Abstract
This paper presents an innovative and efficient methodology for the determination of the solid-state diffusion coefficient in electrode materials with phase transitions for which the assumption of applying the well-known formula from the work of Weppner et al. is not satisfied. This methodology includes a k-means machine learning screening of Galvanostatic Intermittent Titration Technique (GITT) steps, whose outcomes feed a physics-informed algorithm, the latter involving a pseudo-two-dimensional (P2D) electrochemical model for carrying out the numerical simulations. This methodology enables determining, for all of the 47 steps of the GITT characterization, the dependency of the Na(+) diffusion coefficient as well as the reaction rate constant during the sodiation of an NVPF electrode to vary between 9 × 10-18 and 6.8 × 10-16 m(2)·s(-1) and between 2.7 × 10-14 and 1.5 × 10-12 m(2.5)·mol(-0.5)·s(-1), respectively. This methodology, also validated in this paper, is (a) innovative since it presents for the first time the successful application of unsupervised machine learning via k-means clustering for the categorization of GITT steps according to their characteristics in terms of voltage; (b) efficient given the considerable reduction in the number of iterations required with an average number of iterations equal to 8, and given the fact the entire experimental duration of each step should not be simulated anymore and hence can be simply restricted to the part with current and a small part of the rest period; (c) generically applicable since the methodology and its physics-informed algorithm only rely on "if" and "else" statements, i.e., no particular module/toolbox is required, which enables its replication and implementation for electrochemical models written in any programming language.