Dynamic measurement setups for validating piezoelectric energy harvesters in driving conditions

Sustainable power supply to flexible electronics is currently of high interest due to the transition to autonomous and self-driving vehicles. Piezoelectric Energy Harvesters (PEH) can be used as sustainable energy sources by harvesting the electrical power through the material deformation occurring in a tire. In this work, an analytical setup was developed to experimentally validate the energy harvesters for their use in tires. It was designed to measure the harvested electrical energy under simulated driving conditions. The setup includes a Dynamic Mechanical Analysis (DMA) as foundation to simulate the vibrations and dynamic responses occurring in a rolling tire. The dynamic properties and the output voltage from the harvesters were monitored under these sinusoidal conditions. For this, a PEH for tire applications was prepared in a sandwich configuration. It consists of a piezoelectric material, i.e. PolyVinyliDene diFluoride (PVDF) film, inserted in between two layers of electrodes, i.e. elastomers filled with conductive carbon black fillers. The electrical conductivity of elastomeric compounds was measured under dynamic conditions varying dynamic strain, frequencies, and temperatures. Dynamic strain and temperature resulted to be the most significant factors influencing the electrical conductivity of elastomers. Output power from the piezoelectric energy harvester was also measured at varied frequencies and temperatures. Both properties increase considerably the piezoelectric power. This development gives a promising method for analyzing the electro-mechanical properties of conductive and piezoelectric materials and optimizing their performance according to simulated tire-rolling conditions.


