Model reduction of fractional impedance spectra for time–frequency analysis of batteries, fuel cells, and supercapacitors

Joint time–frequency analysis is an emerging method for interpreting the underlying physics in fuel cells,batteries,and supercapacitors.To increase the reliability of time–frequency analysis,a theoretical correlation between frequency-domain stationary analysis and time-domain transient analysis is urgently required.The present work formularizes a thorough model reduction of fractional impedance spectra for electrochemical energy devices involving not only the model reduction from fractional-order models to integer-order models and from high-to low-order RC circuits but also insight into the evolution of the characteristic time constants during the whole reduction process.The following work has been carried out:(i)the model-reduction theory is addressed for typical Warburg elements and RC circuits based on the continued fraction expansion theory and the response error minimization technique,respectively;(ii)the order effect on the model reduction of typical Warburg elements is quantitatively evaluated by time–frequency analysis;(iii)the results of time–frequency analysis are confirmed to be useful to determine the reduction order in terms of the kinetic information needed to be captured;and(iv)the results of time–frequency analysis are validated for the model reduction of fractional impedance spectra for lithium-ion batteries,supercapacitors,and solid oxide fuel cells.In turn,the numerical validation has demonstrated the powerful function of the joint time–frequency analysis.The thorough model reduction of fractional impedance spectra addressed in the present work not only clarifies the relationship between time-domain transient analysis and frequency-domain stationary analysis but also enhances the reliability of the joint time–frequency analysis for electrochemical energy devices.

联合时频分析:以单孔中电荷穿透深度和电流空间分布为例

近年来,联合时频分析再次成为研究热点。超级电容器功率密度高和寿命长,但为了优化平衡功率密度和能量密度,需考虑两个关键因素:(1)多孔基质的比表面积;(2)孔内空间电解质可抵达性。本文采用联合时频分析方法,研究孔内电荷穿透深度及电流空间分布。具体开展了如下工作:(i)在复正弦电流激励下,推导单孔的时域响应和频域响应解析解,由此定义了描述电荷扩散行为的时频特征。(ii)采用联合时频方法,分析了内部参数和外部参数对孔内电荷穿透率的影响,揭示了孔内电荷有限扩散和无限扩散之间的演变规律。(iii)基于穿透率临界值,定义了孔内部参数的临界值,由此判断孔内电荷半无限扩散和有限扩散。本文提出联合时频分析方法,实现了多孔电极中复杂物理化学过程的信息融合,联合时频分析最终殊途同归,并提高诊断可靠性。

Decouple charge transfer reactions in the Li-ion battery

In the development of Li-ion batteries(LIBs)with high energy/power density,long cycle-life,fast charging,and high safety,an insight into charge transfer reactions is required.Although electrochemical impedance spectroscopy(EIS)is regarded as a powerful diagnosis tool,it is not a direct but an indirect measurement.With respect to this,some critical questions need to be answered:(i)why EIS can reflect the kinetics of charge transfer reactions;(ii)what the inherent logical relationship between impedance models under different physical scenes is;(iii)how charge transfer reactions compete with each other at multiple scales.This work aims at answering these questions via developing a theory framework so as to mitigate the blindness and uncertainty in unveiling charge transfer reactions in LIBs.To systematically answer the above questions,this article is organized into a three-in-one(review,tutorial,and research)type and the following contributions are made:(i)a brief review is given for impedance model development of the LIBs over the past half century;(ii)an open source code toolbox is developed based on the unified impedance model;(iii)the competive mechanisms of charge transfer reactions are unveiled based on the developed EIS-Toolbox@LIB.This work not only clarifies theoretical fundamentals,but also provides an easy-to-use open source code for EIS-Toolbox@LIB to optimize fast charge/discharge,mitigate cycle aging,and improve energy/power density.

Capacitive energy storage from single pore to porous electrode identified by frequency response analysis

Rate capability,peak power,and energy density are of vital importance for the capacitive energy storage(CES)of electrochemical energy devices.The frequency response analysis(FRA)is regarded as an efficient tool in studying the CES.In the present work,a bi-scale impedance transmission line model(TLM)is firstly developed for a single pore to a porous electrode.Not only the TLM of the single pore is reparameterized but also the particle packing compactness is defined in the bi-scale.Subsequently,the CES properties are identified by FRA,focused on rate capability vs.characteristic frequency,peak power vs.equivalent series resistance,and energy density vs.low frequency limiting capacitance for a single pore to a porous electrode.Based on these relationships,the CES properties are numerically simulated and theoretically predicted for a single pore to a porous electrode in terms of intra-particle pore length,intra-particle pore diameter,inter-particle pore diameter,electrolyte conductivity,interfacial capacitance&exponent factor,electrode thickness,electrode apparent surface area,and particle packing compactness.Finally,the experimental diagnosis of four supercapacitors(SCs)with different electrode thicknesses is conducted for validating the bi-scale TLM and gaining an insight into the CES properties for a porous electrode to a single pore.The calculating results suggest,to some extent,the inter-particle pore plays a more critical role than the intra-particle pore in the CES properties such as the rate capability and the peak power density for a single pore to a porous electrode.Hence,in order to design a better porous electrode,more attention should be given to the inter-particle pore.

