Heil S R, Holz M
Institut für Physikalische Chemie und Elektrochemie, Universität Karlsruhe, Kaiserstr. 12, Karlsruhe, D-76128, Germany.
J Magn Reson. 1998 Nov;135(1):17-22. doi: 10.1006/jmre.1998.1536.
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.
多孔介质中的电输运在许多纯科学和应用科学领域都起着重要作用。电荷输运的基本微观过程长期以来一直吸引着相当多的理论关注。然而，在微观层面上，到目前为止还没有针对这个问题的实验方法。在本文中，我们通过使用一种合适的多孔系统证明，两种结合的核磁共振方法可以提供这样的首次实验途径。我们应用普通的脉冲场梯度核磁共振方法和特殊的电泳核磁共振（ENMR）技术来测量阳离子（(C4H9)+4）在充满电解质溶液的无序凝胶状介质（葡聚糖LH - 20）中的自扩散系数D+和电迁移率u+。我们发现D+在定性上符合预期的观测时间依赖性，但首次也观测到u+具有这种时间依赖性，这意味着检测到了“反常场辅助扩散”或“反常迁移率”现象。为了测量迁移率的短时间行为，我们提出了一种新的脉冲序列。在三个不同的外部电场E下测量了随时间变化的迁移率。从D+、u+和DH2O的长时间行为可以推导出多孔系统曲折度T的三个独立值。我们发现曲折度T(D+)和T(u+)相等，这首次从实验上证明了爱因斯坦关系（D+≈u+）在无序介质中的有效性。最后，我们讨论了在多孔介质形态学研究中，通过动态成像，“反常场辅助扩散”相对于常用的“反常扩散”可能具有的优势。
