Electrochemical Impedance Spectroscopy Simulation Research Articles

Uncovering accurate values of the polarization resistance in molten fluorides using electrochemical impedance spectroscopy

High-temperature operation and the presence of oxidizing impurities in molten chloride and fluoride salts pose significant corrosion risks to structural alloys in molten salt nuclear reactors. Electrochemical impedance spectroscopy (EIS) offers an operando, real-time method to study the instantaneous corrosion behavior of these materials non-destructively. However, signal noises may originate from sources extraneous to the electrochemical systems that limit the ability to perform quality impedance measurements in low-frequency regime where polarization resistance (Rp) dominates. Using the exposure of pure Cr in molten LiF-NaF-KF containing 1 wt% EuF3 at 600 °C as a model corrosion system, the extent of Non-Uniform Current and Potential (NUCP) distribution during an AC perturbation associate with the disk electrodes is evaluated in terms of two dimensionless correction factors kfRct(=Rct/Reff) and kfCdl(=Cdl/Ceff). Results show that a small area Cr disk electrode increases the transition frequency that marks the dominance of Rp to a conventional terminational frequency above 10−2 Hz, enabling a reliable charge-transfer resistance (Rct) value to be determined via circle fitting of an electrical equivalent circuit model (ECM) model. Experimental results were supported by EIS simulations considering commonly used ECM models that factor in the NUCP effect of disk geometries.

Estimating Parameters of Physics-Based Battery Models – What Machine Learning Can and Cannot Do

With the widespread use of Lithium-ion (Li-ion) batteries in multiple industries, the design space for the electrochemical cells has increased drastically. Li-ion batteries’ design parameters and material properties, such as porosity, electrode thickness, active material loading, and solid phase diffusivities, typically vary substantially due to different design goals and variation in the manufacturing process. Due to the difficulty in obtaining these and other battery cell parameters, many battery management systems used to control and monitor Li-ion batteries opt for the simplified resistor-capacitor circuit-based battery cell representation over using physics-based battery models. However, if these parameters become obtainable, scientists could implement advanced battery management systems using physics-based battery models to capture precisely how the battery performs and degrades in a wide variety of applications. Multiple methods, such as genetic algorithms, statistics, and machine learning, have been attempted for the parametrization and characterization of battery cells to enable accurate battery simulations using physics-based models [1, 2]. However, there are inherent limitations to the type and number of parameters that can be estimated using these methods if only the standard battery cell cycling data is utilized for this purpose. The present work elucidates and quantifies these limitations specifically in the case of machine learning based approach and provides deeper insights into these limitations that may help develop more robust cell characterization protocols. In the present work, model parameters are varied in a continuum-level physics-based model and simulations are performed for: (1) constant current-constant voltage (CC-CV) charging and constant current discharge at different C-rates, and (2) electrochemical impedance spectroscopy (EIS) in the relevant frequency range at multiple states of charge (SOCs). The Single Particle Model (SPM) is used for performing these simulations due to its relative simplicity and small number of parameters. At first, the charge and discharge data are input as training data in a long short-term memory neural network (LSTM NN), and EIS data is input as training data in a convolutional neural network (CNN). Once trained, the machine learning (ML) model uses charge, discharge, and EIS data withheld from the original training data set to predict SPM parameters. The estimated parameters are compared with the true parameters used for SPM charge, discharge, and EIS simulations, and the error in parameter estimation is quantified. A rigorous grid convergence analysis is performed to highlight the importance of ensuring that the spatial discretization error of the model does not influence the parameter estimation accuracy. For the first error quantification, all parameters are varied concurrently to obtain the parameter estimation error that arises from a large, undetermined parameter set. Parameters are then analyzed individually and in clusters related to diffusion, kinetics, and stoichiometric limitations. Further analysis is performed on parameters that could not be estimated with sufficient accuracy, including theoretical explanations for the incurred error and the effect of this error on the internal state predictions.

