Relationship between surface potential and d33 constant in cellular piezoelectric polymers

The development of cellular piezoelectric polymers has shown very promising results thanks to their high d₃₃ piezoelectric constants which make them candidates for many applications. Cellular piezoelectric polymers, known as ferroelectrets, are obtained by means of an activation process which consists in generating an internal dipole with electrostatic charges produced by internal electric discharges. The most common system for this activation process is the application of a corona discharge on the surface of the sample in order to produce a high internal electric field. The theoretical electrostatic model of the process which is widely used is the Sessler model which relates the internal surface charge density, the air and polymer layers thickness, the dielectric permittivity of the polymer and the Young's Modulus of the cellular material to the d₃₃ piezoelectric constant. In our work, we relate the internal charges of the material with the d₃₃ piezoelectric constant by means of a surface potential scanning of cellular polypropylene biaxially stretched samples. Samples were charged by a corona discharge controlled with a triode electrode. Surface potentials were high enough to generate internal discharges and obtain measurable d₃₃ piezoelectric constants but low enough to be measured with spatial resolution by means of a 3 kV electrostatic probe. Surface potential profiles showed some deviations from the expected bell-shape profile due to the internal electric field generated by the internal static charge. These deviations can be numerically related to the measured d₃₃ piezoelectric constant with the electrostatic Sessler model.