Distribution Function Of Relaxation Times Research Articles

Nitrous oxide abatement and valorization in an ammonia-fueled SOFC stack – Nitric oxide and electricity production

Nitrous oxide (N2O) is a harmful gas that strongly impacts climate change. Several strategies for denitrification have been addressed, where the use of solid oxide fuel cells (SOFCs) has been demonstrated to be attractive for N2O reduction and simultaneous electricity production. The reduction of N2O to N2 is studied for the first time at the cathode of an SOFC, where ammonia is supplied to the anode as fuel. A diluted ammonia stream is particularly interesting since it is normally available in HNO3 plants – the most important concentrated source of N2O emission – and is carbon-free. The combined reduction of N2O with the oxidation of NH3 allows the production of nitric oxide (NO) at the anode, a valuable precursor for HNO3 production.This work uses a commercial SOFC stack comprehending six cells, equipped with membrane electrode assemblies of LSM-CGO ‖ yttria-stabilized zirconia (YSZ) ‖ YSZ-NiO. Electrochemical Impedance Spectroscopy (EIS) was successfully employed to characterize the stack performance. Data were analyzed by combining a Distribution Function of Relaxation Times (DFRT) and Equivalent Circuit Models (ECMs), for different operating conditions, namely in terms of temperature and fuel feed composition. Three major processes were identified at the anode: one related to the adsorption/desorption of reactants on the surface of the electrocatalyst, a diffusion process of charge carriers/intermediate species to the triple phase boundary (TPB), and a charge-transfer process at the TPB. The electrochemical production of nitric oxide (NO) was investigated, and a 20 % selectivity towards NO production and an energy stack efficiency of 88 % was obtained. Overall, the current work provides a critical first step toward using SOFC to perform efficient N2O electroreduction using diluted ammonia as fuel.

The relaxation time distribution function for a mineral medium clay soil

The relaxation time distribution function for a mineral medium clay soil

Studying the Effect of Operating Conditions and NO2 Cathode Contamination on PEM Fuel Cells Using Distribution Function of Relaxation Times Analysis.

The effect of NO2, an air pollutant, on the durability of polymer electrolyte membrane fuel cells (PEMFCs) and the affected electrochemical processes in the PEMFC following the contamination were investigated. In-situ Electrochemical Impedance Spectroscopy (EIS) measurements were conducted on PEMFCs under different operating conditions of temperature and relative humidity (RH). NO2 was introduced to the cathode inlet flow. Analyses of the EIS measurements were performed using a genetic algorithm called ISGP (Impedance Spectroscopy by Genetic Programming) to obtain the distribution function of relaxation times (DFRT, a.k.a. DRT) models. Utilizing ISGP enabled us to differentiate the various phenomena in PEMFC and study how they are affected by NO2 contamination. Moreover, the experiments demonstrate the effectiveness of the mitigation method to flush the PEMFC and regenerate its performance after being contaminated, particularly at low operating temperatures. Energy-dispersive X-ray spectroscopy (EDS) technique is performed on the contaminated PEMFC to detect the presence of any nitrogen components in the FC's gas diffusion layer and the catalyst layer post the mitigation step. Cyclic Voltammetry is also performed on the contaminated cell to determine the effect of the contamination on the electrochemically active surface area of the cathode by evaluating the double-layer capacitance.

Detection of invasive ductal carcinoma by electrical impedance spectroscopy implementing gaussian relaxation-time distribution (EIS-GRTD)

Breast cancer detection and differentiation of breast tissues are critical for accurate diagnosis and treatment planning. This study addresses the challenge of distinguishing between invasive ductal carcinoma (IDC), normal glandular breast tissues (nGBT), and adipose tissue using electrical impedance spectroscopy combined with Gaussian relaxation-time distribution (EIS-GRTD). The primary objective is to investigate the relaxation-time characteristics of these tissues and their potential to differentiate between normal and abnormal breast tissues. We applied a single-point EIS-GRTD measurement to ten mastectomy specimens across a frequency range f = 4 Hz to 5 MHz. The method calculates the differential ratio of the relaxation-time distribution function Δγ between IDC and nGBT, which is denoted by ΔγIDC−nGBT, and Δγ between IDC and adipose tissues, which is denoted by ΔγIDC−adipose. As a result, the differential ratio of Δγ between IDC and nGBT ΔγIDC−nGBT is 0.36, and between IDC and adipose ΔγIDC−adipose is 0.27, which included in the α -dispersion at τpeak1=0.033±0.001s. In all specimens, the relaxation-time distribution function γ of IDC γIDC is higher, and there is no intersection with γ of nGBT γnGBT and adipose γadipose. The difference in γ suggests potential variations in relaxation properties at the molecular or structural level within each breast tissue that contribute to the overall relaxation response. The average mean percentage error δ for IDC, nGBT, and adipose tissues are 5.90%, 6.33%, and 8.07%, respectively, demonstrating the model’s accuracy and reliability. This study provides novel insights into the use of relaxation-time characteristic for differentiating breast tissue types, offering potential advancements in diagnosis methods. Future research will focus on correlating EIS-GRTD finding with pathological results from the same test sites to further validate the method’s efficacy.

