The Distribution of Relaxation Times (DRT) analysis gained considerable attention for its ability to reveal detailed information about complex electrochemical processes without requiring a priori knowledge. This review provides a comprehensive insight into different methods of the DRT analysis, their mathematical bases, and the latest approaches to acquiring and analyzing frequency and time domain data. The analysis is based on the deconvolution of frequency domain data into a distribution function of gains at (pre-specified) relaxation times in the time domain, which improves the spectral resolution and separability of electrochemical processes. It provides valuable information about different electrochemical processes on different time scales, making it particularly useful for the characterization of both materials and electrochemical systems. The DRT analysis can be applied to arbitrary spectra containing electromagnetic effects, resistive–capacitive processes, and solid-state diffusion. To enhance process identification, a post-processing step involving peak analysis with Gaussian or RQ-distribution peaks is presented and the assignment of peak patterns induced by distributed processes like solid-state diffusion is discussed. In addition, a step-by-step workflow for the DRT analysis is provided to guide researchers from data acquisition and validation techniques to calculation and interpretation of the distribution function.

The open circuit voltage hysteresis of lithium-ion batteries is a phenomenon that, despite intensive research, is still not fully understood. However, it must be taken into account for accurate state-of-charge estimation in battery management systems. Mechanistic models of the open circuit voltage hysteresis previously published are not suitable for deployment in a battery management system. Phenomenological models on the other hand can only superficially represent the processes taking place. To address this limitation, we propose a probability distributed equivalent circuit model motivated by the physical insights into hysteresis. The model incorporates hysteresis effects that are often disregarded for state estimation, while keeping the computational cost low. Although the parameterization is more demanding, the model has the advantage of providing insight into the internal state of the battery and intrinsically incorporating the effect of path-dependent rate capability.

For the identification of processes in lithium-ion batteries (LIB) by electrochemical impedance spectroscopy, frequency data is often transferred into the time domain using the method of distribution of relaxation times (DRT). As this requires regularization due to the ill-conditioned optimization problem, the investigation of data-driven methods becomes of interest. One promising approach is the Loewner method (LM), which has already had a number of applications in different fields of science but has not been applied to batteries yet. In this work, it is first deployed on synthetic data with predefined time constants and gains. The results are analyzed concerning the choice of model order, the type of processes , i.e., distributed and discrete, and the signal-to-noise ratio. Afterwards, the LM is used to identify and analyze the processes of a cylindrical LIB. To verify the results of this assessment a comparison is made with the generalized DRT at two different states of health of the LIB. It is shown that both methods lead to the same qualitative results. For the assignment of processes as well as for the interpretation of minor gains, the LM shows advantageous behavior, whereas the generalized DRT shows better results for the determination of lumped elements and resistive–inductive processes.

To ensure the safety and performance of lithium-ion batteries (LIBs), a rational design and optimization of suitable cathode materials are crucial. Lithium nickel cobalt manganese oxides (NCM) represent one of the most popular cathode materials for commercial LIBs. However, they are limited by several critical issues, such as transition metal dissolution, formation of an unstable cathode-electrolyte interphase (CEI) layer, chemical instability upon air exposure, and mechanical instability. In this work, coating fabricated by self-assembly of osmotically delaminated sodium fluorohectorite (Hec) nanosheets onto NCM (Hec-NCM) in a simple and technically benign aqueous wet-coating process is reported first. Complete wrapping of NCM by high aspect ratio (>10 000) nanosheets is enabled through an electrostatic attraction between Hec nanosheets and NCM as well as by the superior mechanical flexibility of Hec nanosheets. The coating significantly suppresses mechanical degradation while forming a multi-functional CEI layer. Consequently, Hec-NCM delivers outstanding capacity retention for 300 cycles. Furthermore, due to the exceptional gas barrier properties of the few-layer Hec-coating, the electrochemical performance of Hec-NCM is maintained even after 6 months of exposure to the ambient atmosphere. These findings suggest a new direction of significantly improving the long-term stability and activity of cathode materials by creating an artificial CEI layer.

Lithium deposition (LD) is a parasitic, detrimental side reaction during the charging of lithium-ion batteries with graphite anodes. The kinetic limitations of the intercalation of lithium ions into the host lattice lead to overpotentials, making the metallic deposition thermodynamically favourable. These limitations are especially crucial at low temperatures, high states of charge, and high currents. Hence, lithium deposition becomes the major mechanism for accelerated ageing during fast charging. In our work, the effects of LD on the cell's voltage and thickness are analysed in detail. We show that the dilation behaviour of pouch cells during the charge subsequent relaxation phase can be used to detect LD. A yet undescribed feature in the differential dilation even provides information about the severity of the LD. These findings are verified with the established method of differential voltage analysis during relaxation. Additionally, we propose a Bayes algorithm for the combined use of voltage and dilation data to detect LD even for dilation measurements with strong noise and limited resolution.

Model-based fast charging control of Li-ion batteries requires real-time capable models with a spatial resolution to effectively prevent metallic lithium deposition. In a recent publication we showed that a discrete electrochemical modeling approach in form of a transmission line model is able to precisely describe the dynamic behavior of electrodes in time domain. The model is able to simulate and detect local lithium deposition and fulfills the requirement of real-time capability. On this basis, we study the feasibility of nonlinear model predictive control for fast charging of a graphite electrode. For this purpose, two different approaches for the cost function are introduced. The first approach controls the anode surface potential to a target value close to 0 V vs. Li/Li+, to charge at the maximum rate and thus preventing Li deposition. The cost function can be rewritten explicitly to achieve a minimum computation time. The second approach weighs the charge current, which should be maximized, against the deposition current, which should be minimized. A trade-off between charging time and lithium deposition can be achieved allowing for varied priorities while finding the optimum charging trajectory for the targeted purpose.

During fast charging of lithium-ion batteries with graphite electrodes, kinetic limitations of the desired intercalation process force the Li ions to deposit metallically on the electrode's surface. The degradation process of lithium deposition (LD) leads to rapid capacity fade and may lead to safety-critical conditions. Hence, a reliable and sensitive method for the operando detection of LD is needed that allows to adjust the charging current and to preserve the lifetime of the battery. Differential voltage analysis is a state-of-the-art electrochemical characterisation technique that enables the retrospective detection of LD during relaxation and discharge. However, in its current use it reveals weaknesses in terms of reliability and sensitivity. Our novel, model-based approach distinguishes normal, i.e., after intercalation only, and LD-affected relaxation. Hence, the charging process can be classified as critical or non-critical in terms of accelerated ageing. To test the method on real fast charging cycles, a measurement series with six commercial cells and different applied charging currents is performed, and the subsequent voltage behaviour during relaxation and discharge is investigated. As reference, the irreversible charge loss is measured for each cycle using coulomb counting. A detection algorithm is developed, which shows a remarkable sensitivity and furthermore enables an automated detection of LD.