Introduction
Nowadays, an increasing number of sensors are being integrated into a vehicle to ensure safe driving, consistent operations, and efficient tire performance [1][2][3][4]. The new generation of tires, namely 'smart tires', combines an advanced monitoring system to observe real-time tire performances, e.g. tread wear, temperature or heat build-up and pressure of the running tires. Attempts to further improve the performance of tire sensors have continuously been made. One of the potential attractive features is an integration of a piezoelectric energy harvester in tires. This has currently been researched due to its key advantage of providing a battery-less system to sensors for autonomous operations [5,6].
Piezoelectric Energy Harvester (PEH) is one of the promising technologies that can potentially replace a battery as power source for sensors in tires. Piezoelectricity is a principle in which the mechanical energy introduced to a dielectric material under dynamic deformations (i.e. shear, tension, or compression) is converted into electrical energy [7]. During the running of a vehicle, tires are continuously subjected to dynamic mechanical conditions that involve external forces, deformations, as well as varied vibrations and excitations during their rotation at various temperatures. When a tire is in contact with the road surface, the tire partially flattens at the contact patch, due to external loads and gravity. The contact patch deforms in tension and compression. In addition, the vibrations in running tires occur due to the interactions between the tires and the road surface. Therefore, mounting a PEH in a tire has a potential to produce electrical energy [2,8].
A PEH consists of two components: a piezoelectric material which generates electricity under mechanical stress and applied electrodes on both sides of the piezoelectric material to induce the flow of the electric charges and store them in a capacitor. To be embedded in a tire, both components of the PEH need to have appropriate design and properties i. e. elasticity, durability and stability. They need to withstand the dynamic service conditions of the rolling tires, which involve variable parameters, i.e. loads, strains and temperatures. Therefore, it is essential to evaluate and validate the conductive and piezoelectric properties of newly developed materials under simulated tire-rolling conditions.
A variety of piezoelectric energy harvesters have been investigated for use as supply power to tire sensors by using various approaches like mathematical models, numerical simulations and experiments in laboratory conditions as well as in actual tires [1,4,6,[9][10][11][12][13][14][15][16][17][18][19]. The piezoelectric efficacy is mainly affected by the following parameters: temperature, car speeds, on-road noise excitations/vibrations and vehicle loads/deformations [9,10,16,17]. Various theoretical models reported in literature introduced useful tools to predict the electrical output from PEHs based on the kinematics of a car tire. The strain variation associated with the cyclic deformation of a tire is substantial. The tread and sidewall of a tire deform to a larger extent at the contact patch area compared to other positions. It was proven that the piezoelectric energy harvesters generate the highest amount of electrical power in the middle of the contact patch area [3,20]. It is based on the fact that the contact patch area experiences compressive strain in the radial direction on each side and an additional tensile strain within the area in the circumferential direction, i.e. 0.1-2%. Tire sidewall and wheel rim were not considered as optimal locations in a tire due to an undesired high deformation of the sidewall, a more difficult installation process and low durability [4,13,20]. The sidewall experiences compressive strain in the radial direction, with a deformation that can be as high as 10-50 mm. The feasibility of using a piezoelectric energy harvester in a tire can be assessed by experiments under laboratory conditions and by embedding it into an actual tire [11,12]. The output power from a piezoceramic-based PEH was analyzed on a lab-scale under sinusoidal vibrations and shock-induced excitations, which confirmed the major influence of these two factors on the electricity harvester performance. Van den Ende et al. [15] were able to measure the output power from a piezoelectric harvester using a tensile test machine coupled with an oscilloscope and then directly attaching it to a real tire. Nevertheless, the authors measured a substantial change in output power when varying tensile and compression strain, as well as temperature. Some researchers investigated further piezoelectric material category (ceramics and polymers) and other factors influencing PEHs performance, e.g. optimal location in the tire (wheel rim and inner liner) and road roughness conditions, by embedding the PEHs in actual tires [6,8,13,14,18,19]. In our previous research, a PEH including a piezopolymer polyvinylidene difluoride and an elastomeric electrode in a sandwich structure was developed [21]. Chemical adhesion between both components and a gluing method of the patch to the inner liner of a tire ensure a durable, flexible and stable harvester able to generate enough electricity under tire-rolling conditions, i.e. 28 mW, to power a tire sensor [21]. This gave a good preliminary indication regarding piezoelectric efficiency, durability and installation method of PEH in actual tires.
It was confirmed in literature that the piezoelectric energy harvester is suitable for replacing the batteries in tire sensors. Relevant aforementioned investigations were conducted in actual tires. However, some crucial factors influencing the performance of PEH components, e.g. temperature, vibrations/excitations, vehicle load, and tire deformation, remain unclear. Therefore, in the present work a tool that exploits the piezoelectric and conductive properties of flexible harvesters under dynamic mechanical conditions of tires was successfully developed. This setup allows to study the feasibility of a PEH for powering tire sensors by exploring the effects of solely compression deformation, excitations/ vibrations and temperature. A Dynamic Mechanic Analysis (DMA) is the fundamental instrument employed for this setup as it is well-recognized as an extremely sensitive and efficient dynamic analyzer for polymers and so a most appropriate technique for simulating tire-rolling conditions. The DMA is capable of analyzing the behavior of polymers under various conditions, e.g. static and dynamic strains and stresses, frequencies, and temperatures. Hence, the DMA can give relevant information on viscoelastic properties of the compounds used to manufacture a tire as well as the input data to model and predict the quality of the final tires like rolling resistance, heat build-up, and ice/wet grip. By selecting the proper values of variable parameters like strain, frequency and temperature, DMA can assess the degree of tread deformation under a given load, which is crucial for simulating rolling tire conditions. Therefore, the use of DMA represents a good analytical method to gain a deeper insight into the electro-dynamics of rubbers.
In the present work, analytical setups based on a combination of DMA and electrical circuits were developed to measure the conductive and piezoelectric properties of polymeric materials as a function of frequency and temperature. Conductive elastomers and flexible piezoelectric polymers were prepared and used for evaluating the setups.

Materials
Piezoelectric polymer PolyVinyliDene diFluoride (PVDF) was supplied by PolyK Technologies LLC (Philipsburg, USA) in a form of a 100 μm thick film. The electrical and chemical properties of this polymer film are given in Table 1.
For the surface treatment of PVDF surface, chloroform (99.5%, Sigma-Aldrich, St. Louis, MO) and 3-thiocyanatopropyltriethoxy silane (Si-264 as tradename, Evonik Industries AG, Essen, Germany) were used. This silane is characterized by a sulfur content of 12.5 wt%, an average molecular weight of 263 g/mol and a density of 1 g/cm 3 .

