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ACS Omega
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ACS Omega
2470-1343
American Chemical Society

10.1021/acsomega.4c03625
Article
Analysis and Application of Poly(vinyl alcohol) (PVA) and Polyacrylonitrile (PAN) Nanofiber Membrane-Based Triboelectric Nanogenerators
Pragalathan Subalakshmi †
https://orcid.org/0000-0001-7893-4514
Venugopal Velmurugan *‡
† Department of Chemistry, School of Advanced Sciences, Vellore Institute of Technology, Vellore, Tamil Nadu 632014, India
‡ Department of Micro and Nanoelectronics, School of Electronics Engineering, Vellore Institute of Technology, Vellore, Tamil Nadu 632014, India
* E-mail: vvelmurugan@vit.ac.in.
27 08 2024
10 09 2024
9 36 3780237813
19 04 2024
17 07 2024
09 07 2024
© 2024 The Authors. Published by American Chemical Society
2024
The Authors
https://creativecommons.org/licenses/by-nc-nd/4.0/ Permits non-commercial access and re-use, provided that author attribution and integrity are maintained; but does not permit creation of adaptations or other derivative works (https://creativecommons.org/licenses/by-nc-nd/4.0/).

The triboelectric property of materials is used to harvest energy from intentional or nonintentional sources of vibration. Contact mode freestanding dielectric based nanogenerators (CFTENGs) have many advantages when compared with other modes of triboelectric nanogenerators. The property of dielectric materials plays an important role in the energy harvesting process. In this work, we aim to fabricate nanofiber membranes of poly(vinyl alcohol) (PVA) and polyacrylonitrile (PAN) and study their properties for CFTENGs. The morphology and porosity of both membranes were tested experimentally. The mechanical property is modeled with a representative volume element (RVE) technique to understand its deflection behavior. In addition, an electromechanical model is developed to predict and analyze the behavior of those membranes in the energy conversion process. Our research reveals that the PAN dielectric layer achieves a maximum open circuit voltage of 192 kV compared to the PVA dielectric layer (2.2 kV) in the CFTENG system. In comparison, the dielectric layer of the PAN nanofiber membrane reflects its flexibility to generate electrical energy in a CFTENG with the effect of contact electrification and electrostatic induction under various sources of unused energies for a wide range of applications. Moreover, the same methodology is applied to various sources of vibration, and their performance is reported. With an appropriate power management circuit, we can design a PAN membrane-based TENG for various applications.

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pmc1 Introduction

The widespread use of electronic gadgets makes sense in the development of sustainable power sources. Macro and microelectronic devices are powered using chemical batteries that are hazardous to the environment and have a limited lifetime.1,2 In this context, converting unused energy into electrical energy is an important topic for scientists.3−7 A nanogenerator based on the triboelectric effect of contact electrification and electrostatic induction from mechanical energy to generate electric energy was reported in 2012.8 Triboelectric nanogenerators (TENGs) have broad prospects such as high output energy, high charging and discharging rates, low maintenance, high scalability, simple structures, free of pollution, and cost-effective technology.9−12 TENGs were investigated universally with diverse energy sources, materials, and operation modes due to their low weight and easy fabrication to implement into various applications.13,14 The power supplied from TENGs was demonstrated as a sustainable power source for portable electronic devices, batteries of mobile phones, and other low power systems.15−17 In common, TENGs contain an electrode attached with a dielectric layer and have limitations in their applications. In a freestanding triboelectric nanogenerator (FTENG), contact separation of electrodes with a stacked structure of a dielectric layer will restrict the electric field within stationary electrodes which can be represented as a contact mode freestanding triboelectric layer-based TENG (CFTENG).18 The CFTENG mode has been widely ulitized in wind energy harvesting and self-powering electronics due to its advantages of easy fabrication, low cost, sustainability, and single triboelectric layers without attached electrodes compared to other modes like contact mode and sliding mode TENGs.18−20 To design a TENG for a particular application, the theoretical work is considered as a basic requirement to analyze its electrical output performance. Moreover, it is necessary to understand the mechanical properties of the dielectric layer for TENG-related applications.

