Optimization of dynamic transfer function analysis for impedance spectroscopy and intensity-modulated photo spectroscopy for application to non-stationary and distributed electrochemical systems
Optimierung der dynamischen Transferfunktionsanalyse für die Impedanzspektroskopie und die intensitätsmodulierte Photospektroskopie zur Anwendung an instationären und verteilten elektrochemischen Systemen
Creators: name: Schiller, Karl-Albrecht
Publisher: name: Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU)
Year: 2023
Subjects: impedance spectroscopy
relaxation impedance
ZHIT
CIMPS
solar cells
photo spectroscopy

description: übersetzt von: Optimierung der dynamischen Transferfunktionsanalyse für die Impedanzspektroskopie und die intensitätsmodulierte Photospektroskopie zur Anwendung an instationären und verteilten elektrochemischen Systemen Deutsche Fassung unter: https://open.fau.de/handle/openfau/2365
description: In the evaluation of electrochemical processes, it is popular to measure the electrical impedance of electrodes and cells. Kinetic knowledge, obtainable from the impedance spectra, can be used to extract application-relevant information. Examples are for instance the corrosion rate of materials or process details determining the efficiency of fuel cells or photovoltaic cells. This work aims on the improvement of the impedance related techniques with emphasis on the analysis procedure (Dynamic Transfer Analysis TFA). Moreover, it is proposed to widen the TFA tools for the application on photo-sensitive objects (Intensity Modulated Photo Spectroscopy IMPS). The author performed this work beside his profession as manager and head of research in his company Zahner-Messtechnik in Germany, Kronach. For many cases, application examples for the developed procedures are presented. Usually, they grew in cooperation with universities and external research institutes. Hereby, the leading role was performed by the Department of Materials Science of the Friedrich-Alexander University, Germany, Erlangen, with the chair for surface science and corrosion LKO as a mentor of this work. In analogy to the requests brought to the author from the cooperation partners, the studies are diverse, comprising tasks of verification, recovery and analysis of measured transfer function data, the time dependency of quasi-steady state systems as well as the modeling of photo-electrical systems such as solar cells. Procedures for the estimation of the reliability of experimental TFA data, the determination of the significance and uncertainty of electrochemical parameters (e.g., the electrode polarization resistance or the characteristic values of the diffusion involved), evaluated by the TFA can be considered results of this work. The temporal change of an electrochemical system during the recording time of a spectrum may be a serious experimental obstacle, as drift collides with one of the basic requirements for any TFA, which is the stationarity during the measurement time. Theoretically, the well-known Kramers-Kronig-Transform allows for the detection of parasitic errors caused by the loss of causality due to temporal change, but its computation is questionable. The Logarithmic Hilbert Transform for Two-Poles, referred to as ZHIT, was developed by the author and asserts itself in practice for its uncomplicated numerics and its ruggedness against the limited frequency range of experimental data. Even TFA-data affected by time-drift may be analyzed in a comparably accurate manner. For this, several spectra have to be acquired sequentially and data sets belonging to certain points in time need to be calculated by means of a temporal interpolation. This is demonstrated alongside the ZHIT on non-steady-state systems like corroding Iron in an electrolyte which contains CO2, a fuel cell which is gradually poisoned by carbon monoxide present in the fuel gas, another fuel cell, where the cathode is flooded by reaction water and organic protective coatings on metal under water uptake. The insight into devices for the electrochemical energy conversion like batteries and fuel cells, or into modern solar cells often requires the knowledge of the dynamic properties of distributed systems, as represented by porous structures and non-homogeneous dielectrics, and of their characteristic relaxation behavior. It appeared appropriate to address such phenomena in this work. The temperature relaxation behavior of electrochemical objects like fuel cells or batteries under the influence of electrical current heat is not so commonly known. Therefore, exemplary studies on temperature dependent resistors were performed in this work. As an outcome, the theoretical formulation of the "General Relaxation Impedance" will be presented and discussed together with the experimental results. It is a well-established practice to model the impedance of electrodes by means of electrical equivalent circuits. In contrast, accurate modeling of photo-electrical active objects like solar cells is usually done by individual analytical computations. If one wants to transcribe the modular way of equivalent circuit analysis also to dynamic photo-electric transfer functions, one may introduce a localized photocurrent source as a network component. The author describes his technical realization in an analysis program. A special fitting feature of this program is the so called "TRIFIT-algorithm". It allows the joint best model fit of the three types of experimental data from impedance, dynamic photocurrent- and photo voltage efficiency spectra, which were acquired all from the same system state of the object under test. Compared to the analysis of the isolated spectra, like it is popular in EIS, the relation between the number of known observables and the number of free parameters is increased. This leads to a model close to definiteness with less ambiguity. Experiments in this field were performed by the author on dye-sensitized solar cells "DSSC" based on TiO2 -nanotubes and on Tantalum oxide films created by anodic oxidation of Tantalum metal. By means of the TRIFIT-algorithm the "Bay-West"-model of a porous distributed photocurrent generation, published by a Danish group, could be verified for the photo-anode of the DSSC. Besides this, in cooperation with colleagues from the LKO institute several samples of thin film solar cells were examined. Their charge carrier time constants for diffusion and recombination, evaluated as dynamic efficiency from photocurrent- and photo voltage spectra, could be assigned to the parameters of synthesis and the content of sensitizing dye of the samples. The experimental impedance-, dynamic photocurrent- and photo voltage efficiency spectra of the Tantalum oxide films could be modelled over a wide range of preparation parameters of the anodic oxidation by means of a simple electrical equivalence circuit. It is primarily composed of the photocurrent source, which is embedded in the model of the oxide, containing three characteristic conduction areas with p-, intrinsic- and n-conductivity. This "PIN-model" is presented in the chapter about inhomogeneous dielectrics. For the determination of reliable dynamic photo-voltage and photocurrent spectra, an instrumentation of high-quality standard is necessary. Poor reproducibility or missing calibration of the used light intensity, non-linearity of the light modulation and frequency dependent artefacts have a negative effect on the interpretation of the experimental results. A development of the author, the "Controlled Intensity Modulated Photo Spectroscopy" CIMPS is able to enhance the accuracy of photo-electrochemical transfer function measurements significantly, compared to the literature common usage of current controlled LED as light source. The CIMPS principle will be outlined here, too.