A new insight into the oxygen reduction reaction of the Ca3Co4O9+δ/CGO composite air electrode

The calcium cobaltite Ca3Co4O9+δ (CCO) is an emerging electrode for Solid Oxide Fuel Cells or Solid Electrolyser Cells. Thanks to a thermal expansion coefficient which is in the same range of magnitude than the commonly used electrolytes, it should lead to improved durability. However, because the material suffers of a lack of oxide ion conductivity, it has to be used in composite with an ionic conductor. Displaying good compatability with ceria, first studies were carried out on composite with Ce0.9Gd0.1O1.95 (CGO). At 700 °C, an optimal Area Specific Resistance of 0.5 Ω cm2 was obtained for a 50/50 wt.% CCO/ CGO, 21 μm thick electrode, with CCO powder prepared by a solid-state route whose synthesis method led to large grains compared to the CGO powder. Here, to increase the density of triple-phase boundaries between the gas and the two materials, a CCO powder with smaller grain size was prepared using a citrate route. For screen printed 50/50 wt.% CCO (citrate)/CGO composite electrode deposited on symmetrical cell with a CGO electrolyte, an ASR of 0.35 Ω cm2 was achieved at 700 °C, under air. To go further in the understanding of the oxygen reduction reaction, the cell was then carefully studied at variable temperatures and under variable oxygen partial pressures, combining calculation of the distribution function of relaxation times (DFRT) and complex nonlinear least squares fitting (CNLS) of impedance spectra. At 700 °C, under air, it was shown that 55 % of the ASR was due to the oxygen molecule dissociation and diffusion of atomic oxygen species at the surface of the electrode materials. It was only 37 % at 600 °C. Experiment carried out under 21 % of oxygen in helium proved that gas diffusion was a limiting step at temperature higher that 650 °C whereas the redox of CCO was limiting at lower temperature. When deposited on a commercial anode supported 2R-Cell™ half cell, the maximum power density was improved by 284 %, reaching 532 mW/cm2 at 700 °C with a 50/50 wt.% CCO (citrate)/CGO composite air electrode against 187 mW/cm2 for a 50/50 wt.% CCO (solid-state)/CGO composite air electrode at the same temperature.

Detection of invasive ductal carcinoma in quadrant breast areas by electrical impedance tomography implemented with gaussian relaxation-time distribution (EIT-GRTD)

Invasive ductal carcinoma (IDC) in breast specimens has been detected in the quadrant breast area: (I) upper outer, (II) upper inner, (III) lower inner, and (IV) lower outer areas by electrical impedance tomography implemented with Gaussian relaxation-time distribution (EIT-GRTD). The EIT-GRTD consists of two steps which are (1) the optimum frequency fopt selection and (2) the time constant enhancement of breast imaging reconstruction. fopt is characterized by a peak in the majority measurement pair of the relaxation-time distribution function γ, which indicates the presence of IDC. γ represents the inverse of conductivity and indicates the response of breast tissues to electrical currents across varying frequencies based on the Voigt circuit model. The EIT-GRTD is quantitatively evaluated by multi-physics simulations using a hemisphere container of mimic breast, consisting of IDC and adipose tissues as normal breast tissue under one condition with known IDC in quadrant breast area II. The simulation results show that EIT-GRTD is able to detect the IDC in four layers at fopt = 30, 170 Hz. EIT-GRTD is applied in the real breast by employed six mastectomy specimens from IDC patients. The placement of the mastectomy specimens in a hemisphere container is an important factor in the success of quadrant breast area reconstruction. In order to perform the evaluation, EIT-GRTD reconstruction images are compared to the CT scan images. The experimental results demonstrate that EIS-GRTD exhibits proficiency in the detection of the IDC in quadrant breast areas while compared qualitatively to CT scan images.

