# Piezoelectric and Electromechanical Characteristics of Porous Poly(Ethylene-co-Vinyl Acetate) Copolymer Films for Smart Sensors and Mechanical Energy Harvesting Applications

Chouaib Ennawaoui, Abdelowahed Hajjaji, Cédric Samuel, Erroumayssae Sabani, Abdelkader Rjafallah, Ikrame Najibi, El Mehdi Laadissi, El Mehdi Loualid, Mohamed Rguiti, Abdessamad El Ballouti, et al.

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Chouaib Ennawaoui, Abdelowahed Hajjaji, Cédric Samuel, Erroumayssae Sabani, Abdelkader Rjafallah, et al.. Piezoelectric and Electromechanical Characteristics of Porous Poly(Ethylene-co-Vinyl Acetate) Copolymer Films for Smart Sensors and Mechanical Energy Harvesting Applications. Applied System Innovation, 2021, 4 (3), pp.57. 10.3390/asi4030057. hal-03703173

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Article

# Piezoelectric and Electromechanical Characteristics of Porous Poly(Ethylene-co-Vinyl Acetate) Copolymer Films for Smart Sensors and Mechanical Energy Harvesting Applications

Chouaib Ennawaoui <fnref n="1" />*, Abdelowahed Hajjaji <fnref n="1" />, Cédric Samuel <fnref n="2" />, Erroumayssae Sabani <fnref n="1" />, Abdelkader Rjafallah <fnref n="1" />, Ikrane Najihi <fnref n="1" />, El Mehdi Laadissi ¹ID, El Mehdi Loualid ¹ID, Mohamed Rguiti <fnref n="3" />, Abdessamad El Ballouti <fnref n="1" /> and Azeddine Azim <fnref n="1" />

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**Citation:** Ennawaoui, C.; Hajjaji, A.; Samuel, C.; Sabani, E.; Rjafallah, A.; Najihi, I.; Laadissi, E.M.; Loualid, E.M.; Rguiti, M.; Ballouti, A.E.; et al. Piezoelectric and Electromechanical Characteristics of Porous Poly(Ethylene-co-Vinyl Acetate) Copolymer Films for Smart Sensors and Mechanical Energy Harvesting Applications. *Appl. Syst. Innov.* **2021**, *4*, 57. https://doi.org/10.3390/asi4030057

Academic Editor: Andrey Chernov

Received: 14 July 2021

Accepted: 18 August 2021

Published: 26 August 2021

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**Abstract:** This paper investigates energy harvesting performances of porous piezoelectric polymer films to collect electrical energy from vibrations and power various sensors. The influence of void content on the elastic matrix, dielectric, electrical, and mechanical properties of porous piezoelectric polymer films produced from available commercial poly(ethylene-co-vinyl acetate) using an industrially applicable melt-state extrusion method (EVA) were examined and discussed. Electrical and mechanical characterization showed an increase in the harvested current and a decrease in Young's modulus with the increasing ratio of voids. Thermal analysis revealed a decrease in piezoelectric constant of the porous materials. The authors present a mathematical model that is able to predict harvested current as a function of matrix characteristics, mechanical excitation and porosity percentage. The output current is directly proportional to the porosity percentage. The harvested power significantly increases with increasing strain or porosity, achieving a power value up to 0.23, 1.55, and 3.87 mW/m<fnref n="3" /> for three EVA compositions: EVA 0%, EVA 37% and EVA 65%, respectively. In conclusion, porous piezoelectric EVA films has great potential from an energy density viewpoint and could represent interesting candidates for energy harvesting applications. Our work contributes to the development of smart materials, with potential uses as innovative harvester systems of energy generated by different vibration sources such as roads, machines and oceans.

**Keywords:** porous polymers; piezoelectric effect; poly(ethylene-co-vinyl acetate); mechanical energy harvesting

## 1. Introduction

Piezoelectric materials are optimized for special applications ranging from mechanical structures to electronic devices, from applications in structural health monitoring and aerospace to active vibration damping and the automotive industry [1-4]. Today, piezoelectric polymers have been considered for energy harvesting applications [5-8]. The material has remarkable fatigue resistance and environmental stability [9], but it has not been recognized as a promising energy harvesting material because of its low piezoelectric constants when compared to PZT ceramics [10-12]. Recently, researchers investigated porous piezoelectric polymers consisting of an ionized cellular polypropylene film made by a chemical elaboration method using nitrogen gas [13]. Excellent piezoelectric coefficients up to 2000 pC/N for

