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- Herausgeber: Wiley-VCH
- Kategorie: Fachliteratur
- Sprache: Englisch
Comprehensive resource on the fundamentals, recent research developments, and applications of triboelectric nanogenerators (TENGs)
Triboelectric Nanogenerators delivers a comprehensive overview of a lightweight, low cost, and high-efficiency sustainable mechanical energy harvesting technique that draws from the ambient environment and has high output and extremely flexible structural designs.
The book starts with an introduction on triboelectric nanogenerator technology, then continues to discuss the latest fundamental studies about TENGs, including models of triboelectric effect, the discharge effect, and standardized evaluation. The next part explains new output performance promotion of TENGs for power generation applications, including output promotion through multiple methods, as well as power management and effective energy storage. The last part explores new concepts inspired by the field of TENGs, including applications in sensing, actuation, data science, artificial intelligence (AI), the Internet of Things (IoT), and smart cities.
Written by a team of highly qualified academics with significant research experience in the field, Triboelectric Nanogenerators includes information on:
- Triboelectric charge generation and discharge, highlighting how electrostatic energy is often wasted
- Energy potential of TENGs in comparison to other sources such as lithium-ion batteries and other types of batteries
- Methods to promote and configure output performance, such as through gas environments, liquid-solid interfaces, and electromechanical structures
- High-voltage output from TENGs and its potential for new applications in areas such as breakdown charge triggering, electrospraying, field emissions, and others
Triboelectric Nanogenerators is an essential reference for scientists, engineers, students, and professionals in related fields seeking to understand this exciting energy harvesting technique and gain all of the knowledge needed to help further progress in the field.
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Veröffentlichungsjahr: 2025
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Table of Contents
Cover
Table of Contents
Title Page
Copyright
Preface
Introduction of Triboelectric Nanogenerator
I.1 What is a Triboelectric Nanogenerator (TENG)?
I.2 First‐Principle Theoretical Model
I.3 Equivalent Circuit Models and Basic Operation Modes
I.4 Energy Conversion and Electromechanical Coupling Models
I.5 Summary
References
1 Models of Triboelectric Effect
1.1 Introduction
1.2 Thermionic Emission Method
1.3 Material‐Dependent Charge Transfer Mechanism and Model
1.4 Liquid–Solid Contact Electrification Mechanism
1.5 Environmental and Material Effects on Charge Transfer
1.6 Potential Applications
1.7 Summary
References
2 Discharge Effects in TENG
2.1 Introduction
2.2 Theoretical Studies of Breakdown Discharge in Contact‐Separation‐Based TENGs
2.3 Experimental Verification and Quantitative Measurements
2.4 Photon Generation
2.5 Potential Applications
2.6 Summary
References
3 Figure‐of‐Merit of Triboelectric Nanogenerator
3.1 Introduction
3.2 Effective Maximized Energy Output
3.3 Figure‐of‐Merit
3.4 Output Energy Density
3.5 Environmental and Techno‐Economic Analysis
3.6 Potential Applications
3.7 Summary
References
4 Output Promotion by Environment
4.1 High Vacuum Environment
4.2 High Atmospheric Pressure and High‐Breakdown‐Limit Gas Environments
4.3 Interfacial Liquid Lubrication
4.4 Humidity
4.5 Summary
References
5 DC‐TENG: A New Paradigm
5.1 Introduction
5.2 Basic Principle
5.3 Physical Model
5.4 Optimization Methods for DC‐TENG
5.5 DC‐TENG for Energy Harvesting
5.6 DC‐TENG for Self‐Powered Sensing
5.7 Hybrid of AC‐TENG and DC‐TENG
5.8 Summary
References
6 Promotion of Contact Electrification at Liquid–Solid Interface
6.1 Introduction
References
7 Output Promotion of Triboelectric Nanogenerator by Electromechanical Structures
7.1 Introduction
7.2 Charge Excitation Mechanism
7.3 Other Promotion Strategies
7.4 Summary
References
8 Power Management and Effective Energy Storage
8.1 Introduction
8.2 Theoretical Basis of Energy Management for TENG
8.3 Mechanical Switched Converter
8.4 Electronic Switch Converter
8.5 Transformer Converter
8.6 Conclusion and Perspective
References
9 Tribotronics
9.1 Introduction
9.2 Tribo‐Potential
9.3 Triboelectricity Modulate Field Effect
9.4 Tribotronic Transistor
9.5 Tribotronic Functional Devices
9.6 Conclusion
References
10 Tribophotonics
10.1 Introduction
10.2 Tribophotonics: Concept, Origin, Characteristics, and Potential Applications
10.3 Tribo‐Induced EM‐Wave Generation (TIEG)
10.4 Tribo‐Induced Light Propagation Tuning (TILPT)
10.5 Triboelectrification‐Induced Electroluminescence (TIEL)
10.6 Tribo‐Assisted Spectrometry (TAS)
10.7 Potential Applications and Perspectives
10.8 Challenges and Summary
References
11 TENG‐Based Wearable Biomechanical Sensors and Human–Machine Interface
11.1 Introduction
11.2 TENG‐Based Biomedical Sensing
11.3 TENG‐Based Human–Machine Interface
11.4 Summary
References
12 TENG as the High‐Voltage Source
12.1 Introduction
12.2 Overview of Materials and Universal Methods for TENG's Performance Enhancement
12.3 Artificial Muscle Based on Dielectric Elastomer and TENG
12.4 Microactuators Based on Piezoelectric Ceramics and TENG
12.5 Materials Polarized by the High Voltage Output From TENG
12.6 Electrostatic Manipulator Driven by TENG
12.7 Electrostatic Adsorption and Air Cleaning Based on TENG
12.8 Electronic Excitation and Ion Generation Powered by TENG
12.9 Summary and Perspectives
References
Index
End User License Agreement
List of Tables
Chapter 1
Table 1.1 Summary and comparison of different tribo‐pairs.
Chapter 2
Table 2.1 The dielectric strength for breakdown in selected substances.
Table 2.2 Parameters of the CS mode TENG.
Table 2.3 Experiment parameters of the CFT mode TENG.
Chapter 3
Table 3.1 Parameters of TENGs for calculations.
Table 3.2 Revised FOM of different nanogenerators.
Chapter 10
Table 10.1 Summary of TIEG devices.
Table 10.2 Summary of TILPT devices/hybrid systems.
Table 10.3 Summary of TIEL devices.
List of Illustrations
Introduction
Figure I.1 Equivalent circuit models and basic operation modes of TENGs. (a)...
Figure I.2 The traditional mode (a) and the mode of EDAEC method (b) of the ...
Figure I.3 Comparison of traditional and the EDAEC method on capacitance (a)...
