Using electrochemical impedance spectroscopy in a broad range of applications This book provides the background and training suitable for application of impedance spectroscopy to varied applications, such as corrosion, biomedical devices, semiconductors and solid-state devices, sensors, batteries, fuel cells, electrochemical capacitors, dielectric measurements, coatings, electrochromic materials, analytical chemistry, and imaging. The emphasis is on generally applicable fundamentals rather than on detailed treatment of applications. With numerous illustrative examples showing how these principles are applied to common impedance problems, Electrochemical Impedance Spectroscopy is ideal either for course study or for independent self-study, covering: Essential background, including complex variables, differential equations, statistics, electrical circuits, electrochemistry, and instrumentation Experimental techniques, including methods used to measure impedance and other transfer functions Process models, demonstrating how deterministic models of impedance response can be developed from physical and kinetic descriptions Interpretation strategies, describing methods of interpretating of impedance data, ranging from graphical methods to complex nonlinear regression Error structure, providing a conceptual understanding of stochastic, bias, and fitting errors in frequency-domain measurements An overview that provides a philosophy for electrochemical impedance spectroscopy that integrates experimental observation, model development, and error analysis This is an excellent textbook for graduate students in electrochemistry, materials science, and chemical engineering. It's also a great self-study guide and reference for scientists and engineers who work with electrochemistry, corrosion, and electrochemical technology, including those in the biomedical field, and for users and vendors of impedance-measuring instrumentation.

In this paper, a Nonlinear Electrochemical Impedance Spectroscopy (NLEIS) method is presented that allows capturing the nonlinearity of current and overpotential of a lithium-ion battery individually in charge and discharge direction. A DC bias is applied to the battery to shift its operating point to the nonlinear region of current and overpotential. An alternating current of a low amplitude (AC) is simultaneously superimposed in order to investigate the system additionally in the time domain. NLEIS cell spectra and selected electrode-resolved NLEIS spectra are recorded as a function of state of charge and temperature. Furthermore, Distribution of Relaxation Times (DRT) plots obtained from EIS measurements provide information, which electrochemical processes correlate with the occurrence of nonlinear distortions of current and overpotential. Moreover, the occurrence of overpotentials and their degree of nonlinearity at cathode and anode as a function of the state of charge are determined by current pulse measurements.

Diagnosing battery states such as health, state-of-charge, or temperature is crucial for ensuring the safety and reliability of electrochemical energy storage systems. While some states, such as temperature, may be measured using cheap sensors, accurate diagnosis of battery health metrics usually requires time-consuming performance measurements, making them infeasible for use in real-world operation. These health metrics can be measured during lab-testing and then estimated on-line using predictive life models or via state observer algorithms such as Kalman filters, but these predictive methods should be supplemented by actual measurement of battery health whenever possible to ensure reliability. Rapid measurement of battery health may be done by various types of fast diagnostic techniques such as electrochemical impedance spectroscopy (EIS), which can be performed in only a few minutes and require only a fraction of the energy and power needed for a full charge and discharge measurement. But there is a substantial challenge for estimating battery health using EIS data, as EIS is sensitive to cell temperature, state-of-charge, current, and resting time in addition to health. Thus, utilizing EIS data to predict battery capacity requires correcting for all these additional variables, a task that is extremely difficult to handle analytically. This talk utilizes machine-learning methods to estimate the effectiveness of battery capacity prediction from EIS data, leveraging a data set of hundreds of EIS measurements recorded at varying temperature and state-of-charge throughout a 500-day aging study of 32 commercial, large-format NMC-Graphite lithium-ion batteries. Using EIS as input to machine-learning models is complicated by the nonlinear response of impedance to battery health, temperature, and state-of-charge, as well as the collinearity between the impedance response at neighboring frequencies, which can easily lead to overfit models. To train robust models, features from EIS data need to be extracted from the data or some subset of critical frequencies selected. Many approaches for extracting and selecting features from EIS data from electrochemical analysis and machine-learning fields were identified for analysis: using the entire raw spectra; selection of one, two, or many frequencies from the entire spectra; selecting interesting points from the EIS measurement using domain knowledge; fitting EIS with an equivalent-circuit model; calculating statistics on the raw impedance values; and reducing the dimensionality of the data using unsupervised linear (principal component analysis) and non-linear (uniform manifold approximation and projection) methods. These approaches were rigorously compared using a machine-learning pipeline approach, training linear, Gaussian process, and random forest regression models and quantifying performance using cross-validation as well as a held-out test set. An artificial neural network model trained on the raw spectra was also tested. Promising pipelines were fine-tuned via Bayesian hyperparameter optimization using cross-validation loss and training with class-specific weights to counter data set imbalance. The most reliable method for utilizing impedance in this work was the selection of two optimal frequencies through an exhaustive search, resulting in about 2% mean absolute error on test data for both Gaussian process and random forest model architectures. Interrogation of a variety of models reveals critical frequencies of 100 Hz and 103 Hz for this data set, though the optimal set of frequencies is not necessarily intuitive, i.e., the best performing models are not simply those that use impedance at frequencies that have the highest correlation to the relative discharge capacity. The best performing model is an ensemble model, which is able to predict battery capacity with 1.9% mean absolute error for unseen cells using impedance recorded at a variety of temperatures and states-of-charge.

