Dynamics of charge fluctuations in nanocapacitors: Effects of salt concentration and electrode metallicity from Brownian dynamics

Electric double-layer capacitors (EDLCs) rely on the dynamical response of confined electrolytes to store and release charge, yet the interplay between ion transport, electrostatic interactions, and electrode metallicity remains poorly understood at the nanoscale. In this work, we develop a comprehensive Brownian dynamics framework to compute the frequency-dependent admittance of nanocapacitors, explicitly accounting for salt concentration and the finite screening length of electrodes (modeled via Thomas-Fermi theory). We derive the fluctuation-dissipation relation connecting the dynamics of equilibrium charge fluctuations to the linear response of the system quantified by the frequency-dependent admittance. In particular, we obtain two estimators for the admittance-based on ionic positions and forces-and combine them via a control variate method to reduce statistical uncertainty across all frequencies. Our simulations show that the admittance exhibits a low-frequency regime dominated by capacitive effects and a high-frequency one governed by the ideal Nernst-Einstein conductivity. The crossover between these regimes is characterized by a timescale that depends on both the electrode metallicity and salt concentration, highlighting the role of ion-wall collisions and electrostatic interactions. Comparisons with analytical models show that while mean-field theories capture qualitative trends, they systematically overestimate low-frequency admittance and underestimate high-frequency behavior, underscoring the necessity of explicit ion-ion and ion-wall interactions. This work connects microscopic dynamics to macroscopic electrochemical observables, offering a tool to interpret impedance spectra in nanoscale systems. Beyond charge storage in EDLCs, our framework provides insights for sensing applications in nanofluidic devices, where charge/current fluctuations enable the detection of electrochemically active species.