The equivalent pore radius of charged membranes from electroosmotic flow

The equivalent pore radius of charged membranes has been determined from the electroosmotic transport number of water. In comparison to the hydrodynamic method, the proposed method does not require the knowledge of the tortuosity coefficient and only slightly depends on the assumption concerning the viscosity of pore solution. It depends on the function describing the distribution of ions in the pore (homogeneous, Boltzmann, and modified Boltzmann distributions); however, the discrepancy of the values of radius is within 15%. It has been found that, for membranes of different structures, porosity (0.27–0.47) and ion-exchange capacity (1.3–6.4 mol/dm3 pore solution), the equivalent pore radius is in the range 0.8–2 nm. For Nafion membranes, the radius is 1.1–1.5 nm and lies between the channel and cluster radii estimated by independent methods. The simple experimental setup for automatic measurement of electroosmotic flow is presented.