title: Moderately nonlinear diffuse-charge dynamics under an ac voltage.
abstract: 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 equations for a dilute solution of point-like ions. The solution to these equations is expressed as a Fourier series with a voltage perturbation expansion for arbitrary Debye layer thickness and ac frequency. Here, the perturbation expansion in voltage proceeds in powers of V_{o}/(k_{B}T/e), where V_{o} is the amplitude of the driving voltage and k_{B}T/e is the thermal voltage with k_{B} as Boltzmann's constant, T as the temperature, and e as the fundamental charge. We show that the response of the electrolyte remains essentially linear in voltage amplitude at frequencies greater than the RC frequency of Debye layer charging, D/λ_{D}L, where D is the ion diffusivity, λ_{D} is the Debye layer thickness, and L is half the cell width. In contrast, nonlinear response is predicted at frequencies below the RC frequency. We find that the ion densities exhibit symmetric deviations from the (uniform) 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. For instance, the first nonlinear contribution to the current is O(V_{o}^{3}) which contains the expected third harmonic but also a component oscillating at the applied frequency. We use this to compute a generalized impedance for moderate voltages, the first nonlinear contribution to which is quadratic in V_{o}. This contribution predicts a decrease in the imaginary part of the impedance at low frequency, which is due to the increase in Debye layer capacitance with increasing V_{o}. In contrast, the real part of the impedance increases at low frequency, due to adsorption of neutral salt from the bulk to the Debye layer.
authors.affiliation: Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA.
authors.forename: Robert F
authors.initials: RF
authors.lastname: Stout
authors.affiliation: Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA.
authors.forename: Aditya S
authors.initials: AS
authors.lastname: Khair
mesh_terms: D058266:Dielectric Spectroscopy; D004058:Diffusion; D004560:Electricity; D004573:Electrolytes / Q000737:chemistry*; D008962:Models, Theoretical; D017711:Nonlinear Dynamics; D012996:Solutions; D013696:Temperature
chemical_list: D004573:Electrolytes; D012996:Solutions