Figure I.4 The schematic (a) and equivalent capacitance (b) of SES TENG. (c)...
Figure I.5 The schematic (a) and equivalent capacitance (b) of SFT TENG part...
Figure I.6 Energy flow in the TENG system. (a) The TENG system's energy flow...
Chapter 1
Figure 1.1 Performances of the Ti‐SiO
2
TENG at different temperatures: (a) s...
Figure 1.2 Results of metal/Kapton and Kapton/Kapton tribo‐pairs. The measur...
Figure 1.3 Mechanisms and model for contact electrification. (a) Illustratio...
Figure 1.4 The experiment by Lin et al. to determine the charge transfer mec...
Figure 1.5 The hybrid EDL model with the “two‐step” formation process for CE...
Chapter 2
Figure 2.1 Fundamental mechanisms, behaviors, and studies about discharge ef...
Figure 2.2 Simulations and calculations of the breakdown area. (a) Paschen's...
Figure 2.3 The experiment to demonstrate the existence of air breakdown with...
Figure 2.4 The methods and charge–voltage (
Q
‐
V
) curve of the discharge break...
Figure 2.5 Breakdown discharge results for a CS‐TENG. (a) Schematic diagram ...
Figure 2.6 Breakdown discharge for CFT‐TENG. (a) Schematic diagram of CFT mo...
Figure 2.7 The whole process of the breakdown discharge.
Chapter 3
Figure 3.1 Operation cycles of TENG. (a) Schematic diagram of the LS mode TE...
Figure 3.2 The breakdown areas and maximized energy output per cycle. (a–c) ...
Figure 3.3 The (a) Paschen's curve and (b) maximized energy output per cycle...
Figure 3.4 FOM
S
versus
x
max
for different TENG structures. (a) ∼ (e) FOM
S
fo...
Figure 3.5 Further applications of the proposed method.
Q
–
V
plots of (a) PVD...
Figure 3.6 The output energy density of TENGs considering the breakdown. (a–...
Figure 3.7 The cost and the CO
2
emission distributions of two TENGs. (a) The...
Chapter 4
Figure 4.1 Output promotion of TENG by decreasing atmospheric pressure. (a) ...
Figure 4.2 Output promotion of TENG by increasing atmospheric pressure and a...
Figure 4.3 Output promotion of TENG by interface liquid lubrication. (a) Sch...
Figure 4.4 Output promotion of TENG by humidity. (a,b) Electrical output per...
Chapter 5
Figure 5.1 Working principle of DC‐TENG. (a) Working mechanism of DC‐TENG ba...
Figure 5.2 An equivalent circuit model of DC‐TENG. (a) The simplified struct...
Figure 5.3 The transient physical‐field model of air‐breakdown DC‐TENG. (a) ...
Figure 5.4 Improving triboelectrification. (a) Primary selection rules of tr...
Figure 5.5 Enhancing electrostatic breakdown. (a) Paschen's curves of gas br...
Figure 5.6 The advanced structure design of DC‐TENG. (a) The structural sche...
Figure 5.7 DC‐TENG for energy harvesting. (a) Schematic fabrication process ...
Figure 5.8 DC‐TENG for self‐powered sensing. (a) The schematic structure of ...
Figure 5.9 The relationship of triboelectrification, electrostatic induction...
Figure 5.10 The dual‐mode TENG for energy harvesting and self‐powered sensor...
Chapter 6
Figure 6.1 Temperature effect on the contact electrification between DI wate...
Figure 6.2 Temperature effect on the contact electrification between DI wate...
Figure 6.3 Modification for CE at solid–liquid interface. (a) Molecular stru...
Figure 6.4 The application of L‐S TENG for energy harvesting. (a) energy col...
Chapter 7
Figure 7.1 FOM of TENG. (a) Schematic diagram of LS‐TENG with horizontal sli...
Figure 7.2 Air breakdown in TENG devices. Air breakdown in (a) contact‐separ...
Figure 7.3 Maximum surface charge density of contact‐separated TENG. (a) Ion...
Figure 7.4 Charge pumping for ultrahigh charge density under ambient conditi...
Figure 7.5 Structural design and performance characterization of SCE‐TENG. (...
Figure 7.6 External charge excitation and self‐charge excitation strategies ...
Figure 7.7 Structure and mechanism of CSA‐S‐TENG. (a) The 3D schematic of CS...
Figure 7.8 Structural design and performance characterization of TEL‐TENG. (...
Figure 7.9 Interfacial insulating liquid used to enhance TENG's output perfo...
Chapter 8
Figure 8.1 The advancement history and theoretical basis of power management...
Figure 8.2 Theoretical basis of energy management for TENG. (a) Equivalent c...
Figure 8.3 The power management strategy utilizes series travel switches. (a...
Figure 8.4 Energy management for parallel switching schemes. (a) The working...
Figure 8.5 Energy management scheme based on capacitive conversion. (a) Oper...
Figure 8.6 Energy management scheme based on electronic discharge switch. (a...
Figure 8.7 Power management scheme of electrostatic switch principle. (a) Th...
Figure 8.8 Application demonstration of the mechanical switch energy managem...
Figure 8.9 Power management with integrated circuit. (a) A self‐starting pow...
Figure 8.10 Power management with MOSFET switch. (a) The schematic circuit d...
Figure 8.11 Power management with silicon‐controlled rectifier (SCR) and tri...
Figure 8.12 The power management module with using of a transformer converte...
Figure 8.13 Application demonstration utilizing transformer converter. (a) R...
Figure 8.14 Conclusion and perspectives for power management strategy and ef...
Chapter 9
Figure 9.1 A summary of four major technological drives for electronics: min...
Figure 9.2 Tribo‐potential generation principle of vertical contact separati...
Figure 9.3 Theoretical analysis of the performance of tribotronics MOSFET. R...
Figure 9.4 Theory of nanoscale tribotronics. Reproduced with permission of R...
Figure 9.5 Theory of tribotronic transistor. (a) Structure of the CE‐FET bas...
Figure 9.6 Structure of tribotronic transistor. (a) Structure of the FOTT wi...
Figure 9.7 Tribotronics for information sensing. (a) Basic structure of the ...
Figure 9.8 Tribotronics for active control. (a) Schematic illustration of th...
Figure 9.9 Tribotronics for artificial synapse. (a) The intelligent neuromor...
Figure 9.10 Application prospect of triboelectronics. Reproduced with permis...
Chapter 10
Figure 10.1 The overall illustration of tribophotonics. (a) The general illu...
Figure 10.2 Discharge‐induced displacement‐current‐based fully self‐powered ...
Figure 10.3 Tribo‐induced light color control through tribo‐induced color tu...
