Distribution of electrolytes between membraneous and bulk phases, and the dielectric properties of membraneous water, studied by impedance spectroscopy measurements on dense cellulose acetate membranes

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Abstract
The dielectric properties of dense cellulose acetate (CA) membranes have been determined using impedance spectroscopy. The impedance of the membranes in equilibrium with external salt solutions (10–4–1 mol dm–3) and at varying pH as a function of the frequency of the applied field was measured. From the data, and using classical Donnan theory together with the Nernst–Planck electrodiffusion equations and known dielectric theory, it is possible to find the concentration ratios of the ions between the membranes and the surrounding solution as a function of the external salt concentration, as well as their diffusion coefficients. In addition, the relative permittivities of the membrane matrix and of the solution present in the membrane alveoles, as well as the size of the latter, can be estimated. The results show (1) that there is no qualitative difference between NaCl and KCl. (2) The concentration ratios of the cations and the anions differ very much from unity at low (10–4 mol dm–3) external salt concentration. The cation ratios attain values of several hundred, decreasing rapidly as the external concentration increases. (3) The (relative) permittivity of the solvent inside the membrane is ca. 20, indicating either that the rotational degrees of freedom of the water in the alveoles are, to a considerable extent, hindered compared with normal water, or that the temporary H-bond clusters in pore water are less extended than in bulk water, with a resulting lower effective dipole moment; and (4) the average radius of the alveoles is ca. 6.5 ± 1.0 nm. Our results are at variance with measurements on similar membranes reported a few years ago by Wiggins and van Ryn, J. Macromol. Sci., Part A, Chem., 1986, 23, 875, who found considerable qualitative differences in the behaviour of the two alkali-metal salts. On the other hand, the low relative permittivity estimated for the water in the membrane supports the idea of anomalous water in the membrane alveoles, however, this seems to be caused by the properties and size of the alveoles, rather than by the presence of a particular cation.