This book presents a complete overview of the powerful but often misused technique of Electrochemical Impedance Spectroscopy (EIS). The book presents a systematic and complete overview of EIS. The book carefully describes EIS and its application in studies of electrocatalytic reactions and other electrochemical processes of practical interest. This book is directed towards graduate students and researchers in Electrochemistry. Concepts are illustrated through detailed graphics and numerous examples. The book also includes practice problems. Additional materials and solutions are available online.

This book presents a balance of theoretical considerations and practical problem solving of electrochemical impedance spectroscopy. This book incorporates the results of the last two decades of research on the theories and applications of impedance spectroscopy, including more detailed reviews of the impedance methods applications in industrial colloids, biomedical sensors and devices, and supercapacitive polymeric films. The book covers all of the topics needed to help readers quickly grasp how to apply their knowledge of impedance spectroscopy methods to their own research problems. It also helps the reader identify whether impedance spectroscopy may be an appropriate method for their particular research problem. This includes understanding how to correctly make impedance measurements, interpret the results, compare results with expected previously published results form similar chemical systems, and use correct mathematical formulas to verify the accuracy of the data. Unique features of the book include theoretical considerations for dealing with modeling, equivalent circuits, and equations in the complex domain, review of impedance instrumentation, best measurement methods for particular systems and alerts to potential sources of errors, equations and circuit diagrams for the most widely used impedance models and applications, figures depicting impedance spectra of typical materials and devices, extensive references to the scientific literature for more information on particular topics and current research, and a review of related techniques and impedance spectroscopy modifications.

Whole-cell diagnostic methods and analysis tools are critical for characterizing lithium-ion batteries as we aim to increase the performance and lifetime of these devices while also minimizing safety concerns and cost. Diagnostics of whole-cells can be significantly more complicated than their half-cell counterparts because of the lack of a reference electrode, and complex way two active electrodes interact with each other to yield a whole-cell response. The complexity of whole-cell electrochemical methods adds a further burden to the quality and reproducibility of the experimental data used to validate the performance of whole-cell analysis tools. We create a dataset used in all subsequent analysis that is well replicated and is used to showcase the statistical attributes of a testing regime carried out using Samsung INR 18650-15M cells with NMC | Graphite chemistry aged to different states-of-health (SoH) at different charging rates and temperatures. The dataset includes measurements of open-circuit voltage (OCV) from low C-rate scanning along with differential analysis of OCV and capacity, electrochemical impedance (EIS) and nonlinear electrochemical impedance (NLEIS) measurements. Quadruplicate measurements were taken for nearly all conditions. Using data from our well-characterized cells, we adapt the half-cell Multi-Species, Multi-Reaction (MSMR) model into a whole-cell diagnostic tool via inclusion of whole-cell design parameters and cell charge balance constraints. The whole-cell model is first compared to experiments using literature reference values for the MSMR thermodynamic parameters. To improve fit quality, the MSMR thermodynamic parameters and electrode capacities are simultaneously fit to the OCV and differential voltage data, producing low error, high quality fits to experiments. Bootstrap analysis is performed to show the robustness of the fitting software to experimental noise and data sampling. The MSMR results quantify which insertion reactions are most responsible for capacity loss in each electrode, while also showing how slippage in the lithiation window, changes in useable capacity, and other properties evolve as the cell ages. Finally, in this work, we provided an experimental framework for nonlinear electrochemical impedance spectroscopy (NLEIS). Increasing the input AC signal from the classic small-amplitude linear limit to a moderate amplitude that produces a second harmonic in the output signal (but no other harmonics), then the first-harmonic signal remains a valid representation of the linear response, while the second harmonic signal introduces new physics to the analysis. We show how the second harmonic NLEIS spectra build from, but complements, the Warburg and interfacial charge transfer response of the cell, providing unique insights into the evolution of charge transfer symmetry at low SOC as the cathode ages during cycling. These results launched two additional studies, where we collected the linear and nonlinear impedance response over much tighter SoC ranges to try and explore the emergence of these second harmonic charge-transfer kinetics and higher-order thermodynamic properties. We use traditional equivalent circuit elements to analyze the linear EIS, and then derive nonlinear equivalent circuit elements to model the NLEIS. Here, we also show that with inclusion of thermodynamic information achieved through the MSMR model, these new nonlinear circuit elements can capture the behavior we see in the charge-transfer asymmetry as well as the direction and quadrant that these nonlinear low-frequency may extend into. Finally, we also employ a full-physics pseudo-2-dimensional model, to show the general validity of the results we see from using the simpler, empirical equivalent circuit models.