Electromagnetic Fluctuations at the Nanoscale by Aleksandr I. Volokitin & Bo N.J. Persson

Author:Aleksandr I. Volokitin & Bo N.J. Persson
Language: eng
Format: epub
Publisher: Springer Berlin Heidelberg, Berlin, Heidelberg

(9.50)

where q is the magnitude of the component of the wave vector parallel to surface. We will assume that the liquid consists of ions of two types a and b. The equation of continuity for the ions

(9.51)

where , , where and are the concentration of ions in the presence and absence of the electric field, respectively. To linear order in the electric field

(9.52)

where is the diffusion coefficient, is the mobility and is the charge for ions of type i. The diffusion coefficient and the mobility are related to each other by the Einstein relation: . We consider the case of different ion mobilities differing considerably. In this case, in the calculation of dielectric response it is possible to disregard the diffusion of the less mobile ions. Omitting the index i for the more mobile ions, after substitution of (9.52) in (9.50), we obtain

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