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Computation of distribution of relaxation times by Tikhonov regularization for Li ion batteries: usage of L-curve method
In this paper, the distribution of relaxation times (DRTs) functions are calculated numerically in Matlab for synthetic impedance data from single parallel [Formula: see text] circuit and two parallel [Formula: see text] circuits connected in series, experimental impedance data from supercapacitors...
Autores principales: | , , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Nature Publishing Group UK
2021
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8209233/ https://www.ncbi.nlm.nih.gov/pubmed/34135360 http://dx.doi.org/10.1038/s41598-021-91871-3 |
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author | Paul, T. Chi, P. W. Wu, Phillip M. Wu, M. K. |
author_facet | Paul, T. Chi, P. W. Wu, Phillip M. Wu, M. K. |
author_sort | Paul, T. |
collection | PubMed |
description | In this paper, the distribution of relaxation times (DRTs) functions are calculated numerically in Matlab for synthetic impedance data from single parallel [Formula: see text] circuit and two parallel [Formula: see text] circuits connected in series, experimental impedance data from supercapacitors and α-LiFeO(2) anode based Li ion batteries. The quality of the impedance data is checked with the Kramers–Krönig (KK) relations. The DRTs are calculated within the KK compatible regime for all the systems using Tikhonov regularization (TR) method. Here we use a fast and simple L-curve method to estimate the TR parameter (λ) for regularization of the Fredholm integral equations of first kind in impedance. Estimation of the regularization parameters are performed effectively from the offset of the global corner of the L-curve rather than simply using the global corner. The physical significances of DRT peaks are also discussed by calculating the effective resistances and capacitances coupled with peak fitting program. For instance, two peaks in the DRTs justify the electrical double layer capacitance and ion diffusion phenomena for supercapacitors in low to intermediate frequencies respectively. Moreover, the surface film effect, Li/electrolyte and electrode/electrolyte charge transfer related processes are identified for α-LiFeO(2) anode based Li-ion batteries. This estimation of the offset of the global corner extends the L-curve approach coupled with the Tikhonov regularization in the field of electrochemistry and can also be applied in similar process detection methods. |
format | Online Article Text |
id | pubmed-8209233 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2021 |
publisher | Nature Publishing Group UK |
record_format | MEDLINE/PubMed |
spelling | pubmed-82092332021-06-17 Computation of distribution of relaxation times by Tikhonov regularization for Li ion batteries: usage of L-curve method Paul, T. Chi, P. W. Wu, Phillip M. Wu, M. K. Sci Rep Article In this paper, the distribution of relaxation times (DRTs) functions are calculated numerically in Matlab for synthetic impedance data from single parallel [Formula: see text] circuit and two parallel [Formula: see text] circuits connected in series, experimental impedance data from supercapacitors and α-LiFeO(2) anode based Li ion batteries. The quality of the impedance data is checked with the Kramers–Krönig (KK) relations. The DRTs are calculated within the KK compatible regime for all the systems using Tikhonov regularization (TR) method. Here we use a fast and simple L-curve method to estimate the TR parameter (λ) for regularization of the Fredholm integral equations of first kind in impedance. Estimation of the regularization parameters are performed effectively from the offset of the global corner of the L-curve rather than simply using the global corner. The physical significances of DRT peaks are also discussed by calculating the effective resistances and capacitances coupled with peak fitting program. For instance, two peaks in the DRTs justify the electrical double layer capacitance and ion diffusion phenomena for supercapacitors in low to intermediate frequencies respectively. Moreover, the surface film effect, Li/electrolyte and electrode/electrolyte charge transfer related processes are identified for α-LiFeO(2) anode based Li-ion batteries. This estimation of the offset of the global corner extends the L-curve approach coupled with the Tikhonov regularization in the field of electrochemistry and can also be applied in similar process detection methods. Nature Publishing Group UK 2021-06-16 /pmc/articles/PMC8209233/ /pubmed/34135360 http://dx.doi.org/10.1038/s41598-021-91871-3 Text en © The Author(s) 2021 https://creativecommons.org/licenses/by/4.0/Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) . |
spellingShingle | Article Paul, T. Chi, P. W. Wu, Phillip M. Wu, M. K. Computation of distribution of relaxation times by Tikhonov regularization for Li ion batteries: usage of L-curve method |
title | Computation of distribution of relaxation times by Tikhonov regularization for Li ion batteries: usage of L-curve method |
title_full | Computation of distribution of relaxation times by Tikhonov regularization for Li ion batteries: usage of L-curve method |
title_fullStr | Computation of distribution of relaxation times by Tikhonov regularization for Li ion batteries: usage of L-curve method |
title_full_unstemmed | Computation of distribution of relaxation times by Tikhonov regularization for Li ion batteries: usage of L-curve method |
title_short | Computation of distribution of relaxation times by Tikhonov regularization for Li ion batteries: usage of L-curve method |
title_sort | computation of distribution of relaxation times by tikhonov regularization for li ion batteries: usage of l-curve method |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8209233/ https://www.ncbi.nlm.nih.gov/pubmed/34135360 http://dx.doi.org/10.1038/s41598-021-91871-3 |
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