Derivation and analysis of lattice Boltzmann form of the mild slope equation

The present study investigates the performance of the Lattice Boltzmann Method (LBM) as an alternative numerical method for simulating wave propagation in coastal zones. While formulations like the Mild-Slope Equation (MSE) remain efficient for coastal engineering applications due to their simplicity, LBM offers an explicit numerical solver for partial differential equations (PDEs). LBM utilizes local operations, making it well-suited for Graphics Processing Unit (GPU) acceleration and consequently efficient simulations. This study examines LBM's performance in several benchmark cases, including wave propagation behind a single breakwater, harbor resonance, refraction of long waves over a parabolic shoal, and wave propagation over an elliptic shoal. The Chapman-Enskog multi-scale expansion was used within a popular 2D LBM scheme to derive the relaxation time and equilibrium distribution function. The results showed a good agreement between LBM predictions and benchmark data. Furthermore, LBM demonstrated efficiency in reducing the computation time, achieving a notable 30–50% decrease in CPU time and an 85% reduction when utilizing a GPU.

Procedure for Obtaining the Analytical Distribution Function of Relaxation Times for the Analysis of Impedance Spectra Using the Fox H-Function

Procedure for Obtaining the Analytical Distribution Function of Relaxation Times for the Analysis of Impedance Spectra Using the Fox <i>H</i>-Function

Distribution function of relaxation times: An alternative to classical methods for evaluating the reaction kinetics of oxygen evolution reaction

Reaction kinetics of RuO2 is precisely evaluated by distribution function of relaxation times (DFRT) model using impedance spectroscopy analysis by genetic programming (ISGP). Effective resistances of the Faradaic processes, measured using Electrochemical impedance spectroscopy (EIS) at various overpotentials, were determined utilizing DFRT, by separating and associating three electrochemical phenomena occurring during the reaction. The effective resistances are used to generate a Tafel plot of potential as a function of log1Reff. The classical method, based on linear sweep voltammetry (LSV), to evaluate the Tafel slope is associated with some considerations for accurate results. For RuO2, a reference catalyst, LSV illustrates an average Tafel slope of 182 ± 8 mV/dec while the effective resistance method, estimated using DFRT, shows an average of 181 ± 3 mV/dec. A relative error of 0.3 % between the two methodologies, and a lower standard deviation for DFRT demonstrate the higher precision and effectiveness of ISGP in determining the reaction kinetics via Tafel slope analysis. Therefore, using DFRT with the ability to separate Faradaic from non-Faradaic processes to evaluate the relevant part of the effective resistance, reaction kinetics can be estimated, avoiding shortcomings of the classical Tafel method.

IMPEDANCE SPECTROSCOPY GENETIC PROGRAMMING (ISGP) ANALYSES SETTING PROPER WORKING CONDITIONS OF A POLYMER ELECTROLYTE MEMBRANE FUEL CELL

&#x0D; &#x0D; &#x0D; This study demonstrates application of Impedance Spectroscopy Genetic Program (ISGP) for the investigation of a polymer electrolyte membrane fuel cell (PEMFC). It further demonstrates the procedures to optimize the operating conditions of a single cell in a test station. To do that, the effects of temperature, hydrogen/air, and dew point temperature (DPT) on the cell were examined using an Arbin test station. ISGP followed a two-iteration procedure. First, find an out-of-range peak (at high frequencies) that corresponds to the ohmic (series) resistance of the system. Second, finding the models after subtracting the ohmic resistance from the real part of the measured spectrum. This two- step procedure allows solving a Fredholm equation of the second kind with a reasonable accuracy. The resulting peaks making the distribution function of relaxation time (DFRT) were partially assigned to different physical processes in the PEMFCs. ISGP seeks for a distribution of relaxation times that has the form of a peak or a sum of several peaks, assuming the Debye kernel, where each peak is represented by a known analytic function. As a part of the analysis, the peak areas, which correspond to the contribution of the relevant process to the total impedance, were calculated obtaining tendentious behavior depending on the changing environmental parameters. ISGP of PEMFC results in three peaks. The optimized conditions were found to be the ratio of gas flow fuel to air rate 1:7, fuel cell temperature 60°C and dew point temperature 50°C.&#x0D; &#x0D; &#x0D;

