Dynamic double layer force between charged surfaces

Abstract

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 nonzero time-averaged force, along with a component oscillating with frequency 2ω. The timeaveraged 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 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.

Thermodynamics of Electrical Double Layers with Electrostatic Correlations

“…Looking forward, our analysis of the EDL potential distribution in equilibrium can also be utilized for out-of-equilibrium phenomena such as double layer charging, ,,− electrophoresis, − diffusiophoresis, − , and colloidal stability. , Our formalism and results can be extended to these phenomena by evaluating chemical potential gradients, which can be utilized to derive modified Poisson-Nernst–Planck equations. In fact, the out-of-equilibrium phenomena sometimes can be approximated to be in quasi-equilibrium where our formalism for potential distribution calculations can be directly utilized.…”