Ferroelectret is a cellular polymer foam that is able to convert compressive and bending forces into electrical signals, which 10 can be used for both sensing and energy harvesting. In the past several research groups have proposed theoretical models that 11 relate the output voltage of the ferroelectret to its mechanical deformation. This is particularly useful for sensing applications 12where the signal-to-noise ratio is important. However, for energy harvesting applications, a theoretical model needs to include 13 both the voltage across a resistive load and the duration of the electrical signal as energy is an integral of power over time. In 14 this work, we propose a theoretical model that explains the behaviour of a ferroelectret when used as an energy harvester. This 15 model can be used to predict the energy output of a ferroelectret by knowing its parameters, and therefore optimize the harvester 16 design for specific energy harvesting application. 17 18
Introduction 19A ferroelectret is a thin and flexible porous polymer 20 that can store positive and negative charges in its internal 21 voids after charging. It is then able to convert compressive 22 and bending forces into electrical signals that can be used 23 for both sensing and energy harvesting [1][2][3][4][5][6][7][8][9][10]. Our 24 previous study has demonstrated that the output energy 25 from porous polypropylene (PP) ferroelectret is sufficient 26 to power a low-power wireless sensor chipset [10]. When 27 a ferroelectret is used in energy harvesting applications, its 28 output pulses can be used to charge an energy storage 29 device, such as a capacitor, to store the energy that 30 generated from the mechanical deformation. This is 31 similar in principle to piezoelectric energy harvesting 32 using piezo ceramics [11, 12]. However, ferroelectret 33 materials are flexible and therefore more attractive for 34 wearable applications. 35When ferroelectret is used as the sensing material in a 36 sensor, the magnitude of the output voltage and the signal-37 to-noise ratio are the key design parameters [8,13]. 38 Previous studies [3,[14][15][16] To predict the output energy of a ferroelectret, we 82 propose an electromechanical model that treats the 83 ferroelectret as both a capacitor and a spring-mass-damper 84 system. In this model a ferroelectret can be treated as a 85 capacitor with internal spring that provides restoring force 86 when the applied compressive force is released. 3, 28], its 2 capacitance C will increase as the thickness reduces when 3 a compressive force is applied. Using 33 = and = 4 , the Vout of the ferroelectret can be expressed as 5output voltage when compressed. When the ferroelectret is 1 treated as a capacitor containing charge [where C is the capacitance of the ferroelectret when 7 compressed. Since = ɛ 33 ℎ− ℎ in Figure 3, Eq.(1) can 8 be derived into 9where ɛ33 is the permittivity of the material. Using Eq. (2), 11the Vout of a ferroelectret can be related to its dimensional 12 parameters (b, l, h), thickness deforma...