Imposed currents in galvanic cells
We analyze the steady-state behavior of a general mathematical model for reversible galvanic cells, such as redox flow cells, reversible solid oxide fuel cells, and rechargeable batteries. We consider not only operation in the galvanic discharging mode, spontaneously generating a positive current ag...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
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Elsevier B.V.
2012
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| Online Access: | http://hdl.handle.net/1721.1/69560 |
| _version_ | 1811079996323659776 |
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| author | Biesheuvel, P. M. Soestbergen, M. van Bazant, Martin Z. |
| author2 | Massachusetts Institute of Technology. Department of Chemical Engineering |
| author_facet | Massachusetts Institute of Technology. Department of Chemical Engineering Biesheuvel, P. M. Soestbergen, M. van Bazant, Martin Z. |
| author_sort | Biesheuvel, P. M. |
| collection | MIT |
| description | We analyze the steady-state behavior of a general mathematical model for reversible galvanic cells, such as redox flow cells, reversible solid oxide fuel cells, and rechargeable batteries. We consider not only operation in the galvanic discharging mode, spontaneously generating a positive current against an external load, but also operation in two modes which require a net input of electrical energy: (i) the electrolytic charging mode, where a negative current is imposed to generate a voltage exceeding the open-circuit voltage, and (ii) the “super-galvanic” discharging mode, where a positive current exceeding the short-circuit current is imposed to generate a negative voltage. Analysis of the various (dis-)charging modes of galvanic cells is important to predict the efficiency of electrical to chemical energy conversion and to provide sensitive tests for experimental validation of fuel cell models. In the model, we consider effects of diffuse charge on electrochemical charge-transfer rates by combining a generalized Frumkin-Butler-Volmer equation for reaction kinetics across the compact Stern layer with the full Poisson-Nernst-Planck transport theory, without assuming local electroneutrality. Since this approach is rare in the literature, we provide a brief historical review. To illustrate the general theory, we present results for a monovalent binary electrolyte, consisting of cations, which react at the electrodes, and non-reactive anions, which are either fixed in space (as in a solid electrolyte) or are mobile (as in a liquid electrolyte). The full model is solved numerically and compared to analytical results in the limit of thin diffuse layers, relative to the membrane thickness. The spatial profiles of the ion concentrations and electrostatic potential reveal a complex dependence on the kinetic parameters and the imposed current, in which the diffuse charge at each electrode and the total membrane charge can have either sign, contrary perhaps to intuition. For thin diffuse layers, simple analytical expressions are presented for galvanic cells valid in all three (dis-)charging modes in the two subsequent limits of the ratio δ of the effective thicknesses of the compact and diffuse layers: (i) the “Helmholtz limit” (δ → ∞) where the compact layer carries the double layer voltage as in standard Butler-Volmer models, and (ii) the opposite “Gouy-Chapman limit” (δ → 0) where the diffuse layer fully determines the charge-transfer kinetics. In these limits, the model predicts both reaction-limited and diffusion-limited currents, which can be surpassed for finite positive values of the compact layer, diffuse layer and membrane thickness. |
| first_indexed | 2024-09-23T11:23:50Z |
| format | Article |
| id | mit-1721.1/69560 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T11:23:50Z |
| publishDate | 2012 |
| publisher | Elsevier B.V. |
| record_format | dspace |
| spelling | mit-1721.1/695602022-09-27T19:14:40Z Imposed currents in galvanic cells Biesheuvel, P. M. Soestbergen, M. van Bazant, Martin Z. Massachusetts Institute of Technology. Department of Chemical Engineering Massachusetts Institute of Technology. Department of Mathematics Bazant, Martin Z. Bazant, Martin Z. Biesheuvel, P. M. We analyze the steady-state behavior of a general mathematical model for reversible galvanic cells, such as redox flow cells, reversible solid oxide fuel cells, and rechargeable batteries. We consider not only operation in the galvanic discharging mode, spontaneously generating a positive current against an external load, but also operation in two modes which require a net input of electrical energy: (i) the electrolytic charging mode, where a negative current is imposed to generate a voltage exceeding the open-circuit voltage, and (ii) the “super-galvanic” discharging mode, where a positive current exceeding the short-circuit current is imposed to generate a negative voltage. Analysis of the various (dis-)charging modes of galvanic cells is important to predict the efficiency of electrical to chemical energy conversion and to provide sensitive tests for experimental validation of fuel cell models. In the model, we consider effects of diffuse charge on electrochemical charge-transfer rates by combining a generalized Frumkin-Butler-Volmer equation for reaction kinetics across the compact Stern layer with the full Poisson-Nernst-Planck transport theory, without assuming local electroneutrality. Since this approach is rare in the literature, we provide a brief historical review. To illustrate the general theory, we present results for a monovalent binary electrolyte, consisting of cations, which react at the electrodes, and non-reactive anions, which are either fixed in space (as in a solid electrolyte) or are mobile (as in a liquid electrolyte). The full model is solved numerically and compared to analytical results in the limit of thin diffuse layers, relative to the membrane thickness. The spatial profiles of the ion concentrations and electrostatic potential reveal a complex dependence on the kinetic parameters and the imposed current, in which the diffuse charge at each electrode and the total membrane charge can have either sign, contrary perhaps to intuition. For thin diffuse layers, simple analytical expressions are presented for galvanic cells valid in all three (dis-)charging modes in the two subsequent limits of the ratio δ of the effective thicknesses of the compact and diffuse layers: (i) the “Helmholtz limit” (δ → ∞) where the compact layer carries the double layer voltage as in standard Butler-Volmer models, and (ii) the opposite “Gouy-Chapman limit” (δ → 0) where the diffuse layer fully determines the charge-transfer kinetics. In these limits, the model predicts both reaction-limited and diffusion-limited currents, which can be surpassed for finite positive values of the compact layer, diffuse layer and membrane thickness. 2012-03-02T16:10:00Z 2012-03-02T16:10:00Z 2009-08 2009-03 Article http://purl.org/eprint/type/JournalArticle 0013-4686 0019-4686 http://hdl.handle.net/1721.1/69560 Biesheuvel, P.M., M. van Soestbergen, and M.Z. Bazant. “Imposed Currents in Galvanic Cells.” Electrochimica Acta 54.21 (2009): 4857–4871. en_US http://dx.doi.org/10.1016/j.electacta.2009.03.073 Electrochimica Acta application/pdf Elsevier B.V. Prof. Bazant via Erja Kajosalo |
| spellingShingle | Biesheuvel, P. M. Soestbergen, M. van Bazant, Martin Z. Imposed currents in galvanic cells |
| title | Imposed currents in galvanic cells |
| title_full | Imposed currents in galvanic cells |
| title_fullStr | Imposed currents in galvanic cells |
| title_full_unstemmed | Imposed currents in galvanic cells |
| title_short | Imposed currents in galvanic cells |
| title_sort | imposed currents in galvanic cells |
| url | http://hdl.handle.net/1721.1/69560 |
| work_keys_str_mv | AT biesheuvelpm imposedcurrentsingalvaniccells AT soestbergenmvan imposedcurrentsingalvaniccells AT bazantmartinz imposedcurrentsingalvaniccells |