锂离子电池容量衰减机理和界面反应研究

锂离子电池容量衰减机理和界面反应研究 Capacity Fade Mechanisms and Side Reactions in Lithium-Ion Batteries Pankaj Arorat and Ralph E. White ABSTRACT The capacity of a lithium-ion battery decreases during cycling. This capacity loss or fade occurs due to several different mechanisms which are due to or are associated with unwanted side reactions that occur in these batteries. These reactions occur during overcharge or overdischarge and cause electrolyte decomposition, passive film formation, active material dissolution, and other phenomena. These capacity loss mechanisms are not included in the present lithium-ion battery mathematical models available in the open literature. Consequently, these models cannot be used to predict cell performance during cycling and under abuse conditions. This article presents a review of the current literature on capacity fade mechanisms and attempts to describe the information needed and the directions that may be taken to include these mechanisms in advanced lithium-ion battery models。 lntroduction The typical lithium-ion cell(Fig. 1) is made up of a coke or graphite negative electrode, an electrolyte which serves as an ionic path between electrodes and separates the two materials, and a metal oxide (such as LiCoO2, LiMn2O4, or LiNiO2) positive electrode. This secondary (rechargeable) lithium-ion cell has been commercialized only 学，化工学院化工系 摘 要 锂电池在循环过程中，其容量会逐渐衰减。而出现容量衰减主要 归因于几个不同的机理，这些机理大多与电池内部的界面反应相关，这些 反应持续性的发生在电池的充放电环节，并且引起电解液的分解、钝化膜 的形成、活性材料的溶解等其它现象。关于容量衰减的机理在目前公开的 锂离子电池数学模型的文献中并未加以阐述，因此在锂电池循环过程中和 处于苛刻的条件下，我们无法通过模型来对锂电池的性能作出有效的预测。 本篇文章将陈述容量衰减的机理，并且试着去解释其本质，为构建先进的 锂电池模型指明方向。 概论 传统的锂电池由碳或石墨负极材料、作 为电极间的离子传输通道的电解液、金属氧化物(例如LiCoO2、LiMn2O4、 LiNiO2)正极材料三部分组成，这种二次(可充电)电池已经商业化。依 照这种原理制作的锂电池已 recently.47 Batteries based on this concept have reached the consumer market, and lithium-ion electric vehicle batteries are under study in industry. The lithium-ion battery market has been in a period of tremendous growth ever since Sony introduced the first commercial cell in 1990.With energy density exceeding 130 Wh/kg (e.g., Matsushita CGR 17500)and cycle life of more than 1000 经形成稳定的消费者市场， 同时锂离子动力电池也在进行工业化研究。自从1990年，Sony制造出第 一批商业化电池开始，锂电池市场开始进入繁荣时期。由于具有超过 130wh/kg(matsushita CGR 17500)的能量密度和超过1000次循环的优势， 锂cycles (e.g., Sony 18650)in many cases, the lithium-ion battery system has become increasingly popular in applications ，such as cellular phones, portable computers, and camcorders. As more lithium-ion battery manufacturers enter the market and new materials are developed, cost reduction should spur growth in new applications. Several manufacturers such as Sony Corporation, Sanyo Electric Company, Matsushita Electric Industrial Company, Moli Energy Limited, and A&T Battery Corporation have started manufacturing lithium-ion batteries for cellular phones and laptop computers. Yoda has considered this advancement and described a future battery society in which the lithium-ion battery plays a dominant role. Several mathematical models of these lithium-ion cells have been published.Unfortunately, none of these models include capacity fade processes explicitly in their mathematical description of battery behavior. The objective of the present work is to review the current understanding of the mechanisms of capacity fade in lithiumion batteries. Advances in modeling lithium-ion cells must result from improvements in the fundamental understanding of these processes and the collection of relevant experimental data. 