Enhanced rate capability in lithium-sulfur batteries using hybrid carbon nanotubes and NZFO-coated separator

Developing lithium-sulfur batteries (LiSBs) performance is vital for sustainable development. This study presents an innovative approach to enhance LiSBs performance by fabricating a sulfur composite cathode using hybrid-carbon nanotubes (CNTs) denoted as M/S-CNT and a nickel-zinc ferrite (NZFO)-coated separator. The batteries with modified separators (M/S-CNT-NZFO) exhibited remarkable achievements, showcasing significantly enhanced high-rate capabilities [∼527 mAh/g at 3350 mA/g (2C)] and a substantial reduction in polarization. Cyclic voltammetry analysis revealed a diffusion-controlled dominated charge storage mechanism, and the modified separator effectively improved lithium-ion transportation, leading to a notable decrease in charge transfer resistance observed in the simulation of electrochemical impedance spectroscopy (EIS) spectra. This work highlights the impressive high-rate capability and reduced polarization achieved in the M/S-CNT-NZFO cells. Recognizing that high-rate capability is crucial for fast-charging devices, this approach stands out as a compelling strategy to establish the electrochemical stability of LiSBs in applications demanding rapid charging.

Physics-based simulation of electrochemical impedance spectroscopy of complex electrode microstructures using smoothed boundary method

Electrochemical impedance spectroscopy (EIS) is a widely used technique to measure macroscopic properties of electrodes. However, the underlying connections between the obtained macroscopic properties and electrode microstructures are not well understood because of the complexity of coupled electrochemical mechanisms and microstructure morphologies. In this work, we present a smoothed-boundary-method (SBM) electrochemical simulation framework that allows us to directly simulate the electrochemical dynamics with parameterized material properties and explicit consideration of electrode microstructures, and to extract EIS curves from the electrochemical simulations. This method uses continuous domain parameters to define the complex geometries of electrode particles and electrolyte phase in the interparticle space, thus circumventing the requirement of computational mesh conforming to the complex electrode microstructures in the simulations. The SBM is also utilized to calculate the double-layer capacitance that is required in the physics-based EIS simulations. The effects of the state of charge, salt concentration in electrolyte, and particle size distribution in electrode on the resulting EIS curves are examined using the SBM simulations. This simulation tool allows us to reveal the underlying connections between intrinsic material properties, microstructures, and macroscopic EIS behavior of battery electrodes.

Characteristics of Methyl Cellulose Based Solid Polymer Electrolyte Inserted with Potassium Thiocyanate as K+ Cation Provider: Structural and Electrical Studies

The attention to a stable and ionic conductive electrolyte is driven by the limitations of liquid electrolytes, particularly evaporation and leakage, which restrain their widespread use for electrochemical device applications. Solid polymer electrolyte (SPE) is considered to be a potential alternative since it possesses high safety compared to its counterparts. However, it still suffers from low device efficiency due to an incomplete understanding of the mechanism of ion transport parameters. Here, we present a simple in situ solution casting method for the production of polymer-based electrolytes using abundantly available methylcellulose (MC) doped at different weight percentages of potassium thiocyanate (KSCN) salt. Fourier transform infrared (FTIR), and electrochemical impedance spectroscopy (EIS) methods were used to characterize the prepared samples. Based on EIS simulation and FTIR deconvolution associated with the SCN anion peak, various ion transport parameters were determined. The host MC medium and KSCN salt have a strong interaction, which was evident from both peak shifting and intensity alteration of FTIR spectra. From the EIS modeling, desired electric circuits correlated with ion movement and chain polarization were drawn. The highest ionic conductivity of 1.54 × 10−7 S cm−1 is determined from the fitted EIS curve for the film doped with 30 wt.% of KSCN salt. From the FTIR deconvoluted peak, free ions, ions in contact with one another, and ion aggregates were separated. The extracted ion transport parameters from the EIS method and FTIR spectra of the SCN anion band confirm that both increased carrier concentration and their mobility were crucial in improving the overall conductivity of the electrolyte. The dielectric investigations were further used to understand the conductivity of the films. High dielectric constants were observed at low frequencies for all MC:KSCN systems. The dispersion with a high dielectric constant in the low-frequency band is ascribed to the dielectric polarization. The wide shift of M″ peak towards the high frequency was evidenced by the MC-based electrolyte impregnated with 30 wt.% of KSCN salt, revealing the improved ionic movement assisted with chain segmental motion. The AC conductivity pattern was influenced by salt concentration.

Enrichment-Free Rapid Detection of Phthalates in Chinese Liquor with Electrochemical Impedance Spectroscopy

A non-invasive real-time detection technique for phthalates in Chinese liquor is proposed in this paper. This method is based on the measurement of Faradaic impedance in the presence of a redox probe, [Fe(CN)6]3−/4−, upon the absorption of phthalates to the graphene electrode surface. This absorption activity is according to the π–π stacking interactions between phthalates and the graphene working electrode which allows direct sampling and analyte preconcentration. The absorption of phthalates retards the interfacial electron-transfer kinetics and increases the charge-transfer resistance (Rct). Numerical values of Rct were extracted from a simulation of electrochemical impedance spectroscopy (EIS) spectra with the corresponding equivalent circuit. Cathodic polarization was employed prior to EIS measurements to effectively eliminate the metal ion interference. The results yielded a detection limit of 0.024 ng/L for diethyl phthalate (DEP) with a linear range from 2.22 ng to 1.11 µg. These results indicate a possibility of developing a household sensor for phthalate determination in Chinese liquor.

