(484a) Dynamic Double Layer Force between Charged Surfaces

We develop a theory for the "dynamic double layer force" between charged surfaces in an electrolyte under a time dependent voltage. Specifically, the force between two planar surfaces is calculated within the Poisson-Nernst-Planck framework for dilute electrolytes, accounting for unequal ionic diffusivities. Due to the inherent nonlinear dependence of the force on the electric potential, a sinusoidal voltage oscillating with frequency ω gives rise to a non-zero time averaged force, along with a component oscillating with frequency 2ω. The time-averaged force is always attractive, as expected for surfaces of opposite polarity. However, the instantaneous force switches between attractive and repulsive over an oscillation cycle at certain frequencies. Next, the force is quantified for suddenly-applied and pulsed voltages. In the former case, the force approaches its long-time limit exponentially: on a resistor-capacitor (``RC'') or bulk diffusion time scale for an electrolyte with equal or unequal ionic diffusivities, respectively. The long time decay of the force for a pulsed voltage also decays exponentially on the same timescales. The theory developed here is a dynamic generalization of the equilibrium double layer force, with potential applications to electrochemical devices, force-based spectroscopy, and colloidal directed assembly.