<footnote n="1">¹ Sciences Engineer Laboratory for Energy (LabSIPE), National School of Applied Sciences, Chouaib Doukkali University, El Jadida 24030, Morocco; hajjaji12@gmail.com (A.H.); erroumayssae@gmail.com (E.S.); rjafallah.abdelkader@gmail.com (A.R.); najihi.ikram@gmail.com (I.N.); laadissi.e@ucd.ac.ma (E.M.L.); loualid.m@ucd.ac.ma (E.M.L.); elballouti@hotmail.com (A.E.B.); azim.a@ucd.ac.ma (A.A.)</footnote>

<footnote n="2">² IMT Lille Douai, Institut Mines-Telecom, Univ. Lille, Centre for Materials and Processes, F-59000 Lille, France; cedric.samuel@imt-lille-douai.fr</footnote>

<footnote n="3">³ EA 2443-LMCPA-Laboratory of Ceramic Materials and Associated Processes, Polytechnic University of Hauts-de-France, F-59313 Valenciennes, France; mohamed.rguiti@uphf.fr</footnote>

<footnote>* Correspondence: chouaib.enna@gmail.com</footnote>
specific morphologies and mechanical conditions comparably higher than those of piezo-
ceramics were identified [14,15]. In order to demonstrate the ability of the porous piezoelectric
polymers in a harsh environment, Zhong et al. [16] fabricated PET/EVA/PET laminated films
and ionized them by a corona charging method. The longitudinal piezoelectric coefficient of
the developed generator reached ~6300 pC/N. Zhang et al. [15] showed energy harvesting
applications with this type of cellular material based on piezoelectret fluorocarbon polymers
with a power collected value up to 109 W [16]. Kachroudi et al. [17] examined air-spaced
cantilevers elaborated from a PDMS porous piezoelectric material for energy harvesting
applications. For frequencies ranging from 5 Hz to 200 Hz, the output power reached a
maximum of 136 nW and remained stable at 103 nW.

Different procedures, techniques and methods have been developed and used in
order to prepare the porous polymers, e.g., compression molding [18], extrusion [19,20],
injection [21], solvent casting [22], tape casting [23], and spin coating [24]. Void content
creation techniques provide opportunities to fabricate advanced polymers with greater
physical proprieties and controlled volume as a function of porosity fraction [25]. The
porous piezoelectric ceramics mainly suffer from low mechanical proprieties, high cost
for preparation and limited application fields [26]. Porous piezoelectric polymers can be
described as particles that contain void or gas by a coating or shell and have diameters in
the 1–1000 µm range [27]. Commercial uses for this type of material include functional
textiles, adhesives, cosmetics, medicines, and other medical applications [28,29]. Physical
methods, chemical methods, and physico-chemical methods are the three strategies used
to create porous polymers [30–32]. The physical methods contain techniques such as spray
cooling, spray drying and fluidized bed processes, and the chemical methods contain in
situ polymerization and the solvent extraction/evaporation method. The physico-chemical
methods contain simple and complex methods as well as sol gel technology. After the
elaboration step of polymer foams, gas ionization is an important step to create the pseudo
piezoelectric effect [33–37]. Starting with a polymer film with embedded air cells, internal
charging of air can be carried out through electrical ionization [38]. When a large electric
field is applied across the film, gas molecules in the cells become ionized and opposite
charges are accelerated and implanted on each side of the cells, depending on the applied
electric field direction [39–41]. Such artificially embedded dipoles respond externally
to an applied electrical field or mechanical force similar to piezoelectric material [42].
Porous piezoelectric polymers are also extremely flexible, making them ideal candidates
for mechanical energy harvesters [43]. In this field, commercially available poly(ethylene-
co-vinyl acetate) (EVA) could be of great interest, with an intrinsic low modulus and high
flexibility similar to elastomeric materials [44]. The EVA matrix shows a high compatibility
with pores, making them an excellent candidate for incorporation of electrical macro-
dipoles [45].

In order to achieve the above-mentioned purpose, our prior studies have been per-
formed on EVA porous piezoelectric polymers [46]. SEM analysis has been realized to
determine the homogeneity of gas cells’ distribution in the EVA matrix. A good distribu-
tion of cells/voids in the EVA matrix has been obtained for all fabricated films. Various
means of increasing the intrinsic characteristics of the copolymers were also studied and
demonstrated the simplicity and advantage of working in the pseudo-piezoelectric effect.

