Continuum modeling of charging process and piezoelectricity of ferroelectrets

Ferroelectrets in the form of electrically charged micro-porous foams exhibit a very large longitudinal piezoelectric coefficient d(33). The structure has hence received wide application interests as sensors particularly in acoustic devices. During charging process, electrical breakdown (Paschen breakdown) takes place in the air pores of the foam and introduces free charge pairs. These charges are separated by electrostatic forces and relocated at the interfaces between the polymer and the electrically broken-down medium, where they are trapped quasistatically. The development of this trapped charge density along the interfaces is key for enabling the piezoelectricity of ferroelectrets. In this article, an internal variable based continuum model is proposed to calculate the charge density development at the interfaces, whereas a Maxwell stress based electromechanical model is used for the bulk behavior, i.e., of the polymer and of the medium where the Paschen breakdown takes place. In the modeling, the electrostatic forces between the separated charge pairs are included, as well as the influence of deformation of the solid layers. The material models are implemented in a nonlinear finite element scheme, which allows a detailed analysis of different geometries. A ferroelectret unit with porous expanded polytetrafluoroethylene (ePTFE) surrounded by fluorinated ethylene propylene is studied first. The simulated hysteresis curves of charge density at the surfaces and the calculated longitudinal piezoelectric constant are in good agreement with experimental results. Simulations show a strong dependency of the interface charge development and thus the remnant charges on the thicknesses of the layers and the permittivity of the materials. According to the calculated relation between d(33) and the Young's modulus of ePTFE, the value of the Young's modulus of ePTFE is identified to be around 0.75 MPa, which lies well in the predicted range of 0.45 to 0.80 MPa, determined from the dielectric resonance spectra in the work of Zhang et al. [X. Q. Zhang et al., J. Appl. Phys. 108, 064113 (2010)]. To show the potential of the models, it is also applied to simulation of ferroelectrets with a lens shape. The results indicate that the electrical breakdown happens in a sequential manner, and the local piezoelectric coefficient varies with position. Thereby, the middle point on the surface exhibits the maximum d(33). The simulation results obtained by the proposed models will provide insight for device optimization. (C) 2013 AIP Publishing