The most preferred TENG materials are polyimide (PI), polytetrafluoroethylene (PTFE), polypropylene (PP), polydimethylsiloxane (PDMS), polyvinylidene fluoride (PVDF), polyvinyl chloride (PVC), polyacrylonitrile (PAN), cellulose, polyurethane (PU), and poly(vinyl alcohol) (PVA). These polymeric materials were structured differently such as nanofibers, thin films, and aerogels to analyze the performance of TENGs.21 The performance of the TENGs depends on the surface characteristics of the triboelectric layer. The surfaces with structures like pyramids, sheets, wires, pores, and nanowires exhibit better performance than unpatterned surfaces.22 The interfacial micro and nanostructure deformation of triboelectric layers has an impact on the force and voltage relationship in TENGs.23,24 Several research studies are ongoing on using nanostructured triboelectric layers for a wide range of self-powering systems.

Nanofiber structures were developed for numerous applications including energy harvesting technologies owing to its parallel advantages such as high surface volume ratio, lightweight, flexible, and porous structure.25,26 Nanofiber structured materials can be fabricated using the electrospinning technique due to their ease of fabrication.27 Typically, nanofiber membranes have the strong potential of providing stable and repeated signals with consistent time intervals.28 Among polymer materials in triboelectric series, PVA and PAN polymers were chosen based on their functional groups. Poly(vinyl alcohol) (PVA) and polyacrylonitrile (PAN) polymers have the attractive polar groups namely a hydroxyl group (−OH) and a nitrile group (−CN) respectively.29 The PVA and PAN-based nanofiber membranes were widely utilized in filtration, wound dressing, photocatalytic degradation, and tissue engineering applications due to their excellent characteristics.30−34

Moreover, electrospun PVA and PAN-based nanofiber membranes were investigated as a friction layer in various kinds of TENG applications due to their flexibility, ultrathin nature, and stretchability.35−38 Nanofiber-based TENGs have been developing to generate electricity with a wide range of deformations such as twisting, knee bending, holding, deflection by breathing, and friction by human motions (running, walking, and jumping).39−41 Therefore, along with the material selection, material structure and the mechanical properties of materials will play an important role in achieving the stable electrical output response of TENGs under external forces. In our proposed CFTENG mode, the dielectric layer will deflect back and forth to make contact and separate with top and bottom electrodes under external forces and will generate power. This kind of mode has been emerging in wind energy harvesting; authors generate the output voltage based on fluttering of dielectric films to make contact and separate with top and bottom electrodes under different ranges of wind flow as external mechanical forces with various kinds of structural designs.42

As a consequence, there is a need to investigate and understand the mechanical properties of the membrane as a dielectric layer prior to practical applications in the CFTENG mode. The mechanistic studies of thin nanofibers using instrumentation have limitations due to the fine nature of the nanofibers, which can easily be damaged during testing and it may be expensive sometimes and complex.43 The numerical analysis is preferred to predict the results accurately and can be implemented in future applications. The mechanical behavior of membranes may vary based on the orientation of internal fibers, diameter of single fibers, and porosity of membranes. The mechanical properties of nonwoven-structured nanofiber membranes can be evaluated with the structural geometry parameter of membrane using the representative volume element (RVE) technique among other models due to the complicated structure of nanofibers. This technique is to study the mechanical behavior of intricate structures of fibers in the membranes on a micro scale to obtain macro scale resultants under uniaxial forces.44−46 In addition, the dynamic behavior of the membranes was simulated and analyzed by integrating the electromechanical model of single degree of freedom (SDOF) with TENGs under a standard step load. This simulation facilitates an understanding of the connection between the movement of a dielectric layer and electrical efficiency under a frequency response and the damping effect of triboelectric layers. The authors examined the dynamic movement of triboelectric layers under vibration of the TENG system to understand the electrical efficiency by coupling the electromechanical model with the system.47,48

In this work, the objective is to analyze the deflection behavior and electrical performance of electrospun nanofiber membranes to utilize as a dielectric layer in the CFTENG mode for a stable mechanical to electrical energy conversion process. Experimentally, we spun the pristine polymer materials such as PVA and PAN as nanofiber membranes from the electrospinning unit and studied their morphology, fiber orientations, and porous nature. Theoretically, the first part of the analytical work has detailed information on the mechanical behavior such as uniform bending under a uniaxial force and the damping effect of membrane under vibration from force using simple, and existing strategies of RVE methodology and electromechanical coupling model for the CFTENG mode, respectively. The second part involves analyzing the electrical characterization of nanofiber membranes using a fundamental theoretical concept based on the CFTENG mode. In the future, this simple and flexible CFTENG system has been constructed to elucidate the power generating principle with time dependent and independent characteristics.