电池在移动电话、手提电脑、便携式摄像机等设备领域得到更加广泛 的应用。随着更多的锂电池生产商进入市场，新型材料也被陆续开发出来， 同时成本控制也成为新产品增长的关键因素。像索尼电器、三洋电器公司、 松下电器、莫里能源有限公司(加拿大)、日本A&T电器公司都已经 在移动电话和便携式电脑等产业开始锂电池应用商业化。Yoda也已经认识 到锂电池的发展趋势，并且在将来的电池能源时代，锂离子电池将扮演者 关键的角色。 关于锂离子电池的数学模型，已经有相关文献进行阐 述，然而遗憾的是至今没有一篇文献能就容量衰减机理进行明确解释，而 本文将会在锂电池容量衰减机理进行详细阐述。先进的锂电池模型必须建 立在加深对这些过程的基本理解和实验数据的整理归纳的基础之上。 Some of the processes that are known to lead to capacity fade in lithium-ion cells are lithium deposition (overcharge conditions), electrolyte decomposition, active material dissolution, phase changes in the insertion electrode materials, and passive film formation over the electrode and current collector surfaces. Quantifying these degradation processes will improve the predictive capability of battery models ultimately leading to less expensive and higher quality batteries. Significant improvements are required in performance standards such as energy density and cycle life, while maintaining high environmental,safety, and cost standards. Such progress will require considerable advances in our understanding of electrode and electrolyte materials, and the fundamental physical and chemical processes that lead to capacity loss and resistance increase in commercial lithium-ion batteries. The process of developing mathematical models for lithiumion cells that contain these capacity fade processes not only provides a tool for battery design but also provides a means of understanding better how those processes occur. 一些常见的引起锂电池容量衰减的因素包括1、锂枝晶的生成(过充 电压条件下)2、电解液分解3、活性材料的溶解4、电极材料嵌锂过程中 发生相变5、电极材料和集流体表面钝化膜的形成。对以上这些降解过程 进行量化，将能够提升电池模型的电池容量，并最终制造出成本低、质量 好的电池，能量密度和循环寿命是作为提升电池性能的重要指标，同时电 池的安全性能、环境友好程度、成本标准也是衡量电池的指标。在此过程 中，我们需要对电解液和电极材料有更深层次的理解，并且对商业化锂电 池体系中引起容量衰减、阻抗增加的基本物理原理和化学过程做出进一步 探究。构建包含这些容量衰减因素的锂电池数字模型不仅能为锂电池的设 计提供帮助，更为探究这些因素如何发生提供方法。 Present Lithium-Ion Battery Models The development of a detailed mathematical model is important to the design and optimization of lithium secondary cells and critical in their scale-up. West et al. developed a pseudo two-dimensional model of a single porous insertion electrode accounting for transport in the solution phase for a binary electrolyte with constant physical properties 如今的锂离子电池模型 一种详细的数字模型的构建对于锂离子二次电池的结构和性能优化 显得极其重要，并且在后续的电池比例扩大过程中起到决定性的作用。西 方学者首先构建出一种虚拟的二维模型，在该模型中，存在and diffusion of lithium ions into the cylindrical electrode particles. The insertion process was assumed to be diffusion limited, and hence charge-transfer resistance at the interface between electrolyte and active material was neglected. Later Mao and White developed a similar model with the addition of a separator adjacent to the porous insertion electrode.These models cover only a single porous electrode; thus, they do not have the advantages of a full-cell-sandwich model for the treatment of complex, interacting phenomena between the cell layers. These models confine themselves to treating insertion into TiS2. with the kinetics for the insertion process assumed to be infinitely fast. Spotnitz et al.accounted for electrode kinetics in their model for discharge of the TiS2 intercalation cathode. The galvanostatic charge and discharge of a lithium metal/solid polymer separator insertion positive electrode cell was modeled using concentrated-solution theory by Doyle et al.The model is general enough to include a wide range of separator materials, lithium salts, and composite insertion electrodes. Concentrated-solution theory is used to 着单一的多孔可嵌入的电极， 它能够保证具有常数物理性质的二元电解液在液态环境中传输，并且能让 锂离子在电极的球形颗粒中扩散，锂离子的嵌入过程被认为是扩散能力有 限的，因此在电解液和电极材料界面形成的电荷转移电阻通常是被忽略不 计的。