Relaxation time for the ionic current in a nematic cell under a large electric field.

We evaluate the ionic relaxation time of a nematic cell subjected to a potential difference, V0 , very large with respect to VT=KBT/q=0.025 V, where KBT is the thermal energy, and q the electrical charge of the ions, assumed monovalent. The analysis is performed by assuming that the mobilities of the positive and negative ions are the same, and that the ions can be considered pointlike. We show that, for V0>>VT, the relaxation time tends to the time of flight of the ions. In our analysis the ionic charges are assumed to form two surface layers responsible for a partial screening of the external field. In this framework, the evolution of the surface-charge density is determined by a simple differential equation related to the conservation of the ions number. According to our calculations, the relaxation time of the surface density of ionic origin, and of the electrical potential close to the electrodes, depends on the applied voltage, in agreement with the experimental observations.