In-Out Cylindrical Triboelectric NanogeneratorsBased Energy Harvester
Ahmed Zaky1, Akram Ahmed1, Passant Ibrahim1, Basant Mahmoud1, and Hassan Mostafa1,2
1 Nanotechnology Engineering Department, University of Science and Technology at Zewail City, October Gardens, Egypt.2 Electronics and Communication Engineering Department, Cairo University, Giza 12613, Egypt.
Abstract—The arising need for self-powered devices havedriven the research towards new energy harvesting techniques,especially the mechanical energy. Triboelectric nanogenerators(TENGs) are considered a very promising technique for har-vesting mechanical energy. However, most of the studies in theliterature have been focusing on rectangular TENGs with witha scarce research in cylindrical configurations. In this paper, anovel In-Out cylindrical TENG mode is proposed to serve asa potential candidate for different applications. A FEM modelis constructed using COMSOL-Multiphysics to characterize thedevice intrinsic properties such as open circuit voltage Voc(x) andshort circuit charges Qsc(x). Furthermore, an analytical modelis developed to obtain a closed form (V-Q-x) relation with itsaccuracy validated against the FEM model. The results show anexcellent agreement with an average error of 5.2% due to FEMlimitations, which was a motivation for establishing a Verilog-A model as a circuit element to describe the mode’s behaviorunder different loading conditions and explore its ability to beintegrated into different applications.
Index Terms—Triboelectric Nanogenerators, CylindricalTENG, Energy Harvesting, COMSOL, Verilog-A.
I. INTRODUCTION
Nowadays, there have been many efforts to obtain alterna-tive energy sources to the traditional ones and transfer to cleanrenewable energies. Moreover, portable electronic devices areconsidered a crucial part of people’s daily life as they havea lot of functions that conveniently fulfill their daily needs,however, it is an urgent need to find an energy source for themother than batteries, due to their limited lifetime and potentialhazards [1]. Therefore, researchers started to propose self-powered systems that avail the ambient mechanical energy,as it exists in a wide range and has high operability.
The existing techniques to harvest mechanical energy are,for example, the electromagnetic generators, electret gener-ators, and piezoelectric generators, however, each one hasdrawbacks like heavy components and low efficiency [2]. Therecently introduced approach, based on combining the contactelectrification and electrostatic induction, is the TriboelectricNanogenerators (TENGs). TENGs have shown unique traits;for instance, high efficiency, low weight, relatively cheapmaterials, and simple fabrication, which make them a potentialpower source to self-powered portable devices [2,3]. TENGsbasically have four fundamental modes, which all of them arebased on rectangular configurations [2].
Other interesting structures of TENGs are the cylindricalones. One example for them is the Rotating cylindrical TENG
which has coaxial rotating cylindrical structure to harvest ro-tational mechanical energy homologous to an electromagneticgenerator [4].
Throughout this study, a novel In-Out cylindrical TENGis introduced, starting from its mechanism, followed by theCOMSOL simulation and its results, reaching the derivationof its analytical model, followed by the Verilog-A model andfinally the results of the model is discussed in details.
II. PROPOSED CYLINDRICAL MODEL
The proposed model consists of four layers as a dielectric todielectric system, the two dielectrics serve as tribo-pairs withtwo metal electrodes as shown in Fig. 1. A distance x betweenthe tribo-pairs is varied upon applying a mechanical forceon either of the tribo-pairs, such that contact electrificationoccurs at x=0. During the transient contact time, static chargedensities having opposite polarities of +σ and -σ are createdon the surfaces of the tribo-pairs. It could be considered thatcharges are uniformly distributed on the surface at macro scalewith negligible decay due to the excellent properties of thedielectrics [5]. Upon separating the tribo-materials, chargeswith a magnitude of Q will be transferred from one electrode toanother such that one electrode will have a +Q charge and theother will have -Q charge and therefore, a potential differenceis created between the two electrodes. The motion along thedirection of x is bounded by a maximum displacement of xmax
between the tribo-pair to maintain the stability of the structureand the efficiency of charge transfer [6].
Therefore, the potential difference between the two elec-trodes can be represented by a superposition of two differentpotential values. The first is the potential difference due tothe polarized triboelectric charges denoted as Voc(x), and thesecond is the potential difference originated from the alreadytransferred charges Q between the two electrodes. If it isassumed that no triboelectric charges, the structure can beconsidered as a typical capacitor with the voltage across itgiven by Q/C(x), where C(x) is the capacitance between theelectrodes. Therefore, the total potential difference betweenthe two electrodes is given by:
V = − |Q| /C(x) + Voc(x) (1)
Equation (1), known as (V-Q-x) relation, is the fundamentalgoverning equation of any TENG structure. To fully char-acterize a particular TENG structure operating in a given
Fig. 1. Device structure of the proposed TENG model with the used materialsin simulation. The figure is not to scale, as metal electrodes are much thinnerthan dielectrics.
mode, both Voc(x) and C(x) need to be known explicitly andsubstituted directly in (1).