To continue in the same research area, the objective of this study is to evaluate the
energy harvesting by EVA porous polymers in order to increase the conversion abilities of
porous piezoelectric polymers. The goals of the next sections are to: (i) characterize mechan-
ical and piezoelectric proprieties of these materials with their mechanical/thermal stability,
and (ii) use a theoretical model and experimental setup to demonstrate the possibility of
using the cellular EVA piezoelectric for mechanical energy harvesting applications.
## 2. Materials, Process, and Characterizations

### 2.1. Materials Preparation

The matrix material used in this study was a poly(ethylene-co-vinyl acetate) random copolymer (EVA, Greenflex® FC45F) supplied by ENI Versalis Spa (Milan, Italy). The EVA used has a vinyl acetate content of 14 wt.%. The cellular EVA films were produced by a melt-state coextrusion process using 0%, 1%, and 2% of Hydrocerol® ITP848 (Clariant, Muttenz, Switzerland) as a chemical foaming agent (CFA). The as-produced films had a thickness of around between 160 and 310 µm. You can find more information on film elaboration and morphological analysis in our previous work [46].

### 2.2. Electrical Charging/Ionization Process

To create piezoelectric properties in our porous polymer films, a high voltage was applied perpendicular to the material surface to charge the encapsulated gas in the foams (air) and create electrical macro-dipoles. To charge the porous copolymer samples, a high-resolution sputter coater coats the film with a silver electrode on both surfaces (12 nm thick) under high vacuum, and then subjects it to DC electric fields E of 10 kV/mm.

High voltage was delivered by a voltage amplifier of gain 1000 (TREK10/10 B, Trek Inc., Lisses, France). Input was controlled by a function generator (Agilent 33220A, Santa Clara, CA, USA). The sample had a surface area of 400 mm², and the electrical charges were injected for a duration of 15 min. Figure 1 gives a schematic representation of the electrical ionization process. The electrical charging process was performed in silicone oil. The silicone oil used in the experiment is a dielectric liquid consisting of polydimethylsiloxane with a purity specially controlled for use in electrical engineering.

<figure><img src="image_5.png" /><figcaption>**Figure 1.** Illustration of electrical ionization process using DC generator.</figcaption></figure>

### 2.3. Physical Characterizations

The porosity, foam, or void content of porous polymer materials is an important parameter that must be measured with a high precision balance (OHAUS® ADVENTURER™, NJ, USA) ($m = 10^{-4}$ g). The porous films' Young's modulus was determined using a computer-controlled EM MODEL 00 UNIVERSAL testing machine (ERM-automatismes, Carpentras, France) with a 20 kN load cell [47].

The longitudinal piezoelectric coefficient of electrically ionized cellular EVA film is determined using a piezometer (model YE2730). A HP 4284A LCR meter was used to do the dielectric measurements (Agilent Technologies, Santa Clara, CA, USA).

### 2.4. Experimental Harvesting Energy Test

For the active energy harvesting system investigated within the scope of this study, electric energy parameters were performed. The setup for characterizing the current and voltage collected by flexible materials is shown schematically in Figure 2. These measurements were made with a one-degree-of-freedom table. The material is held in
place by two jaws, one of which is movable and attached to the table through a degree of freedom, while the other is immovable and connected to the force sensor.

<figure><img src="image_6.png" /><figcaption>**Figure 2.** Schematic illustration of the experimental setup for the energy harvesting measurements.</figcaption></figure>

The NewPort table was controlled using a computing process. It is possible to obtain a wide range of strain over a wide frequency band. At $f_m = 4$ Hz, the film was stretched with maximum transverse strain amplitudes of 0.25%, 0.50%, and 0.75%. The output from the current and voltage harvested by the piezoelectric materials were monitored using Stanford Model SR 570 (Stanford Research Systems Inc., Sunnyvale, CA, USA) and Scope Gw INSTEK GDS-2074A (INSTEK, New Taipei City, Taiwan), respectively.

**3. Results and Discussions**

**3.1. Mechanical Characterization**

The material used in this work is a thin film flexible multilayer structural device with an EVA film between 160 and 320 µm. The device is then encapsulated in between two thin EVA protective layers without pores. The multilayer material is sandwiched in between two 12 nm thin film metal electrodes (Figure 3). The film compositions are summarized in Table 1.

