具有广义Boltzmann因子的双电层结构的Gouy-Chapman-Stern模型
On the Gouy-Chapman-Stern model of the electrical double-layer structure with a generalized Boltzmann factor
摘要：
通过Gouy-Chapman-Stern（GCS）方法对平面金属/电解质结处的双电层（EDL）结构的经典处理是基于将静电势与净平均电荷密度相关联的泊松方程。假设扩散层中的离子浓度遵循玻尔兹曼分布定律，即$\propto \exp(-\tildeψ)$，其中$\tildeψ$是无量纲静电势。然而，即使在平稳平衡，其中变量的平均超过了大量的基本随机事件，偏离平均值的预期。在这项研究中，我们评估的EDL的行为，假设一些小的扰动叠加在上面的玻尔兹曼分布的离子浓度使用Tsallis非广泛的统计框架。由此，我们假设离子浓度与$ [ 1- (1-q) \tildeψ]^{{1}/{(1-q)}} = \exp_q({- \tildeψ})$成比例，其中$q$是表征系统统计的实参数。我们推导出的解析表达式，并提供计算结果的EDL结构，这取决于参数$q$的值可以显示出传统的反钟形曲线的水溶液和钟形曲线观察到的离子液体的整体微分电容。
英文摘要：
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.
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