  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.
