流子不仅仅分布在注入端附近而且还有一小部分能够传输到另一端,而低迁移率的载流子只分布在其注入端附近;当μn、μp的大小相差不大时,载流子传输情况就介于两者之间。当μn/μp的比值变化时,电场强度的极大值向载流子迁移率小的注入端偏移。     

不同溶剂中硝基苯胺分子非线性光学性质的研究

在含时密度泛函理论水平上研究了溶剂对硝基苯胺分子非线性光学性质的影响 .溶剂效应通过极化连续模型来研究 .首先采用极化连续模型在密度泛函理论水平上优化了硝基苯胺分子在溶剂中的几何结构 ,从而研究了溶剂引起硝基苯胺分子几何结构的变化 .然后采用极化连续模型在含时密度泛函理论水平上计算了不同溶剂中硝基苯胺分子的激发态能量和电偶极矩 ,并利用两态模型首次给出了不同溶剂中二次谐波振荡过程的一阶非线性超极化率的色散关系 .计算结果表明 ,极性溶剂对硝基苯胺分子的非线性光学性质有较大的影响 .在低的辐射场频率下 ,理论给出的一阶非线性超极化率的色散关系和实验结果符合得较好 .最后对所得结果从理论上给出了可能的解释并讨论了两态模型的可靠性 .     

Excellent thermoelectric performance in weak-coupling molecular junctions with electrode doping and electrochemical gating

Excellent thermoelectric performance in molecular junctions requires a high power factor, a low thermal conductance, and a maximum figure of merit(ZT) near the Fermi level. In the present work, we used density functional theory in combination with a nonequilibrium Green's function to investigate the thermoelectric performance of carbon chain-graphene junctions with both strong-coupling and weak-coupling contact between the electrodes and the molecules. The results revealed that a room temperature ZT of 4 could be obtained for the weak-coupling molecular junction, approximately one order of magnitude higher than that reached by the strong-coupling junction. The reason for this is that strong interfacial scattering suppresses most of the phonon modes in weak-coupling systems, resulting in ultralow phonon thermal conductance. The influence of electrode width,electrode doping, and electrochemical gating on the thermoelectric performance of the weak-coupling system was also investigated, and the results revealed that an excellent thermoelectric performance can be obtained near the Fermi level.     

Structure of a planar electric double layer containing size-asymmetric ions: density functional approach

We have studied the structure of the electrolytes with asymmetries in charge and size near a charged planar electric double layer by a density functional theory. In the present theory, the hard-sphere contribution has been approximated as the direct pair correlation function with the coupling parameter, whereas the electronic contribution has been approximated as the mean-spherical approximation in the bulk phase. This theoretical approach for the size-symmetric and size-asymmetric electrolytes displays a good agreement with the simulation results over a wide range of surface charge densities and electrolyte concentrations. However, the accuracy between the present theory and the simulation results slightly deteriorates for the highly size-asymmetric electrolytes and the multivalent electrolytes. In these cases, the performance of the present theory is comparable to those of the simplified extension of the Poisson–Boltzmann theory and the modified Poisson–Boltzmann theory. The calculated result indicates that the surface charge distribution function, which was introduced as an indicator for studying the charge reversal, layering effect, and surface charge amplification in a planar electric double layer, describes the electronic properties of a planar electric double layer well.     

基于电化学模型的锂离子电池多尺度建模及其简化方法

锂离子电池的精确建模和状态估计对于电动汽车电池管理系统非常重要,准二维(P2D)电化学模型由于计算复杂,难以直接应用于电池管理的参数在线估计和实时控制中.本文基于多孔电极理论和浓度理论,提出一种考虑锂离子液相动力学的简化准二维(SP2D)模型.忽略锂离子孔壁流量沿电极厚度方向的变化求解SP2D模型所描述的锂离子电池锂浓度分布,基于锂离子电池电化学平均动力学行为求解固相和液相电势变化,推导出电池电压计算的简化表达式;采用恒流、脉冲以及城市循环工况放电电流对比分析了严格P2D模型与SP2D模型的终端电压和浓度分布.结果表明:SP2D模型在保持较高计算精度的同时,可显著提高计算效率.     

