Transient behaviour of facilitated transport through liquid membranes

Abstract

During the transient period of facilitated transport of a permeant across a thin liquid film, the ratio of the concentrations of the carrier at the two ends of the film as a function of time has a shape which is sensitive to the values of the physicochemical parameters. In certain systems involving ionic carriers, the above concentration ratio can be related to a conveniently measurable electrical potential difference, ΔV, across a pair of electrodes attached to the two faces of the liquid film. Bdzil et al. measured ΔV vs. time for NO FeCl 2FeCl 3—formamide system and observed that it goes through a maximum (ΔV max), before reaching the asymptotic value corresponding to the steady state, ΔV s. In the present paper, we solve numerically the species conservation equations, which describe the transients of the facilitated transport in the film, when the reversible reaction occurring in the film is of the form: A↑ + B = P (where A is the permeant and B and P are the carrier and permeant—carrier complex, respectively). The analysis takes into account: (i) the electrical effects which arise when B and P are ions of different diffusion coefficients and (ii) the effect of a second electrolyte added to the film to provide the cations which participate in an electrode reaction with the carrier ions. On this basis, an explanation is provided for the overshoot observed experimentally by Bdzil et al. in the ΔV vs. time curve. Such a maximum is exhibited by systems for which the time scales of diffusion and backward reaction in the film are of comparable magnitude. (Of course, for viable facilitation, the characteristic times of the forward and backward reactions should also be comparable.) The profile of ΔVvs. time is very sensitive to the values of the kinetic constants as well as the diffusion coefficients of the species A, B, and P. Therefore, measurements of ΔV vs. time (or equivalently the ratio of concentrations of the carrier on the two sides of the film as a function of time) can provide a more accurate method of determining the above parameters than those based on flux measurements.