2 Experimental Section

2.1 Materials

Poly(vinyl alcohol) (PVA) with molecular weight of 89 000–98 000 g/mol, polyacrylonitrile (PAN) with molecular weight of 150 000 g/mol, and the DMF solvent were purchased from Sigma-Aldrich and used without any modification.

2.2 Fabrication of the Nanofiber Membrane

To fabricate the membrane by electrospinning, the corresponding polymeric solution was prepared. For the PVA membrane, 10 wt % PVA powder was dissolved in hot water by maintaining at 70 °C overnight to prepare the solution. For the PAN membrane, 6 wt % PAN powder was dissolved in DMF as the solvent at room temperature overnight to prepare the homogeneous solution.

As shown in Figure 1a. the solution of PVA and PAN is loaded using a flow pump controller. Here, with a voltage of 22 kV, both PVA and PAN nanofiber membranes were fabricated on the drum collector with a distance of collector-to-needle tip of 12 cm and a solution flow rate of 0.5 mL/h at room temperature in an electrospinning instrument. The nanofibers were spun on aluminum (Al) foil, which is wrapped on a collector. The inset image of Figure 1a represents the spun nanofiber membrane.

Figure 1 (a) Schematic of electrospinning technique. (b,c) SEM images of PVA and PAN nanofiber membranes. (d,e) and (f,g) Their corresponding fiber diameter distribution (AD - average diameter of fiber; SD - standard deviation of fiber diameter) and fiber orientation distribution.

2.3 Morphological Studies

SEM analysis was performed to analyze the morphology, fiber diameter, and fiber orientation distribution (FOD) of the membrane. Figure 1 presents the analysis of membrane morphology, fiber diameter, and fiber orientation by showing the SEM images of membranes. The PVA and PAN fibers were aligned randomly without any defects such as beads and strings, which can be confirmed from Figure 1b,c. The fibers without beads have a high tensile strength due to their higher cohesion points. The average diameter (AD) of fiber was measured to be 97.5 and 268 nm for PVA and PAN nanofiber membranes respectively using IMAGE J software. The standard deviation (SD) of PVA and PAN are 26.25 and 68.47 nm, respectively. The majority of PVA fibers are in the range of 60–120 nm, and PAN fibers are in the range of 150–350 nm, as shown in Figure 1d,e. The orientation of the fiber was obtained as shown in Figure 1f,g and analyzed using Orientation J to predict its mechanical behavior. It was observed that the maximum count of nanofibers aligned in the same direction (0°) in the PAN membrane compared to the PVA membrane where the nanofibers were oriented randomly (50° and −50°). The formation of aligned nanofibers is due to the variation in the conductivity of the solution.49 A stable charged jet path is formed if the polymer solution has high conductivity. The PAN solution has higher conductivity (16 500 μS/cm) than PVA (1275 μS/cm).50,51 So, the PAN nanofibers are more aligned.50,51 The aligned nanofiber membrane has higher mechanical properties than the randomly oriented nanofibers.52,53 Hence, the PAN membrane has higher mechanical properties in comparison to PVA membrane.

2.4 BET Specific Surface Area Analysis

The surface area and pore size distribution of the spun PVA and PAN nanofiber membranes were analyzed using the nitrogen (N2) adsorption and desorption measurements (Brunauer–Emmett–Teller, BET) carried out at 77K temperature.