Conductive elastomeric compounds for electrical conductivity measurements
All conductive elastomeric compounds were prepared using a twosteps procedure in an internal mixer (Brabender Plastograph EC plus, Brabender GmbH & Co KG, Germany), at 80 • C as starting temperature and 75% as fill factor. The rotor speed and mixing time were selected at 100 rpm and 10 min, respectively, based on the results of a preliminary study. NR was initially masticated for 1 min. Then carbon black and oil were added in two portions, each one mixed for half of the pre-set filler mixing time. For the remaining 2 min, the rest of the ingredients (e.g. 6PPD, TMQ, ZnO and stearic acid) were added and mixed. The compounds were then discharged and sheeted out on a two-roll mill for 2 min at 2 mm nip width (Polymix 80 T, Schwabenthan-Maschinen GmbH & Co. KG, Berlin, Germany) and kept overnight before sulfur and TBBS were added to the compound on the above mentioned two-roll mill at 50 • C for 5 min. The vulcanization characteristics of the compounds were analyzed using a Rubber Process Analyzer (RPA 2000, Alpha Technologies, Ohio, USA). Each measurement was done for 20 min at 160 • C at a frequency of 1.667 Hz and an oscillating shear angle of 0.5 • . Conductive elastomeric compounds were cured in a cylindrical shape at t c95 values at 160 • C in a Wickert press WLP 1600 at 100 bar (Wickert Maschinenbau GmbH, Landau, Germany) by using 4 mm-thick steel sheets with cavities of 10 mm as diameter.

Piezoelectric energy harvester for piezoelectric measurements
Piezoelectric energy harvesters were prepared by adhering a surface modified PVDF film (Table 1) with the conductive elastomeric compounds (Table 2). A surface modification of the piezoelectric PVDF film was carried out to improve the interfacial adhesion between the PVDF film and the conductive elastomeric compounds. First, the PVDF film was treated with oxygen plasma using a plasma reactor Plasma-Prep II (SPI Supplies, West Chester, Pennsylvania, USA) consisting of a plasma vacuum chamber, in which the PVDF film was placed. A mechanical vacuum pump (Oerlikon, Lafert S.p.A., Piave, Italy) reduced the pressure inside the chamber to around 100-200 mTorr. After reaching this pressure, the chamber was refilled with oxygen gas. A Radio Frequency (RF) power at 13.56 MHz was applied to the chamber to excite and charge the oxygen molecules by turning them into oxygen radicals. The film was treated with this oxygen plasma for 15 min at room temperature. After this, the PVDF film surface is expected to be randomly covered with hydroxyl and carbonyl groups which are highly reactive towards silanes. The silanization of the oxygen-treated PVDF film was carried out using the silane coupling agent 3-thiocyanatopropyltriethoxysilane. For this, the PVDF film, directly after the plasma treatment, was placed in a desiccator under vacuum at room temperature with 3 ml of 3thiocyanatopropyltriethoxysilane silane in a small Petri dish for 24 h. The film was fixed with a holder to fully expose both sides of the film to the silane vapor. More details of this methodology are reported in Refs. [21][22][23].
After the silane treatment, the PVDF films were assembled in between two layers of conductive elastomeric compounds. Novel molds were designed for the vulcanization of piezoelectric harvester in a cylindrical shape by using Solidworks software; the components are shown in Fig. 1a. The molds were made of structural steel and they include a bottom plate in which 2 mm-thick steel sheets were placed. Each sheet has cylindrical cavities with 10 mm as diameter in which unvulcanized rubber was placed. An upper plate is then needed to exert pressure on the compounds and cure it. In between the two sheets, a 0.1 mm PVDF film was inserted in order to obtain the configuration as shown in Fig. 1b. Piezoelectric energy harvesters in sandwich design were cured using compression molding in a press at 160 • C to their t c95 in cylindrical shapes with a diameter of 10 mm.

Setups for electro-dynamic characterizations
The conductivity and piezoelectricity of the investigated materials were characterized using in-house developed setups. They consisted of a Dynamic Mechanical Analyzer (DMA) to simulate the dynamic mechanical conditions of running tires. The DMA used in this work was the DMA Gabo Eplexor 9 (Netzsch Gabo Instruments GmbH, Ahlden, Germany). DMA is used to determine the viscoelastic properties of elastomeric samples under static and dynamic excitation. Static and dynamic loads, frequency and temperature can be varied. When a sinusoidal deformation is applied, the elastomeric sample response is time-delayed due to the viscoelastic properties. For elastic materials, the modulus of elasticity is the complex modulus E*, defined as a combination of the storage modulus E' (elastic part) and the loss modulus E'' (viscous part).  The ratio of loss modulus and storage modulus is called tan δ.
The measurements were performed in compression mode with a preconditioning of 3.5 N as load, following two methodologies: (1) a temperature sweep from − 120 to 120 • C at frequencies of 10 and 100 Hz; (2) a frequency sweep from 0.1 to 100 Hz at 25 • C. The dynamic analyses were developed based on the assumption for a certain car, selected as an example by considering its weight and tire series typically used for this car. The applied load on each tire was estimated for such a car and the analysis conditions were simulated by DMA, i.e. 10% as static strain and 2% as dynamic strain [24]. It is worth remarking that the static and dynamic strains of compression were 0.5% at a temperature lower than − 35 • C which is the glassy region of the selected rubber. To determine the repeatability of these dynamic analyses, three individually prepared conductive and PEH samples at the center point were measured.

