Kinetic analysis of lithium intercalating systems: cyclic voltammetry Sergey Yu. Vassiliev a , Eduard E. Levin a , Victoria A. Nikitina a,b, * a M.V. Lomonosov Moscow State University, Leninskie Gory 1/3, Moscow 199991, Russia b Skolkovo Institute of Science and Technology, Moscow 143026, Russia A R T I C L E I N F O Article history: Received 26 November 2015 Received in revised form 22 December 2015 Accepted 25 December 2015 Available online 30 December 2015 Keywords: electrochemical kinetics cyclic voltammetry lithium-ion intercalation numerical modeling rate constant A B S T R A C T General model for the description of electrochemical behavior of lithium ion intercalating materials is formulated on the basis of fundamental physicochemical principles. Kinetic and transport parameters for selected well-known electrode materials (LiMn 2 O 4 and LiCoO 2 ) are evaluated from numerical modeling and fitting of cyclic voltammetry responses. Good agreement between calculated and experimental voltammograms in the wide range of potential scan rates proved the self-consistency of the proposed model. The applied formalism allows for the correct choice of model assumptions and accurate determination of kinetic and transport parameters of intercalating materials. ã 2015 Elsevier Ltd. All rights reserved. 1. Introduction Intensive research in the field of lithium ion intercalating systems over the last decades resulted in the design of hundreds of active material and electrolyte systems for practical battery applications. Given the high priority of achieving maximum capacity, energy density, and rate characteristics of the Li-ion batteries, the focus of the majority of studies on the cycling efficiency and charge-discharge characteristics of the active materials is not surprising. Fundamental studies on the diffusion and phase-separation mechanisms [1,2] as well as on the charge- transfer kinetics [3] in Li-ion systems are rather rare. These studies in particular are aimed at constructing physically sound and experimentally verified models of diffusion and kinetics of the Li- ion transfer, which are likely to affect the whole methodology of material design, or at least rationalize experimental observations. Another complicated task is precise and physically adequate determination of transport and kinetic parameters of materials under investigation. Today this problem is far from being solved. In spite of very common application of well-established techniques for diffusion coefficient determination (PITT, GITT), the scatter in diffusion coefficient values given in literature for the same materials exceeds 3–5 orders of magnitude. The possibility of kinetic or mixed reaction rate control in most cases is not discussed due to the relative complexity of accurate kinetic analysis. Models conventionally applied to determine electrode material transport characteristics are typically based on analytical for- mulations developed in the semi-infinite diffusion geometry. In this case, quantitative analysis is possible in the short-time domain at the beginning of the transient curve. In this procedure the choice of the moment of time, when diffusion layer reaches the center of the (de)lithiating particle and the semi-infinite diffusion condition is violated, is rather arbitrary. Moreover, the effect of the particle size distribution on the transient shape is also commonly ignored. No accurate attempts to construct a model description of the electrode material electrochemical response in the finite diffusion limit with consideration of the real particle size distribution in the composite electrode have been performed so far, to our knowledge. Most of the research on intercalation processes modeling focuses on the description of galvanostatic charge-discharge curves [4–23], which are not very informative and generally do not permit the analysis of reaction rate limiting step and material kinetic parameters determination. The attempts to model cyclic voltammetry response of lithium intercalating systems are rare [24]. Studies aimed at semiempirical modeling of the electrode charge-discharge characteristics in an operating battery dominate the field [see e.g. 6–13], while analysis of transport and kinetic properties of the material itself attracts less attention. Moreover, most of the researchers choose LiFePO 4 as a model system, which shows two-phase coexistence behavior in a wide potential range. However, this system is far from the most convenient one for model testing and development, as its response should include the nucleation contribution, which is statistical in its nature and, in * Corresponding author at: M.V. Lomonosov Moscow State University, Chemical Faculty, Department of Electrochemistry, Leninskie Gory 1/3, Moscow, 199991, Russia. E-mail address: nikitina@elch.chem.msu.ru (V.A. Nikitina). http://dx.doi.org/10.1016/j.electacta.2015.12.172 0013-4686/ ã 2015 Elsevier Ltd. All rights reserved. Electrochimica Acta 190 (2016) 1087–1099 Contents lists available at ScienceDirect Electrochimica Acta journa l home page : www.e lsevier.com/loca te/ele cta cta