(Keynote) On Interpretation of Impedance Spectroscopy Data

Impedance spectroscopy represents a rich area of science that has been applied to many research disciplines, including those associated with corrosion and corrosion control, energy systems, and biological systems. In laboratory settings, impedance has been used to study the kinetics and mechanisms of electrochemical reactions. Impedance spectroscopy has also been applied in industrial applications to quality control and corrosion monitoring and constitutes the basis of a class of sensors [1].Impedance spectra are easily measured by used of modern instrumentation. The difficulty lies in interpretation of impedance spectra in terms of physically meaningful information. While graphical methods [2], distribution of relaxation times analyses [3], and measurement model analyses [4] can guide model development, interpretation is generally based on use of a deterministic model that describes the physics of the system under study [5]. Such models may be coupled with electrical circuits that account for the double layer formed at the electrified interface and for the electrolyte resistance. The deterministic model approach is often perceived as being much more complicated than use of electrical circuits alone because it requires mathematical expertise.In general, interpretation of the impedance response requires both a quantitative evaluation of the error structure of the impedance measurement and insight into the physics and chemistry of the system under study. Analysis of the error structure yields a standard deviation for the stochastic errors, which can be used to weight subsequent regressions. The error analysis also identifies the range of frequencies that are consistent with the Kramers–Kronig relations and are, therefore, suitable for regression analysis. The physical insight is used to guide the interpretation model development. It should be noted that interpretation models are not unique. The models may suggest other experiments which can be used to reject the proposed model. Greater confidence may be assigned to a model that explains a variety of experimental observations.The objective of this paper is to review our work on interpretation of impedance data, including the identification and quantification of the error structure associated with impedance spectroscopy measurements. The presentation makes use of a program that allows users to access the power of the measurement model concept and to fit custom process models [6].References S. Wang, J. Zhang, O. Gharbi, V. Vivier, M. Gao, and M. E. Orazem, “Electrochemical Impedance Spectroscopy,” Nat. Rev. Methods Primers, 1, 41 (2021), 1-21.M. E. Orazem, and N. Pébère, and B. Tribollet, “Enhanced Graphical Representation of Electrochemical Impedance Data,” J. Electrochem.Soc., 153 (2006), B129-B136.B. A. Boukamp, “Distribution (Function) of Relaxation Times, Successor to Complex Nonlinear Least Squares Analysis of Electrochemical Impedance Spectroscopy?” J. Phys. Energy, 4 (2020), 042001.H. Liao, W. Watson, A. Dizon, B. Tribollet, V. Vivier, and M. E. Orazem, “Physical Properties Obtained from Measurement Model Analysis of Impedance Measurements,” Electrochim. Acta, 354 (2020), 136747.V. Vivier and M. E. Orazem, “Impedance Analysis of Electrochemical Systems,” Chem. Rev., 122 (2022), 11131-11168.W. Watson and M. E. Orazem, EIS: Measurement Model Program, ECSArXiv, 2020, https://ecsarxiv.org/kze9x/.

Comprehensive study of functional properties and electrochemical performance of layered lanthanum nickelate substituted with rare-earth elements

The present work is devoted to the comparative study of the absolute oxygen content, thermal expansion, electrical conductivity, and electrochemical performance of the La1.6Ln0.4NiO4+δ (Ln = La, Pr, Nd, Sm, Eu) complex oxides. The thermal expansion coefficients, obtained for the La1.6Ln0.4NiO4+δ compact samples, have approved thermomechanical compatibility of the materials with the Sm0.2Ce0.8O1.9 electrolyte. The highest conductivity value is found to be 107 S cm−1 at 420 °C for the La1.6Sm0.4NiO4+δ sample. The results of scanning electron microscopy, performed after the cycle of measurements on two-layer electrodes with the La1.6Ln0.4NiO4+δ functional layers and the LaNi0.6Fe0.4O3−δ (LNF) collector layers, have demonstrated the stability of the electrode structure under the measurement conditions and the maintenance of high average porosity for both layers. The minimum polarization resistance value, equal to 0.64 Ω cm2 at 700 °C, has been measured for the La1.6Eu0.4NiO4+δ electrode sintered at 1200 °C. Comprehensive distribution function of relaxation times (DFRT or DRT) analyses of the impedance data has been performed to establish the rate-limiting stages of the electrode reaction. Oxygen kinetic parameters calculated in the framework of the Adler-Lane-Steele (ALS) model with considering the microstructural parameters are shown to correlate well with those obtained from the isotope exchange data.