Figure 10.4 Tribo‐assisted spectrometry (TAS). (a) Microplasma driven by TEN...
Chapter 11
Figure 11.1 An overview of TENG‐based wearable biomechanical sensors and HMI...
Figure 11.2 TENG‐based biomechanical sensors in pulse monitoring. (a) Self‐p...
Figure 11.3 TENG‐based biomechanical sensors in respiration monitoring. (a) ...
Figure 11.4 TENG‐based biomechanical sensors in joint movement monitoring. (...
Figure 11.5 TENG‐based HMIs in eye movement monitoring. (a) Eye motion trigg...
Figure 11.6 TENG‐based HMIs in voice/auditory recognition. (a) A self‐powere...
Figure 11.7 TENG‐based HMIs in gesture recognition. (a) Rotation sensing and...
Figure 11.8 TENG‐based HMIs in touch/tactile recognition. (a) Ionic communic...
Chapter 12
Figure 12.1 Combination of TENG and electrically response materials/devices ...
Figure 12.2 Surface modification of friction materials. (a,b) SEM images of ...
Figure 12.3 (a) Maximum saturated charge density between FEP (without corona...
Figure 12.4 Enhancement of TENG's voltage performance by charge injection me...
Figure 12.5 Enhancement of TENG's Voltage Performance by Charge Supplement. ...
Figure 12.6 Self‐powered artificial muscle and intelligent switch based on a...
Figure 12.7 Intelligent optical modulator by coupling TENG and dielectric el...
Figure 12.8 An effective method for operating the TENG‐DEA system and theore...
Figure 12.9 Optical modulated active microactuator based on planar sliding T...
Figure 12.10 Triboelectric micromotor based on a micromotor and a triboelect...
Figure 12.11 Self‐powered trace memorized storage based on triboelectrificat...
Figure 12.12 Liquid–liquid triboelectric nanogenerator based on liquid dropl...
Figure 12.13 TENG as an electrostatic actuator for the manipulation of tiny ...
Figure 12.14 Self‐powered drug delivery system based on TENG. (a,b) The illu...
Figure 12.15 The manipulation of microfluidics by TENG in a microfluidic sys...
Figure 12.16 Self‐powered anode bonding system driven by TENG. (a) Circuit d...
Figure 12.17 A self‐powered air purifier for removing particulate matter fro...
Figure 12.18 TENG‐based air filter for efficient particulate matter removal....
Figure 12.19 Oil purification system based on high voltage TENG. (a) Schemat...
Figure 12.20 Field emission powered by TENG. (a) A schematic of an emitter, ...
Figure 12.21 Mass spectrometry powered by TENG. (a,b) Schemes of the ion gen...
Figure 12.22 Triboelectric field‐induced plasma discharge based on TENG. (a)...
Figure 12.23 Plasma excitation based on TENG. (a) The schematic illustration...
Guide
Cover
Table of Contents
Title Page
Copyright
Preface
Begin Reading
Index
End User License Agreement
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Triboelectric Nanogenerators
Technology, Applications, and Commercialization
Yunlong Zi, Hengyu Guo, Jie Wang, Chi Zhang, Xiangyu Chen, and Qing Zhao
Authors
Yunlong ZiHong Kong University of Science and Technology (Guangzhou)Guangzhou, GuangdongChina
Hengyu GuoChongqing UniversityChongqingChina
Jie WangBeijing Institute of NanoenergyBeijingChina
Chi ZhangBeijing Institute of NanoenergyBeijingChina
Xiangyu ChenBeijing Institute of NanoenergyBeijingChina
Qing ZhaoChongqing UniversityChongqingChina
Cover Image: © Carlos Barros/Getty Images
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© 2025 WILEY‐VCH GmbH, Boschstraße 12, 69469 Weinheim, Germany
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All rights reserved (including those of translation into other languages, text and data mining and training of artificial technologies or similar technologies). No part of this book may be reproduced in any form – by photoprinting, microfilm, or any other means – nor transmitted or translated into a machine language without written permission from the publishers. Registered names, trademarks, etc. used in this book, even when not specifically marked as such, are not to be considered unprotected by law.
Print ISBN: 978‐3‐527‐35042‐1ePDF ISBN: 978‐3‐527‐83788‐5ePub ISBN: 978‐3‐527‐83789‐2oBook ISBN: 978‐3‐527‐83790‐8
Preface
Since its invention, triboelectric nanogenerator (TENG) has experienced development for over 10 years, like a big tree grown from a tiny seed. 10 years ago, we were still working on the basic modes, fundamental theories, evaluation standards, etc. Five years ago, we studied mechanisms and designs that can enhance the output performance of TENGs. Nowadays, TENG has become a well‐recognized energy harvesting technology with output energy density of 105 J/m3 level while the peak power density can achieve 15 MW/m2, and scientists are working on TENG's applications in various scenarios. As recommended by authors, we believe the topics selected are important research topics in TENG, which may not only contribute to the development of science in TENG, but also promote the applications. The significance and the related questions of these chapters are stated below:
Chapters 1
and
2
state how the triboelectric charge was generated and discharged, which highlights the charge transfer flow in TENG. In the meanwhile, an issue worthy to discuss is how the energy conversion in TENG was completed at the beginning, and how a large portion of the electrostatic energy was wasted if they were not used in applications.
Chapter 3
regarding the standardization of TENG is touching a key question of TENG, that is how much energy can TENG provide? The provided standards are all related the output energy density of TENG, which is now around 10
5
J/m
3
. As comparison, the lithium ion battery can achieve around 10
9
J/m
3
, while the limit of the breakdown discharge of materials is around 10
8
J/m
3
, which means we may still have some gaps to catch.
Chapters 4
–
8
discuss about different methods to promote and/or config the output performance of TENGs. The gas environment can impact the breakdown discharge limits as well as equivalent resistance of among triboelectric layers and electrodes. Liquid–solid interface may provide a way for triboelectric charge generation with little energy waste in friction. Electromechanical structures may provide means to excite the charge in circles until breakdown limit. DC‐TENG provides a new design that can directly supply direct current output. The power‐management and energy storage systems provide solutions to manage and store the generated power, which is also necessary in the system.
Chapters 9
–
12
outlook four new related research areas, which are all related to potential applications. Tribotronics utilizes TENG to serve as a gate voltage, which can be triggered by simply touching. Tribophotonics couples the triboelectricity as the power source and photonics as the wireless transmission means, targeting at self‐powered wireless systems. Combined with artificial intelligence (AI), sensing systems based on TENG mechanisms will become more accurate, with advantages of high signal‐to‐noise ratio. High‐voltage output from TENG, with thousands or even tens of thousands volts in voltage, may be a new application area that is promising to trigger breakdown discharge, electrospray, field emission, etc.