Operando EQCM-D with Simultaneous in Situ EIS: New Insights into Interphase Formation in Li Ion Batteries.

An operando electrochemical quartz crystal microbalance with dissipation monitoring (EQCM-D) with simultaneous in situ electrochemical impedance spectroscopy (EIS) has been developed and applied to study the solid electrolyte interphase (SEI) formation on copper current collectors in Li ion batteries. The findings are backed by EIS simulations and complementary analytical techniques, such as online electrochemical mass spectrometry (OEMS) and X-ray photoelectron spectroscopy (XPS). The evolution of mass and the mechanical properties of the SEI are directly correlated to the electrode impedance. Electrolyte reduction at the anode carbon active material initiates dissolution, diffusion, and deposition of reaction side products throughout the cell and increases electrolyte viscosity and the ohmic cell resistance as a result. On Cu the reduction of CuO x and HF occurs at >1.5 V and forms an initial LiF-rich interphase while electrolyte solvent reduction at <0.8 V vs Li+/Li adds a second, less rigid layer on top. Both the shear storage modulus and viscosity of the SEI generally increase upon cycling but-along with the SEI Li+ diffusion coefficient-also respond reversibly to electrode potential, likely as a result of Li+/EC interfacial concentration changes. Combined EIS-EQCM-D provides unique prospects for further studies of the highly dynamic structure-function relationships of electrode interphases in Li ion batteries.

Electrochemical impedance spectroscopy study of membrane fouling characterization at a conductive sub-stoichiometric TiO2 reactive electrochemical membrane: Transmission line model development

This work presents a non-invasive and non-destructive electrochemical impedance spectroscopy (EIS) method for studying membrane fouling at a sub-stoichiometric TiO2 reactive electrochemical membrane (REM). An asymmetric, ceramic, ultrafiltration REM is studied through EIS simulations, that are based on a mathematical transmission line model (TLM). The TLM is developed to interpret EIS data and is shown to be sensitive to fouling at multiple interfaces of the REM (outer surface, active and support layers). Mathematical interpretation of penetration depth of the alternating voltage signal allows a determination of the characteristic frequencies associated with different layers of the membrane. The simulation results of membrane fouling mechanisms, such as monolayer adsorption and pore constriction at either active or support layer, and intermediate pore blockage at the outer surface produce distinguishable EIS spectra. Simulation results suggest that interpreting EIS spectra by the TLM is a useful technique for spatially characterizing membrane fouling and determining prevalent fouling mechanisms at a conductive membrane surface.

Two-dimensional modeling of a polymer electrolyte membrane fuel cell with long flow channel. Part II. Physics-based electrochemical impedance analysis

The state-of-the-art electrochemical impedance spectroscopy (EIS) calculations have not yet started from fully multi-dimensional modeling. For a polymer electrolyte membrane fuel cell (PEMFC) with long flow channel, the impedance plot shows a multi-arc characteristic and some impedance arcs could merge. By using a step excitation/Fourier transform algorithm, an EIS simulation is implemented for the first time based on the full 2D PEMFC model presented in the first part of this work. All the dominant transient behaviors are able to be captured. A novel methodology called ‘configuration of system dynamics’, which is suitable for any electrochemical system, is then developed to resolve the physical meaning of the impedance spectra. In addition to the high-frequency arc due to charge transfer, the Nyquist plots contain additional medium/low-frequency arcs due to mass transfer in the diffusion layers and along the channel, as well as a low-frequency arc resulting from water transport in the membrane. In some case, the impedance spectra appear partly inductive due to water transport, which demonstrates the complexity of the water management of PEMFCs and the necessity of physics-based calculations.