Electrical conductivity measurements
Concerning the electrical properties, the voltage was measured during the temperature and frequency sweeps of DMA. To measure the electrical conductivity of the materials, copper plates with electrical wires were attached to the upper and lower parts of the specimen (i.e. cylindrical sample containing conductive elastomeric compounds) to create a connection with the electrical measuring devices. The attachment of the copper plates to the compression clamp of the DMA is shown in Fig. 2. To avoid an electrical short circuit, the specimen needs to be isolated from the metal clamps. Therefore, the clamps were covered with Kapton tape, i.e. polyimide (PrintTec, Geldermalsen, the Netherlands).
The electrical conductivity of the elastomeric compounds was determined by transmitting a specific current, where the voltage between two copper plates attached to both ends of the conductive elastomeric compounds was measured. The measurement setup included a Direct Current (DC) power supply (0-30 V, 3 A, TENMA, Farnell House, Leeds, UK) to transmit an electrical current to the specimen and a voltage module (Model NI-9215, National Instruments, Austin, TX, USA) to monitor the corresponding voltage drop over a shunt resistor placed in series with the specimen. A circuit with a shunt resistor was used to divert a small part of the current flow and to detect the current across the circuit. Thereby, the conductivity of the specimen was calculated. A compact-DAQ chassis (Model cDAQ-9171, National Instruments, Austin, TX, USA) connected the voltage module (Model NI-9215, National Instruments, Austin, TX, USA) to a USB port and recorded the changes in voltage using computing software. In Fig. 2a the electrical circuit for the conductive measurements is shown.
The measured voltage was used to calculate the electrical conductivity, as expressed by the following equation [25]: The voltage drop over the sample is the difference between the voltage from the power supply (V PS , i.e. 4 V for the tests) and the voltage measured by the module (V S ). The current I s was calculated using Ohm's law by inserting the voltage output from the specimen (V out ) and the value of the resistance (R) of the resistor load. The DMA registered the distance l between the copper plates, i.e. the thickness of the sample during the measurement, while the cross-sectional area A i is calculated considering the cylindrical shape of the specimen, i.e. 10 mm diameter.

Piezoelectric measurements
With the same concept as the conductivity measurement setup, the output voltage generated by the piezoelectric patch was monitored. To measure the output voltage of the materials, copper plates with electrical wires were attached to the upper and lower parts of the specimen (i.e. cylindrical sample containing sandwich design) to create a connection with the electrical measuring devices and the clamps were covered with Kapton tape for the electrical insulation of the specimen. For this piezoelectric measurement, the electrical circuit was simplified: Fig. 2b. It included a shunt resistor placed in series with the specimen to divert the current flow generated by the specimen across the voltage module. The PVDF film in a piezoelectric patch produces electrical charges that move to the patch surface. Then, the conductive elastomer layers enable the transport of the generated electrical current to a voltage module, used to monitor the output voltage. The application of sinusoidal stresses to the piezoelectric patch leads to sinusoidal voltages due to the generation of Alternating Current (AC). The power output (P, μW/cm 2 ) of the piezoelectric patch is calculated using Equation (2) [26]: Where <V 2 > is the average of the squared generated voltage in the dynamic phase while the calculation of the cross-sectional area includes the exact dimensions of cylindrical shape of the specimen. The maximum amount of power is reached when the resistor value (R) is equal to the internal resistance of the piezoelectric patch. Therefore, the effect of the resistor value on the output power was investigated.

