A study of the subdiffusion of small molecules in charged polyelectrolyte multilayers

A theoretical approach has been developed here to describe the slow diffusion of small charged molecules of sodium dithionite (S₂O₄^2-) in polyelectrolyte multilayers (PEMs) composed of polyallylamine hydrochloride (PAH) and polystyrene sulfonate (PSS), which is demonstrated here to be a case of subdifussion. Diffusion is measured experimentally by recording the quenching of the fluorescence of (7-nitrobenz-2-oxa-1,3-diazol-4yl) amino (NBD) labelled PAH layers assembled on silica particles by flow cytometry. NBD is reduced when it encounters dithionite leading to the disappearance of the fluorescence. The fluorescence decay curves show a slow diffusion of dithionite, that does not follow classical Fickean law. Dithionite diffusion in the PEMs is shown to be a non-Markovian process and the slow diffusion can be described via diffusion equations with fractional time derivatives. Results are explained assuming subdifussion of dithionite in the PEMs, as a result of the trapping of the negatively charged dithionite in the positively charged layers of PAH.