et optimisation de récupérateurs d'énergie cinétique miniatures avec triboélectrets

Keywords: Modélisation, simulation Récupérateurs d'énergie cinétique, Tribo-électrets, Modélisation, Simulation, Optimisation, Modification du potentiel de surface Modeling, simulation, and optimization of miniature tribo-electret kinetic energy harvesters Kinetic energy harvesters, Tribo-electrets, Modeling, Simulation, Optimization, Surface potential modification

Harvesting energy from the ambient environment is a good sustainable and complementary power supply solution in some consumer electronics, distributed wireless sensor networks, wearable or implantable devices, "Internet of Things" systems with lots of nodes, etc. in comparison with batteries. The ubiquitous kinetic energy in various motions and vibrations is one of the most available energy sources for such a purpose. The electret kinetic energy harvesters (E-KEHs) is one type of electrostatic kinetic energy harvesters using electrets (dielectrics with quasi-permanent charges) as the biasing voltage source, which can generate electricity based on the electrostatic induction effect when the capacitance of the E-KEHs is changed by the motions/vibrations. This thesis aims to investigate the transitory output characteristics of E-KEHs by both theoretical simulations and experimental measurements and to optimize the efficiency and output power of E-KEHs by tribo-charging and other methods adapted to their output characteristics, which are significant to improving the performance of E-KEHs. Firstly, the amplitude-variable output characteristics of a contact-separation (CS) mode E-KEH in transitory working cycles are investigated via the simulation results based on a detailed equivalent circuit model. These amplitude-variable output characteristics are attributed to the lag of the charge-transfer cycle behind the excitation motion cycle. The influences of both the initial condition and the load resistance on the variation in the output voltage peaks of a tribo-electret KEH (TE-KEH) are studied in detail and verified by both simulated and experimental data of a CS mode TE-KEH made with polytetrafluoroethylene (PTFE) electret film.

Résumé : La récupération d'énergie ambiante représente une solution durable et complémentaire, par rapport aux batteries, en termes d'alimenter certains produits électroniques grand public, des réseaux de capteurs distribués sans fil, des dispositifs portables ou implantables, des systèmes "Internet of Things" avec beaucoup de noeuds, etc.. Les mouvements humains et les vibrations mécaniques sont des sources d'énergie les plus disponibles à cet effet. Les dispositifs collectant de l'énergie cinétique à petite échelle sont appelés récupérateurs d'énergie cinétique (RECs). Les RECs avec électrets (E-RECs) sont RECs électrostatiques qui utilisent des électrets (diélectriques avec charges quasi permanentes) comme source de tension de polarisation, et qui peuvent générer de l'électricité grâce à l'effet d'induction électrostatique lorsque la capacitance des E-RECs varie du fait des mouvements/vibrations. L'objectif de cette thèse est d'étudier les caractéristiques de sortie transitoires des E-RECs à la fois par des simulations théoriques et par des mesures expérimentales, et d'optimiser l'efficacité et la puissance de sortie des E-RECs par charge triboélectrique ainsi que d'autres méthodes adaptées à leurs caractéristiques de sortie, qui sont essentielles pour améliorer la performance des E-RECs. Tout d'abord, les caractéristiques de sortie à amplitude variable d'un E-REC en mode contact-séparation (CS) dans des cycles de travail transitoires sont examinées via les résultats de la simulation basés sur un modèle de circuit équivalent détaillé. Ces caractéristiques de sortie à amplitude variable sont attribuées au décalage du cycle de transfert de charge par rapport au cycle de mouvement d'excitation. Les influences de la condition initiale et de la résistance de charge sur la variation des pics de tension de sortie d'un tribo-électret REC (TE-REC) en mode CS réalisé avec un film électret en polytétrafluoroéthylène (PTFE) one été étudiées en détail et vérifiées à la fois par simulations et expériences. Deuxièmement, une méthode d'optimisation du temps de contact est utilisée pour améliorer la puissance de sortie et l'efficacité du TE-REC en mode CS avec une résistance de charge de 100 MΩ. L'énergie convertie théorique maximale par cycle de travail du TE-REC est analysée. Nous avons aussi étudié les influences de plusieurs facteurs défavorables qui généralement réduiraient la conversion d'énergie par cycle de travail du TE-REC. L'optimisation de l'intervalle d'air maximal et la méthode tribo-charge sont également utilisées pour améliorer la puissance moyenne sortie du TE-REC avec une surface de 4 cm × 4 cm, de 150 μW à ~503 μW. Enfin, une méthode innovante et facile a été développée pour charger le film polymère électret en éthylène propylène fluoré (FEP) par pelage de ruban adhésif, sans utiliser de source de haute tension électrique. La distribution du potentiel de la surface du film de FEP est fortement modifiée après plusieurs pelages au ruban adhésif. Par conséquence, la tension et le courant de sortie des TE-REC fabriqués avec le film FEP traités sont beaucoup améliorés. Pour un TE-REC flexible d'une surface de 64 cm2 soufflé par du vent, une amélioration évidente d'environ 692% de la puissance de sortie, correspondant 2,5 μW à environ 19,8 μW, a été obtenue par cette méthode.

