Simulation of Electrochemical Double Layer Formation with Complex Geometries

Abstract

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 ∼ 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.

Multiphysics Electrochemical Impedance Simulations of Complex Multiphase Graphite Electrodes

“…Thus, the numerical accuracy is not discussed in this article. The specific capacitance stemming from double-layer formation on the particle surfaces was calculated separately by solving the Nernst–Planck–Poisson (NPP) equations as in refs and . The total response current consists of reactive and capacitive currents.…”

Heterointerfaces: Unlocking Superior Capacity and Rapid Mass Transfer Dynamics in Energy Storage Electrodes

“…Consequently, the current density can be further enhanced. Equation 3 can be used to describe the current density (J i ) at the heterointerfaces: [30] where J i represents species i's current density, D i its diffusion coefficient, ∇c i its concentration gradient, z i its charge number, u i its mobility, F the Faraday constant, c i its concentration, and ∇ϕ the electric potential gradient (ϕ). The equation can be explained as follows: The term −D i ∇c i represents the diffusion current caused by the concentration gradient, while the term −z i u i Fc i ∇ϕ represents the migration current caused by the electric potential gradient.…”

Complex Electrode Microstructure Simulations using a Smoothed Boundary Method with Adaptive Mesh Refinement

“…In this work, octree and quadtree AMR 28,[39][40][41] were used to generate the grid systems in 3D and 2D, respectively. A brief description of octree AMR is provided here.…”

“…We use FDM to solve the governing equations, with the stencil of a variable-coefficient second-order derivative operator in 3D as 41,43 where the subscripts W, E, S, N, B, and T indicate the west, east, south, north, bottom, and top directions, respectively, the subscript C indicates the center node, u i are the values at different nodes, and s i are the distance from the center node to its (direct or virtual) neighbors in the i direction. ξ i = (ψ i + ψ C )/2 is the average value of ψ between the center node and its (direct or virtual) neighbor.…”