Investigating particle size effects on NMR spectra of ions diffusing in porous carbons through a mesoscopic model

Characterizing ion adsorption and diffusion in porous carbons is essential to understand the performance of such materials in a range of key technologies such as energy storage and capacitive deionisation. Nuclear Magnetic Resonance (NMR) spectroscopy is a powerful technique to get insights in these systems thanks to its ability to distinguish between bulk and adsorbed species and to its sensitivity to dynamic phenomena. Nevertheless, a clear interpretation of the experimental results is sometimes rendered difficult by the various factors affecting NMR spectra. A mesoscopic model to predict NMR spectra of ions diffusing in carbon particles is adapted to include dynamic exchange between the intra-particle space and the bulk electrolyte surrounding the particle. A systematic study of the particle size effect on the NMR spectra for different distributions of magnetic environments in the porous carbons is conducted. The model demonstrates the importance of considering a range of magnetic environments, instead of a single chemical shift value corresponding to adsorbed species, and of including a range of exchange rates (between in and out of the particle), instead of a single timescale, to predict realistic NMR spectra. Depending on the pore size distribution of the carbon particle and the ratio between bulk and adsorbed species, both the NMR linewidth and peak positions can be largely influenced by the particle size.