Abstract
A theoretical approach has been developed here to describe the slow diffusion of small charged molecules of sodium dithionite (S2O42−) 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.
Highlights
A theoretical approach has been developed here to describe the slow diffusion of small charged molecules of sodium dithionite (S2O42−) in polyelectrolyte multilayers (PEMs) composed of polyallylamine hydrochloride (PAH) and polystyrene sulfonate (PSS), which is demonstrated here to be a case of subdifussion
We aim to advance on our understanding of the diffusion of charged small molecules in PEMs, and we propose a different theoretical framework for analysing experimental results based on the assumption that diffusion is non-Markovian and the slow diffusion can be described via diffusion equations with fractional time derivatives[13,14,15,16]
As was shown in our previous w orks[11,12] the diffusion of charged small molecules, in this case dithionite, in PEMs cannot be described in the framework of the classical Fickean diffusion
Summary
A theoretical approach has been developed here to describe the slow diffusion of small charged molecules of sodium dithionite (S2O42−) in polyelectrolyte multilayers (PEMs) composed of polyallylamine hydrochloride (PAH) and polystyrene sulfonate (PSS), which is demonstrated here to be a case of subdifussion. The unique architecture of PEMs, consisting of a layered structure where alternating layers bear opposite charges, makes them a fascinating system to study the diffusion of charged molecules. These would be facing alternating attractive and repulsive interactions while diffusing through the film. Dithionite was used to quench the fluorescence of the nitrobenzoxadiazole (NBD) dye molecules, which were covalently linked to PAH chains assembled on top of colloidal particles. We demonstrated that dithionite diffusion in PEMs does not follow an exponential law and can be considered as atypical
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