Persistent internal polarization and distribution of activation energies

Electrical surface charge density and decay are influenced by the surface and bulk properties of the material that serves as the charge carrier. Persistent internal polarization (PIP) is one of the influencing factors. A better understanding of this effect is of direct interest in electrophotography. PIP can be produced by electrical, thermal, optical, and penetrating radiation activation, separately, or jointly. Experimental aspects are complex, due to the superposition of a variety of factors which by themselves are incidental. It seems important to coordinate these various aspects and obtain an interpretation in terms of a general concept. In a previous paper, Gross presented a theory of linear PIP for the case of electrical and thermal activation (electret behavior) in which all observable functions are expressed in terms of a distribution function of activation energies of the elements influenced by the external stimulant. In this paper this theory is applied to a group of materials, like carnauba wax or polymers, that are characterized by a wide distribution of activation energies. Experimental evidence indicates that the number of elements in a given energy interval increases with increasing energy, and leads to an exponential law for the distribution function. The consequences of this situation are examined and a consistent description of all pertinent aspects of thermally activated PIP is obtained.