High-temperature impedance properties of Sr1-xCaxTiO3 ceramics for lead-free capacitor applications

ABSTRACT Lead-free Sr0.6Ca0.4TiO3 ceramic was prepared by solid-state reaction route. X-ray diffraction technique showed the phase purity and identified the orthorhombic perovskite structure. Scanning Electronic Microscopy observation evidenced homogeneous morphology and dense microstructure. Electrical conduction and dielectric relaxation mechanisms at high temperature have been studied by complex impedance measurement techniques over a wide range of frequencies and temperatures, from 100 Hz to 1 MHz and from 573 K to 783 K. Fitting of impedance measurements allowed us to study grains and grain boundaries electrical characteristics and their contribution to the conduction and dielectric relaxation processes in the ceramic. Electrical conduction in grains is due to oxygen vacancy jumps for temperatures below 733 K and to polarons above 763 K. Electrical DC conductivity in grains and grain boundaries is mainly due to oxygen vacancies. Impedance measurements and relaxation time distribution function calculations show non-Debye-type relaxation effects for both grains and grain boundaries.

Interpretation of the resistance of Li7La3Zr2O12 – Li2O–B2O3–SiO2 composite electrolytes for all–solid–state batteries using the distribution of relaxation times technique

Solid electrolytes based on Li7La3Zr2O12 are promising membranes for all–solid–state batteries. However, the main parameters of all transport stages in composite and doped Li7La3Zr2O12 could not be determined by conventional impedance fitting. A tremendous assistance in the analysis of impedance spectra over the past few years has become the method of distribution of relaxation times (DRT). In the present study, a composite electrolyte Li7La3Zr2O12 – Li2O–B2O3–SiO2 was investigated by impedance spectroscopy. A detailed analysis of the impedance spectra by DRT showed that the additional peak appears on the DRT function with the introduction of glass; this interfacial resistance is responsible for the transfer of lithium ions across the Li7La3Zr2O12/glass interface. The resistance, capacitance and relaxation frequency of all the transport stages in the composite electrolytes were determined based on the analysis of the DRT functions. It was found that the Li7La3Zr2O12/glass resistance decreases with increasing fraction of glassy additive. It was established that the DRT technique can be successfully used to deeper understanding of the transport stages of lithium ions in composite and doped solid electrolytes for all–solid–state batteries.

Analysis of Impedance Spectra of a Lithium Electrode by the Distribution of Relaxation Times

The possibility of analyzing the electrochemical impedance spectra of lithium–lithium cells using the Distribution of Relaxation Times (DRT) function is studied. A comparative analysis of the electrochemical impedance spectra of lithium–lithium cells obtained during long-term storage at a constant temperature and at different temperatures was performed using the method of either equivalent electrical circuits or the DRT function. The analysis of the impedance of lithium–lithium cells by the DRT function is shown to allow estimating the number of layers in the surface film on the lithium electrodes and evaluating their physical parameters—the resistance and capacitance. It has been established that with a long exposure of lithium–lithium cells at the temperature of 30°C, the number of layers in the surface film and its resistance decreased. With the increase in the temperature, the physical properties of the layers of the surface film are differentiated and its total resistance decreased. The analysis of the electrochemical impedance spectra of lithium–lithium cells by the DRT functions is more informative than the method of equivalent electrical circuits.

Electrochemical properties of double molybdate LiSm(MoO4)2 ceramics with ultra-low sintering temperature

A novel double molybdate LiSm(MoO4)2 composition was prepared through a conventional solid-state ceramic route for its potential application as a solid-state Li+-ion conductor for low-loss dielectric ceramics. Ceramic disks were prepared by uniaxial pressing and sintered at the low temperature of 620 °C. Phase formation was confirmed through powder X-ray diffraction (XRD), which was indexed to the tetragonal crystal system with a Scheelite-type structure. Laser Raman spectroscopy showed that the MoO42− tetrahedra in the LiSm(MoO4)2 material are more regular, suggesting high symmetry for the compound. Scanning Electron Microscopy (SEM) revealed the formation of polygonal grains with an average grain size of less than 1 μm. The electrochemical properties of the ceramic system were investigated by Electrochemical Impedance Spectroscopy (EIS) in O2, air, and Ar (250 °C – 500 °C). Data were systematically analyzed using an Equivalent Circuit Model (EQM) combined with a Distribution Function of Relaxation Times (DFRT) analysis. The results revealed the coexistence of both a delocalized (long-range conductivity) and a localized (dipole relaxation) phenomenon, mainly distinguishable at lower temperatures (i.e., for T ≤ 350 °C) and in a pure O2 atmosphere. This localized phenomenon was tentatively attributed to the presence of trapped hole-vacancy pairs with reduced mobility. Conversely, at higher temperatures in O2 (i.e., for T ≥ 350 °C) and in the whole temperature range in less oxidizing conditions (air and Ar), such a localized phenomenon was no longer observed, as a likely result of a decrease in hole concentration with decreasing oxygen partial pressure (pO2). The current work, thus, underscores a different perspective for the development and characterization of ceramic-based solid-state Li+-ion conductors for their application as low-loss dielectric ceramics.

