Verification of a model for the d33-coefficient of ferroelectrets

An existing model for the piezoelectric d₃₃-coefficients of charged cellular polymers (ferroelectrets) is tested with experimental data obtained from two different cellular polypropylene (PP) materials. The model assumes the cellular film to consist of plane parallel layers of solid and gaseous material with the surfaces of the solid layers charged in a specific way. Films of charged cellular PP are expanded by a pressure treatment. Subsequently, due to viscoelastic relaxation, the thickness of the films decreases, thus causing a change of their Young´s modulus Y. Values of Y are obtained from interferometric measurements of the thickness resonance frequency. Together with the measured thickness of the solid layers and air layers in the material, the d₃₃-coefficients can be determined from the model. These values are compared with experimental results for d₃₃ also obtained inter-ferometrically by means of the inverse piezoelectric effect. Very good agreement between the calculated and measured d₃₃-coefficients and their change with film thickness and time is obtained.