Simulation of Electrochemical Double Layer Formation with Complex Geometries

A novel method is introduced to simulate the formation of electrochemical double layers on complex electrode particle geometries. Electrochemical double layers play the most crucial role in electrical energy storage of supercapacitors and in capacitive deionization (desalination) devices. The double-layer region usually spans 20 to 50 nanometers, whereas other significant length scales, e.g., particle size or inter-particle space in electrodes, are in tens to hundreds of microns. Thus, a direct numerical simulation in the continuum scale must resolve the ionic concentration and potential gradients in spatial scales across 3 similar to 4 orders of magnitude difference and is highly challenging. In this paper, we use the smoothed boundary method that defines complex microstructures with a continuous domain-parameter function to reformulate the Nernst-Planck-Poisson equations and solve the reformulated governing equations on adaptively refined meshes. The method allows for accurate simulations of arbitrarily complex geometries with resolutions spanning from nanometers in the double layer to micron/millimeters in the particle/electrode scales. The results show that ions first rapidly adsorb onto or are repelled from the particle surfaces, followed by long-distance diffusion to alleviate the concentration gradient until the system reaches the steady state. The concentration and potential evolutions highly depend on the particle geometries.