<figure><img src="image_7.png" /><figcaption>**Figure 3.** Description of the composition of pseudo-piezoelectric cellular EVA films. The mechanical tests' objective is to describe the macroscopic behavior of the three compositions studied in the static and dynamic case, then establish the relationship between this macroscopic and the microscopic material characteristics.</figcaption></figure>
<table><caption>**Table 1.** Film compositions before and after extrusion operation.</caption><thead><tr><th rowspan="2">Samples</th><th colspan="3">Before Extrusion</th><th colspan="2">After Extrusion</th></tr><tr><th>Ethylene (%)</th><th>Vinyl Acetate (%)</th><th>Hydrocerol (%)</th><th>Poly(Ethylene-co-Vinyl Acetate) (%)</th><th>Porosity (%)</th></tr></thead><tbody><tr><td>EVA 0</td><td>86</td><td>14</td><td>0</td><td>100</td><td>0</td></tr><tr><td>EVA 1</td><td>85</td><td>14</td><td>1</td><td>63</td><td>37</td></tr><tr><td>EVA 2</td><td>84</td><td>14</td><td>2</td><td>35</td><td>65</td></tr></tbody></table>

The objective of the mechanical tests is to describe the macroscopic behavior of the three compositions studied in the static and dynamic case, then establish a relationship between these macroscopic and the microscopic material characteristics.

The Young's modulus according to the pourcentage of porosity was evaluated. The results presented in Figure 4 show that Young's modulus of the material decreases in the presence of porosity, as a typical result obtained with porous materials. The test was performed on four rectangular samples with a crosshead speed of 10 mm/min at room temperature.

<figure><img src="image_8.png" /><figcaption>**Figure 4.** (a) Applied force as a function of machine displacement of EVA 0%, EVA 37% and EVA 65%. (b) Young's modulus as a function of porosity percentage.</figcaption></figure>

Figure 4 reports the mechanical properties as a function of cellular morphology. It is clear that for EVA compositions, the values decrease linearly with pore content (about 29, 25 and 20 MPa for 0%, 37% and 65% of pores, respectively). For the same condition to each film, EVA 65% generates bigger strains than EVA 37% and EVA 0%. Raising the percentage of gas cells raises the quantity of mechanical energy absorbed by the materials, thus increasing the material flexibility. This flexibility is due to the shape and the gas cell number, which create sensitivity to the mechanical stress.

The cyclic mechanical loading at various frequencies is measured using the dynamic mechanical analysis technique (DMA). For testing, a porous EVA is placed into the DMA's tensile grips. The sample is then subjected to a predefined maximum tensile stress, which elongates the material. The material is returned to zero force at the end of one cycle. All of the experiments were carried out at room temperature (25 °C).

Figure 5a,b represent the stress-strain hysteretic response of porous EVA when exposed to frequencies of 4 and 20 Hz, respectively. Each frequency was subjected to six separate tests. The average of the six experiments is shown in Figure 5. When porous piezoelectric EVA is exposed to cyclic mechanical stress, it develops hysteretic behavior. Microstructural changes such as cell morphology, matrix mechanical proprieties, and other potential permanent microstructural changes such as cracking cause the hysteretic response under the mentioned loading conditions.
<figure><img src="image_9.png" /><figcaption>**Figure 5.** Stress–strain hysteretic response of EVA 0% (Black curve), EVA 37% (Red curve) and EVA 65% (Blue curve) with various cycles. (a) 4 Hz and (b) 20 Hz.</figcaption></figure>

## 3.2. Influence of Environment Temperature and Time on the Piezoelectric Properties

The goal of this subsection is to test the piezoelectric properties' stability of the cellular EVA. The first experiment consists of measuring the piezoelectric constant as a function of the environmental temperature. The purpose of this experiment is to show the effect of temperature on the material. The first phase in the experiment was to apply a gradual temperature rise while maintaining constant pressure (5 MPa). The temperature was gradually raised from 0 to 180 °C, with a 20 °C increment every 10 min. The second experiment is to measure the piezoelectric constant as a function of time. The objective of this experiment is to show the capacity of the material to store electrical charges. An experimental measurement of the $d_{33}$ piezoelectric coefficient as a function of time and temperature is shown in Figures 6 and 7. Figure 6 presents the changing of the piezoelectric constant with depoling temperature for several silicone oil-ionized samples.

