Title: Investigating the effect of particle size distribution and complex exchange dynamics on NMR spectra of ions diffusing in disordered porous carbons through a mesoscopic model

Abstract: Ion adsorption and dynamics in porous carbons is crucial for many technologies such as energy storage and desalination. Nuclear Magnetic Resonance (NMR) spectroscopy is a key method to investigate such systems thanks to the possibility to distinguish adsorbed (in-pore) and bulk (ex-pore) species in the spectra. However, the large variety of magnetic environments experienced by the ions adsorbed in the particles and the existence of dynamic exchange between the inside of the particles and the bulk renders the intepretation of the NMR experiments very complex. In this work, we optimise and apply a mesoscopic model to simulate NMR spectra of ions in systems where carbon particles of different sizes can be considered. We demonstrate that even for monodisperse systems, complex NMR spectra, with broad and narrow peaks, can be observed. We then show that the inclusion of polydispersity is essential to recover some experimentally observed features, such as the co-existence of peaks assigned to in-pore, exchange and bulk. Indeed, the variety of exchange rates between in-pore and ex-pore environments, present in experiments but not taken into account in analytical models, is necessary to reproduce the complexity of experimental NMR spectra.