随后Later Mao和White构建出另外一种相似的模型，此模型中， 在多孔的嵌入电极相邻处加入隔膜。这些模型中都只包含一个多孔电极， 因此它们不像“三明治”模型那样具备层间相互作用合成处理的优势。在 这些模型中，它们将自己定位为TiS2的嵌入处理，并且认为该嵌入过程中 的动力学是无限快的，其中Spotnitz学者对TiS2嵌入式正极在放电过程中 的电极动力学进行过相关研究。 Doyle学者通过溶液浓度理论构建出由 锂金属/固态聚合物隔膜/可嵌入的活性材料三部分组成的恒流充放电体系。 该模型一般包括广泛的隔膜材料、锂盐和复合式插入电极。溶液浓度 理论则可以解释粒子传输 describe the transport processes, as it has been concluded that ion pairing and ion association are very important in solid polymer electrolytes.This approach also provides advantages over dilute solution theory to account for volume changes. Butler-Volmertype kinetic expressions were used in this model to account for the kinetics of the charge-transfer processes at each electrode. The positive 过程，并且认为在固态聚合物 电解质环境中，离子的配对和结合是相当重要的，相对于稀溶液理论，这 种模型在体积变化上具备优势。,这个模型要运用Butler-Volmertype运动 学公式去计算每个电极中电荷转移过程中的动力学。electrode insertion process was described using Pick's law with a constant lithium diffusion coefficient in the active material. The volume changes in the system and film formation at the lithium/polymer interface were neglected and a very simplistic case of constant electrode film resistances was considered. Long-term degradation of the cell due to irreversible reactions (side reactions) or loss of interfacial contact is not predictable using this model. Fuller et al developed a general model for lithiumion insertion cells that can be applied to any pair of lithium-ion insertion electrodes and any binary electrolyte system given the requisite physical property data. Fuller et al's work demonstrated the importance of knowing the dependence of the open-circuit potential on the state of charge for the insertion materials used in lithium-ion cells. The slopes of these curves control the current distribution inside the porous electrodes, with more sloped open-circuit potential functions leading to more uniform current distributions and hence better utilization of active material. Optimization studies were carried out for the Beilcore plastic lithium-ion system.The model was also used to predict the effects of relaxation time on multiple charge-discharge cycles and on peak power. Doyle et al.modified the dual lithium-ion 在正极材料的嵌入过程中，利 用菲克定理来计算活性材料中锂离子扩散系数，整个体系中体积变化和锂 与聚合物界面形成的钝化膜均忽略不计，但是会将电极界面电阻作为恒量 纳入考虑范围。通过这种模型，我们无法预测由不可逆反应(副反应)或 界面接触损失引起的持续性衰减。 富勒等人构建出锂离子嵌入式电池的 综合性模型，这种模型能兼容各种类型的锂离子嵌入式电极和二元电解液 形成的体系，这能测定出我们想要的物理属性数据。富勒等人的工作阐述 了理解充电状态的开路电压对于锂离子电池嵌入材料应用的重要性。通过 这些曲线的斜率可以控制多孔电极内部的电流分布，利用开路电压曲线函 数来更好的统一电流分布，因此使活性材料得到更好的使用，而关于贝尔 塑料锂离子电池系统的最优化设计已经完成，这个模型可以预测由弛豫时 间给电池多次充放电循环和峰值功率带来的影响。 Doyle学者修改了双电 model to include film resistances on both electrodes and made direct comparisons with experimental cell data for the LixC6/LiPF6, ethylene carbonate/dimethyl carbonate (EC/DMC), Kynar FLEX/LiyMn2O4 system. Comparisons between data and the numerical simulations suggested that there is additional resistance present in the system not predicted by present models. The discharge performance of 极锂离子电池模型， 他考虑到两电极表面的钝化膜阻抗，并且制备出LiC6/LiPF6 EC/DMC(阿柯玛 股份有限公司)/LiyMn2O4电池体系测试出的相关比对数据，对比实验数据 和数字模型可以得出在该系统中出现的附加阻抗，而这个阻抗无法the cells was described satisfactorily by including either a film resistance on the electrode particles or by contact resistances between the cell layers or current-collector interfaces. One emphasis of this work was in the use