In light of the four parts as stated above, we can see that TENG is experiencing a rapid development in the past five years. Compared with the book Triboelectric Nanogenerators published in 2016 by Springer, the contents of this book cover more in‐depth mechanism studies, discuss more methods to promote/regulate the output performance, and expands more applications with new research directions proposed. Hopefully with this new book, readers can understand the progress in this exciting field, and facilitate mutual communications among scientists, engineers, students, and public, which may end up with better utilization of TENG technology to serve the people's life.
Introduction of Triboelectric Nanogenerator
I.1 What is a Triboelectric Nanogenerator (TENG)?
To meet the rapidly increased energy demands of the Internet of Things (IoT) and modern smart cities, a new type of energy harvesting technology, nanogenerator, has been invented to provide sustainable power source by collecting energy from the ambient environment. In them, the triboelectric nanogenerator (TENG), which is based on the coupling of triboelectrification and electrostatic induction effects, is focused in recent years [1–6]. This emerging technology was predicted to play a critical role in harvesting low‐frequency energy such as body motion energy and ocean‐wave energy [7–9]. Due to its advantages of lightweight, low cost, and high efficiency, plenty of research has demonstrated the great potential of TENGs on numerous applications [10–13].
The term “nanogenerator” is defined as an emerging type of technology that can convert small‐scale mechanical and thermal energy into electricity. Different from traditional generators, nanogenerator usually utilizes Maxwell's displacement current initiated by the static charges, which were generated by triboelectric, piezoelectric, and pyroelectric effects, to drive effective energy conversion [14, 15]. TENG is the major type of nanogenerator which utilizes the charge generated in triboelectric effect, which is also the most powerful energy harvester in nanogenerators.
I.2 First‐Principle Theoretical Model
Traditionally, it is believed that TENG is operated based coupling effects of triboelectrification and electrostatic induction. Triboelectrification (triboelectric effect) describes the origin of the static charges, while electrostatic induction explains the power generation. However, further theories from fundamental physics are still required to understand the operation of TENG.
Wang demonstrated the first‐principle theoretical models from Maxwell's displacement current [14, 15]. Maxwell's equations are shown below:
Here, D = εE is the electric displacement field, B is the magnetic field vector, E is the electric field, H is the magnetic field strength, J is the current density, and ρ is the volume charge density. The term ∂D/∂t can be also written as JD, as named Maxwell's displacement current. Wang proposed an additional polarization term PS in the electric displacement field due to the static charge generation in nanogenerator, and thus JD can be written as:
Therefore, the volume charge density ρ and current density J can be redefined as ρ′ and J′, respectively:
And they still satisfy the charge conversion and continuation equation:
Through this displacement current as the driving force in nanogenerators, the conduction current can be driven on the external load, forming a complete loop. And then, the output characteristics of TENGs can be further discussed in theoretical models such as Displacement Current Theory model [16, 17], quasi‐electrostatic model [18–20], and Distance‐Dependent‐Electric‐Field (DDEF) mode [21–23], which can be used to calculate electric potential and power generation accurately.
I.3 Equivalent Circuit Models and Basic Operation Modes
I.3.1 Equivalent Circuit Models
As stated above, the TENG is operated based on the additional displacement current term, originating from the static charge generated from triboelectric effect. The maintained opposite static charge in triboelectric surfaces determines the inherent capacitive behavior of the TENG. At the open‐circuit condition, the potential difference VOC accumulated between electrodes originates from the additional polarization term PS, as a function of the displacement x of the moving part in TENG. In the meanwhile, if we assume no charge generation in TENG, the device can be treated as a pure capacitor with capacitance C determined by x as well. So in the generalized case, the output voltage V and the charge transfer Q between electrodes are determined by the equivalent circuit of a voltage source VOC(x) in parallel with a capacitor C(x) as shown in Figure I.1a, with the governing equation described by: [2, 24]
Figure I.1 Equivalent circuit models and basic operation modes of TENGs. (a) Basic equivalent circuit of TENG.
Source: Reproduced with permission of [2], 2015 © Elsevier.
(b–e) The theoretical models of contact‐separation (CS), lateral‐sliding (LS), single‐electrode (SE), freestanding triboelectric‐layer (FT) modes TENGs. (f) The EDAEC method for quantitatively analysis of all modes of TENG.
Source: Reproduced with permission of [26], 2019 © Royal Society of Chemistry.
In short‐circuit condition, full charge transfer (QSC) can be obtained as driven by the voltage source, and hence: [25]
From such the V‐Q‐x relationship, we can derive the lumped parameter equivalent circuit mode, which can be used to predict characteristics of TENGs in different modes.
TENG has four basic operation modes: contact‐separation (CS), lateral sliding (LS), single electrode (SE), and freestanding triboelectric layer (FT), with detailed structures shown in Figure I.1b–e. In them, SE and FT modes can be further divided into SE contact (SEC), SE sliding (SES), sliding FT (SFT), and contact FT (CFT) modes, depending on whether they are triggered by contact separation or sliding motions. These modes have their own equivalent circuit models available for simulations and theoretical calculations. Here, a universal method for quantitative analysis of all modes of TENG is used for analysis, as shown in Figure I.1f [26]. This method is based on the edge approximation‐based equivalent capacitance (EDAEC). The equivalent capacitance models are used to demonstrate charge distributions on each electrode. Due to contact electrification, static triboelectric charges – Qtribo,χ will be dispersed on the dielectric surface χ after contacting the metal electrodes. According to charge conservation, the metal electrodes would have the same amount of opposite‐sign charges in total [27–29]. By defining the charges distributed on electrodes 1 and 2 as Q1 and Q2, respectively, the relation can be given below:
Under short‐circuit conditions, two electrodes would have the same potential. For simplicity, the two electrodes and the dielectric surface can be defined as node 1, 2 and surface χ (can be different letters for different surfaces), with capacitance between them as Cχ1,total and Cχ2,total, respectively, as shown in Figure I.1. Therefore, the following equation can be obtained.
Thus, the short‐circuit equilibrium charges Q1 and Q2 on electrodes 1 and 2, respectively, are given as: [30]
Sum symbol ∑ is used here to indicate the charge contributions from different surfaces. And then:
From the equations above, the working mechanism of TENGs can be easily illustrated. When the distance between surface a and electrode 2 is zero the capacitance across them would be much larger than that across electrode 1 (Cχ2,total ≫ Cχ1,total). Most of the positive tribo‐charges would be attracted to electrode 2. Q2 is close to Qtribo and Q1 is approximately zero. On the other hand, when the distance is quite large, the capacitance across surfaces a and electrode 2 would be much smaller than that across electrode 1 instead (Cχ1,total ≫ Cχ2,total). So Q1 is close to Qtribo and Q2 is approximately zero. Thus, QSC(x) can be calculated by the difference between Q1(x) and Q1(0) or between Q2(x) and Q2(0), and the total capacitance C(x) = Cχ1,totalCχ2,total/(Cχ1,total + Cχ2,total). According to this EDAEC method the charge distributed on each electrode could then be quantitatively calculated.