Figure 2 shows the nitrogen (N2) adsorption and desorption isotherms of PVA and PAN membranes analyzed to determine the specific surface area of BET and pore size membranes. The isotherm profiles (Figure 2a,b) of PVA and PAN resemble the type IV isotherm under IUPAC classification, and its relative pressure hysteresis curve is close to unity, indicating the mesoporous nature of membranes.54−56 The surface areas of PVA and PAN membranes obtained from the BET test are 887.102 and 1010.577 m2/g, respectively. From the Barret–Joyner–Halenda (BJH) method, the distribution of pore size was measured for fabricated nanofiber membranes. The PVA membrane has the porous ranging between 1.5 and 11 and 16 nm whereas the PAN membrane has pores of 1.4–11 nm, 16, and 29 nm. From the PVA and PAN curves as shown in Figure 2c,d, the ranges of pore size indicated the micropores or mesopores nature. Moreover, the calculated average pore diameter of PVA and PAN membranes further confirms the mesoporous nature of membranes with values of 5.24 and 6.6 nm, respectively. The pore volumes of PVA and PAN membranes are 2.484 and 3.127 cc/g, respectively.

Figure 2 (a,b) Nitrogen adsorption–desorption isotherm profiles of PVA and PAN membranes. (c,d) Pore size distribution curve of PVA and PAN.

3 Results

3.1 Theoretical Analysis of the Nanofiber Membrane

The electrical performance of the TENG system is dependent on the deflection behavior of the dielectric tribolayer under the external force. It is necessary to understand the mechanical characteristics of the nanofiber membrane.

3.1.1 Representative Volume Element Method and Deflection Studies of the Nanofiber Membrane

In this section, the uniform bending of nanofiber membranes under a uniaxial load is analyzed using the representative volume element (RVE) methodology. RVE adopts a process of taking into account a statistically homogeneous representation of a heterogeneous material to analyze the mechanical behavior. In our analysis, the RVE modeling of nanofibers include the factors affecting mechanical behaviors such as porosity, fiber alignment, dimensions of single nanofiber and membrane.57,58 The analysis is based on assumptions such as the internal structure of the membrane has randomly aligned fibers with the same fiber diameter without any beads, as revealed in Figure 3a. The membrane is circular in shape and is analyzed for the tensile relationship in rectangular RVE cut. The analysis details are discussed below.

Figure 3 (a) RVE diagram of the membrane. (b) Schematic of RVE of nanofiber membrane. (c) Deflection of the circular membrane under a uniform load. (d,e) Deflection profile of PVA and PAN nanofiber membranes under uniform force. (f) Influence of porosity in deflection of the PVA membrane.

The rectangular part of the membrane, which is shown as a colored area in Figure 3b with the parameters such as L as the length and W as the width, forms an RVE unit cell. Those fibers with the ends of overlaying and coinciding in the cross-section of membranes will contribute to resist the given tensile force owing to its insignificant adhesion between the nanofibers. Since there are fibers in a particular portion, the testing outcomes of this tensile test will depend on the fragment of nanofibers that will be the actual area of abcd of the membrane as shown in Figure 3b.59

Thus, the fragment of nanofibers can be represented by,1

where, Al is the area of the membrane and Aμ is the RVE area.

Finding the tensile stress using eq 1 involves membrane thickness (T) of RVE, the stress of individual fibers (σf), and porosity (P). The stress (F) of a tensile membrane including the RVE cut area stretches in a direction and can be obtained using eq 2.2

Figure 3c shows that the clamped circular membrane (radius, a) has an out of plane behavior (W’) under a uniform loading, and expression z represents the out of plane deformation.60,61

For finding the deflection (W’) of the membrane for an applied force, eqs 1 and 2 can be developed and used.

Since our sample is circular in shape, it results in the deflection of3

Eq 3 involves the pressure (P), young’s modulus (E), the thickness of membrane (L), poisson’s ratio (ν), and membrane radius (a). The tensile strength of the nanofiber membrane can be analyzed for various porosities, thicknesses, and sizes.

The deflection of the membrane has a contribution of every single nanofiber. The membrane’s deflection is found maximum at the center for a uniform load as shown in Figure 3c. This profile is based on eq 3 as shown in Figure 3c. Both membranes show uniform bending at the center, and a similar profile is observed. We vary the force acting on it, and the maximum displacement formed is to be 2 mm at a force of 334 700 and 35 415 MPa for PVA and PAN membranes, respectively. According to eq 3, it can be observed that the effect of Young’s modulus of the membrane plays an important role in the bending behavior which is represented in Figure 3d,e. Based on eq 2, the deflection is directly proportional to the porosity. So, we anticipated high porosity in both the membranes. The predicted values are shown in Figure 3f. For both PVA and PAN membranes, the deflection decreases with respect to the load. For instance, 86% of the porosity membrane yields a deflection of 2 mm under a pressure of 32 935 Pa.

