Polarizability of the ionic cloud around a charged membrane sheet

The polarizability of the ionic cloud around a charged membrane sheet parallel to the surface is calculated. The membrane is modeled as an infinitely thin and long strip of width 2d'. The Poisson-Boltzmann equation is solved with an external electric field as a perturbation. The polarizability is given in closed integral form, with numerical results. At higher salt concentration the polarizability varies approximately as kappa(-3), where kappa is the Debye-Hückel constant. The given theoretical result can account for the a.c. electrodichroism of purple membrane suspensions.