RESEARCH ARTICLE 1 Voltammetric behaviour of LMO at the nanoscale: a map of reversibility and diffusional limitations E.M. Gavilán-Arriazu* [a],[b] , M.P. Mercer [c],[d] , D.E. Barraco [b] , H.E. Hoster [c],[d] and E.P.M. Leiva* [a] [a] Dr. E.M. Gavilán-Arriazu and Prof. E.P.M. Leiva Departamento de Química Teórica y Computacional Facultad de Ciencias Químicas, Universidad Nacional de Córdoba, INFIQC, Córdoba, Argentina E-mail: maxigavilan@hotmail.com E-mail: ezequiel.leiva@unc.edu.ar [b] Dr. E.M. Gavilán-Arriazu and Prof. D.E. Barraco Facultad de Matemática, Astronomía y Física, IFEG-CONICET Universidad Nacional de Córdoba Córdoba, Argentina [c] Dr. M.P. Mercer and Prof. H.E. Hoster Department of Chemistry, Lancaster University, Bailrigg, Lancaster, United Kingdom [d] Dr. M.P. Mercer and Prof. H.E. Hoster ALISTORE European Research Institute CNRS FR 3104, Hub de l’Energie, 80039 Amiens, France Supporting information for this article is given via a link at the end of the document Abstract: Understanding and optimization of single particle rate behaviour is normally challenging in composite commercial lithium-ion electrode materials. In this regard, recent experimental research has addressed the electrochemical Li-ion intercalation in individual nanosized particles. Here, we present a thorough theoretical analysis of the Li + intercalation voltammetric behaviour in single nano/micro- scale LiMn2O4 (LMO) particles, incorporating realistic interactions between inserted ions. A transparent 2-dimensional zone diagram representation of kinetic-diffusional behaviour is provided that allows rapid diagnosis of the reversibility and diffusion length of the system dependent on particle geometry. We provide an Excel file where the boundary lines of the zone diagram can be rapidly recalculated by setting input values of the rate constant,  0 and diffusion coefficient, . The model framework elucidates the heterogeneous behaviour of nanosized particles with similar sizes but different shapes. Hence, we present here an outlook for realistic multiscale modelling of real materials. Introduction By now, lithium ion (Li-ion) batteries are well optimized in terms of capacity, proving successful in portable electronics, electric vehicles and potentially even stationary storage [1–5] . On the other hand, the key factors governing the rate performance of the electrodes are not fully understood. In particular, a proper description of Li-ion intercalation in nanosized materials is of primary importance for battery electrode design to inform how size and geometry impact on rate performance and lifetime. Most research has been focused on the behaviour of composite electrodes, where the contribution of particles with different sizes and shapes, together with the influence of agglomeration and the binder, plays an important role [6,7] . This approach circumvents analysis of single particle behaviour because the contribution of each particle to the total behaviour results in a collective average in electrochemical responses. The spinel cathode LiMn2O4 (LMO) presents a good rate performance, moderate theoretical capacity and high abundance, potentially making this chemistry suitable for stationary storage applications. However, in spite of the previous extensive research on composite microsized particles used in commercial cathodes [8,9] , the redox behaviour of individual nanosized particles practically remains a virtually unexplored research area. Figure 1. Cyclic voltammograms (i) for particles a and b, with the corresponding SEM images (ii). Reproduced with permission from reference [10] . John Wiley & Sons Copyright © 2011. CC BY 4.0. Remarkably, LMO ensembles of nanosized particles have been found to exhibit higher reversibility and better performance than the micrometric counterpart, but the origin of this improvement was not clear [11] . The recent work of Tao et al. [10] , set a precedent by measuring cyclic voltammograms for individual LiMn2O4 particles of nanometric size using scanning electrochemical cell microscopy (SECCM), getting well resolved voltammetric features at scan rates as high as 1 V/s. Two cyclic voltammograms from this work, (a-i) and (b-i), for individual particles and the