I.3.2 CS Mode TENG
CS mode TENG was the original type TENG demonstrated in early‐stage studies [1, 3]. Based on triboelectric materials used, the CS‐mode TENG can be divided into two types: dielectric/dielectric contact and dielectric/metal contact. However, since there is no fundamental difference in operation mechanism between these two types, we just take the dielectric/metal contact type as an example, with the model shown in Figure I.1b. The dielectric layer with a thickness of d and relative dielectric constant εr is directly facing metal surface as one electrode, and another electrode is attached on the backside of the dielectric layer. Under external excitation, the displacement x is defined as vertical distance between two surfaces. After triboelectric effect, the surface charge density −σ was generated in the dielectric surface a with area S = w × L, making Qtribo = Sσ. By choosing the minimum achievable charge reference state (MACRS) [30], with the charge transfer of Q, the top electrode (electrode 2) is with total charge of Q2 = Sσ−Q, and the bottom electrode (electrode 1) is with total charge of Q2 = Q. As shown in Figure I.1f‐I, the two electrodes and the dielectric layer surface form two capacitances: Ca2,total (x) is the capacitance between electrode 2 and the dielectric surface a, depending on x; and Ca1,total is the capacitance between the dielectric surface a and electrode 1, which is a fixed value which can be considered as parallel‐board capacitance. If S ≫ x2, the capacitance Ca2,total(x) can be also considered as parallel‐board capacitance Ca2(x) without considering the edge effect, and we can derive:
While if the edge effect is considered, the total capacitance of Ca2,total(x) should include capacitance contributions from edge effects Ca2edge(x) in parallel, as shown Figure I.1f‐I. Based on previous studies, this capacitance can be estimated as: [31]
With that, we can calculate numerous values for QSC(x), C(x), and VOC(x), obtaining the governing equation.
I.3.3 LS Mode TENG
Traditionally, by assuming the parallel‐board capacitance model, the total capacitance C(x) fully depends on the capacitance of the covered part between electrodes 1 and 2, as described in Figures I.1c and I.2a [24, 32, 33]. The length L and the width w of the electrodes and dielectric layers are all defined as 100 mm. The dielectric layer with the thickness of d0 is stacked on electrode 1 and the gap between the dielectric layer and the sliding electrode 2 is defined as d. The total capacitance C(x), which is based on a traditional unlimitedly large plane, can be described as the equations below:
Figure I.2 The traditional mode (a) and the mode of EDAEC method (b) of the LS mode TENG. The comparison of transferred charge by traditional and EDAEC methods (c–e). The comparison of short‐circuit current by traditional and EDAEC methods.
Source: Reproduced with permission of [26], 2019 © Royal Society of Chemistry.
And the equivalent capacitance of C(x) can also be described as the series connection of Cb1(x) and Cb2(x), in which:
Here, a new analytical EDAEC model is built, taking the capacitance of edge effect into consideration, to quantitatively describe the TENG's outputs. The real equivalent capacitance of C(x) is shown in Figure I.2b, which includes three parts. Part 1 shows the edge capacitance Ca2(x) between the surface a (dielectric layer) and electrode 2, and the capacitance Ca1(x) between surface a and electrode 1. Ca2(x), which is almost a constant, is quite small when comparing to Ca1(x). Therefore Ca2(x) can be approximated as a small constant through:
Part 2 in Figure I.2b shows the edge capacitance C12d between electrode 1 and electrode 2, which is also considered as a small constant for easy calculation. And Part 3 shows the capacitance C1b2 based on traditional parallel‐board capacitance model between the covered part of electrode 1 and electrode 2.
Therefore, the total capacitance C(x) can be calculated as:
With triboelectric charge density σ, total triboelectric charge on surface sections a and b can be defined as the equations below:
Under the short‐circuit (SC) condition, electrode 1 and electrode 2 will have the same electrical potential. Therefore, the total charges on each electrode can be derived from Equation (I.10) by overlapping electrostatically induced charges from Qa and Qb:
Therefore, the total charges on electrode 1 Q1 can be calculated as:
When x = 0 is assigned to be the initial state, the initial Q1 is defined as:
The transferred charges QSC is equal to the change of the charge on electrode 1, therefore the transferred charge QSC can be calculated as the difference between the induced charges Q1(x) and the initial state charges Q1(0) on electrode 1. The short‐circuit charge QSC can be calculated by the equation below.
In the equation above, Za is a constant when the structure is fixed:
It should be noticed that the first item of QSC has a linear relationship with displacement x, representing the part of σwx from traditional method. The second item of QSC is a non‐linear item, and the third item is a constant.
Traditionally, the graph of traditional QSC has a strictly linear relationship with x. However, in the new EDAEC method, as we consider the edge effect, the QSC does not have a strictly linear relationship with the displacement. As shown in Figure I.2c, the graph of QSC has a flatter start at the beginning (Figure I.2d), and then the slope of QSC will increase until it has almost the same slope with the traditional graph when d = 0 (Figure I.2e). In order to validate the above theoretical derivation, an LS mode TENG model is simulated by finite element method (by COMSOL Multiphysics software package), and the corresponding results are plotted in Figure I.2c–e. It should be emphasized that the theoretically calculated QSC by COMSOL simulation is closer to that from our EDAEC model than traditional QSC. According to the results of QSC, the graph of current and displacement is also plotted with a constant sliding speed of 0.01 m/s. Unlike the traditional graph which gives constant current, the EDAEC method shows that the current would be much lower when x is small and then sharply increase to the traditional value (in Figure I.2f). These results demonstrate that our EDAEC model which considers the edge effect is more suitable when describing the LS mode TENG.
With the total capacitance C(x) and the short‐circuit charge QSC known, the open‐circuit voltage can be obtained. The capacitance calculated by the EDAEC method is demonstrated to be more accurate than traditional values (Figure I.3a) as compared to the COMSOL results. The open‐circuit voltages are also plotted in Figure I.3b, which gradually increase with displacement x, and increase sharply when x is quite close to L. The total capacitance of the LS TENG will be zero according to the traditional method at x = L. At this position, the open‐circuit voltage will be infinitely large, which is far away from the real situation. The EDAEC method takes the edge capacitance into consideration, and thus the open‐circuit voltage can be accurately calculated even when x = L. Compared to traditional calculation, the EDAEC method shows that the voltage will give a result which is more consistent with that by COMSOL, as shown in Figure I.3b.