of the battery model for the design and optimization of the cell for particular applications using simulated Ragone plots. Thermal modeling is very important for lithium batteries because heat produced during discharge may cause either irreversible side reactions or melting of metallic lithium, Chen and Evans carried out a thermal analysts of lithiumion batteries during charge-discharge and thermal runaway using an energy balance and a simplified description of the electrochemical behavior of the system.Their analysis of heat transport and the existence of highly localized heat sources due to battery abuse indicated that localized heating may raise the battery temperature very quickly to the thermal runaway onset temperature, above which it may keep increasing rapidly due to exothermic side reactions triggered at high temperature. Pals and Newman developed a model to predict the thermal behavior of lithium metal-solid polymer electrolyte cells and cell stacks. This model coupled an integrated energy balance to a fullcell-sandwich model of the electrochemical behavior of the cells. Both of these models emphasized the importance of considerations of heat removal and thermal 通过现有的模型进行预测。 在将活性材料表面的钝化膜阻抗和电极间的接触阻抗或集电器的界面阻 抗纳入考虑范围后，该电池的放电性能令人满意。此项工作的重点是利用 模拟Ragone图来进行电池设计和最优化应用。 热反应建模也是锂电池的 重要组成部分，通常认为在放电过程中产生的热量将会导致不可逆的副反 应和金属锂的溶解。Chen和Evans两人制备出一套关于锂电池热分解系统， 当电池处于充放电状态或热失控状态，通过能量平衡和简单描述该系统的 电化学行为来构建模型，他们关于由电池滥用引起的热量传输分析和局部 温度过高的理论表明:局部升温可能会很快地引起电池温度升高以致电池 热失控，超出设定温度后，高温将会引发放热性界面反应从而使整个电池 的温度急剧上升。Pals和Newman也构建出一种模型，利用该模型可以预 测金属固态聚合物电解质电池和电池推的热反应，这个模型将综合能量平 衡系统与 “三明治”式的全电池模型 control in lithium-polymer battery systems. 相联接，从而测定整个电池 的电化学行为，以上所有模 型均强调锂离子聚合物电 池系统的热散失和热控制 的重要性。 Verbrugge and Koch developed a mathematical model for lithium intercalation processes associated with a cylindrical carbon microfiber. They characterized and modeled the lithium intercalation process in single-fiber carbon microelectrodes including transport processes in both phases and the kinetics of charge transfer at the interface. The primary purpose of the model was to predict the Verbrugge和Koch构建成 一个关于锂离子嵌入圆柱形碳纤维的数字化模型，该模型可以表征并且可 以模拟锂离子在单个碳纤维电极中的嵌入过程。包括锂离子在两相中的传 输和界面传输动力学，该模型主要意图是为了预测嵌入的potential as a function of fractional occupancy of intercalated lithium. The overcharge protection for a Li/TiS2, cell using redox additives has been theoretically analyzed in terms of a finite linear diffusion model by Narayanan et al。 Darling and Newman modeled a porous intercalation cathode with two characteristic particle sizes.They reported that electrodes with a particle size distribution show modestly inferior capacity-rate behavior and relaxation on open circuit is substantially faster when the particles are uniformly sized. Nagarajan et al modeled the effect of particle size distribution on the intercalation electrode behavior during discharge based on packing theory.They observed that during pulse discharge, an electrode consisting of a binary mixture displays higher discharge capacity than an electrode consisting of singlesized particles. The current from the smaller particles reverses direction during the rest period which cannot be observed in the case of an electrode comprised of the same-sized particles. Recently Darling and Newman made a first attempt to model side reactions in lithium batteries by incorporating a solvent oxidation side reaction into a lithium-ion battery model, Even though a simplified treatment of the oxidation reaction was used, their model was able to make several interesting conclusions about self-discharge processes in these cells and their impact on positive electrode state-of-charge. 