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Unformatted text preview: 10.626 Electrochemical Energy Systems Spring 2011 MIT, M. Z. Bazant Problem Set 4 Electrolytes Due: Lecture 28 1. Ambipolar diffusion in a concentrated solution. Consider a quasi-neutral, concen- trated binary electrolyte. The ions have charges z e , non-constant mobilities M (which could depend on position or concentrations), and electro-chemical potentials = k B T ln( c ) z e where ( c + ,c ) are concentration-dependent chemical activity coecients. (a) Express the current density J in terms of the potential and salt concentration c = z + c + = z c . (b) Derive a nonlinear diffusion equation for c , with a correction depending on J and t + , where t + is the transference number of cations 1 (c) Simplify your result for the case of a solid electrolyte, modeled as an ideal solution of ions and vacancies in a lattice of volume v per site. Assume that the transition state for diffusion excludes two sites (before and after a particle...
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This note was uploaded on 11/27/2011 for the course CHEMICAL E 20.410j taught by Professor Rogerd.kamm during the Spring '03 term at MIT.
- Spring '03