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

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 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.

Detecting mechanical indentation from the time constants of Li-ion batteries

Lithium-ion batteries pose severe hazards if their safety is compromised. Previous work has shown that mechanical damage to the battery may not affect its voltage, capacity, or other primary specifications. Therefore, currently, there is no method to check the integrity of battery cells inside an electric vehicle battery pack once it has been subjected to a shock or impact. Here, we report a method to detect mechanical damage to Li-ion cells from their electrical response. We formulate the distribution function of relaxation times (DRT) by a series of passive electrical elements consisting of inductors, resistors, and capacitors. Using our DRT formulation and criteria, we show that the indented cells have substantially different high-frequency time constant characteristics than the control group. This non-invasive method has the potential for detecting hazardous mechanical damage to the batteries of electric vehicles after a road crash or impact landings of drones.

Polarization resistance of the Ruddlesden-Popper nickelates Lan+1NinO3n+1 (n = 1, 2, 3): Comparative analysis using the distribution of relaxation times method

The Ruddlesden-Popper layered nickelates La2NiO4+δ (n = 1, LN21), La3Ni2O7-δ (n = 2, LN32) and La4Ni3O10-δ (n = 3, LN43) were studied as electrodes in symmetrical cells based on Ce0.8Sm0.2O2-δ (SDC) at various temperatures (600 ≤ T ≤ 800 °C) and oxygen partial pressures (−3 ≤ log(P(O2)/P0) ≤ −0.67). Electrochemical Impedance Spectroscopy (EIS) of the selected Lan+1NinO3n+1/SDC cells with similar microstructure reveals that the polarization resistance of the electrodes gradually increases with increasing n, namely by ≈0.75 Ω cm2 at 800 °C in air. The Distribution Function of Relaxation Times (DFRT) analysis of the obtained data shows that the polarization resistance of Lan+1NinO3n+1 includes four distinguishable contributions RHF (1), RHF (2), RMF and RLF. The Ri resistances at fixed temperatures and P(O2) were determined by fitting the obtained impedance spectra using the equivalent circuit consisting of electrolyte resistance and a series of R-CPE elements. Based on the analysis of the Ri = f(T, P(O2)) dependences, the RHF (1), RHF (2) resistances are assigned to the charge transfer through the interfaces and RMF, RLF are interpreted as “chemical” part of the impedance, i.e. ionic transport in the electrode and oxygen dissociation at the electrode surface, respectively. Comparison of the obtained resistances shows that RMF dominates the polarization resistance meaning that ionic transport in the electrodes is the slowest stage of the electrochemical reaction at the studied temperatures in air. The increase in the number of perovskite layers deteriorates ionic diffusion and promotes oxygen dissociation. As RMF > RLF, this leads to an increase in the overall polarization resistance from 0.75 Ω cm2 for LN21 to 2.25 Ω cm2 for LN43 at 800 °C in air.

Distribution functions of magnetic moments and relaxation times for magnetic fluids exhibiting controllable microstructure evolution

The paper presents experimental and numerical studies of laboratory magnetic fluid samples that differ significantly from each other by dispersion compositions (particle size distributions). We propose and justify a new technique for describing the magneto-granulometric properties of magnetic fluids. Our approach is based on the analysis of distribution functions of magnetic moments and their relaxation times. It can be used to determine the magnetic response of any magnetic fluid with arbitrary particle size distribution f(x) and arbitrary microstructure, including magnetic fluids undergoing phase transition. No intermediary representation of the f(x) function is needed. It is shown that a priori standard distribution functions f(x) cannot describe the ferrofluid microstructure features, specifically those related to the formation of nanoparticle aggregates. The distributions of magnetic moments and their relaxation times were obtained by means of a regularized numerical inversion of experimental static magnetization and dynamic susceptibility curves. These distributions contain full information about the microstructure of ferrofluids. Analysis of the distribution curves showed the temperature-dependent evolution of the ferrofluid microstructure in the zero applied magnetic field: particle aggregates form or disintegrate and magnetic moment relaxation mechanism changes depending on the temperature.