3.1.2 Time Response Analysis of the Nanofiber Membrane

Furthermore, our TENG model is coupled with electromechanical modeling to simulate the dynamic response of the electrospun membrane under a force as represented in eq 4. Here, the system can be modeled by single degree of freedom (SDOF), and there is a strong coupling between the electrode and the dielectric in terms of energy conservation. This model is used to predict the maximum output energy under ideal conditions of a certain TENG.62,63 The equivalent SDOF model of the CFTENG is represented in Figure 4a.

Figure 4 (a) Equivalent SDOF model for the CFTENG. (b) Schematic illustration of SDOF model of dielectric CFTENG. (c) Simulated time response of the nanofiber membrane.

The SDOF model suitably represents the behavior of the membrane’s deflection due to the application of force and it consists of three elements such as mass (m) with the support of spring constant (k) and damping coefficient (c) as shown in Figure 4b.

The governing equation for the system is4

5

6

ζ is a damping ratio; we tried to investigate the time response of the film for various values of m, k, and c. The classical form of outputs can be grouped under these three categories: (i) undamped, (ii) underdamped, and (iii) overdamped systems based on the damping coefficient (ζ). The relationship can be realized using eq 6 for the nanofiber membrane.

We subject the membrane to a step input and analyze the response. We could pick up three distinct cases, ζ > 1, ζ = 1, ζ < 1 as shown in Figure 4c. By applying the force (F) of 2.5 N, the displacement of the membrane has been carried out with constant values for the parameters m as 0.6 g, k as 1.25 N m–1, and varying the c as 1.73, 3.73, and 5.73 g/s. The resulting graph indicates an underdamped system that gives a fast response when compared to others. The drawback of the membrane is that it will overshoot and vibrate when it is closer to the electrode. So, it may need time to settle. There could not be a regular electrical output at the time of contact between electrodes.

In other cases, when ζ > 1 is an overdamped system without any oscillation, but it takes time to reach the output; hence, the membrane will move slowly and the derived voltage response also becomes slow. The intermediate is ζ = 1, which is critically damped and this also suffers in poor response time but still it is better than an overdamped system. For a continuous analysis, we repeated the load based on the time response and results as shown in Figure 4c.

3.1.3 Spring Constant Studies of the Nanofiber Membrane

The deflection of the nanofiber membrane depends on its flexibility nature, and it was challenging with its porosity. To predict the flexibility of the membrane, the spring constant study is carried out in this section. The spring constant of the membrane can be studied with dependence on porosity of it as shown in Figure 5. This study helps to fabricate the appropriate nanofiber membrane, which is attributed to achieve quick and dynamic response of membrane in the TENG system. The spring constant (K) of the porous membrane is calculated using eq 7 with varying P based on the value of the spring constant (K0) of the nonporous structure.64,657

Figure 5 Variation of the spring constants of PVA and PAN nanofibers with respect to porosity.

where the spring constant K0 values of nonporous PVA and PAN membranes are 19 821.2 and 86 800 N m–1 respectively. m is the power exponent that controls the spring constant rate with the porosity.

The porosity of the membrane has an inverse relationship with the spring constant. Since we have the possibility of variation in the porosity of the membrane, it will affect the spring constant. At the same time, due to changes in porosity, the damping of the membrane will also vary.

3.2 Analysis of CFTENG Structure

In this section, the electrical performance of our proposed TENG mode is analyzed. The working mechanism is represented in Figure 6a.

Figure 6 (a) Working mechanism of the CFTENG. (b) Typical theoretical model of dielectric layer of CFTENG. (c) Equivalent circuit model of an electrostatic system of dielectric layer of CFTENG. (d) An equivalent circuit of the TENG.

