dorsal/arxiv
View SchemaCurrent-Voltage Relations for Electrochemical Thin Films
| Authors | Martin Z. Bazant, Kevin T. Chu, B. J. Bayly |
|---|---|
| Categories | |
| ArXiv ID | physics/0406075 |
| URL | https://arxiv.org/abs/physics/0406075 |
Abstract
The dc response of an electrochemical thin film, such as the separator in a micro-battery, is analyzed by solving the Poisson-Nernst-Planck equations, subject to boundary conditions appropriate for an electrolytic/galvanic cell. The model system consists of a binary electrolyte between parallel-plate electrodes, each possessing a compact Stern layer, which mediates Faradaic reactions with nonlinear Butler-Volmer kinetics. Analytical results are obtained by matched asymptotic expansions in the limit of thin double layers and compared with full numerical solutions. The analysis shows that (i) decreasing the system size relative to the Debye screening length decreases the voltage of the cell and allows currents higher than the classical diffusion-limited current; (ii) finite reaction rates lead to the important possibility of a reaction-limited current; (iii) the Stern-layer capacitance is critical for allowing the cell to achieve currents above the reaction-limited current; and (iv) all polarographic (current-voltage) curves tend to the same limit as reaction kinetics become fast. Dimensional analysis, however, shows that ``fast'' reactions tend to become ``slow'' with decreasing system size, so the nonlinear effects of surface polarization may dominate the dc response of thin films.
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"abstract": "The dc response of an electrochemical thin film, such as the separator in a\nmicro-battery, is analyzed by solving the Poisson-Nernst-Planck equations,\nsubject to boundary conditions appropriate for an electrolytic/galvanic cell.\nThe model system consists of a binary electrolyte between parallel-plate\nelectrodes, each possessing a compact Stern layer, which mediates Faradaic\nreactions with nonlinear Butler-Volmer kinetics. Analytical results are\nobtained by matched asymptotic expansions in the limit of thin double layers\nand compared with full numerical solutions. The analysis shows that (i)\ndecreasing the system size relative to the Debye screening length decreases the\nvoltage of the cell and allows currents higher than the classical\ndiffusion-limited current; (ii) finite reaction rates lead to the important\npossibility of a reaction-limited current; (iii) the Stern-layer capacitance is\ncritical for allowing the cell to achieve currents above the reaction-limited\ncurrent; and (iv) all polarographic (current-voltage) curves tend to the same\nlimit as reaction kinetics become fast. Dimensional analysis, however, shows\nthat ``fast\u0027\u0027 reactions tend to become ``slow\u0027\u0027 with decreasing system size, so\nthe nonlinear effects of surface polarization may dominate the dc response of\nthin films.",
"arxiv_id": "physics/0406075",
"authors": [
"Martin Z. Bazant",
"Kevin T. Chu",
"B. J. Bayly"
],
"categories": [
"physics.chem-ph"
],
"title": "Current-Voltage Relations for Electrochemical Thin Films",
"url": "https://arxiv.org/abs/physics/0406075"
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