Electrical transport in a disordered medium: NMR measurement of diffusivity and electrical mobility of ionic charge carriers.

Electrical transport in porous media plays an important role in many fields of pure and applied science. The basic microscopic processes of the charge transport have attracted considerable theoretical interest for a long time. However, on a microscopic level there was up to now no experimental access to this problem. In the present paper we demonstrate, by using a suited porous system, that two combined NMR methods can offer such a first experimental access. We apply common PFG NMR methods and the special electrophoretic NMR (ENMR) technique for the measurement of self-diffusion coefficient D+ and electric mobility u+ of a cation ((C4H9)+4) in a disordered gel-like medium (Sephadex LH-20) filled with electrolyte solution. We find a, qualitatively expected, observation time-dependence of D+, but for the first time such a time-dependence is also observed for u+, which means the detection of the phenomenon of "anomalous field assisted diffusion" or "anomalous mobility." For the measurement of the short-time behavior of the mobility a new pulse sequence is presented. The time-dependent mobilities were measured at three different external electrical fields E. From the long-time behavior of D+, u+, and DH2O three independent values for the tortuosity T of the porous system could be derived. We find equality of the tortuosities T(D+) and T(u+), which represents a first experimental proof of the validity of the Einstein relation (D+ approximately u+) in a disordered medium. Finally, we discuss advantages of the possible use of "anomalous field assisted diffusion" over the commonly used "anomalous diffusion" in morphology studies by dynamic imaging in porous media.