Staff Publications

Staff Publications

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    'Staff publications' is the digital repository of Wageningen University & Research

    'Staff publications' contains references to publications authored by Wageningen University staff from 1976 onward.

    Publications authored by the staff of the Research Institutes are available from 1995 onwards.

    Full text documents are added when available. The database is updated daily and currently holds about 240,000 items, of which 72,000 in open access.

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Record number 440297
Title Validity of the Boltzmann equation to describe Donnan equilibrium at the membrane–solution interface
Author(s) Galama, A.H.; Post, J.W.; Cohen Stuart, M.A.; Biesheuvel, P.M.
Source Journal of Membrane Science 442 (2013). - ISSN 0376-7388 - p. 131 - 139.
Department(s) Sub-department of Environmental Technology
Physical Chemistry and Colloid Science
Publication type Refereed Article in a scientific journal
Publication year 2013
Keyword(s) ion-exchange membrane - dielectric exclusion model - fixed charge groups - nanofiltration membranes - transport-properties - capacitive deionization - partition equilibrium - sulfonated polymers - spherical colloids - cylindrical pores
Abstract To describe Donnan equilibrium at the membrane–solution interface, the simplest approach uses the classical Boltzmann equation, based on a mean-field description of ions as ideal point charges, in combination with the assumption of fully overlapped electrical double layers in the membrane pores. We test the Boltzmann equation by measurement of the equilibrium counterion and co-ion concentration in densely charged membranes equilibrated with various NaCl solutions (0.01–3 M). To obtain a good fit of data it was found necessary to express the membrane charge and ion concentration per volume of aqueous solution phase in the membrane, and to include a volume-exclusion term in the Boltzmann relation. A discrepancy between theory and experiment data is found at low external NaCl concentrations. Similar deviations from the Donnan model have been reported for over half a century, but do not yet have a convincing explanation. Agreement between experiment data and theory at low external NaCl concentrations is obtained when we model the desorption experiment taking into account the role of H+ and OH- ions in closing the charge balance, and postulating the presence in the membrane of a tiny amount of fixed groups with a charge opposite to overall fixed membrane charge.
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