锂离子数量和电动势函数关系。在 Nareyamal等学者构建的有限线性扩散模型中，理论分析了可以通过氧化 还原添加剂来对Li/TiS2电池进行过充保护的结论。 Darling和Newman 构建成两种不同粒径尺寸的多孔嵌入式正极模型，他们表明当材料的颗粒 尺寸分布不不均匀时，将会导致较低的容量保持率和较快的自放电现象。, Nagarajan等学者研究了在充放电过程中颗粒尺寸分布对嵌入式电极的影 响,，他们发现在放电过程中，二种粒度混合电极要比单一尺寸颗粒电极 具有更高的放电容量。在后期放电过程中，小颗粒里面形成的电流将会改 变方向，而这种现象在粒径分布均匀的电极里面不会存在。最近Darling 和Newman开始尝试构建锂电池副反应模型，他们的想法是在锂电池模型 中引入溶液氧化副反应系统，尽管对氧化反应进行了简单处理，但他们的 模型仍然在电池自放电过程以及它对正极电极充电状态的影响方面能得 出一些有价值的结论。 A number of models having varying degrees of sophistication have been developed for lithium rechargeable batteries. For the most part, these models consider the ideal behavior of the systems, neglecting the phenomena that lead to losses in capacity and rate capability during repeated charge-discharge cycles. Fundamental models of these latter phenomena are less common because these processes are not 关于锂离子二次电池 已经构建出不同程度复杂性的模型，然而它们大部分都只是电池的理想状 态，而忽略了在充放电循环过程中引起容量衰减和容量保持率下降的内部 因素。关于后面这些现象的模型原理也不尽相同，因为这些过程as well understood. Also, models of failure modes in batteries do net usually have general applicability to a wide range of systems. However, the importance of these phenomena in the safe and efficient operation of high-energy lithium-ion batteries requires that they be incorporated into future battery models. Capacity Fading Phenomenon Side reactions and degradation processes in lithium-ion batteries may cause a number of undesirable effects leading to capacity loss. Johnson and White have shown that the capacities of commercial lithium-ion cells fade by ca. 10-40% during the first 450 cycles.A flow chart describing many of the processes leading to capacity fade is shown in Fig. 2. In Fig. 3, the capacity fade processes are shown on half-cell discharge curves. This gives a clearer picture of the processes by demonstrating where each is expected to manifest itself during operation of the battery Below, we discuss each of these processes in some detail, after first discussing the general topic of capacity balance. Capacity Balancing in Lithium-Ion Cells Lithium-ion cells operate by cycling lithium ions between two insertion electrode hosts having different insertion energies. For optimum performance, the ratio of the lithium-ion capacities of the two host materials should be balanced. Capacity balancing refers to the optimization of the 还没有被完全解释清楚，同 样那些失败的电池模型则没有在广泛的体系中得到应用，然而对于高能量 锂电池的安全性和效率性能的重要性来讲，它们仍然有可能纳入到未来的 电池模型中。 容量衰减现象 锂电池中的界面反应和衰减过程将会 引起一系列负面影响导致容量衰减。Johnson和White展示了商业锂电池 在450此循环后容量衰减10%~40%，如图2为一些导致容量衰减过程的流 程图，如图3为半电池容量衰减过程的放电曲线。通过放电曲线可以清楚 的向我们演示过程。在电池工作期间，我们可以预测该电池每一点的状态。 以下我们将详细讨论每一个过程，随后将讨论容量平衡主题。 锂 电池容量平衡 在锂电池循环过程中，两个嵌入电极有着不同的嵌入能 量，为了达到最佳的性能，两电极的材料重量需要相互匹配。容量平衡是 指通过对两电极材料质量进行最优化匹配，使得材料处 mass loading in the two electrodes to achieve the maximum capacity (or energy) from the battery under conditions of steady cycling. Due to the practical importance of this subject for maximizing cell performance, as well as the safety implications with poorly balanced cells, this subject has been discussed in the literature by several authors。 The condition for balanced capacities in a 于稳定循环状态时，电池能释 放出最大容量。由于最大限度地提高电池的性能和较差平衡电池的安全性 能两个主题具有实际意义，有关作者已经在文献中进行过讨论。 