Diffuse-charge effects on the transient response of electrochemical cells
We present theoretical models for the time-dependent voltage of an electrochemical cell in response to a current step, including effects of diffuse charge (or “space charge”) near the electrodes on Faradaic reaction kinetics. The full model is based on the classical Poisson-Nernst-Planck equations w...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
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American Physical Society
2010
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| Online Access: | http://hdl.handle.net/1721.1/58745 |
| _version_ | 1826196628445331456 |
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| author | van Soestbergen, M. Biesheuvel, P. M. Bazant, Martin Z. |
| author2 | Massachusetts Institute of Technology. Department of Chemical Engineering |
| author_facet | Massachusetts Institute of Technology. Department of Chemical Engineering van Soestbergen, M. Biesheuvel, P. M. Bazant, Martin Z. |
| author_sort | van Soestbergen, M. |
| collection | MIT |
| description | We present theoretical models for the time-dependent voltage of an electrochemical cell in response to a current step, including effects of diffuse charge (or “space charge”) near the electrodes on Faradaic reaction kinetics. The full model is based on the classical Poisson-Nernst-Planck equations with generalized Frumkin-Butler-Volmer boundary conditions to describe electron-transfer reactions across the Stern layer at the electrode surface. In practical situations, diffuse charge is confined to thin diffuse layers (DLs), which poses numerical difficulties for the full model but allows simplification by asymptotic analysis. For a thin quasi-equilibrium DL, we derive effective boundary conditions on the quasi-neutral bulk electrolyte at the diffusion time scale, valid up to the transition time, where the bulk concentration vanishes due to diffusion limitation. We integrate the thin-DL problem analytically to obtain a set of algebraic equations, whose (numerical) solution compares favorably to the full model. In the Gouy-Chapman and Helmholtz limits, where the Stern layer is thin or thick compared to the DL, respectively, we derive simple analytical formulas for the cell voltage versus time. The full model also describes the fast initial capacitive charging of the DLs and superlimiting currents beyond the transition time, where the DL expands to a transient non-equilibrium structure. We extend the well-known Sand equation for the transition time to include all values of the superlimiting current beyond the diffusion-limiting current. |
| first_indexed | 2024-09-23T10:31:19Z |
| format | Article |
| id | mit-1721.1/58745 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T10:31:19Z |
| publishDate | 2010 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/587452022-09-30T21:35:20Z Diffuse-charge effects on the transient response of electrochemical cells van Soestbergen, M. Biesheuvel, P. M. Bazant, Martin Z. Massachusetts Institute of Technology. Department of Chemical Engineering Bazant, Martin Z. Bazant, Martin Z. We present theoretical models for the time-dependent voltage of an electrochemical cell in response to a current step, including effects of diffuse charge (or “space charge”) near the electrodes on Faradaic reaction kinetics. The full model is based on the classical Poisson-Nernst-Planck equations with generalized Frumkin-Butler-Volmer boundary conditions to describe electron-transfer reactions across the Stern layer at the electrode surface. In practical situations, diffuse charge is confined to thin diffuse layers (DLs), which poses numerical difficulties for the full model but allows simplification by asymptotic analysis. For a thin quasi-equilibrium DL, we derive effective boundary conditions on the quasi-neutral bulk electrolyte at the diffusion time scale, valid up to the transition time, where the bulk concentration vanishes due to diffusion limitation. We integrate the thin-DL problem analytically to obtain a set of algebraic equations, whose (numerical) solution compares favorably to the full model. In the Gouy-Chapman and Helmholtz limits, where the Stern layer is thin or thick compared to the DL, respectively, we derive simple analytical formulas for the cell voltage versus time. The full model also describes the fast initial capacitive charging of the DLs and superlimiting currents beyond the transition time, where the DL expands to a transient non-equilibrium structure. We extend the well-known Sand equation for the transition time to include all values of the superlimiting current beyond the diffusion-limiting current. Materials Innovation Institute M2i (Project No. MC3.05236) National Science Foundation (U.S.) (Contract No. No. DMS-0855011) National Science Foundation (U.S.) (Contract No. DMS-0842504) 2010-09-29T12:52:25Z 2010-09-29T12:52:25Z 2010-02 2009-10 Article http://purl.org/eprint/type/JournalArticle 1539-3755 1550-2376 http://hdl.handle.net/1721.1/58745 van Soestbergen, M., P.M. Biescheuvel, and M.Z. Bazant. "Diffuse-charge effects on the transient response of electrochemical cells." Physical Review E 81.2 (2010): 021503. © 2010 The American Physical Society en_US http://dx.doi.org/10.1103/PhysRevE.81.021503 Physical Review E Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf American Physical Society APS |
| spellingShingle | van Soestbergen, M. Biesheuvel, P. M. Bazant, Martin Z. Diffuse-charge effects on the transient response of electrochemical cells |
| title | Diffuse-charge effects on the transient response of electrochemical cells |
| title_full | Diffuse-charge effects on the transient response of electrochemical cells |
| title_fullStr | Diffuse-charge effects on the transient response of electrochemical cells |
| title_full_unstemmed | Diffuse-charge effects on the transient response of electrochemical cells |
| title_short | Diffuse-charge effects on the transient response of electrochemical cells |
| title_sort | diffuse charge effects on the transient response of electrochemical cells |
| url | http://hdl.handle.net/1721.1/58745 |
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