Figure I.3 Comparison of traditional and the EDAEC method on capacitance (a) and voltage (b). The insets are the magnified graph of the dotted part. (c) The relationship between transferred charges at short‐circuit and the separation distance d. (d) The relationship between open‐circuit voltage and the separation distance d. (e) The relationship between transferred charges at short‐circuit and the thickness of dielectric layer d0. (e) The relationship between open‐circuit voltage and the thickness of dielectric layer d0.
Source: Reproduced with permission of [26], 2019 © Royal Society of Chemistry.
According to Equation I.24, the transferred charge QSC is also affected by the TENG's structural parameters, for example, the distance d between the dielectric material and electrode 2, and the thickness d0 of the dielectric material. Therefore, the short‐circuit transferred charges and open‐circuit voltages with different gap d is also demonstrated in Figure I.3c,d. It is obvious that the slopes of QSC and VOC against the change of x become much smaller when the gap d increases. This result can explain experimental phenomenon of why the outputs (QSC and VOC) of the LS TENG become quite low when the gap between the dielectric material and electrode 2 is larger than a threshold value. The thickness d0 of the dielectric material will also affect the LS TENG's outputs, as shown in Figure I.3e,f. The QSC against x will become a bit smaller when the dielectric thickness d0 increases, while the VOC will become much larger due to the decrease in the total capacitance. These results are also compared with the simulation results by COMSOL, which shows a high degree of agreement. Based on the above analysis, the EDAEC method, by considering the edge effect, shows high accuracy in calculating the capacitance C(x), short‐circuit charge QSC and open‐circuit voltage VOC of LS mode TENGs under different conditions. It should be emphasized that this EDAED method is quite important for the grating structured TENGs. Because the electrode sizes of the grating structured TENGs are much smaller than other sliding TENGs, the electrodes could not be regarded as the traditional unlimitedly large plane anymore. Therefore, the influence of the side‐effect capacitance will become much more significant. The short‐circuit charge of the grating structured TENGs is no longer a straight line [34].
I.3.4 SE Mode TENG
SE mode TENG is a design that utilizes only one electrode to collect output and connect to the external device, getting rid of the moving electrode which may bring limitations in applications. However, in practical applications, the other connection node of the external devices is always connected to the ground, so the ground should be considered as a reference electrode for SE‐TENGs. Here we will introduce models for SEC and SES modes TENGs.
(1) SEC mode TENG
We take the conduct‐to‐dielectric SEC TENG as an example, with the structure shown in Figure I.1d. The output of dielectric‐to‐dielectric SEC TENG will be slightly different, but they follow similar characteristics. The top dielectric serves as the moving part, with the bottom surface a taking charge density of ‐σ, and the surface area of S = w × L, making Qtribo = Sσ. The electrodes in TENG and the ground are marked as nodes “1” and “2”, respectively. The gap between the electrode and the ground is g, while the displacement of the dielectric is x which is defined as the gap between the dielectric bottom surface a and the electrode. By choosing the minimum achievable charge reference state (MACRS), with the charge transfer of Q, the electrode is with total charge of Q1 = Sσ−Q, and the ground is with total charge of Q2 = Q. As shown in Figure I.1f‐V, the electrode, dielectric surface a, and reference electrode forms 2 capacitances: Ca1 is the capacitance between the electrode and the dielectric surface a, depending on x, which is infinite at x = 0; Ca2 is the capacitance between the ground and the dielectric surface a, depending on x. In this mode, the direct capacitance C3 between the electrode and ground should also be considered, except the short‐circuit condition [25]. The actual capacitance between the electrode and ground can be obtained by considering the connections among the three capacitances:
Therefore, according to Eqs. I.7, I.10, and I.11, the short‐circuit charge can obtained as:
Please note that in SEC TENG, if we use the parallel‐board capacitance for these capacitances, there will be no output, since the edge effects play an important role in SEC TENG. We can use Equation (I.16) to calculate these capacitances, obtaining numerous values for QSC(x), C(x), and VOC(x), and the governing equation.
(2) SES mode TENG
Owing to only one electrode, it is difficult for researchers to quantitatively describe output performances of the SES TENG [25]. The EDAEC method mentioned above can solve this problem. The mode in Figure I.4a is designed to demonstrate the working principle of the SES TENG, as the ground could be regarded as the second electrode of the single‐electrode TENG. Similar to the method described before, the metal electrode 1 and the dielectric layer are defined with length L = 100 mm and width w = 100 mm. The distance between dielectric layer and electrode 1 is defined as d, and the distance between the dielectric layer and the ground is defined as dg. The surrounding environment connected to the ground will have an effect to the dg, which could be regarded as a big conductive box containing the SES TENG.
Figure I.4 The schematic (a) and equivalent capacitance (b) of SES TENG. (c) The relationship of transferred charges with the displacement. (d) The relationship of open‐circuit voltage with the displacement. (e,f) The relationship between transferred charges at short‐circuit (e) and open‐circuit voltage (f) with the distance between the dielectric layer and the ground dg.
Source: Reproduced with permission of [26], 2019 © Royal Society of Chemistry.
The equivalent capacitance of Ctotal is shown in Figure I.4b, which includes three parts, including the capacitances between electrode 1 and the ground electrode via surfaces a (Ca1 and Cag), and b (Cb1 and Cbg). Because the ground electrode is surrounding the dielectric layer, therefore there are several in‐parallel capacitances Cbg,n between the dielectric layer and each surrounding surface, and Cbg is the total capacitance. And C1gd is the direct capacitance between electrode 1 and the ground electrode. The capacitance can be defined by the following equations.
According to the EDAEC we described before, the edge capacitance Cb1 is quite small as compared with other capacitances. Therefore, Cb1 can be approximated as a small constant. The total capacitance could be defined as:
After contact electrification, the upper surface of the dielectric layer would be filled with triboelectric charges. Under short‐circuit conditions, the total charges on electrode 1 can be calculated by the following equations.
In the equation above, to facilitate the calculation, the constant is defined as:
Thus, the short‐circuit charge QSC can be calculated by the equation below.
Due to the characteristics of the single electrode TENGs, the short‐circuit charge QSC is noticeably lower than the total charges on the electrode 1 Qtotal, which is equal to the total triboelectric charge of the dielectric layer. From Figure I.4c, at x = L, the short‐circuit charge QSC only reaches around 70% of the total movable charge Qtotal. This phenomenon could explain why the output power or the efficiency of SE TENG is quite lower than LS or SFT TENG. To validate the above equations, a SES TENG model is simulated by COMSOL. The transferred charge from the equation and the numerical results simulated from COMSOL are plotted in Figure I.4c which are quite consistent with our model.
