Kinetic Aspects of Donnan Membrane Technique for Measuring Free Trace Cation Concentration

Abstract

Addition of ion complexation ligands in the acceptor solution in the Donnan membrane technique (DMT) can lower its detection limit for free metal ion concentration in natural samples. In this paper, the influence of added ligands on the transport behavior of trace ions in DMT was studied using numerical and analytical models and experimental tests. The results show that addition of ligands in the acceptor can significantly influence the time to reach the Donnan membrane equilibrium. Depending on several factors, the flux can be controlled by the diffusion in the stagnant solution film at the solution−membrane interface, by the diffusion in the membrane, or by both. The conditions under which the diffusion in the solution film or in the membrane becomes the rate-limiting step are discussed and approximate analytical solutions for some special cases are presented. Very low concentrations of free metal ion can be measured using the ligand complexation DMT. Depending on the degree of complexation in the sample, the measurement can be based on either the Donnan membrane equilibrium (when the complexation degree is low) or the kinetic interpretation of the ion transport (when the complexation degree is high).