<figure><img src="image_10.png" /><figcaption>**Figure 6.** Piezoelectric coefficient as a function of depolarization temperatures charged in the silicone oil at room temperature.</figcaption></figure>
<figure><img src="image_11.png" /><figcaption>Figure 7. Piezoelectric coefficient as a function of time after ionization process charged in the silicone oil at room temperature.</figcaption></figure>

The principal experimental results demonstrate that when temperature rises, the piezoelectric coefficient remains stable until it reaches a critical limit, at which point the piezoelectric constant reduces. The pores consolidate beyond this point, and the film loses its cells, as well as the local dipoles that provide the pseudo piezoelectric effect. The phase transition solid-liquid temperature is observed when the piezoelectric constant begins to decrease. Thermal depolarization shows a remarkable difference between a sample which contains charges in the defaults without pores (EVA 0%) and a sample which contains ionic dipoles with porous structure (EVA 37% and EVA 65%).

Figure 7 illustrates the temporal evolution of the piezoelectric coefficient, which was measured outside of the laboratory. After the relaxation period, the measurements were collected at room temperature. The d33 piezoelectric coefficient value for EVA 65% reduced from 5.1 to 4.5 pC/N from 0 to 65 h, after which it stabilized at 4.5 pC/N. However, these piezoelectric activities were unstable, and a reduction was observed 65 h after the ionization step. Moreover, the charge in cellular EVA remained constant after this time.

### 3.3. Energy Harvesting Study

#### 3.3.1. Piezoelectric Harvested Current Model

The goal of modeling is to express the current harvested by a piezoelectric material in temporal domain. Modeling the effect of piezoelectric materials is written in the form of the following two fundamental equations. The piezoelectric constitutive equations of direct and converse effects are given below [14]:

$$S = s^E \times T + d_t \times E \qquad (1)$$

$$D = d_t \times T + \varepsilon^T \times E \qquad (2)$$

where S, T, D, E, ε^T, d and s^E are, respectively, the strain, the stress, the electric displacement, the electric field, the dielectric permittivity, the piezoelectric coefficient and the compliance.

It is possible to express the T stress as a function of strain S using Equation (1), given by:

$$T = \frac{S - d_t \times E}{s^E} \qquad (3)$$
By substituting the expression of Equation (3) into Equation (2), the electrical displacement can be expressed as follows:

$$D = d_t \times \frac{S - d_t \times E}{s^E} + \varepsilon^T \times E \quad (4)$$

It is known that the expression of current harvested and electrical displacement is:

$$I = A \times \frac{\partial D}{\partial t} \quad (5)$$

A is the metalized surface of the polymer. Substituting Equations (4) into (5) gives:

$$I = A \times \left( \varepsilon^T - \frac{d_t^2}{s^E} \right) \frac{\partial E}{\partial t} + A \times \frac{d_t}{s^E} \frac{\partial S}{\partial t} \quad (6)$$

$\frac{\partial E}{\partial t}$ and $\frac{\partial S}{\partial t}$ are the time variation of the electrical field and strain as a function of time variation, respectively.

The electrical field output of the polymer across the load resistance is defined by the term:

$$E_R = -\frac{R \times I}{h} \quad (7)$$

where R the electrical resistance and h is the thickness of the polymer film.

The relation between Y material Young's modulus and the compliance is $Y = \frac{1}{s_{11}^T}$, so substituting Equation (7) into (6) gives:

$$I(t) = -A(\varepsilon^T - Yd_t^2)\frac{R}{h} \times \frac{\partial I}{\partial t} + A \times Yd_t \times \frac{\partial S}{\partial t} \quad (8)$$

Transforming Equation (8) into frequency domain, we can obtain the current I as:

$$I(p) = \frac{A \times Yd_t \times p}{1 + A(\varepsilon^T - Yd_t^2)\frac{R}{h} \times p} S(p) \quad (9)$$

Applying the transformation of inverse Laplace to Equation (9), we obtain the current harvested expression:

$$I^{-1}\{I(p)\} = I(t) = \frac{hYd_t}{(\varepsilon^T - Yd_t^2)R} \left( \gamma(t) - \frac{h}{A(\varepsilon^T - Yd_t^2)R} \exp\left(-t\frac{h}{A(\varepsilon^T - Yd_t^2)R}\right) \right) S(t) \quad (10)$$

with the governing equation of mechanical motion being:

$$S(t) = S_M \sin(2\pi f_M \times t) \quad (11)$$

where $S_M$ and $f_M$ are maximum transverse strain and mechanical excitation frequency, respectively.