With the total capacitance Ctotal and the short‐circuit charge QSC known, the open‐circuit voltage can be obtained by Equation (I.7). The open‐circuit voltage from the equation and the results simulated from COMSOL are plotted on the same graph to compare, in Figure I.4d. The theoretical calculation coincides with numerical simulation, which demonstrates the accuracy of the proposed theoretical model.
According to Equation (I.34), the distance dg between the dielectric material and the ground electrode will significantly affect the transferred charge QSC. Therefore, the transferred charge and open‐circuit voltage with different distance dg is also demonstrated in Figure I.4e,f. It is interesting to notice that the slope of QSC will be much smaller when the distance dg increases, while VOC will be much larger.
I.3.5 FT Mode TENG
FT TENG is another two‐electrode TENG design that can make both electrodes keep static, while the high output performance can be guaranteed [30]. It can also be distinguished from CFT and SFT modes.
(1) CFT mode TENG
The CFT can also be divided by the different material selections as dielectrics or conductors, while their output characteristics are quite similar. Here, we just introduce a typical one with the dielectric freestanding layer and metal electrodes, as shown in Figure I.1f‐III. The dielectric freestanding layer serves as the moving part, with the top and bottom surfaces a and b taking charge density of −σ for each, and the surface area of S = w × L, making Qtribo,a = Qtribo,b = Sσ. The top and bottom metal electrodes are marked as nodes “1” and “2”, respectively. The gap between the electrodes is g, while the displacement of the dielectric layer is x, which is defined as the distance between the bottom dielectric surface b and the bottom electrode 2. The dielectric thickness is d with relative dielectric constant εr. As shown in Figure I.1f‐III, the electrodes 1, 2, and dielectric surfaces a, b can form 3 capacitances: Ca1 is the capacitance between the top electrode 1 and the dielectric surface a, depending on g−x, which is infinite at x = g; Cab is the capacitance of the dielectric layer, which is a constant estimated by the parallel‐board capacitance; Cb2 is the capacitance between the electrode 2 and the dielectric surface b, depending on x, which is infinite at x = 0.
Q1 and Q2 of this CFT TENG can be derived as the sum of charge contributed from two charged surfaces a and b, and then:
And then:
So VOC(x) can be also calculated correspondingly. If S ≫ g2, the capacitance Ca1(x) and Cb2(x) can be also considered as parallel‐board capacitances without considering the edge effect, and we can derive:
If the edge effect is considered, the total capacitance of these two capacitors should include capacitance contributions from edge effects in parallel, as shown in Figure I.1f‐III. Based on previous studies, this capacitance can be estimated by Equation (I.16). With that, we can calculate numerous values for QSC(x), C(x), and VOC(x), obtaining the governing equation.
(2) SFT mode TENG
The capacitance caused by edge effect in sliding FT (SFT) TENG is significant and brings a much more obvious influence than that for LS TENG. The simplest structure of the SFT TENG, shown in Figure I.1e, consists of two adjacent metal electrodes (length: L = 100 mm, width: w = 100 mm) with a gap g and a movable dielectric layer with identical size to each electrode. The dielectric layer is placed above the electrodes at a distance of d. Due to impact of the edge capacitance, the sliding displacement of the TENG can be divided into three sections according to x, 0 < x < g (Part 1, Figure I.5a,b), g ≤ x ≤ L (Part 2, Figure I.5c,d), and L < x < L + g (Part 3), which is symmetric to Part 1. Therefore, both the short‐circuit transferred charge QSC (Figure I.5e,f) and open‐circuit voltage (Figure I.5g,h) can be divided into 3 parts correspondingly: the first flat part corresponding to 0 < x < g, the second linear‐like part corresponding to g ≤ x ≤ L and the third flat part corresponding to L < x < L + g.
Figure I.5 The schematic (a) and equivalent capacitance (b) of SFT TENG part 1. The schematic (c) and equivalent capacitance (d) of SFT TENG part 2. (e) The total transferred charges of three parts with the displacement. (f)The magnified graph of the dotted part 1 of (e). (g) The total open‐circuit voltage of three parts with the displacement. (h) The magnified graph of the dotted part 1 of (g). (i,j) The relationship between transferred charges at short‐circuit (i) and open‐circuit voltage (j) with the separation distance d. (k,l) The relationship between transferred charges at short‐circuit (k) and open‐circuit voltage (l) with the gap g.
Source: Reproduced with permission of [26], 2019 © Royal Society of Chemistry.
When g ≤ x ≤ L, the total capacitance (Figure I.5c) consists of the capacitances between electrodes via surfaces a (Ca1 and Ca2), b (Cb1 and Cb2), and c (Cc1 and Cc2), and the direct capacitance between electrodes (C12d). Traditionally, only Ca1 and Cc2 are considered, which can be given by the following equations.
Similar to the Equation (I.19) of LS TENG, Ca2 and Cc1 are quite small, which can be approximated as small constants. Due to the structural symmetry, Cb1 is equal to Cb2, thus Yb = Cb2/Cb1 = 1. Therefore, according to the charge distribution Equation I.10, the charge distributed on the electrode 1 can be defined as:
When the distance d is fixed, Yb, Za, and Zc are considered as constants, for convenience of the calculation:
Therefore, the charge distributed on the electrode 1 can be defined as:
With x = 0 assigned to be the reference state, the short‐circuit charge QSC can be calculated by the equation below.
It should be emphasized that the second part of QSC does not have a strict linear relationship with the displacement. Because the constants Za and Zc are quite small, thus the items Za2/(L−x + Za) and Zc2/(x−g + Zc) do not have a significant influence on the QSC, resulting that the QSC seems to have a linear relationship with the displacement when (g ≤ x ≤ L).
When the distance d = 0, the Za and Zc are zero and QSC can be simplified as.
This equation demonstrates that when the distance d is zero, part 2 of QSC has a linear relationship with the displacement x.
