Simulation of space charge deposition by barrier discharges in piezoelectric polymer foams

Fig. 2 shows the deposited space charge as a function of pressure p and void height. When V reaches its positive maximum in the charging cycle for the second time, the larger voids (with heights above approx. 12 μm) are charged with a density in excess of 1 mC/m². The charging of smaller voids is strongly dependent on pressure, as shown by the Paschen curves in the inset of Fig. 3. As p is increased above 100 kPa, their breakdown field decreases towards a minimum, allowing these voids to be charged. However, if p is increased past the minimum of E_c, the increase in the breakdown field reduces the deposited charge according to (1). Therefore, the piezoelectric coefficient shows a pronounced maximum when plotted as a function of pressure (Fig. 3). For cellular polypropylene (PP) film from VTT Processes, Finland (OW50 grade), the optimum charging pressure is 274 kPa, while for inflated PQ-50 film (Nan Ya Plastics, Taiwan), a value of approx. 170 kPa was found. At this pressure, d₃₃ has increased its value at atmospheric pressure by 50 to 120% (depending on the material), in good agreement with experimental findings [10]. After V is brought back to zero, the field generated by the deposited charges causes secondary breakdowns (so-called back discharges [11]), reducing the effective charge density. Again, elevated pressure is beneficial as the higher critical field in the large voids reduces the amount of back discharging.