Abstract
We study the linear stability of transient electrodeposition in a charged random porous medium, whose pore surface charges can be of any sign, flanked by a pair of planar metal electrodes. Discretization of the linear stability problem results in a generalized eigenvalue problem for the dispersion relation that is solved numerically, which agrees well with the analytical approximation obtained from a boundary layer analysis valid at high wavenumbers. Under galvanostatic conditions in which an overlimiting current is applied, in the classical case of zero surface charges, the electric field at the cathode diverges at Sand’s time due to electrolyte depletion. The same phenomenon happens for positive charges but earlier than Sand’s time. However, negative charges allow the system to sustain an overlimiting current via surface conduction past Sand’s time, keeping the electric field bounded. Therefore, at Sand’s time, negative charges greatly reduce surface instabilities and suppress dendritic growth, while zero and positive charges magnify them. We compare theoretical predictions for overall surface stabilization with published experimental data for copper electrodeposition in cellulose nitrate membranes and demonstrate good agreement between theory and experiment. We also apply the stability analysis to how crystal grain size varies with duty cycle during pulse electroplating.
Highlights
The MIT Faculty has made this article openly available
Some examples in hydrodynamics include the Orr-Sommerfeld equation that predicts the dependence on Reynolds number of the transition from laminar flow to turbulent flow[4,5,6,7] and the electroconvective instability that causes the transition of a quasiequilibrium electric double layer to an nonequilibrium one that contains an additional extended space charge region.[8]
The root causes of the widely publicized lithium-ion batteries (LIBs) failures in two Boeing 787 Dreamliners in January 2013 were not conclusively identified,[102] there is no doubt that safety is of paramount importance in both lithium metal batteries (LMBs) and LIBs, which requires a thorough understanding of dendrite formation
Summary
In 2004 and 2005, Monroe and Newman included additional mechanical effects such as pressure, viscous stress and deformational stress to the linear stability analysis of electrodeposition, which provided more stabilization beyond that provided by surface energy.[156,157] For a steady-state base state, in 2014, Tikekar, Archer and Koch studied how tethered immobilized anions provide additional stabilization to electrodeposition by reducing the electric field at the cathode and, after making some approximations, derived analytical expressions for the dispersion relation for small and large current densities.[158]. We apply the linear stability analysis to compare theoretical predictions and experimental data for copper electrodeposition in cellulose nitrate membranes,[180] and use the stability analysis as a tool for investigating the dependence of crystal grain size on duty cycle during pulse electroplating
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