Assessment of the electro-dynamic setups
First of all, the impact of the required electrical connections at the DMA to measure the electricity was evaluated. Therefore, the influence of the clamps with and without Kapton tape and copper plates on the electrical properties of the samples analyzed in compression mode was investigated. This was done by using a conductive elastomer compound (Table 2) and the setup/specimen for conductive measurement (prepared according to paragraph 2.2.1 and measured according to paragraph 2.3.1). Fig. 3 shows the complex modulus (E*) and the tan δ of NR filled with 15 vol% of CCB in a temperature range of − 120 to 120 • C at a frequency of 10 Hz.
The results show that the presence of Kapton tape and copper plates does not considerably affect the measurements of the complex modulus and tan δ. In this range of temperatures, the differences in the output values are negligibly small, ascertaining that this setup can be utilized for determining the conductivity and piezoelectricity of the materials.

Progress of conductive measurement in dynamic conditions
Firstly, the conductive elastomeric compounds of the PEH sandwich design were investigated. Conductive elastomeric compounds operate in various conditions, such as diversified mechanical loads, temperatures and frequencies during their service life in rolling tires. Fig. 4 shows a typical example of a simultaneous record of the applied dynamic force and the resulting voltage at set parameters.
Before starting the measurement, all conductive elastomeric compounds were conditioned with a pre-load of 3.5 N in order to overcome the impact of deformation history on the measurements, i.e. Mullins effect [27]. After having applied this pre-load (Fig. 4a), the measurement starts by applying static and dynamic strains, of 10% and 2%   respectively, as shown in Fig. 4b. When the specimen is a conductive elastomeric compound, filled at least with a critical amount of conductive carbon black (i.e. at 50% percolation threshold), the sinusoidal dynamic load causes a periodic disruption of filler network due to the oscillating deformation, resulting in an alternating connection and disconnection of the filler particles. It results in a sinusoidal voltage as well. This concept was recently studied in detail by Bhagavatheswaran et al. [28]. They studied the piezoresistive properties of elastomeric compounds. In carbon black and carbon nanotubes filled elastomers under dynamic strain, the filler network disrupted and recovered harmoniously, increasing and decreasing the interparticle distances and causing the sinusoidal changes in electrical conductivity over time.
Applying a static and dynamic strain on a conductive elastomeric compound causes the rearrangement of filler network due to an increased internal friction in the material [29]. Measurements of electrical conductivity of conductive elastomers as a function of volume fraction of CCB, called percolation plot, for two values of dynamic strains, 1 and 2%, are shown in Fig. 5. The electrical conductivity was calculated from the voltage measured over time at 100 • C and 100 Hz. In this way, the deformation history was neglected and the conductivity was calculated after ca. 60 min, when the voltage reached a plateau. In this plot, it is possible to distinguish three zones: (1) the insulation region, at a low filler amount and low conductivity; (2) the percolation region with a sharp increase in conductivity and a transition of the material from insulator to conductor; (3) and the conductive region at a high filler amount and high conductivity. Based on these trends, a crossover point in the percolation region can be identified. In the conducting zone, the conductivity increases by ca. 2 orders of magnitude at the higher dynamic strain. This is due to the fact that dynamic deformation affects the physical contact between the particles, implying a decreasing tunneling gap between carbon black particles and increased charge carriers transfer across this conductive path. In the insulating region, the conductivity decreases ca. 1 order of magnitude at higher dynamic strain. This might be because a continuous filler network is not formed at this stage and a higher dynamic strain increases the tunneling distance across the conductive path.