Reply to comments on “Intrinsic limitations of impedance measurements in determining electric double layer capacitances” by H. Wang, L. Pilon [Electrochimica Acta 63 (2012) 55

In the commentary to our paper [Electrochimica Acta 63 (2012) 55], Roling and Drüschler raised a very important issue regarding the measurements and comparison of the differential and integral capacitances retrieved using electrochemical impedance spectroscopy (EIS). They clearly explained that EIS measures differential capacitance rather than integral capacitance. The present letter aims to correct our previous study. It also clarifies the fact that cyclic voltammetry (CV) and galvanostatic methods can measure both differential and integral capacitances. Similar confusion exists in the literature on electrical energy storage devices and may explain discrepancies reported when measuring the capacitances of supercapacitors using EIS, CV, or galvanostatic methods. Finally, our original paper, for the first time, solved a modified Poisson–Nernst–Planck model with a Stern layer for simulating EIS. It also presented an interpretation of “capacitance dispersion” and a scaling analysis of electric double layers in EIS simulations. The model, scaling analysis, and the associated results were not affected by the confusion pointed out by Roling and Drüschler.

Electrochemical Impedance Spectroscopy (EIS) Applied to Study to Aluminum Alloys Degradation in Saline Solution

The electrochemical impedance spectroscopy (EIS) has been used to evaluate the behavior of alloys immersed in marine environment. This work presents the versatility of EIS technique to identify the formation of corrosion products and the different electrode processes than can be carried out on the interface metal-electrolyte when the aluminium alloys are in contact with a saline media (NaCl 0.5 M). After the time exposition, the samples were analyzed by X-Ray Diffraction (XRD), Scanning Electronic Microscopy (SEM) and EIS simulation with equivalent circuits (EEC) to propose a corrosion mechanism, and the results of these observations was the possible formation of an oxide film and a diffusion process across this film. The equivalent circuit selected from the simulation of experimental results takes in consideration a process with activation and mass transport control.

Electrochemical impedance spectroscopy (EIS) modelling of different behaviours of Ni and Ni oxide thin films for corrosion prevention in sour media

PurposeThe purpose of this paper is a theoretical modeling use of electrochemical impedance spectroscopy (EIS) technique for different cases that could describe the possible electrochemical behaviour on steel coated with metallic and oxide thin films (of nickel) deposited by magnetron sputtering, and compare them to know if the theoretical analysis resembles the real case. It is extremely important to clarify that such simulations do not consider the use of the constant phase element (CPE) for the analysis. Therefore, the goal for the theoretical models should be to gain acceptance in electrochemical research.Design/methodology/approachIn order to obtain the equivalent circuits to explain the different possible behaviours of the films and their protective properties in sour media, EIS experimental data were correlated with data from the simulation software. The different nickel and nickel oxide thin films were tested after their deposition by magnetron sputtering on low‐carbon steel and after they had then been exposed to the sour media electrolyte of NaCl 3 wt% + H2S (saturated).FindingsThe EIS simulation starts from the laboratory evaluation of nickel and nickel oxide thin films as anticorrosive protection for low‐carbon steel exposed to sour media. From these results, it is found that the nickel and nickel oxide films could adopt seven different behaviours, and all are possible to occur.Practical implicationsThe equivalent circuits proposed will give an insight into the corrosion phenomena for different metals coated with thin films and exposed to sour media, because all of the simulations are made on the basis of real EIS results.Originality/valueThe electrical analysis in the simulation diagram did not consider the use of the CPE to adjust the plots. In consequence, the values of all parameters for the seven different adjustments obtained through the simulations establish a reference for the explanation of the corrosion phenomena. They are also a tool with which to predict the possible behaviour of a thin film deposited on metal and exposed to electrolytes that are as aggressive as sour media.

Analysis of specification of an electrode type sensor equivalent circuit on the base of impedance spectroscopy simulation

Simulation of electrochemical impedance spectroscopy (EIS) based on a LabVIEW model of a complex impedance measuring system in the frequency domain has been investigated to specify parameters of Randle's equivalent circuit, which is ordinarily used for electrode sensors. The model was based on a standard system for EIS instrumentation and consisted of a sensor modelled by Randle's equivalent circuit, a source of harmonic frequency sweep voltage applied to the sensor and a transimpedance amplifier, which transformed the sensor current to voltage. It provided impedance spectroscopy data for different levels of noise, modelled by current and voltage equivalent noise sources applied to the amplifier input. The noise influence on Randle's equivalent circuit specification was analysed by considering the behaviour of the approximation error. Different metrics including absolute, relative, semilogarithmic and logarithmic based distance between complex numbers on a complex plane were considered and compared to one another for evaluating this error. It was shown that the relative and logarithmic based metrics provide more reliable results for the determination of circuit parameters.