Poling kinetics in polar amorphous polymers containing space charge

Polar amorphous polymers available in sheets are readily made into planar capacitors with parallel thin film electrodes on opposite surfaces. They may be poled in this form using a process called thermopoling where a specimen is heated to a temperature near its glass transition temperature T, a voltage V is applied across the electrodes, and the specimen is cooled below T before V is removed. In the s absence of space charge, the electric field E in the specimen of thickness d is homogeneous and has the initial value V/d. The electric polarization P induced by thermopoling is then homogeneous. In practice, however, space charge is almost always present during poling. This charge may be pre-existing or be injected during poling and its mobility may be strongly dependent on temperature. The volume-density of space charge p may then vary spatially and temporally during poling and the resulting E and P no longer can be homogeneous. In those cases, poling kinetics are important in establishing the final polarization distribution P(x). In this paper, we develop mathematical relations among the spatially and/or temporally varying quantities v(t), E(x,t), and p(x,t) where x is a coordinate measuring distance from the initially positive electrode and t is the time.