Modeling of piezoelectric coupling coefficients of soft ferroelectrets for energy harvesting

Recently, Fluoroethylenepropylene (FEP) tubes have been thermally fused to form ferroelectrets with a parallel-tunnel structure with well-defined air gaps thereby improving their applicability for energy harvesting applications. These structures exhibit mechanical and electric properties, mostly depending on their geometry, which result in structure-specific longitudinal and transversal piezoelectric coupling coefficients (d₃₃ and d₃₁). This work presents a finite element model able to describe the mechanical-to-electrical coupling of FEP parallel tunnel structures. The focus of the presented paper, however, lies singularly on the coefficient d₃₃, neglecting the transversal coupling coefficient d₃₁. The coupling coefficient d₃₃ is calculated in three main steps. First, the induced charge on the electrode's surface for the unloaded state is determined. Second, the deformation of the structure due to an external force applied in thickness direction is computed. Third, the modified shape is used to determine the electrode's charge variation. The model correctly predicts the experimental values for the Young's moduli in the range of 0.6 MPa to 0.9 MPa, within 10 %. The piezoelectric coefficient d₃₃ is predicted for two internal charge densities, namely 3 x 10^-4 C/m² and 5 x 10^-4 C/m². The respective d₃₃ coefficients are 110 and 240 pC/N. This is in excellent agreement with measured values of 120 and 180 pC/N, respectively. The results prove the finite element model to be suitable to calculate the piezoelectric coupling coefficients for different types of geometries.