In the contact mode freestanding TENG (CFTENG), the dielectric is sandwiched with suitable spacers between two electrodes. In a normal state, the dielectric layer and two electrodes are at a particular distance and have no charges on their surfaces. After the external force is applied, the membrane surface will deflect slowly against an electrode to make contact between them. An equal magnitude of oppositive charges is created on their surfaces due to the contact electrification effect (Figure 6a.i). When the dielectric layer is partially separated from an electrode, the potential difference will form between them, which makes the charges flow from one electrode to another electrode through the external circuit and generate the current due to the electrostatic induction effect (Figure 6a.ii). When the dielectric layer is completely separated from an electrode, an electrostatic equilibrium can be obtained, and there is no movement of charges through the external circuit (Figure 6a.iii). The dielectric layer and another electrode make contact again, and the charges flow back through the external circuit and generate current (Figure 6a.iv). When the dielectric layer makes contact between the electrodes repeatedly, the charges will move back and forth from one electrode to another electrode through the external circuit and generate an alternative current (AC) signal. The electrical output response of this TENG under a periodic motion is modeled using LTspice.

3.2.1 V– Q–x Relationship in the TENG

The membrane and electrodes arranged in the TENG can be modeled with three capacitors in series whose equivalent capacitance is given by the CFTENG. The CFTENG is based on a lumped component representation of a variable capacitor.

Based on the conventional theory of capacitance with d0 is the effective thickness, S is the area, x(t) is the time dependent distance of the dielectric layer, the capacitances (C1, C2, and C3) between the electrodes as the total capacitance (CTENG) of CFTENG can be expressed in eq 8.8

The voltage with charge density σ depends on the nanofiber membrane (dielectric) distance x(t) as represented in eq 9, and the equation of open circuit voltage (Voc or VTENG) of the CFTENG system is represented in Figure 6b.9

The output voltage (V) of any TENG mode is systematically examined using the below equation which involves the basic V–Q–x relationship.6710

This V–Q–x relationship equation has capacitance (C) between the electrodes, transferred charge (Q) between electrodes, and open-circuit voltage (Voc) of our mode which is a function of separation distance (x) between the electrodes.

From eq 10, the equivalent circuit of a TENG is modeled as a series connection of voltage source (VTENG) and time varying capacitance (CTENG) which is represented based on lumped-component circuit theory as shown in Figure 6d.66

3.2.2 Electrical Output Characteristics of PVA and PAN Nanofiber Membranes

Based on the mechanical studies and the time response, we selected a critically damped mode of response and applied the same to predict the output of the TENGs.

We applied a periodic input to the whole TENG system and maintained the distance between the electrodes and the dielectric layer. Based on the magnitude and frequency of the periodic input, the output is analyzed. Table 1 lists the parameters used for simulation.

Table 1 Parameters Used to Simulate CFTENG

parameters	PVA dielectric layer	PAN dielectric layer	
dielectric	εr = 1.99, d = 0.0001 m, d0 = 0.0000503 m	εr = 3.2, d = 0.0001 m, d0 = 0.00003125 m	
area size of dielectrics S	0.005 m2	0.005 m2	
maximum separation distance, xmax	0.004 m	0.004 m	
tribo surface charge density, σ68,69	10 μC m–2	0.85 mC m–2	
velocity v	0.1 ms–1	0.1 1 ms–1	
VTENG	1.1294 × 106x(t) V	0.0960 × 109x(t) V	
VOCMAX	2.2 kV	192 kV	
CTENG			
CTENG,MAX	89 × 10–10 F	142 × 10–9 F	
CTENG,MIN	2 × 10–11 F	2 × 10–11 F	

In reference to the equivalent circuit of TENG (Figure 6d), the equivalent voltage source is a function of conductivity, dielectric constant, and the separation distance x. So we could simulate the voltage profile for both PVA and PAN nanofiber membranes as dielectric layers by fixing the maximum distance between the electrodes as 4 mm. The other parameters used to simulate is given in Table 1. The simulated circuit is referenced in Figure 7a.

Figure 7 (a) LTspice circuit of voltage–controlled voltage source. (b,c) Simulation of open circuit voltage of PVA and PAN dielectric layers.

VTENG of the dielectric layer in the system can be obtained using the equation, and their parameter values from Table 1.

