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The classical treatment of the electrical double-layer (EDL) structure at aplanar metal/electrolyte junction via the Gouy-Chapman-Stern (GCS) approach isbased on the Poisson equation relating the electrostatic potential to the netmean charge density. The ions concentration in the diffuse layer are assumed tofollow the Boltzmann distribution law, i.e. $\propto \exp(-\tilde{\psi})$ where$\tilde{\psi}$ is the dimensionless electrostatic potential. However, even instationary equilibrium in which variables are averaged over a large number ofelementary stochastic events, deviations from the mean-value are expected. Inthis study we evaluate the behavior of the EDL by assuming some smallperturbations superposed on top of its Boltzmann distribution of ionconcentrations using the Tsallis nonextensive statistics framework. With thiswe assume the ion concentrations to be proportional to $ [ 1- (1-q)\tilde{\psi}]^{{1}/{(1-q)}} = \exp_q({- \tilde{\psi}})$ with $q$ being a realparameter that characterizes the system's statistics. We derive analyticalexpression and provide computational results for the overall differentialcapacitance of the EDL structure, which, depending on the values of theparameter $q$ can show both the traditional inverse bell-shaped curves foraqueous solutions and bell curves observed with ionic liquids.

On the Gouy-Chapman-Stern model of the electrical double-layer structure with a generalized Boltzmann factor