The linear response of a symmetric binary ionic liquid confined between two parallel, blocking electrodes is analyzed under the influence of electrostatic correlations $L_c$ while systematically comparing the effects of two distinct interfacial boundary conditions: the Bazant–Storey–Kornyshev (BSK) boundary condition, corresponding to the vanishing correlation limit, and the de Souza-Bazant (dSB) boundary condition, which incorporates finite electrostatic correlation effects at charged electrode surfaces. In contrast to conventional weakly nonlinear models involving thin-double-layer scalings based on small parameters ${\lambda }_D/L\ll 1$ or $\sqrt{{\lambda }_D{L}_c}/L\ll 1$, where ${\lambda }_D$ denotes the Debye screening length and $L$ is the half-cell thickness, the present formulation accommodates double layers of arbitrary width. Using matched asymptotic expansions at leading order, both the frequency-dependent response and the equilibrium response are derived in the asymptotic limit $\varepsilon =L_c/L\ll 1$. This separation of length scales gives rise to interfacial dynamics and equilibrium characteristics that are not captured by standard Debye-based asymptotic models. In particular, the frequency response exhibits a low-frequency inductive behavior manifested by a negative real impedance, a negative complex capacitance, and a nonmonotonic phase response, with these effects being significantly enhanced under the dSB boundary condition. The origin of the inductive regime is linked to the emergence of a low-frequency chemical-inductor contribution, which introduces an intrinsic slow dynamical process. Together with the fast Debye timescale serving as the reference scale, this leads to a coupled fast–slow dynamical structure that becomes increasingly pronounced with growing electrostatic correlation length $L_c$. A scaling analysis in the low-frequency regime further identifies a distinguished intermediate relaxation timescale $L_c^2/D$ in the strong-correlation regime, where $D$ denotes the diffusion coefficient of the ion species. At equilibrium, the dSB boundary condition likewise predicts a nonclassical negative differential capacitance that is absent under the BSK boundary condition.

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• Boundary layers
• Nonlinear dynamics in fluids
• Complex fluids