The equivalent voltage is as follows:

for the PVA dielectric layer, VTENG = 1.1294 × 106x(t)

for the PAN dielectric layer, VTENG = 0.0960 × 109x(t)

Since we consider a periodic load with a maximum velocity of 0.1 ms–1, we could get a maximum output, i.e., VOCMax as 2.2 kV and 192 kV for PVA and PAN dielectric layers, respectively. 0.1 ms–1 is the typical wind speed that can be exerted by a normal human being during the breathing process. The profile of the graph is shown in Figure 7b,c. We consider a sinusoidal oscillation of the TENG at a frequency of 25 Hz. The voltage generated becomes dependent on the periodic oscillation of the dielectric layer.

Based on the assumption that the vibration is periodic in nature, we simulated the TENG structure by subjecting it to the same. The period of vibration was taken as 25 Hz which is a similar range to a human heartbeat.

The TENG with a periodic input can be modeled as a voltage dependent voltage source as shown in Figure 8a. This will make VTENG and CTENG parameters dependent on the periodic movement.

Figure 8 (a) Schematic of TENG system. (i) Simulation of voltage across capacitor for (b) PVA and (c) PAN dielectric layers. (ii) The voltage across the load resistance for PVA and PAN dielectric layers with R of (d,e) 1 GΩ and (f,g) 10 GΩ.

Based on the eqs 8 and 9, CTENG and VTENG of the capacitor voltage (Vc) of the TENG system is independent of the charge density of the dielectric layer. Vc of the system with PVA and PAN dielectric layer for different charge densities has been simulated.

The variable capacitance CTENG is a function of the surface area (actual) and the relative distance between the electrodes and the dielectric layer.

We calculated the same values for the frequency and contact area of 5 mm2. The initial capacitance is found to be 89 × 10–10 and 2 × 10–11 F for PVA and PAN respectively. The corresponding maximum voltages of the capacitor (Vc) are 2.2 kV and 192 kV for PVA and PAN respectively as shown in Figure 8(i)-b,c. and are equal to their VOCMAX values. We assume that the entire surface is in contact with the electrode, as shown in Figure 7a. By utilizing the parameter values in Table 1 with the equation , the CTENG of the system of both PVA and PAN dielectric layers can be calculated as follows:

for the PVA dielectric layer,

for the PAN dielectric layer,

By applying the x(t) value from zero to maximum, it is observed that when the x(t) is 0, the triboelectric capacitance reaches a maximum value, and when the x(t) is maximum, the capacitance value will be minimum.

Figure 8(ii) shows the voltage across the resistor (Vr) for resistance of 1 and 10 GΩ, that drops to the minimum value (zero) after the transients. The steady state was attained much earlier with a load of 1 GΩ for both membranes. This is due to the time constant (RC) of the circuit, whereas it takes 1 s to reach the steady state for a load resistance of 10 GΩ. Figure 8(ii)d,e shows the Vr peak for R = 1 GΩ for PVA and PAN dielectric layers, and Figure 8(ii)f,g shows the peak for R = 10 GΩ for PVA and PAN. It is observed that the Vr decreases when R increases; it represents the increase in charging time.

To know the effect of variation in the load and the power transferred to the load. We varied the load from 100 kΩ to 100 MΩ. Figure 9a,b. shows that upon increasing the resistance, the voltage values will be increased as 680 V for PVA and 57 kV for the PAN dielectric layer, respectively. Figure 9c,d shows that the current decreases as the resistance increases . The maximum current of TENG is achieved at the lowest resistance of 100 kΩ as 16.5 μA and 1.8 mA for PVA and PAN respectively. The maximum power transfer happened at 100 MΩ for both membranes.

Figure 9 Effect of load resistances. (a,b) Voltage across the load resistor. (c,d) Current through the load resistor.

The calculated power generation of these membranes reaches 0.004624 W (PVA) and 32.49 W (PAN).

3.2.3 Energy Harvesting from Other Sources

Similarly, we have analyzed a wide range of wasted mechanical energy sources and their corresponding energy produced. Table 2 reveals the obtained results under different ranges of frequencies. It starts from a minimum frequency of 0.16 Hz (human breath) to a maximum frequency of 50 Hz (engine idling). With a suitable load, the minimum output power of PVA and PAN is calculated as 0.000121 and 0.0121 W respectively at 0.16 Hz, and the maximum output power as 0.6561 W (PVA) and 39.69 W (PAN) at 50 Hz. The minimum power generation of both membranes can be used for powering portable electronic gadgets.