锂 电池容量平衡的条件为活性物质质量比γ，它lithium-ion cell can be written in terms of a ratio γ of active masses in the electrodes. Written as a ratio of positive to negative electrode masses, this expression is This equation says that the desired mass ratio depends on the relative coulombic capacities of the two electrodes (C is in units of mAh/g) and the amount of cyclable lithium in each. The cyclable lithium is quantified in terms of the range of lithium stoichiometry in the insertion electrode that can be cycled reversibly with the notation that Δx refers to the range of negative electrode stoichiometry and Δy to the positive electrode. For some insertion materials, which have several plateaus over which lithium can be inserted and deinserted, one may choose to cycle over only a limited range of stoichiometry for reversibility or safety reasons. In these cases, the stoichiometric range entered in the above formula would be reduced from its maximum value. 表示正极活性材料质量与负极活性材料质量之比，公式如下: 这个公示表明所需的质量比取决于两电极相对库伦容量(C的单位为 mAh/g)和每个循环过程中的脱嵌锂量。可循环锂量是指在嵌入电极能进 行可逆脱嵌的锂离子，可以用Δx表示负极化学计量学的范围，Δy表示正 极化学计量学范围，相对于一些嵌入材料，它在锂离子进行嵌入和脱出过 程中会形成一段电压平台，考虑到电池的可逆性和安全性能，我们可以选 择在一个有限的锂量范围内进行循环，在这些情况下，上述公式中输入的 化学计量范围将从它的最大值开始降低。 For example, consider the case of a lithium-ion cell having a petroleum coke negative electrode and a lithium manganese oxide spinel positive electrode. By choice, we can assign useful ranges of stoichiometries for the two electrode materials of 0.61 for the coke and 0.83 for the lithium manganese oxide. These stoichiometric ranges correspond to the following electrochemical processes: 例如，以石油焦炭负极材料和尖晶石型锰酸锂正极材料组装成的锂电 池，我们分别为两个电极材料设定锂离子化学计量，其中负极为0.61，正 极为0.83。以上化学计量符合以下电化学过程: The active mass ratio needed to cycle these two materials in the manner shown here is equal to 1.85. This is calculated by using the theoretical capacities of both positive and negative electrode (C+ = 148 mAh/g and C ,=372 mAh/g), equal to F divided by the molecular weight of the electrode material in its discharged state。 The situation above describes an “ideal” lithium-ion cell in which the capacity balance does not change over the life of the cell. For an ideal cell, the initial lithium capacity available for cycling is constant over the life of the battery .Unfortunately the true case in actual lithium-ion batteries is more complicated than this, and side reactions and secondary processes are able to perturb the capacity balance from its ideal state. The actual optimized active mass ratio is ca. 2.05-2.15 for the coke/LiMn2O4 system, which corresponds to 14% excess capacity in the positive electrode. This excess capacity is a measure of the amount of lithium needed to form a stable film over the electrode surfaces. A major process that affects the capacity balance is the initial formation period needed to passivate carbon-based electrodes. It is now well known that carbonaceous lithium insertion electrodes have irreversible capacity associated with the initial charging cycles.This irreversible capacity loss is thought to result in the formation of a lithium 如上两种材料的循环方 式，此时的活性物质比为1.85。可以通过正负极的理论容量(C，=148mAh/g， C,=372mAh/g)等同于F,除以放电状态的电极材料分子量。 所谓理想 的锂离子电池条件为在电池的使用过程中，其平衡容量不会发生改变。例 如在理想的锂电池体系中，在电池的整个循环过程中有效初始容量作为可 逆循环容量，恒定不变。遗憾的是，现实中锂离子电池则复杂许多。界面 反应和继发过程将会破坏其平衡容量的理想状态，在焦炭/LiMn2O4电池体 系中，实际最优活性质量比大约为2.05~2.15，对应于正极材料中14%的剩 余容量。这种多余的锂量主要用于在电极表面形成稳定的界面膜，碳基电 极的钝化层初步形成时期将会是影响容量平衡的重要过程。