Substituting Equation (11) into (10), the current expression as a function of time and mechanical cycle excitation is expressed in the form:

$$I(t) = \frac{hYd_tS_M}{(\varepsilon^T - Yd_t^2)R} \left( \gamma(t) - \frac{h}{A(\varepsilon^T - Yd_t^2)R} \exp\left(-t\frac{h}{A(\varepsilon^T - Yd_t^2)R}\right) \right) \sin(2\pi f_M \times t) \quad (12)$$

This harvested current depends on the level of mechanical strain, excitation frequency, material dimensions, electrical load and material proprieties. To validate this principle, an experimental study was performed. In order to predict output performances for charged porous films, the physical parameters of Equation (12) are presented in Table 2.
<table><caption>**Table 2.** Synthesis of materials' physical properties.</caption><thead><tr><th>Material Proprieties</th><th>EVA 0%</th><th>EVA 37%</th><th>EVA 65%</th></tr></thead><tbody><tr><td>Young Modulus (MPa)</td><td>29</td><td>25</td><td>20</td></tr><tr><td>Depolarization Temperature (°C)</td><td>74</td><td>67</td><td>61</td></tr><tr><td>Strain limit (%)</td><td>24</td><td>27</td><td>31</td></tr><tr><td>Piezoelectric Coefficient d<sub>33</sub> (pC/N)</td><td>2.2</td><td>4.2</td><td>5.1</td></tr><tr><td>Time after deionization</td><td>30 h</td><td>33 days</td><td>59 days</td></tr><tr><td>Relative Permittivity</td><td>3.6</td><td>5.1</td><td>5.7</td></tr></tbody></table>

### 3.3.2. Energy Harvesting Results

During the energy harvesting studies, experimental measurements are taken to determine the electrical properties of porous EVA. To validate the proposed modeling approach provided in the preceding part, the three compositions are examined in order. More examples are provided to demonstrate the feasibility and usefulness of EVA porous piezoelectric polymers in the situation of complex mechanical conditions and realistic energy harvesting devices.

Figures 8–10 present the evolution of the electrical parameters (current and voltage harvested) as a function of time according to the applied strain using the three compositions of EVA. After analyzing the figures, it is clear that the electrical parameter increases by increasing the rate of deformation. For example, to obtain a value of the recovered current of 371 pA, it is necessary to apply a deformation of 0.75% in the case of EVA 0%; on the other hand, for porous structures (EVA 37%), it suffices to apply only 0.25%. For a strain of 0.75%, we can obtain a current of 320 pA by the EVA 0% instead of 1027 pA by the EVA 37% or 1692 pA by the EVA 65%. These results clearly show that increasing the porosity represents one of the best solutions for improving the electromechanical conversion of polymers in the pseudo piezoelectric mode.

<figure><img src="image_12.png" /><figcaption>**Figure 8.** Electrical characteristics harvested by EVA 0% as a function of time under a transverse displacement with various values of strain $S_M$. (a) current harvested with $S_M$: 0.25%, (b) voltage harvested with $S_M$: 0.25%, (c) current harvested with $S_M$: 0.50%, (d) voltage harvested with $S_M$: 0.50%, (e) current harvested with $S_M$: 0.75%, (f) voltage harvested with $S_M$: 0.75%.</figcaption></figure>
<figure><img src="image_13.png" /><figcaption>**Figure 9.** Electrical characteristics harvested by EVA 37% as a function of time under a transverse displacement with various values of strain $S_M$. (a) current harvested with $S_M$: 0.25%, (b) voltage harvested with $S_M$: 0.25%, (c) current harvested with $S_M$: 0.50%, (d) voltage harvested with $S_M$: 0.50%, (e) current harvested with $S_M$: 0.75%, (f) voltage harvested with $S_M$: 0.75%.</figcaption></figure>

<figure><img src="image_14.png" /><figcaption>**Figure 10.** Electrical characteristics harvested by EVA 65% as a function of time under a transverse displacement with various values of strain $S_M$. (a) current harvested with $S_M$: 0.25%, (b) voltage harvested with $S_M$: 0.25%, (c) current harvested with $S_M$: 0.50%, (d) voltage harvested with $S_M$: 0.50%, (e) current harvested with $S_M$: 0.75%, (f) voltage harvested with $S_M$: 0.75%.</figcaption></figure>

In the case of EVA 65%, the current delivered is well multiplied by a factor of 8 compared to EVA 0%. This suggests that the higher the porosity, the greater the current that can be harvested. The results obtained clearly show that increased strain has a remarkable influence on the voltage and current in the case of porous piezoelectric materials. The properties of the internal gas of porous films directly influence the electrical properties.

