Extended Distribution of Relaxation Time Analysis for Electrochemical Impedance Spectroscopy

Kobayashi, Kiyoshi; Suzuki, Tohru

doi:10.5796/electrochemistry.21-00111

Cited by 13 publications

(14 citation statements)

References 38 publications

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“…Additionally, the DFRTs are shown in Figure 7c,d. Comparing the peak position with that of the symmetric Li || Li cell, the static peak (1st peak) around 215 Hz corresponds to the surface film effect resulting from Li ion movement 54 and dispersion over time. For the p-Si@C anode, the peak has 42% lower resistance after 5 cycles compared to that of pristine Si at open circuit voltage condition.…”

Section: ■ Results and Discussionmentioning

confidence: 99%

Si@C Core–Shell Nanostructure-Based Anode for Li-Ion Transport

Wang

Chung

Chi

et al. 2023

ACS Appl. Nano Mater.

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Silicon-based anode materials are gaining popularity in lithium-ion battery research due to their high theoretical specific capacity compared to the conventional graphite anode. However, the commercialization of silicon-based anode materials has been hampered by their limited electronic conductivity and significant volume expansion. To address these challenges, our strategy was conducted to prepare porous silicon@carbon (p-Si@C) nanocomposites as an anode material using a simple aqueous solution method. In this work, nitrogen-containing p-phenylenediamine was chosen as the carbon source for synthesizing the nanostructured p-Si@C composites. The excellent electrochemical performance can be achieved, with over 100 cycles, a specific capacity of 624 mAh g −1 , and a high Coulombic efficiency of 97.2%. These promising results were attributed to efficient Li-ion transport and low volume expansion, which are confirmed by the distribution function of relaxation time plots coupled with impedance spectroscopy technique, followed by the calculation of the expansion rate obtained from the SEM cross-sectional image. Hence, our work not only clearly provides a simple yet valuable method for the preparation of nanostructured silicon-based anode material with good electrochemical performance but also demonstrates its potential for industrial battery-grade development.

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Section: ■ Results and Discussionmentioning

confidence: 99%

Si@C Core–Shell Nanostructure-Based Anode for Li-Ion Transport

Wang

Chung

Chi

et al. 2023

ACS Appl. Nano Mater.

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“…6,8,11 To overcome these challenges, the distribution of relaxation times (DRT) has emerged as a complementary method enabling the identification of the characteristic timescales in EIS spectra. [12][13][14][15][16][17] Explicitly, within the DRT analysis framework, the impedance model, Z f , DRT ( ) is fashioned to originate from relaxations, leading to the following expression: 10,11,18…”

Section: Greek Letters γmentioning

confidence: 99%

Selecting the Regularization Parameter in the Distribution of Relaxation Times

Maradesa

Wan

et al. 2023

J. Electrochem. Soc.

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Electrochemical impedance spectroscopy (EIS) is used widely in electrochemistry. Obtaining EIS data is simple with modern electrochemical workstations. Yet, analyzing EIS spectra is still a considerable quandary. The distribution of relaxation times (DRT) has emerged as a solution to this challenge. However, DRT deconvolution underlies an ill-posed optimization problem, often solved by ridge regression, whose accuracy strongly depends on the regularization level λ. This article studies the selection of λ using several cross-validation (CV) methods and the L-curve approach. A hierarchical Bayesian DRT (hyper-λ) deconvolution method is also analyzed, whereby λ_0, a parameter analogous to λ, is obtained through CV. The analysis of a synthetic dataset suggests that the values of λ selected by generalized and modified generalized CV are the most accurate among those studied. Furthermore, the analysis of synthetic EIS spectra indicates that the hyper-λ approach outperforms optimal ridge regression. Due to its broad scope, this research will foster additional research on the vital topics of hyperparameter selection for DRT deconvolution. This article also provides, through pyDRTtools, an implementation, which will serve as a starting point for future research.

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“…Methods to extract distribution function of relaxation times.-The available strategies for DRT extraction are based on regularization techniques, 2,3,[6][7][8][9]4 Fourier filtering, 10,11 evolutionary programming [12][13][14] grammatical evolution, 15 maximum entropy model, 16 Monte Carlo techniques, 17 deconvolution using deep neural networks 18 and Finite Gaussian Processes. 19,20 Interestingly enough, only a few of the listed aforementioned regularization approaches apply the Levenberg-Marquardt algorithm (LMA) to extract the applicable DRT profiles from EIS data.…”

Section: Z G E I E E Dy G Y I E Dymentioning

confidence: 99%

“…19,20 Interestingly enough, only a few of the listed aforementioned regularization approaches apply the Levenberg-Marquardt algorithm (LMA) to extract the applicable DRT profiles from EIS data. 6,7,9 Herein, we are focused on both the LMA regularization and on the Jacobian matrix approximation; and thus, we have revisited several DRT strategies 3,6,7,9 that are of keen interest (Scheme 1).…”

Section: Z G E I E E Dy G Y I E Dymentioning

confidence: 99%

Extraction of Distribution Function of Relaxation Times by using DRT-RBLM Tools: A New Approach to Combine Levenberg-Marquardt Algorithm and Radial Basis Functions for Discretization Basis

Kunaver¹,

Rojec²,

Subotić³

et al. 2022

J. Electrochem. Soc.

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Electrochemical impedance spectroscopy (EIS) is a powerful tool for the analysis of different power sources and various materials. One of the methods used for studying EIS data is the distribution function of relaxation times (DRT). EIS data can be converted into a Fredholm integral of the first kind, and DRT extraction is known to be an inverse ill-posed problem. Herein, a new strategy to extract DRT by applying the Levenberg-Marquardt algorithm (LMA) is proposed. The Jacobian matrix appearing in LMA is partially numerically approximated by applying the radial basis function as a basis for the discretization. DRT data are smoothed by the application of the finite difference matrix and the negative values are avoided by the limits application. The tests conducted with \textcolor{black}{ZARCs/FRACs} synthetic data show that the extracted DRT profiles correspond well to their analytical counterparts. The application of LMA in solving Fredholm integral equation of the first kind (i.e., DRT extraction) resulted in the automatic tuning of the regularization parameter. The aforementioned findings show that by modifying LMA it is possible to both solve the Fredholm integral equation of the first kind in a completely data-driven way and to obtain the applicable DRT data for general EIS study.

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Extended Distribution of Relaxation Time Analysis for Electrochemical Impedance Spectroscopy

Cited by 13 publications

References 38 publications

Si@C Core–Shell Nanostructure-Based Anode for Li-Ion Transport

Si@C Core–Shell Nanostructure-Based Anode for Li-Ion Transport

Selecting the Regularization Parameter in the Distribution of Relaxation Times

Extraction of Distribution Function of Relaxation Times by using DRT-RBLM Tools: A New Approach to Combine Levenberg-Marquardt Algorithm and Radial Basis Functions for Discretization Basis

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