众所周知，含 碳的锂插入电极的不可逆容量与其最初充电周期息息相关，我们认为损失 的不可逆容量是由 conducting solid electrolyte interface (SEI) layer on the surface of the carbon, while in the process consuming some portion of the cyclable lithium ions in the cell. The loss of cyclable lithium to create this passivation layer has a profound impact on the capacity balance in the cell because it can remove a significant portion of the cyclable lithium depending on the type 于在碳材料表面形成了锂 离子固体电解质界面层(SEI)。在这个过程中电池中的部分循环锂离子将 会被消耗，而它形成的钝化层将会对电池的容量平衡产生深远的影响，因 为它将会根据碳的使用类型of carbon used. If the cyclable lithium in the cell is reduced due to side reactions of any type, the capacity balance is changed irreversibly and the degree of lithium insertion in both electrodes during cell cycling is changed. Consider the case of the initial carbon passivation process that occurs on all lithium-ion cells using carbon-based electrodes. The cell is assembled initially in the discharged state, with the carbon free of lithium and the metal oxide positive electrode at its maximum lithium content. The amount of lithium in either electrode can be represented as shown in Fig. 4, which illustrates the difference between the ideal and actual carbon/LiMn2O4 lithium-ion system during the first few cycles. In an ideal lithium-ion cell (Fig. 4a), all of the lithium should be intercalated into the negative electrode from the positive electrode during the first charge. Similarly all of the lithium ions should be intercalated back into the positive electrode during the first discharge. In an actual lithium-ion cell, upon charging the cell for the first time, some portion of the lithium removed from the LiMn2O4 positive electrode goes into the irreversible film formation reaction while the remainder inserts into the carbon structure. The capacity due to the irreversible reaction is represented 去消耗很大部分的循环 锂离子。, 如果电池中的锂离子逐渐减少，那得归因于电池体系内各种 界面反应。在电池循环过程中，容量平衡是不可逆地变化，并且锂离子在 两电极中嵌入深度也在改变，考虑到所有使用碳基电极的锂离子电池都存 在初始碳钝化过程，电池最初是在放电状态下组装成的，包括未嵌锂的碳 和最大锂量的金属氧化物活性电极。如图4所示则表示两电极中的锂离子 数量，这了在焦炭/LiMn2O4电池体系中，前几次循环过程中，理想状 态和实际情况有较大差异。 如图4a为理想的锂电池模型，在第一次充电 过程中，所有从正极脱嵌的锂离子都将嵌入负极中，同样在首次放电过程 中，所有的锂离子将会回嵌到正极材料中，然而在实际的电池体系中，在 首次充电过程中，部分从正极脱嵌的锂离子将会用于不可逆的成膜反应， 而余下的锂离子则会嵌入到碳结构中，如图4b下方的小方块则表示 不可逆反应所消耗的容 schematically in Fig. 4b by the smaller box below the negative electrode. After the cell is finished charging to some arbitrary cutoff voltage, the positive electrode has been delithiated to the extent possible under the charging conditions and the negative electrode is as full of lithium as possible given the amount of positive electrode mass available. Ideally the lithium content in the carbon at 量，当电池在任意的截止电 压范围内完成充电后，在该充电条件下正极电极中的锂离子已经尽可能的 脱嵌完成，负极电极则尽可能的嵌入正极提供的有效锂离子。理想情况下， 此时碳负极的锂量处于最大值，同样我们可以认为this point is at its maximum safe value. Also, we can imagine that the passivation layer is fully formed on the initial charging cycle, having consumed a certain amount of cyclable lithium irreversibly. When this cell is now discharged for the first time, the total quantity of lithium available for discharge is equal only to the amount of lithium reversibly inserted into the carbon electrode. Hence, the initial irreversible lithium lost cannot be recovered or utilized. The discharge proceeds until all of the reversible lithium is removed from the carbon electrode. At this time, the stoichiometry in the positive electrode will not reach its initial value upon cell assembly due to the capacity lost on the initial charging cycle. This situation is reflected in Fig. 4 in the bottom diagram. If the cell operates without any additional side reactions for the rest of its life, it will still never utilize the full range of stoichiometry available in the positive electrode. Thus for the above carbon/LiMn2O4 system it is safe to cycle within the limits of Δx = 0.61 (x varying from 0 to 0.61) and Δy = 0.83 (y varying from 0.17 to 1.0) as shown in Fig. 4. It should be remembered that these Δx and Δy values are cell and material specific. 