Modeling the Lithium Ion/Electrode Battery Interface Using Fick’s Second Law of Diffusion, the Laplace Transform, Charge Transfer Functions, and a [4, 4] Padé Approximant
This work investigates a one-dimensional model for the solid-state diffusion in a LiC6/LiMnO2 rechargeable cell. This cell is used in hybrid electric vehicles. In this environment the cell experiences low frequency electrical pulses that degrade the electrodes. The model’s starting point is Fick’s s...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | International Journal of Electrochemistry |
| Online Access: | http://dx.doi.org/10.1155/2015/496905 |
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| author | John H. Summerfield Charles N. Curtis |
| author_facet | John H. Summerfield Charles N. Curtis |
| author_sort | John H. Summerfield |
| collection | DOAJ |
| description | This work investigates a one-dimensional model for the solid-state diffusion in a LiC6/LiMnO2 rechargeable cell. This cell is used in hybrid electric vehicles. In this environment the cell experiences low frequency electrical pulses that degrade the electrodes. The model’s starting point is Fick’s second law of diffusion. The Laplace transform is used to move from time as the independent variable to frequency as the independent variable. To better understand the effect of frequency changes on the cell, a transfer function is constructed. The transfer function is a transcendental function so a Padé approximant is found to better describe the model at the origin. Consider ∂c(r,t)/∂t=D∂2c(r)/∂2r+(2/r)(∂c(r)/∂r). |
| format | Article |
| id | doaj-art-93abb190a3364f9ab336084420380a4e |
| institution | Kabale University |
| issn | 2090-3529 2090-3537 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Electrochemistry |
| spelling | doaj-art-93abb190a3364f9ab336084420380a4e2025-02-03T01:29:57ZengWileyInternational Journal of Electrochemistry2090-35292090-35372015-01-01201510.1155/2015/496905496905Modeling the Lithium Ion/Electrode Battery Interface Using Fick’s Second Law of Diffusion, the Laplace Transform, Charge Transfer Functions, and a [4, 4] Padé ApproximantJohn H. Summerfield0Charles N. Curtis1Missouri Southern State University, 3950 Newman Road, Joplin, MO 64801, USAMissouri Southern State University, 3950 Newman Road, Joplin, MO 64801, USAThis work investigates a one-dimensional model for the solid-state diffusion in a LiC6/LiMnO2 rechargeable cell. This cell is used in hybrid electric vehicles. In this environment the cell experiences low frequency electrical pulses that degrade the electrodes. The model’s starting point is Fick’s second law of diffusion. The Laplace transform is used to move from time as the independent variable to frequency as the independent variable. To better understand the effect of frequency changes on the cell, a transfer function is constructed. The transfer function is a transcendental function so a Padé approximant is found to better describe the model at the origin. Consider ∂c(r,t)/∂t=D∂2c(r)/∂2r+(2/r)(∂c(r)/∂r).http://dx.doi.org/10.1155/2015/496905 |
| spellingShingle | John H. Summerfield Charles N. Curtis Modeling the Lithium Ion/Electrode Battery Interface Using Fick’s Second Law of Diffusion, the Laplace Transform, Charge Transfer Functions, and a [4, 4] Padé Approximant International Journal of Electrochemistry |
| title | Modeling the Lithium Ion/Electrode Battery Interface Using Fick’s Second Law of Diffusion, the Laplace Transform, Charge Transfer Functions, and a [4, 4] Padé Approximant |
| title_full | Modeling the Lithium Ion/Electrode Battery Interface Using Fick’s Second Law of Diffusion, the Laplace Transform, Charge Transfer Functions, and a [4, 4] Padé Approximant |
| title_fullStr | Modeling the Lithium Ion/Electrode Battery Interface Using Fick’s Second Law of Diffusion, the Laplace Transform, Charge Transfer Functions, and a [4, 4] Padé Approximant |
| title_full_unstemmed | Modeling the Lithium Ion/Electrode Battery Interface Using Fick’s Second Law of Diffusion, the Laplace Transform, Charge Transfer Functions, and a [4, 4] Padé Approximant |
| title_short | Modeling the Lithium Ion/Electrode Battery Interface Using Fick’s Second Law of Diffusion, the Laplace Transform, Charge Transfer Functions, and a [4, 4] Padé Approximant |
| title_sort | modeling the lithium ion electrode battery interface using fick s second law of diffusion the laplace transform charge transfer functions and a 4 4 pade approximant |
| url | http://dx.doi.org/10.1155/2015/496905 |
| work_keys_str_mv | AT johnhsummerfield modelingthelithiumionelectrodebatteryinterfaceusingfickssecondlawofdiffusionthelaplacetransformchargetransferfunctionsanda44padeapproximant AT charlesncurtis modelingthelithiumionelectrodebatteryinterfaceusingfickssecondlawofdiffusionthelaplacetransformchargetransferfunctionsanda44padeapproximant |