Table 2 Simulated Results of Power Harvested from Other Sources of Vibration

 	 	Power generated (W)	
vibration sources	frequency (Hz)	PVA nanofiber membrane	PAN nanofiber membrane	
normal respiration rate of human (10–20 breaths/min)	0.16–0.33	0.000121–0.000441	0.0121–0.0441	
human motion70	1–3	0.003025–0.014641	0.3025–1.2769	
walking (60 steps/min)	1	0.003025	0.3025	
jogging (90 steps/min)	1.5	0.005476	0.5041	
running slowly (120 steps/min)	2	0.008281	0.7396	
running quickly (180 steps/min)	3	0.014641	1.2769	
hand tapping	4–5	0.0256–0.038025	1.8225–2.56	
water waves of low frequency	1–2	0.003025–0.008281	0.3025–0.7396	
engine shake (Idling vibration)	20–50	0.2025–0.6561	14.44–39.69	

4 Discussion

Since we assumed a free-standing membrane as a dielectric layer which oscillates between two metal electrodes, the output is also alternative in nature. The membrane’s mechanical behaviors such as Young’s modulus and spring constant decide the nature of the oscillations produced due to certain loads acting on the TENG. The membrane can be modeled as a second order system, and it can be tuned properly to give a vibration-free oscillation. This vibration-free oscillation results in a ripple free voltage that can enhance the quality of the voltage generated. This is possible by keeping the damping factor close to one. In terms of electrical characteristics, the charge density plays a major role in the conversion process. Since we used bare PVA and PAN solutions, there is a possibility of improving the electrical output by making composites with metal nanoparticles.

The TENG should be in a position to be an independent power source. So we extended our study by connecting various loads. As a basic law, the source resistance should be equal to the load resistance to deliver the maximum power. We tried to extend the study further by correlating various sources of vibration and their corresponding power generation capacities. Our analysis shows that the spun PVA membrane has random nanofiber orientation, whereas the PAN membrane has aligned nanofibers. Due to their orientation, the mechanical properties of the PAN membrane are higher than those of the PVA membrane. In the theoretical results of CFTENG, the output voltage of the PAN membrane was achieved as 192 kV due to its charge density (0.85 mC m–2), whereas the PVA membrane has 2.2 kV. Hence, the spun dielectric layer of PAN nanofiber membrane offers a good approach in energy harvesting technologies. All the above-mentioned analyses can be realized with suitable hardware.

5 Conclusion

Energy harvesting from ambient vibrational sources can be carried out by using triboelectric materials. We report an experiment based on PVA and PAN nanofiber membranes that are used as a dielectric layer in TENGs. We carried out the mechanical analysis of PVA and PAN nanofiber membranes spun by the electrospinning method based on the representative volume element (RVE) method. The fibers in the membrane are uniform in size, and the orientation of the fibers is narrow for the PAN nanofiber membrane. PVA membrane has the random nanofiber orientation, whereas PAN membrane has aligned nanofibers. Due to their orientation, the mechanical properties of the PAN membrane are higher than those of the PVA membrane. The mechanical analysis showed a good response for certain loads and damping. In the comparison to the maximum open-circuit voltage, the PAN membrane generated 192 kV because of a higher charge density (0.85 mC m–2), whereas the PVA membrane could generate 2.2 kV. So, the spun dielectric layer of PAN nanofiber membrane offers a good approach in energy harvesting technologies. The modeling is extended to other sources of vibrations, and the energy supplied is also estimated.

The authors declare no competing financial interest.

Acknowledgments

The authors would like to acknowledge Vellore Institute of Technology (VIT), Vellore for providing us the support in publishing this paper, Centre for Nanotechnology Research, VIT, Vellore for providing lab facilities to carry out the experimental work. Further, the authors wish to thank CeNSE, Indian Institute of Science, Bengaluru, funded by the Ministry of Human Resource Development (MHRD), Ministry of Electronics and Information Technology (MeitY), and Nanomission, Department of Science and Technology (DST), Govt. of India for SEM characterization.
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