钝化层是在初始循环过程中形成的，并且不可逆的消耗了一定数量的 可循环锂离子。 当电池完成首次充电之后，那么可用于放电的总的锂量 则相当于嵌入到碳负极的可逆容量，因此初始损失的不可逆锂离子将不能 被回嵌或利用，放电过程则直到所有的可逆锂从碳负极中脱出为止，此时 由于首次充电周期中容量的损失，正极电极的电化学计量比则无法达到其 初始值。这种情况如图4中底部图表所示，如果在后续循环过程中，该电 池没有任何额外的界面反应，它将不会利用到正极电极有效的全部化学计 量比。因此，对于以上焦炭/LiMn2O4电池体系而言，如图4当Δx=0.61(x 的范围为0~0.61)Δy=0.83(y的范围为0.17~1)时，该电池将能安全地 循环，需要强调的是此处的Δx和Δy值为电池和材料的特征值。 The range of stoichiometries accessed in the negative electrode in this example depends on the positive to negative mass ratio parameter γ. If the ideal value of yγhad been used to fabricate this example cell, the initial loss of lithium due to the irreversible passivation process would prevent the carbon electrode from being fully utilized to an extent that depended directly on the amount of irreversible capacity that the particular carbon electrode material exhibited. Rather than let this happen, the common procedure is to assemble cells having a greater than theoretical amount of positive-electrode mass, thus allowing for losses of cyclable lithium during operation by initially providing extra lithium. One method of providing the extra lithium without increasing the cathode mass is to use overlithiated manganese oxide (Li1+xMn2O4) spinel electrodes as proposed by Tarascon et al 此例子红负极电极使用 化学计量范围取决于正负极质量比参数γ，如果按照理想的γ制备电池时， 由于不可逆钝化过程中损失的锂将会防止碳电极被充分利用的程度,，而 这个程度直接依赖于特定的碳电极材料表现出不可逆容量，为了避免这种 情况的发生，一般方法是在装配电池时，加入超过理论质量的正极材料， 为电池工作期间消耗的可循环锂提供额外的锂离子，另外可以通过合成富 锂锰酸锂尖晶石材料(Li1+xMn2O4)，而不是增加材料质量来提供额外的 锂离子，这种观点由Tarascon和Peramunage学 and Peramunage et al. Even with side reactions and irreversible capacity losses, the desired mass ratio can still be calculated via a formula analogous to the above one, although we must now include in the negative electrode capacity an additive contribution due to the passivation process. Referring to this contribution as Cirr (mAh/g), the capacity balancing condition can be 者提出。 即便存在界面反应和不可逆容量的损失，但是我们仍然 可以通过一个类似上面的公式来计算出所需的质量比，虽然我们必须将由 钝化反应引起的负极容量的影响考虑在内。我们将这影响记为 Cirr (mAh/g)，其expressed as For example, in the case of a lithium-ion cell fabricated using a carbon (petroleum coke) negative electrode and a lithium manganese oxide spinel positive electrode, the actual mass ratio desired for optimum utilization of the two electrodes is about 14% larger than its theoretical value. This excess capacity is a measure of the amount of lithium needed to form a stable film over the electrode surfaces. The active mass ratio for the graphite/LiMn2O4 system is ca. 2.4-2.45. Smaller mass ratios will prevent full utilization of the negative electrode whereas larger mass ratios present a safety hazard because the negative electrode can be overcharged (more lithium is available to insert into the electrode than is desirable). Overall cell performance such as energy density is maximized at the optimum mass ratio only. It should also be apparent that there is a relationship between the expected overcharge and overdischarge processes and the cell's capacity balance. For example, in the case of the lithium manganese oxide spinel