A. COMSOL Model
COMSOL-Multiphysics 5.3 software is used as a FEM tomodel the 3-dimensional structure of the proposed model. Allthe used design parameters are listed in Table I, however thechoice of those parameters depends on the application at whichthe harvester will be deployed at. The structure was surroundedby air to model the real life situation, and the required physicsis used to obtain Voc(x) and Qsc(x), the results of such a studyis shown in Fig. 3.
B. Analytical Model
Based on electrodynamics, both Voc(x) and C(x) can bederived in order to achieve a closed form (V-Q-x) relation.In this subsection, a detailed analytical model is introduced,which will help in understanding the terminal behavior of sucha model and serve as a seed for implementing the device usingcircuit models.
1) Voc(x) Derivation: Basically open circuit conditionsrequires that the total charge at each electrode must = 0. Ifwe assumed an initial movement of the inner cylinder with adistance x, the overlapped distance between the two cylinderswill be (l−x). Let’s define A and B to be the surface charges
TABLE IPARAMETER SET USED THROUGHOUT COMSOL SIMULATION.
Device length l 10 mmThickness of the dielectrics d1, d2 220 µm
Thickness of the metal electrodes dm 10 µmRelative dielectric constants εr1, εr2 2.1, 4
Surface charge density σ 10 µC
Average velocity v 1 ms−1
densities at the overlapped regions on the inner and outerelectrodes respectively. Hence,
∑Qinner = σ × 2πR1x+A× 2πR1(l − x) = 0 (2)
∑Qouter = −σ×2π(R2+d2)x+B×2π(R2+d2)(l−x) = 0
(3)Therefore, A and B equal to:
A =−σx
(l − x), B =
σx
(l − x)(4)
Mainly there are two electric field components both direct-ing towards the center. E1 is between the second dielectricand inner electrode while E2 is between outer electrode andfirst dielectric. The magnitude of these electric fields can bedetermined by applying the fundamental gauss law.∮
E · dA =Qencε
(5)
First, we start with determining E1, with ρ being the gaussradius, E1 is defined over R1 ≤ ρ < R2, so:
−E1 × 2πρ(l − x) =A× 2πR1(l − x)
ε0εr1(6)
Hence E1 equals to:
E1 =−AR1
ρε0εr1(7)
Similarly, E2 can be found by applying gauss law overR2 ≤ ρ < (R2 + d2), so:
−E2 × 2πρ(l − x) =A× 2πR1(l − x)
ε0εr2− σ × 2πR2(l − x)
ε0εr2
+σ × 2πR2(l − x)
ε0εr2(8)
It’s found that second and third terms are equal in magni-tudes with having different signs, therefore:
E2 =−AR1
ρε0εr1(9)
By taking the effects of E1 and E2 into account Voc nowcan be determined as follows:
(10)VOC = −
∫ R2
R1
E1.dρ−∫ (R2+d2)
R2
E2.dρ
=A×R1
ε0εr1×
(∫ R2
R1
1
ρ.dρ+
∫ (R2+d2)
R2
1
ρ.dρ
)By evaluating the integral, and substituting with A from (4)
Voc equals to :
VOC =σxR1
(l − x)ε0×
ln(R1
R2
)εr1
+ln(
R2
(R2+d2)
)εr2
(11)
1119
With (11), the second term in (1) is obtained and thereforeC(x) is still required for having a complete model, which willbe done in the following subsection.
2) C(x) Derivation: The total capacitance, Ct, betweenthe two electrodes can be seen as a series connection of twocapacitors, one capacitor between the outer electrode and firstdielectric, C1, while the other is the capacitor between seconddielectric and inner electrode, C2.
Considering the case of two concentric cylinders with onedielectric between them, we have from (5):
E =Qenc
ε× 2πρ(l − x)(12)
Assuming a is the radius of the inner cylinder while b is theradius of the outer cylinder, then E defined over a ≤ ρ < b .
