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. $\propto exp(-\tilde{\psi })$ where $\tilde{\psi }$ 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 ${[1-(1-q)\tilde{\psi }]}^{1∕(1-q)}={exp}_q(-\tilde{\psi })$ 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.

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规律，即$\propto 经验值(-\tilde{\psi })$ 在哪里 $\tilde{\psi }$是无量纲的静电势。然而，即使在变量在大量基本随机事件上取平均值的平稳均衡中，也会出现与平均值的偏差。在这项研究中，我们通过使用 Tsallis 非广延统计框架假设一些小扰动叠加在其离子浓度的玻尔兹曼分布之上来评估 EDL 的行为。有了这个，我们假设离子浓度与${[1-(1-q)\tilde{\psi }]}^{1∕(1-q)}={经验值}_q(-\tilde{\psi })$ 和 $q$是表征系统统计数据的真实参数。我们推导出分析表达式并提供 EDL 结构的整体微分电容的计算结果，这取决于参数的值$q$ 可以显示水溶液的传统反钟形曲线和离子液体观察到的钟形曲线。