In recent years, joint time-frequency analysis has once again become a research hotspot. Supercapacitors have high power density and long service life, however, in order to balance between power density and energy density, two key factors need to be considered: (i) the specific surface area of the porous matrix; (ii) the electrolyte accessibility to the intra-pore space of porous carbon matrix. Electrochemical impedance spectra are extensively used to investigate charge penetration ratio and charge storage mechanism in the porous electrode for capacitance energy storage. Furthermore, similar results could be obtained by different methods such as stable-state analysis in the frequency domain and transient analysis in the time domain. In this work, a joint time-frequency analysis method is proposed to study the charge penetration depth and current spatial distribution in the pore. In detail, the following work has been carried out: (i) Excited by a complex sinusoidal current, the analytical solutions in the time domain and the frequency domain for the single pore are resolved, and the time-frequency characteristics describing the charge diffusion behavior are defined. (ii) Using the joint time-frequency method, the influences of the internal and external parameters on the charge penetration ratio in the single pore are quantitatively analyzed, and the evolution trend between the finite and semi-infinite diffusion of the charge inside the single pore is revealed. (iii) Based on the critical value of the penetration rate, the critical value of the internal parameters of the single pore is defined as well, and the semi-infinite diffusion and finite diffusion of the charge inside the pore are judged. Based on the above analyses, it can be seen that the frequency domain analysis regards the single pore as a whole and examines the charge transfer characteristics at different frequencies; however, the time domain analysis regards the single pore as a distributed parameter system, examining the evolution of charges at different spatial locations over time. Joint time-frequency analysis successfully completes information fusion and ultimately achieves the same goal. Furthermore, the joint time-frequency method can improve the reliability of diagnosis for the complicated porous electrode in electrochemical systems. In a word, the joint time-frequency analysis method proposed in this paper can achieve the information fusion for complex physio-chemical processes, which not only achieves the similar insights with different efforts, but also improves the diagnosis reliability for the complicated porous electrode in the electrochemical energy systems.

Standard electron-transfer rate constant is one of the intrinsic properties for an electrochemical reaction, which is significant in the study of electrode kinetics. It is a key criterion for one to clarify the mechanism and pathway of a specific electrochemical reaction, and to screening and design the electrocatalysts and battery materials. Herein, we will introduce the measuring methods of rate constant for electrode reactions, including polarization curve, rotating disk electrode, ultramicroelectrode, scanning electrochemical microscopy, electrochemical impedance spectroscopy, current step, potential step and cyclic voltammetry, etc., to provide a guide to investigate electrode kinetics for graduate students and researchers in the related fields.

This study identifies, for the first time, critical calculation errors made by Nathan Lewis and his co-authors, in their study presented on May 1, 1989, at the American Physical Society meeting in Baltimore, Maryland. Lewis et al. analysed calorimetrically measured heat results in nine experiments reported by Martin Fleischmann and his co-authors. According to the Lewis et al. analysis, each of the experiments, where calculated for no recombination, showed anomalous power losses. When we used the same raw data, our corrected calculations indicate that each experiment showed anomalous power gains. As such, these data suggest the possibility of a new, energy-producing physical phenomenon.

Redox potentials and acidity constants are key properties for evaluating the performance of energy materials. To achieve computational design of new generation of energy materials with higher performances, computing redox potentials and acidity constants with computational chemistry have attracted lots of attention. However, many works are done by using implicit solvation models, which is difficult to be applied to complex solvation environments due to hard parameterization. Recently, ab initio molecular dynamics (AIMD) has been applied to investigate real electrolytes with complex solvation. Furthermore, AIMD based free energy calculation methods have been established to calculate these physical chemical properties accurately. However, due to the low efficiency of ab initio calculations and the high computational costs, AIMD based free energy calculations are limited to systems with less than 1000 atoms. To solve the dilemma, machine learning molecular dynamics (MLMD) is introduced to accelerate the calculations. By using machine learning method to construct one-to-one mapping from structures to computed potential energies and atomic forces, molecular dynamics can be carried out with much low costs under ab initio accuracy. In order to achieve the MLMD based free energy calculation, a new scheme for machine learning potential (MLP) should be introduced to collect training datasets. By combining the free energy perturbation sampling method and concurrent learning scheme, the training datasets can be collected along the reaction’s pathway (insertion of an electron or a proton) with high efficiency and the free energy calculations based on MLMD show good accuracy in comparison with AIMD simulation. This paper describes how to constructing machine learning potential for free energy calculation through the automated workflow, and how to use MLMD to compute accurate free energy differences and corresponding physical chemical properties.