Time-frequency analysis of Li solid-phase diffusion in spherical active particles under typical discharge modes

Li transient concentration distribution in spherical active material particles can affect the maximum power density and the safe operating regime of the electric vehicles(EVs). On one hand, the quasiexact/exact solution obtained in the time/frequency domain is time-consuming and just as a reference value for approximate solutions;on the other hand, calculation errors and application range of approximate solutions not only rely on approximate algorithms but also on discharge modes. For the purpose to track the transient dynamics for Li solid-phase diffusion in spherical active particles with a tolerable error range and for a wide applicable range, it is necessary to choose optimal approximate algorithms in terms of discharge modes and the nature of active material particles. In this study, approximation methods,such as diffusion length method, polynomial profile approximation method, Padé approximation method,pseudo steady state method, eigenfunction-based Galerkin collocation method, and separation of variables method for solving Li solid-phase diffusion in spherical active particles are compared from calculation fundamentals to algorithm implementation. Furthermore, these approximate solutions are quantitatively compared to the quasi-exact/exact solution in the time/frequency domain under typical discharge modes, i.e., start-up, slow-down, and speed-up. The results obtained from the viewpoint of time-frequency analysis offer a theoretical foundation on how to track Li transient concentration profile in spherical active particles with a high precision and for a wide application range. In turn, optimal solutions of Li solid diffusion equations for spherical active particles can improve the reliability in predicting safe operating regime and estimating maximum power for automotive batteries.

Permafrost carbon cycle and its dynamics on the Tibetan Plateau

Our knowledge on permafrost carbon(C)cycle is crucial for understanding its feedback to climate warming and developing nature-based solutions for mitigating climate change.To understand the characteristics of permafrost C cycle on the Tibetan Plateau,the largest alpine permafrost region around the world,we summarized recent advances including the stocks and fluxes of permafrost C and their responses to thawing,and depicted permafrost C dynamics within this century.We find that this alpine permafrost region stores approximately 14.1 Pg(1 Pg=1015g)of soil organic C(SOC)in the top 3 m.Both substantial gaseous emissions and lateral C transport occur across this permafrost region.Moreover,the mobilization of frozen C is expedited by permafrost thaw,especially by the formation of thermokarst landscapes,which could release significant amounts of C into the atmosphere and surrounding water bodies.This alpine permafrost region nevertheless remains an important C sink,and its capacity to sequester C will continue to increase by 2100.For future perspectives,we would suggest developing long-term in situ observation networks of C stocks and fluxes with improved temporal and spatial coverage,and exploring the mechanisms underlying the response of ecosystem C cycle to permafrost thaw.In addition,it is essential to improve the projection of permafrost C dynamics through in-depth model-data fusion on the Tibetan Plateau.

中国草地生态系统固碳能力及其提升途径

准确评估草地生态系统固碳速率、提升其碳汇能力对于深入认识国家尺度陆地生态系统碳源汇特征及其固碳潜力具有重要意义。通过梳理文献,本文总结了我国草地碳汇大小、空间格局及其未来趋势,并提出了提升草地碳汇的可能途径。结果发现,不同研究对我国草地碳源汇特征的估算差异较大,大小介于-3.4~17.6 Tg C year^(-1)(1 Tg=10^(12)g),中值为13.0 Tg C year^(-1)。模型预测未来全球变化背景下我国草地碳汇呈增加趋势,由1970s—2010s的12.8 Tg C year^(-1)(不同研究结果的范围:-3.6~18.0 Tg C year^(-1))增加至2050s的29.0 Tg C year^(-1)(10.3~50.0 Tg C year^(-1))。通过构建退化草地恢复技术体系、加强重大生态工程、自然保护区和人工草地建设、利用碳汇植物提升荒漠化草地碳汇、以及实施有效的生态奖补政策等手段,有望进一步提升草地固碳能力。未来亟需在草地碳通量长期联网观测、碳循环关键过程对全球变化响应和反馈机制、数据—模型融合等方面加强研究,以降低草地碳汇估算中的不确定性。此外,还需加强草地退化和恢复过程中碳循环观测和模拟研究,从而针对性地恢复退化草地碳汇功能,为我国实现“碳中和”国家战略目标提供科技支撑。

Effects of Al^3+ on the microstructure and bioflocculation of anoxic sludge

The aluminum ions generated from mining aluminum,electrolytic aluminum and the industrial production of aluminum-based coagulants(such as AlCl3 and Al2(SO4)3)enter sewage treatment plants and interact with activated sludges.An anaerobic/anoxic/oxic(A2^O)process was used to reveal the effects of Al^3+on the pollutant removal efficiencies,bioflocculation and the micro structure of sludge.The results showed that a low concentration of Al^3+improved the pollutant removal efficiencies and increased the sludge particle size.However,a high concentration of Al^3+hindered microbial flocculation and reduced the pollutant removal efficiencies.With a 10 mg/L Al^3+addition,the chemical oxygen demand(COD),total nitrogen(TN)and NH4+-N increased by 3%,16%and 27%,and reached as high as 68%,60%and 87%,respectively.At the same time,the dehydrogenase activity,flocculation ability(FA)and contact angle of the sludge reached their maximum levels at 41.3 mg/L/hr,45%and 79.63°,respectively.The specific surface area of the sludge decreased to 7.084 m2/g and the sludge pore size distribution shifted to concentrate in the me soporous range.Most of Al^3+was adsorbed on the surface of sludge,changing the physicochemical properties and physical structure of the sludge.