Hence,
(13)V = −
∫ b
a
E.dρ = − Qencε× 2π(l − x)
∫ b
a
1
ρdρ
=Qenc
ε× 2π(l − x)ln(
a
b)
So,
C =QencV
=Qenc
Qenc
ε×2π(l−x) ln(ab )=ε× 2π(l − x)
ln(ab )(14)
Applying same analysis for C1 defined over R1 ≤ ρ < R2
and for C2 defined over R2 ≤ ρ < R2 + d2, we have:
C1 =ε0εr1 × 2π(l − x)
ln(R1
R2
) , C2 =ε0εr2 × 2π(l − x)
ln(
R2
(R2+d2)
) (15)
Then, the total capacitance seen between the two electrodesis:
Ct = (1
C1+
1
C2)−1 =
ε0 × 2π(l − x)
ln(
R1R2
)εr1
+ln(
R2(R2+d2)
)εr2
(16)
With (11) and (16) determined, the total potential generatedacross the TENG terminals can be determined by substitutinginto (1) to get a closed form (V-Q-x) relation:
(17)
V = − |Q| / ε0 × 2π(l − x)
ln(
R1R2
)εr1
+ln(
R2(R2+d2)
)εr2
+σxR1
(l − x)ε0
×
ln(R2
r1
)εr1
+ln(
(R2+d2)R2
)εr2
(18)
V =
(− Q
ε0 × 2π(l − x)+
σxR1
ε0(l − x)
)
×
ln(R1
R2
)εr1
+ln(
R2
(R2+d2)
)εr2
Equation (18) shows the closed form (V-Q-x) relation, which
characterize the output voltage seen across the terminals of theTENG.
C. Verilog-A Model
As depicted from (1), a TENG structure can be modeledby a lumped parameter equivalent circuit model as an idealarbitrarily time-varying voltage source Voc(x(t)) serially con-nected to a capacitor C(x(t)) as shown in Fig. 2. Consideringthe simplest case of a pure resistive load, the (V-Q-x) relation-ship can be expressed as follows:
Rd
dtQ(x(t)) = V = − 1
C(x(t))×Q(x(t))+VOC(x(t)) (19)
Where R is the equivalent resistance as seen at the TENGterminals. Clearly, the solution of this differential equation in(19) can be complicated for more complex loads including ac-tive elements (e.g., transistors and diodes). Hence, it becomesso tedious to solve these equations analytically or even usingfinite element packages such as COMSOL to solve the systemon the device level. So, a Verilog-A model is introduced withthe same approach in [7] to enable the integration of TENGswith different applications and circuits using various circuitsimulation tools (e.g., Cadence Virtuoso).
III. RESULTS AND DISCUSSIONS
Scrutinizing the results of the analytical model and theCOMSOL simulation, a comparison between them was neededto demonstrate a well established verified model. The results ofCOMSOL simulation showing 3D-Potential distribution, Qscand Voc along with analytical model is depicted in Fig.3 (a),(b) and (c) respectively. Clearly, the short circuit charge shownin Fig. 3 (b) indicates a monotonic increase with increasingthe gap distance between the tribo-pairs. This is actually canbe seen from (18), at V = 0, Qsc = σ × 2πR1x. Fig. 3 (c)shows the variation of open circuit voltage which indicatesan exponential increase with increasing the gap distance withVoc ideally approaches infinity as x approaches l, which canbe seen from (11).Voc and Qsc, exhibit an average error of 4.3%, 6% re-
spectively, between the FEM - results and analytical model
Fig. 2. Schematic representation of TENG equivalent circuit with an arbitraryload [7].
1120
Fig. 3. COMSOL simulation results along with a comparison with analytical model: (a). 3D potential distribution, (b). Short circuit charges Qsc(x), (c).Open circuit voltage Voc(x).
results, which can be justified by the limitations in FEMsimulation such as that, COMSOL doesn’t include a physicsfor triboelectric effect so an additional air layer of 10 µm isadded between the tribo-pairs to enable the simulation.
The accuracy of the developed analytical model was amotivation for constructing a Verilog-A model to investigatethe characteristics of the harvester under different loadingconditions. A case of simple resistive load is investigated inFig. 4. The impact of the gap distance on the I and V isdepicted in Fig. 4 (a) and (b) at different resistance values.The same parameters in Table I is used except for σ = 200µC, as obtained from experimental setup in [2], is used forpower calculation to develop the sense of values comparison.The results show Isc at R = 0, equals to ≈ 87 nA, and a
Fig. 4. Verilog-A model of the proposed harvester: (a) I(x) vs separationdistance at different resistor values. (b) V (x) vs separation distance atdifferent resistor values. (c) Average delivered power to the load resistor.
Voc at R = ∞, equals to ≈ 1.4 KV . A peak power of 5.5mW is observed at R = 3 GΩ.
IV. CONCLUSION
This paper presents, a novel In-Out cylindrical TENG as anew operating mode. The device is implemented in COMSOLMultiphysics to obtain Voc and Qsc as the characteristic intrin-sic parameters. Furthermore, an analytical model is developedto obtain a closed form (V-Q-x) relation. The accuracy ofthe analytical model is verified against the FEM model, theresults shown an excellent agreement of an average errorof 5.2%. A Verilog-A model is developed based on theobtained (V-Q-x), and the terminal, current, voltage and poweris simulated showing a peak of 5.5 mW at a load of 3GΩ,which is considered a very promising results compared to otherconfigurations proposed in the literature.
ACKNOWLEDGMENT
The authors would like to thank the supporting and fundingagencies. This research was partially funded by ONE Lab atCairo University, Zewail City of Science and Technology, andKAUST.
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