Figure 11 illustrates the dependence of current and voltage harvested using three compositions of porous EVA. The simulation behavior predicted by the proposed model
Equation (12) has been compared with the experimental setup of the power harvested by cellular polymers. In this figure, the points present the experimental results, and the curve presents the developed theoretical model.

<figure><img src="image_15.png" /><figcaption>**Figure 11.** Porosity content influence on the electrical characteristics harvested by cellular EVA with three values of strain $S_M$: 0.25%, 0.50% and 0.75%. (a) Voltage harvested; (b) current harvested.</figcaption></figure>

The values of 123, 241, and 320 pA were obtained, respectively, with 0.25%, 0.50%, and 0.75% of strain using EVA 0% at 4 Hz. In the case of EVA 37%, harvested current values at 4 Hz of 371, 620 and 1027 pA were obtained, respectively, with 0.25%, 0.50% and 0.75% of strain. For EVA 65%, harvested current values at 4 Hz of 497, 938 and 1692 pA were obtained, respectively, with 0.25%, 0.50% and 0.75% of strain.

Figure 11 shows a linear relationship between electrical properties and porosity. At the microscopic level, each cell is regarded as a generator containing a number of macro-dipoles. EVA 65% composition has more gas foams than EVA 37% composition. As a result, raising the proportion of space content in gas cells increases the number of macro-dipoles. For that, EVA 65% is a more sensible mechanical force compared to EVA 37% and EVA 0%. However, the increase in harvested current of the copolymer with an increase in the porosity that could be captured could be confirmed by the theoretical model with an error range between 0.3% and 5%. The harvested current significantly increases with increasing strain or porosity, achieving a high current value up to 1627 pA for EVA 65%. The same dependence is observed for the voltage harvested. These results demonstrate that porous materials are electrically and mechanically stable. As a result, it is evident that these porous polymers will be used in mechanical applications, particularly in the manufacture of energy harvesters and smart sensors based on vibration effect.

The results' analysis makes it possible to study the influence of the pores created in the polymer matrix. It also makes it possible to examine the dependence of these parameters on the mechanical applied stress and frequency range. This analysis was carried out with the aim of optimizing the operating interval for a better application in the field of sensor, actuation or vibratory energy harvesting.

4. Conclusions

This work presented the mechanical, physical, and morphological Poly(ethylene-co-vinyl acetate) (EVA) properties for different void concentrations. Additionally, the effect of porosity on the Young's modulus, piezoelectric coefficient, and the impact of physical properties of the co-polymer were analyzed.

Three different percentages of porosity were used to create and test porous piezoelectric polymers for energy harvesting. The theoretical model and experimental results were
found to be in good agreement. Various methods of improving the inherent properties of the polymers were also investigated, demonstrating the simplicity and usefulness of operating using pseudo-piezoelectric behavior. Porous piezoelectric polymers have been shown to possess significant mechanical energy that can be harvested. It can be concluded that the porosity has a significant effect on the mechanical proprieties of the piezoelectric porous polymers, and on the current, voltage and power in turn. Future research will focus on developing new systems and combining hybridization with other materials to improve the performance of harvested energy.

**Author Contributions:** Conceptualization, C.E., A.H., C.S., E.S., A.R., I.N. and M.R.; Data curation, C.E.; Formal analysis, C.S., A.R., E.M.L. (El Mehdi Laadissi) and E.M.L. (El Mehdi Loualid); Funding acquisition, A.H. and C.S.; Investigation, A.R. and I.N.; Methodology, A.H., C.S., E.M.L. (El Mehdi Laadissi) and A.E.B.; Project administration, A.H., A.E.B. and A.A.; Resources, C.E., E.S. and M.R.; Software, C.E., A.R., E.M.L. (El Mehdi Laadissi) and E.M.L. (El Mehdi Loualid); Supervision, A.H., A.E.B. and A.A.; Validation, C.S., I.N. and M.R.; Visualization, A.A.; Writing—original draft, C.E. and E.S.; Writing—review and editing, C.E., A.H. and C.S. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.

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