Growing Porous Layers

Abstract

The precipitation of ions generated at an electrode, operating at a constant current, with ions of the adjacent electrolytic solution has been modeled as a growing porous layer. The thickness of the layer as a function of time for short times is given by a power series expansion of time. The long-time solution was determined by a numerical calculation on a digital computer. A criterion for linear growth rate as a function of time is given.Moving boundary problems, such as melting-freezing, evaporation-condensation, and purification of materials, involving heat and mass transfer have been treated in depth (1-7). A moving boundary problem is encountered in the field of electrochemistry when ions being generated at an electrode, operating at a constant current, form a precipitate with ions of the adjacent electrolytic solution. The resulting precipitate forms a growing porous layer on the electrode. Studies of anodic dissolution of various metals which form porous coatings (8) can be considered examples of growing porous layers. In the case of silver, a porous layer occurs only after a nonporous layer has been formed or when large currents are employed (9, 10). Jackson and Blomgren (11) studied the anodic dissolution of lithium in a 1M solution of A1C13 in propylene carbonate and observed a growing porous layer of LiC1. Other examples of growing porous layers are the oxidation of tungsten (12) and the scaling of metals (13). In the following analysis, the thickness of a growing porous layer as a function of time is determined, and a criterion for linear growth rate as a function of time is given.

Capacity Fade Mechanisms and Side Reactions in Lithium‐Ion Batteries

“…Finally, if the film has some porosity or if it is not a pure cation conductor, then diffusion limitations inside the film might also be included. 172 Electrolyte decomposition reactions-A large number of different solvent and salt combinations are used in lithium-ion batteries. Because of the complexity of the mechanisms of salt and solvent oxidation and reduction reac-tions, it is not possible at present to create a general model [80] that can treat all possible systems.…”

Modeling for the scale-up of a lithium-ion polymer battery

“…The functional form depends on the polarization characteristics of the electrodes. In this study, the following polarization expression used by Tiedemann and Newman [29] and Newman and Tiedemann [20] was adopted…”

Mixed-Conduction Model for Stainless Steel in a High-Temperature Electrolyte: Estimation of Kinetic Parameters of Inner Layer Constituents

“…In the absence of representative information on the pore diameter and tortuousity, and also of reliable data on the crystallite size of the outer layer, the growth of this layer can be formally treated as a diffusion process in a matrix constituted of the outer layer crystals and the electrolyte in-between. Similar treatments for a porous oxide layer have already been presented 16 and also discussed by some in relation to incorporation of foreign species into the growing film on construction materials in nuclear power plants. 2 It must be stressed, however, that the approach to porous layer growth outlined in the present paragraph is purely formal and can by no means be considered analogous to the solid-state growth mechanism of the inner layer discussed in previous paragraphs.…”