Distortable Double Well. A Prototype for the Analysis of Relaxation Spectra

Abstract

The origin of dielectric relaxation spectra is frequently not the rotation of dipoles as visualized in the Debye and Onsager models but the reversible transfer of ions or electrons between equilibrium sites. The displacement of such charge carriers corresponds to a reversal of dipole moments and had been treated previously as a shifting of charges between fixed equal or unequal double wells. The reversal of dipole moments in condensed phases, however, frequently has decisive after effects: The electrical unbalance created leads to a compensating action of the surroundings, lowering the free energy and tending to freeze in the charge in the occupied well site. Thus the double well becomes unequal because of the reaction of the embedding medium. This model of a distortable double well is here treated, first in its stationary state with and without superposed dc field and then in its ac response, under the simplifying assumption that the surroundings react by an exponentially decaying distortion described by a time constant and final well depth. The characteristics of the model are that it incorporates the equal and unequal fixed double well as special cases but in addition shows an inherent distribution of relaxation times and—for long observation periods—an anomalously large polarizability, since eventually the wells can be turned with their deepened sites in the favorable field direction.