Analysis of the electrolyte diode. Electro-diffusion and chemical reaction within a hydrogel reactor

A reaction–diffusion system describing the electrolyte diode is investigated. This consists of a chemically crosslinked polyvinylalcohol (PVA) hydrogel cylinder in which a pH gradient is provided by having an acid and a base maintained at constant concentrations in reservoirs at each end of the one-dimensional reactor. A potential difference of a given strength is also applied across the gel cylinder. Previous experimental studies of the current–voltage characteristics (CVC) have shown two distinct cases, depending on whether a positive or negative potential difference was applied. The slopes of the linear current–voltage response curve are substantially different in the two cases, that in the 'forward' case being typically several orders of magnitude greater than that in the 'backward' case. Thus the system behaves like a semiconductor diode. The stationary concentration distribution for the different ions is described by a system of reaction–diffusion equations involving migration caused by the electric field. An approximate solution of these equations, using a simplified model, is presented and compared with results obtained by solving the full system numerically. The concentration profiles obtained from the numerical solution confirm the validity of the simplified model.