Effects of temperature and frequency
The effects of temperature and frequency on electrical conductivity measured in dynamic conditions were also investigated. For these measurements, five different amounts of the CCB were selected, based on the finding from Fig. 5: unfilled compound and 9 vol% of CCB (insulating region), 11 vol% of CCB (percolation region), 15 and 17 vol% of CCB (conducting region). To determine the repeatability, three individually prepared conductive elastomeric compounds filled with 15 vol % of CCB were measured and the standard deviation of electrical conductivity was 5%. Fig. 6a and b show tan δ and electrical conductivity as a function of temperature from − 120 to 120 • C.
Based on the tan δ curve, it is possible to distinguish the glassy region (below − 62.5 • C), glass transition region (from − 62.5 to 12.5 • C) and rubbery region (from 12.5 to 120 • C). The temperature has a strong impact on the electrical conductivity of the conductive elastomeric compounds. Elevated temperatures accelerate the transfer of charge carriers across the conductive path. This concept is mainly valid in the rubbery region due to the higher flexibility of the material in this state. Noteworthy, there are different trends of the electrical conductivity in the glass transition region of the compounds. Compound in the percolation zone (i.e., 11 vol% of CCB) shows a sharp decrease in the electrical conductivity in the glass transition region. Due to the limitation of the setup, it is not possible to measure a value of conductivity lower than 10 − 10 S/cm. Thus, it was not possible to investigate in this study the sharp decreases of electrical conductivity in the glass transition region for compounds in the insulation zone (i.e., 9 vol%). As shown in Fig. 6c, the glass transition phenomenon results in the coexistence of rubbery and glassy polymeric chains and morphological change of filler network. In the range of temperature from − 62.5 to − 37.5 • C, the electrical conductivity decreases as rubbery polymeric chains are present next to the glassy chains, affecting the mobility of charge carriers across the carbon black particles and the tunneling effect. From ca. − 37.5 • C, the electrical conductivity increases as in this region the compound is characterized by solely rubbery polymeric chains and an increased free volume [30,31]. This implies higher mobility of charge carriers inside the compounds leading to a filler network orientation with a lower tunneling gap across the conductive path and thus an increased electrical conductivity. This phenomenon has a much lower impact in the case of compounds in the conducting zone; the conductive elastomeric compound filled with 17 vol% of CCB shows a continuously increasing trend with rising temperature. This is probably due to the fact that the amount of conductive filler is much larger, and the higher free volume for the glassy-to-rubbery transition has a negligible effect on the conductivity. This concept agrees with the results reported in literature [28,32].
In the whole temperature range, the electrical conductivity of the compounds increases with increasing CCB amount, due to a more extensive filler network. To provide a deeper insight into how the filler network affects this phenomenon, Fig. 7 shows the electrical conductivity as a function of volume fraction of carbon black at different temperatures in the three different regions. In the rubbery region, higher temperature causes a decrease in percolation threshold and an increase of conductivity in the conductive region. This confirms the acceleration of the charge carrier across the conductive path and a decreased percolation threshold. In the glass transition region, the fitting does not reach a plateau, as in the other regions. As above-mentioned, the glass transition affects the mobility of charge carriers and the percolation threshold. Thus, a higher amount of carbon black is needed in the material to be conductive in this region.   8 shows the electrical conductivity as a function of frequency from 0.1 to 100 Hz at room temperature. In the entire investigated range of frequencies, the electrical conductivity increases with the carbon black amount, as in the results of the temperature sweep analysis (Fig. 6, rubbery region). Additionally, the conductivity of all compounds seems to be not affected by the frequency. This is commonly called Direct Current (DC) conductivity and it is associated with the diffusion process of charge carriers across the conductive path [29,33].

Progress of piezoelectric measurement in dynamic conditions
After the confirmation of the negligible influence of the electrical circuit presence and after the optimization of the conductive elastomeric compound, the measurement device is now settled, ready to be used for the characterization of the PEH. The applied static and dynamic loads cause a deformation of the repeating units (CH 2 -CF 2 ) in piezoelectric polymer PVDF, forming dipole moments inside the material and consequently charges generation. The conductive elastomeric compounds are present on each side of the PVDF film to induce the flow of the electrical charges. The structure of the piezoelectric energy harvester at its original state is shown in Fig. 9a. Both surfaces of the piezoelectric material are characterized by opposite charges. When a compressive strain is applied (in Fig. 9b), the dipoles deflect, leading to a weakening of the internal dipole moments and their polarity. Consequently, the positive-charged surface attracts the electrons via the electrical circuit connected to both electrodes. When the strain is removed, the charges flow in the opposite direction. During the DMA measurements, when a sinusoidal dynamic load is applied to the material, the resulting voltage follows a sinusoidal trend as well. The positive and negative peaks of the voltage are caused by the flow of the charges between the upper and lower conductive layers of the PEH. Fig. 9 shows the progress of the piezoelectric measurement of a harvester, i.e. PVDF sandwiched by NR filled with 15 vol% of CCB, during a frequency sweep in the range of 0.1-100 Hz. With increasing frequency, a lower voltage is generated when the dynamic load is applied and, in turn, a lower power, which can be calculated using Equation (2). This is due to the vibrational displacements of dipoles of the piezoelectric material (see Fig. 11).
To harvest power from piezoelectric harvesters, the device needs to be connected to a resistor load. The output power from the piezoelectric harvester is maximized when the resistor load matches the internal resistance of the piezoelectric material. Thus, the effect of the resistor load on a PVDF-based harvester was firstly investigated. Five different resistor loads (see Fig. 2b) were tested for the piezoelectric measurements, i.e. 1.5, 2.2, 3.9, 4.7 and 10 MΩ. Fig. 10 shows the output power at 25 • C and 100 Hz from the piezoelectric harvester patch having PVDF and the conductive elastomeric compound NR filled with 15 vol% of CCB. This conductive elastomeric compound was selected as it corresponds to the minimum amount of carbon black above which there is no any meaningful change of electrical conductivity (see Figs. 6 and 7).
To determine the repeatability, three individually prepared piezoelectric harvester patches were measured at 4.7 MΩ and the standard deviation of electrical conductivity was 5%. The generated output power across a resistor load gradually increases to reach a maximum and then decreases with further increasing resistance. In the experiments performed with the resistors listed above, the maximum electrical power of 1.44 μW/cm 2 was obtained with a resistor of 4.7 MΩ. In the electrical circuit for piezoelectric measurements (Fig. 2b), the resistor load is in series with the piezoelectric harvester. Thus, the electrical current  generated by the piezoelectric patch goes through the resistor load. The output is then maximized only when the resistor load is close to the internal resistance of the piezoelectric harvester. The resistor with a load value of 4.7 MΩ was selected for further analyses of the piezoelectric patches prepared with different conductive elastomeric compounds.

