Diffusion layer thickness in a membrane system as determined from voltammetric and chronopotentiometric data

Abstract

The thickness of the diffusion boundary layer (DBL) in solution near the surface of an ion-exchange membrane is compared at current densities (δ0) much less than the limiting value and at the limiting current density (δlim). The initial linear part of the current-voltage curve (CVC) of the membrane and the initial part of its chronopotentiogram are used to calculate δ0. Values of δ0 are found in a flow-through cell with an active membrane area of 2 × 2 cm2 and 0.02 M NaCl solution for three membranes: AMX, Nafion-117, and MK-40. It is shown that δ0 is more than 20% less for Nafion-117 than for AMX and MK-40. Values of δ0 are close together for the latter two membranes and do not differ greatly from the value calculated from convective diffusion theory (the Leveque equation). In all cases, δ0 is significantly greater than δlim found from the value of the limiting current density by the method of intersecting tangents, which are drawn to the initial segment of the CVC and to the sloping plateau. The effects that determine the dependence of DBL thickness on not only hydrodynamic conditions, but also the state of the membrane surface, are discussed. The principal phenomenon responsible for the decrease in DBL thickness with increasing current is termed coupled convection, more likely, electroconvection. Among the significant properties of the surface are singled out its electrical heterogeneity and degree of hydrophobicity. The different rate of electroconvection near cation- and anion-exchange membranes is related to the Stokes radius of the counterions. The latter explains the well-known observation in the literature that the limiting current density in dilute NaCl solutions is approximately the same for cation- and anion-exchange membranes in spite of the fact that the mobility of Cl− ions is approximately 1.5 times higher than that of Na+ ions.