(503f) Moderately Nonlinear Diffuse Charge Dynamics Under an AC Voltage

The response of a symmetric binary electrolyte between two parallel, blocking electrodes to a moderate amplitude AC voltage is quantified. The diffuse charge dynamics are modeled via the Poisson-Nernst-Planck (PNP) equations for dilute solutions of point-like ions. The solution to these equations is expressed as a Fourier series with a voltage perturbation expansion for arbitrary diffuse layer thickness and AC frequency. Here, the perturbation expansion in voltage is in powers of V_o /V_T, where V_T is the thermal voltage and Vo is the amplitude of the driving voltage. We show that the response remains essentially linear in voltage amplitude at frequencies greater than the RC frequency of diffuse layer charging (D/λL, where D is the ion diffussivity, λ is the diffuse layer thickness, and L is half the cell width) but becomes nonlinearly voltage dependent at frequencies below the RC frequency. We find that the ion densities exhibit symmetric deviations from the equilibrium density at even orders of the voltage amplitude. This leads to the voltage dependence of the current in the external circuit arising from the odd orders of voltage. We use this to derive a nonlinear generalized impedance for moderate voltages. The first correction is a second order voltage dependent term which predicts a decrease in the complex part of the impedance. This is consistent with the predicted increase in the static diffuse layer capacitance from Gouy-Chapman theory.