论文标题
在带有广义玻尔兹曼因子的电气双层结构的小木马 - chapman-sern模型上
On the Gouy-Chapman-Stern model of the electrical double-layer structure with a generalized Boltzmann factor
论文作者
论文摘要
通过Gouy-Chapman-sern（GCS）方法在平面金属/电解质连接处进行电气双层（EDL）结构的经典处理是基于将静电电位与净平均电荷密度相关的泊松方程。假定弥漫层中的离子浓度遵循Boltzmann分布定律，即$ \ propto \ exp（ - \tildeψ）$，其中$ \tildeψ$是无尺寸的静电电位。但是，即使在固定平衡中，变量在大量基本随机事件上平均，也会期望与平均值偏差。在这项研究中，我们通过假设使用Tsallis nonextistion统计框架在其玻尔兹曼（Boltzmann）的离子浓度分布之上进行了一些小小的扰动来评估EDL的行为。因此，我们假设离子浓度与$ [1-（1-q）\tildeψ]^{{1}/{（1- q）}} = \ exp_q（{ - \ \tildeψ}）$，带有$ q $是描述系统统计数据的真实参数。我们得出分析表达，并为EDL结构的总体差分电容提供了计算结果，根据参数$ Q $的值，该电容均可显示传统的逆钟形曲线，用于水溶液和用离子液体观察到的钟形曲线。
The classical treatment of the electrical double-layer (EDL) structure at a planar metal/electrolyte junction via the Gouy-Chapman-Stern (GCS) approach is based on the Poisson equation relating the electrostatic potential to the net mean charge density. The ions concentration in the diffuse layer are assumed to follow the Boltzmann distribution law, i.e. $\propto \exp(-\tildeψ)$ where $\tildeψ$ is the dimensionless electrostatic potential. However, even in stationary equilibrium in which variables are averaged over a large number of elementary stochastic events, deviations from the mean-value are expected. In this study we evaluate the behavior of the EDL by assuming some small perturbations superposed on top of its Boltzmann distribution of ion concentrations using the Tsallis nonextensive statistics framework. With this we assume the ion concentrations to be proportional to $ [ 1- (1-q) \tildeψ]^{{1}/{(1-q)}} = \exp_q({- \tildeψ})$ with $q$ being a real parameter that characterizes the system's statistics. We derive analytical expression and provide computational results for the overall differential capacitance of the EDL structure, which, depending on the values of the parameter $q$ can show both the traditional inverse bell-shaped curves for aqueous solutions and bell curves observed with ionic liquids.
