| Diffusion at arrays of randomly distributed active sites Giovanni Pireddu1; Irina Svir2; Alexander Oleinick3; Christian Andre Amatore4; 1CNRS, ECOLE NORMALE SUPERIEURE, SORBONNE UNIVERSITY, Paris, France; 2ECOLE NORMALE SUPERIEURE, DEPARTMENT CHEMISTRY, PARIS, France; 3CNRS, Paris, France; 4CNRS & PSL, FRENCH ACADEMY OF SCIENCES, Paris, France; PAPER: 113/Battery/Regular (Oral) SCHEDULED: 11:55/Tue. 29 Nov. 2022/Similan 2 ABSTRACT: Many practical systems at micro- and nanoscale can be represented as arrays of active sites distributed randomly [1]. As shown previously these systems can be efficiently addressed theoretically by using Voronoi diagrams [2, 3] which allows facile tessellation of the system into the unit cells around each active sites. The overall current flowing in the system can then be evaluated by modelling diffusion-reaction processes inside every unit cell and summing the contributions from individual active sites. Although this approach is tempting by its simplicity and efficiency [3] one should bear in mind that Voronoi diagram representing the unit cells by polygonal prisms remains approximation and as each approximation remains valid only under certain conditions. In this work [4] we show that even for the case of diffusion limited electron transfer (ET) the actual shapes of the unit cells are more complicated and depend on the local configuration of the neighbouring active sites. This was exemplified on the small patches of the random arrays with band-like and disk-like active sites via simulations and in the case of band-like active sites confirmed by analytical derivations. Importantly, by comparing the total array current obtained by employing Voronoi tessellation and simulation of the system without any approximations we found that they agree well (relative error ca. 5% or less). At the same time, the individual contributions from the active sites are reproduced with a much larger relative error [4]. The latter suggests that in the case of kinetic control or reaction mechanisms that are more complicated than simple ET the diffusion-reaction competition between the active sites may become even stronger eventually leading to significant deviations from the total current predicted on the basis of the Voronoi approximation. This is currently investigated in our team. References: [1] O. Sliusarenko, A. Oleinick, I. Svir, C. Amatore. J. Electrochem. Soc. 167, 2020, 013530. [2] T. J. Davies and R. G. Compton. J. Electroanal. Chem. 585, 2005, 63. [3] O. Sliusarenko, A. Oleinick, I. Svir, C. Amatore. ChemElectroChem 2, 2015, 1279. [4] G. Pireddu, I. Svir, A. Oleinick, C. Amatore, in preparation. |
