Deconvolution of immittance data: Some old and new methods
Section snippets
Background
Both electrocatalysis and immittance spectroscopy data usually involve distributions of relaxation times or activation energies, but because methods of estimating such distributions, called deconvolution or inversion, are thought to be difficult to apply or not readily available, such techniques for aiding in understanding physico-chemical processes present in materials are often underutilized. A list of acronym definitions, including ones for fitting models, is included at the end of the
Least-squares deconvolution methods
The regularization method, essentially a non-parametric approach, involves a regularization parameter whose value is chosen to ameliorate inversion problems by a kind of smoothing process, one that necessarily introduces some inaccuracy in DRT estimation. Here emphasis is on the PLS approach for estimating an unknown DRT, g(τ) or a transformation of it [13]. It involves expressing the frequency-response data, I(ω), as an integral from zero to infinity over g(τ)/[1 + iωτ], or temporal data, f(t),
PLS inversion approaches
The 2002 PLS publication of Ref. [14] stated that methods of obtaining information about DRTs were not well developed and proposed “a method for identification, from impedance spectra, of the distribution of time constants associated with activation or relaxation processes.” Their approach, although not so mentioned, is just a version of the PLS one described much earlier by others and instantiated in the PLLS and PNLLS approaches included in the widely used LEVM program and its predecessor,
Acronym definitions
- CNLS
complex non-linear least squares
- DIA
differential impedance analysis [7], [25]
- DRT
distribution of relaxation times
- KK
Kronig–Kramers transform relations
- LEVM
CNLS fitting and inversion program [10]
- PLS
parametric least squares
- PLLS
parametric linear least squares
- PNLLS
parametric non-linear least squares
- PWT
proportional weighting [10]
- UWT
unity weighting [10]
General
- CD
Cole–Davidson response function defined at the impedance level (see Section 3.2.3.1)
- K1
conductive-system Kohlrausch frequency-response model (see
Single and composite frequency-response fitting models
Acknowledgements
We thank Dr. P. Lunkenheimer for providing the present CKN data and he and Dr. B.A. Boukamp for valuable comments and suggestions. The work of Dr. E. Tuncer was sponsored by the US Department of Energy, Office of Electricity Delivery and Energy Reliability, Superconductivity Program for Electric Power Systems, under Contract No. DE-AC05-00OR22725 with Oak Ridge National Laboratory, managed and operated by UT-Battelle, LLC.
References (27)
J. Comput. Phys.
(2000)Inverse Probl.
(2000)- et al.
IEEE Trans. Dielect. Electr. Insulat.
(2001) - et al.
IEE. Proc. Sci. Meas. Technol.
(2003) - et al.
J. Appl. Phys.
(2006) Ann. Phys.
(1907)Ann. Phys.
(1913)- et al.
Theory of Electric Polarization
(1996) J. Chem. Phys.
(1995)- et al.
IEEE Trans. Electr. Insul.
(1988)
J. Electroanal. Chem.
Solid State Ionics
Cited by (25)
Drying-rewetting cycles in ordinary Portland cement mortars investigated by electrical impedance spectroscopy
2018, Construction and Building MaterialsCitation Excerpt :A general circuit for fitting the experimental data, without the need of a priori assumptions, is a Voigt circuit with a certain number of pairs elements in parallel (RC) connected in series. Any set of impedance data can be fitted to a circuit with sufficient number of (RC) [45–48]. This circuit also serves to: i) check if the experimental data fulfil the Kramers-Kronig relations, ii) obtain the time constant of each (RC) (τ = RC) and iii) estimate continuous distributions with some approximate results [45].
Two-dimensional impedance data analysis by the distribution of relaxation times
2017, Journal of Energy StorageCitation Excerpt :While the ECM fitting procedure is straightforward owing to the availability of standard software packages, it suffers from ambiguity since it requires detailed a priori knowledge of the system to obtain physically meaningful results. This problem can be mitigated by transforming frequency domain impedance data into the relaxation time domain [10,11], which does not require any assumptions about the investigated system apart from the kernel. The transformation directly provides a distribution of physical processes, which gives rise to the impedance response of a system, and it is possible to determine the number of processes that can be distinguished given the sensitivity of the data [12].
New approach for the calculation of impedance spectra out of time domain data
2011, Electrochimica ActaCitation Excerpt :This is achieved by (i) an optimization of the window function, (ii) a transformation of the time domain data using a straight line sequence, (iii) a variable sampling rate, and (iv) a stepwise evaluation within sections. It is worth mentioning that it is possible to calculate the DRT directly from the recorded time domain data as pointed out in Ref. [19], for example with the LEVM software [20]. However, this technique fails, if the system under test shows capacitive behavior as Li-ion batteries do.
Studies on LiFePO<inf>4</inf> as cathode material using impedance spectroscopy
2011, Journal of Power SourcesStudies on LiFePO<inf>4</inf> as cathode material using impedance spectroscopy
2011, Journal of Power SourcesA compartmental model describing changes in progesterone concentrations during the oestrous cycle
2009, Journal of Dairy Research