Prediction of the carrier-mediated cation flux through polymer inclusion membranes via fundamental thermodynamic quantities: complexation study of bis(dodecyloxy)calix[4]arene-crown-6 with alkali metal cations

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Abstract
In a systematic study of alkali metal cation transport through a polymer inclusion membrane (PIM) with calixcrown carriers, a model that postulates diffusion-limited flux successfully describes PIM transport behavior. The model developed herein is based on an ion-pair extraction equilibrium at the PIM interface and provides a convenient tool for the quantitative understanding and interpretation of the transport data. Cation permeability coefficients can be easily determined and used for the quantitative correlation of fluxes employing a range of aqueous and PIM compositions. The described approach can be readily extended to competitive-transport experiments. Transport of a single cation as well as several cations in a competitive experiment was related to the stability constants of the carrier-metal complexes and the Gibbs energies of ion partitioning between source and membrane phases. The expected dependence of Cs+ ion transport on the Gibbs energy of anion partitioning was validated in a series of 8 univalent anions. Accordingly, the permeability coefficient once determined for a given metal salt, carrier, and PIM provides the basis for the prediction of the transport fluxes under different initial conditions if the thermochemical quantities which govern the complexation and distribution of the metal species into the membrane phase are known or can be estimated. In support of these efforts, a calorimetric study was carried out to obtain thermodynamic parameters for the complexation of bis(dodecyloxy)calix[4]arene-crown-6 with alkali metal ions in acetonitrile.