Side-chain effects on the capacitive behaviour of ionic liquids in microporous electrodes

Classical density functional theory (cDFT) is used to investigate electrosorption of ionic liquids in porous electrodes within the framework of a coarse-grained model. The purpose of this study is to clarify the influence of the side alkyl chains of imidazolium cations on the electric double layer (EDL) capacitance that was studied in a number of recent investigations but with contradictory trends. For an ionic liquid near a planar electrode, cDFT predicts that the capacitance falls by extending the alkyl chain length of cations because neutral segments reduce the packing density of counterions thus the charge density. The side-chain effect is more complicated for ionic liquids in micropores owing to space-charge competition. Adding neutral segments to imidazolium cations always reduces the capacitance in cases where the surface electrical potential of micropores is sufficiently large. However, the capacitance shows a nonmonotonic dependence on the alkyl chain length at intermediate surface potentials. Surprisingly, addition of neutral segments to the cations has the most pronounced effect on the EDL capacitance in cases when the surface potential is positively charged. These findings challenge the conventional assumption that the alkyl side chains of imidazolium ions only negatively impact ionic liquid performance in charge storage.     

Study of solid electrolyte polarization by a complex admittance method

The polarization behavior of zirconia-yttria solid electrolyte specimens with platinum electrodes has been studied over a temperature range of 400° to 800°C and a wide range of oxygen partial pressures. The complex admittance of these specimens was determined over a frequency range from d.c. to 100kHz. An analysis of these data in the complex admittance plane indicated the presence of three polarizations: (1) an electrode polarization characterized by a double layer capacity and an effective resistance for the overall electrode reaction, O₂(gas) + 2e(platinum) O²⁻ (electrolyte); (2) a capacitive-resistive electrolyte polarization, probably corresponding to a partial blocking of oxygen ions at the electrolyte grain boundaries by an impurity phase there; and (3) a pure ohmic electrolyte polarization.     

Impurities and solid electrolyte failure

A thermodynamically based model is used to assess the effects of the formation of a layer of lowered ionic conductivity and increased electronic conductivity on the applied voltage at which solid electrolyte failure is to be expected. Such a layer can result from electrolyte contamination with electrode impurities. It is found that when a significant electrolyte resistivity increase is produced, electrolyte failure can be initiated by a mechanism that deposits sodium internally in the solid electrolyte. The results stress the necessity of operating solid electrolyte cells, such as Na/S, in a manner that minimizes electrode contamination.     

Analysis of electron recombination in dye-sensitized solar cell

A steady-state numerical model of dye-sensitized solar cell is based on continuity and transport equations for electrons, iodide and triiodide ions. The cell model consists of an active layer, where photovoltaic effect including diffusion of electrons in mesoporous TiO₂ and ions in electrolyte takes place, and a bulk electrolyte layer, where only ions diffuse. Exponential distribution of trap states in TiO₂ and Gaussian distributions of energy levels in the electrolyte within active layer are included in modeling of the recombination dynamics, according to Shockley-Read-Hall statistics and Marcus-Gerischer electron transfer theory. Recombinations at the front contact and a voltage drop at the platinum covered back contact are included in the model. Simulation results are compared with the measured current-voltage characteristics at different light intensities. In particular, light intensity dependence of open circuit voltage is studied over 4 decades. Optimization of cell efficiency regarding active layer and electrolyte layer thickness is carried out. Simulation results show that best efficiency is achieved when electrolyte layer thickness is minimized as much as possible and that active layer thickness is traded off with respect to recombination rates and/or diffusion limited current determined with the selection of the electrolyte.     

Evaluation of the electrical capacitance of M,O2/O2− interfaces (M=Pt, Au, Pd, In2O3; O2− = zirconia based electrolyte) exhibiting constant phase element behavior

The behavior of the electrode systems M,O₂/O² (M = porous Pd, Pt, A and dense In₂O₃; O²⁻ = ZrO₂-based single-crystal solid electrolyte) was studied by means of impedance measurements. The examination of the Pt,O₂/O²⁻ electrode system showed that the constant phase element (CPE) can be attributed to a nonuniform distribution of current at the electrode surface. It was observed that the CPE parameters n and B in the expression Y_CPE = B (jω)ⁿ may be related by B=(C_dl)ⁿ (R_Ω)_n-1, where C_dl is the double layer capacitance and R_Ω the resistance of the electrolyte in the cell. Then, C_dl of the electrode - electrolyte interface could be determined. The specific C_dl of the oxidized noble metals and india electrodes is nearly one order of magnitude lower than C_dl of the electrodes in the metallic state. The C_dl value of all the electrodes studied depends little or is independent of temperature and oxygen pressure. It is concluded that the Helmholtz model of double layer structure does not contradict the C_dl behavior.