Effects of temperature and frequency
The output power derived from the sandwich-designed harvester PVDF and the conductive elastomeric compounds filled with 11, 15 and 17 vol% was measured as a function of frequency and temperature with a resistance load of 4.7 MΩ. The results are shown in Fig. 11. To determine the repeatability, three individually prepared piezoelectric harvester patches including PVDF and conductive elastomeric compound filled with 15 vol% of CCB were measured. The standard deviation of electrical conductivity was 5%. Fig. 11a indicates that the output power increases at elevated frequencies, because there is a higher number of mechanical excitations to the material in a given timespan, activating the dipoles inside the PVDF film more frequently. It is reported that a value of frequency exists, called resonant frequency, in which the piezoelectric material has the highest efficiency [34]. This resonance frequency depends on the materials themselves and the mechanical load. The maximum power of the investigated piezoelectric harvester is found at 100 Hz, the highest frequency value of the DMA used in this study. By increasing the temperature (Fig. 11b), the generated power rises considerably. This behavior confirms the already observed phenomena (Fig. 6b) that the temperature increases considerably the electrical conductivity. Additionally, the piezoelectric effect increases with increasing temperature due to the higher mobility of dipoles in the PVDF film, resulting in higher power output. The piezoelectric patch within the conductive elastomeric compound NR filled with 17 vol% of CCB provides the highest generated electricity due to the highest value of conductivity.

Conclusions
Novel setups to characterize the components of piezoelectric energy harvester (PEH) under simulated conditions of tires were successfully developed. The setups include a DMA coupled with electrical circuits. These analyses lead to a better understanding of the main factors influencing the electrical conductivity of elastomers and the output voltage from piezoelectric materials. Moreover, by selecting the parameters in DMA for simulating the tire-rolling conditions, piezoelectric energy harvester components were studied and optimized.
The electrical conductivity of elastomers is enhanced via the socalled mechanism tunneling effect, by the addition of carbon black. Increasing carbon black amounts and dynamic strain level results in the electrical conductivity increase due to a reduced tunneling distance. The electrical conductivity of elastomeric compounds (used as electrodes of PEH) showed a strong temperature dependency. The compounds with an amount of carbon black below and at the percolation threshold lost their electrical properties in the glass transition region, but the conductivity increased again with increasing temperature. This phenomenon is attributed to the chain and segmental mobility and structural change of filler in this region. In the investigated range of frequencies, i.e. 0.1-100 Hz, the electrical conductivity shows a frequency-independent trend.
PVDF film with 0.1 mm thickness was sandwiched between two layers of elastomeric conductive compound to form a flexible piezoelectric energy harvester. With the developed setup it was possible to select a resistor load in order to maximize the output power and determine a temperature and frequency range in which the output power is the highest.

Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Data availability
Data will be made available on request.