When 0 < x < g, the total capacitance consists of the capacitances between electrodes via surfaces a (Ca1 and Ca2) and b (Cb1 and Cb2) and the direct capacitance between electrodes (C12d). Figure I.5f shows that the QSC of part 1, as the framed part in Figure I.5e, increases slowly at the beginning and then much faster. The EDAEC method mentioned above can be used to quantitatively describe the non‐linear relationship of the QSC. The equivalent capacitance of the SFT TENG when 0 < x < g is demonstrated in Figure I.5b. Due to the edge capacitance Cb2 or Ca2 between the surface b or a of the dielectric material and electrode 2, quite a bit of charges will be induced to distribute on electrode 2, causing the slow non‐linear increase. According to the charge distribution Equation (I.3), as the x increases, the ratio of Cb2/Cb1 will be bigger, causing more and more charges transferred to electrode 2. This non‐linear increasing phenomenon could not be quantitatively explained without considering the edge capacitance. The charge distributed on the electrode 1 could be given as:
The QSC for L < x ≤ L + g (Part 3) can be directly given due to the symmetry of it to that for 0 ≤ x < g (Part 1), and then the charge distributed on the electrode 1 could be given as:
Thus, the short‐circuit charge QSC can be calculated by the equation below.
In order to validate the above theoretical calculation, an SFT TENG model is simulated by COMSOL, which also takes the edge effect into consideration, and the corresponding results are plotted in Figure I.5e,f. It should be emphasized that the QSC from Equation (I.23) is consistent with the simulated QSC by COMSOL.
When the distance d = 0, the Za and Zc are zero and QSC can be simplified as.
The total capacitance Ctotal and the short‐circuit transferred charge QSC have already been quantitatively given, and thus the open‐circuit voltage can be obtained. The voltage is also divided into three parts according to x, as shown in Figure I.5g. Due to the edge capacitance, there is a slow‐increase part of Part 1 (0 < x < g) as shown in Figure I.5h. The voltage of Part 2 (g ≤ x ≤ L) has a linear‐like relationship with the x. Due to the increasing edge capacitance effect, the increase of the voltage of Part 3 (L < x < L + g) will turn flat again.
According to Equation (I.50), the short‐circuit transferred charge QSC is also affected by the TENG's structural parameters, for example, the distance d between the dielectric material and the electrodes, and the gap g between the two electrodes. Therefore, the transferred charge and open‐circuit voltage with different distance d and gap g are also demonstrated in Figure I.5i–l. The slope of Qsc and Voc become a little smaller when the distance d increases, as shown in Figure I.5i,j.
When the gap g becomes larger, the ratio of part 1 and part 3 become larger. And thus the influence of edge capacitance becomes more significant. As a result, the non‐linear part becomes more obvious, and the flat parts of QSC at both ends are much more noticeable. Besides, the total capacitance will decrease due to the increase of the gap g. The total transferred charge remains the same during the whole process. Therefore, the open‐circuit voltage will increase, as shown in Figure I.5l. Meanwhile, the portions of parts 1 and 3 also become larger. The results simulated by COMSOL are also presented, which are well‐consistent. Based on the above analysis, the new method shows high accuracy in describing the short‐circuit charge QSC and open‐circuit voltage VOC of SFT TENGs.
I.4 Energy Conversion and Electromechanical Coupling Models
As an energy system, TENG can either collect tiny energy in the environment to provide power for some electronic devices or act as a self‐driven sensor [35–38]. It is crucial to study how to improve the efficiency and performance of TENG. In 2019, Xu et al. proposed a concept to study the efficiency of TENG from the perspective of energy flow [5]. As shown in Figure I.6a, the energy of TENG starts from harvesting external mechanical energy as input. Then it is converted into internal electrostatic energy in TENG and finally transformed into electrical power. It should be noted that the force (F) integral to the displacement (x) represents the mechanical energy input, and the V‐Q plot demonstrates the energy output. Therefore, the total efficiency of TENG can be given by:
Figure I.6 Energy flow in the TENG system. (a) The TENG system's energy flow, force‐displacement (F‐x), and voltage‐charge (V‐Q) plots.
Source: Reproduced with permission of [5], 2019 © Elsevier.
(b) 3D model of an oscillator triggers a contact separation mode TENG. (c) Schematic of a TENG system involving mechanical and electrical parameters.
Source: Reproduced with permission of [54], 2022 © John Wiley & Sons.
Moreover, the TENG energy harvesting system mainly involves three parts: an excitation source such as human motion or vehicle vibration, an energy harvesting device, and an interface circuit. As a dynamic system, a TENG system experiences oscillating energy flow, which means that studying the efficiency of TENG should fully consider the energy input and output simultaneously. In Figure I.6b, we choose the most widely used CS mode TENG as an example [1], where the whole system consists of a CS‐TENG fixed at the excitation source. Here, spring is necessary because it can ensure that the upper electrodes of the TENG can be separated smoothly after contact. This electromechanical coupling system is modeled as an equivalent lumped‐parameter one degree of freedom (DOF) dynamic system (Figure I.6c), whose mechanical governing equation is shown below:
Where m, c, k, and Fe are the equivalent mass, damping, stiffness, and electrostatic force. And the method explaining how to calculate the electrostatic force has been introduced in our work [5]. Solving the above Eqs. (I.53) and (I.6) and can guide us to calculate the TENG efficiency and optimize its output. Based on such electromechanical coupling models, multiple efforts have been devoted to studying dynamic behaviors of the TENG systems, as well as output promotion [6,39–43].
However, the actual situation is much more complicated. For example, (1) The electrostatic force is relatively weak compared to other parties, which is mainly because the surface charge density of TENG is not high enough [13, 44]. (2) The friction force needs to be carefully considered. On the one hand, TENG needs contact electrification to maintain the surface charge; on the other hand, friction as a dissipative force results in low output efficiency of the TENG [45, 46]. Therefore, a trade‐off in contact intimacy is needed. (3) The structure of TENG is not limited to the basic four fundamental modes but also involves hybrid modes whose dynamic behavior is more complex [47–49]. (4) Collision issues are also important, as the strong nonlinear collision force wastes energy and makes our model invalid [40, 50]. (5) The vibration source in the natural environment is usually irregular, while the theoretical simulation is based on simple harmonic vibration, which may also cause inaccurate results [51–53].
I.5 Summary
This introduction discusses the basic theoretical models of TENG, which are considered simple but effective based on equivalent capacitances. Compared to models based on electric fields such as displacement current model, quasi‐electrostatic model, and DDEF model, the EDAEC model may lack some details in a local electric field or a little variation on the calculated voltage, while the calculated accuracy from EDAEC model has been high enough to be close to the simulation results demonstrated by COMSOL Multiphysics [26]. In the meanwhile, EDAEC model shows a much simpler in calculation process compared to electric field‐based models, even though the equivalent capacitances from parasitic effects need to be carefully determined.
On the other hand, the energy conversion process of TENG is a key mechanism to understand the physical principles of TENG, and how to promote the output performances. However, the introduction here is still a very ideal situation without considering energy waste during conversion. In the following chapters, we will cover some key energy waste pathways including discharge and frictional energy waste, and discuss how to prevent this energy waste, ultimately making a breakthrough on the output limit of TENGs.
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