Secondly, based on the analysis of the amplitude-variable output characteristics, a contact time optimization method is used to improve the output power and efficiency of the CS mode TE-KEH with a large load resistance of 100 MΩ. The theoretical maximum output energy per working cycle of the TE-KEH is analyzed. Several usually unfavorable factors that would reduce the practical output energy per working cycle of the TE-KEH are discussed. The maximum air gap optimization and the tribo-charging methods are also used together to further improve the average output power of the 4 cm × 4 cm sized TE-KEH from ~150 μW to ~503 μW. At last, an innovative and facile tape-peeling tribo-charging method is developed to charge the fluorinated ethylene propylene (FEP) polymer film to make electrets without using any high voltage source. The surface potential distribution of the FEP film is apparently changed after several tape-peeling tribocharging treatments. Consequently, the output voltage and current of TE-KEHs made with the FEP film are greatly improved. For a 64 cm2 sized flexible TE-KEH to harvest kinetic energy from wind, an apparent ~692% improvement in the output power from ~2.5 μW to ~19.8 μW was obtained by the tapepeeling charging method. This page is intentionally left blank.

EM Electromagnetic

Chapter 1 General background and introduction

1
Chapter 1 General background and introduction

Background

Harvesting energy from the ambient environment is a good choice to prolong the life time or even become the power supply in consumer electronics, distributed wireless sensor networks (WSN), wearable or implantable devices, Internet of Things (IoT) systems with lots of nodes, etc. [START_REF] Mitcheson | Energy harvesting from human and machine motion for wireless electronic devices[END_REF][START_REF] Roundy | Energy scavenging for wireless sensor nodes with a focus on vibration to electricity conversion[END_REF][START_REF] Dell'anna | State-of-the-art power management circuits for piezoelectric energy harvesters[END_REF]. Especially with the development of electronic technology, electronic devices have a general trend of miniaturization with lower power consumption [START_REF] Wang | Triboelectric nanogenerators[END_REF], making it possible to build autonomous self-powered systems powered by energy harvesters, reducing the maintenance and environmental problems caused by drained batteries. Four main ambient energy sources exist in our environment: radiant energy (light, radio-frequency radiations), mechanical energy (vibrations, movements, and deformations), thermal energy (temperature gradients or variations), and chemical energy (chemistry, biochemistry). Each of them has a different power density range in different environments. The type of energy source to be used should be chosen according to the local environment and the power consumption of the load circuit [START_REF] Boisseau | Electrostatic conversion for vibration energy harvesting[END_REF].

Chapter 1 General background and introduction

2
Outdoor sunlight is usually considered to be the most powerful ambient energy source as shown in However, for some situations without enough light but with abundant mechanical energy sources, kinetic energy harvesters (KEHs) could be suitable for extending the lifetime of power source [START_REF] Roundy | Energy scavenging for wireless sensor nodes with a focus on vibration to electricity conversion[END_REF] or building self-powered systems. Different from the kinetic energy recovery system (KERS) which harvests kinetic energy of a vehicle under braking [7], KEHs mainly convert small-scale kinetic energy from motions and vibrations into electricity with the power of microwatt to a milliwatt.

And the dimension of KEHs in any direction is usually below 10 cm, that's why they are usually described as "miniature". In this thesis, KEHs are defaulted to be miniature without special statement. Three common types of KEHs, i.e. the electromagnetic, piezoelectric, and electrostatic, will be introduced in section 1.2.

Different types of kinetic energy harvesters (KEHs)

Electromagnetic KEHs

Electromagnetic (EM) generators are basically used almost in every power station except the photovoltaic ones. They are based on Faraday's law of induction i.e.

"The electromotive force around a closed conductive path equals the negative of the time rate of change of the magnetic flux enclosed by the path." [START_REF] Jordan | Electromagnetic waves and radiating systems[END_REF] as expressed by the equation , where E is the electromotive force, Ψ is the total magnetic flux linkage enclosed by the conductive path, n is the number of turns of the conductive coil that forms the conductive path, is the magnetic flux enclosed by the conductive coil, t is time.

쮀 쮀 (1-1)

Chapter 1 General background and introduction 3 Electromagnetic KEHs (EM-KEHs) are based on the same fundamentals but with smaller scales. They are made with at least one conductive coil which is relatively movable to at least one magnet, with two typical architectures: magnet in line and magnet across coil [START_REF] Brand | Micro energy harvesting[END_REF]. The conductive coil usually has multiple turns to get a considerable electromotive force. And the internal resistance of the electromagnetic KEHs is low due to the conductive nature of the coil. Huge EM generators can output remarkable power at the magnitude up to ~1000 MW [10] by using an intense magnetic field and numerous turns of coils. While for miniature EM-KEHs, the magnetic field and turns of coils are usually constrained by the limitations in the volume, cost, weight, etc., and they are often designed to have a high mechanical quality factor to harvest energy from low-amplitude vibrations, but that leads to a narrow bandwidth of EM-KEHs [START_REF] Zhu | General model with experimental validation of electrical resonant frequency tuning of electromagnetic vibration energy harvesters[END_REF].

To widen the bandwidth of EM-KEHs, Sari et al. [START_REF] Sari | An electromagnetic micro power generator for wideband environmental vibrations[END_REF] designed an arrayed EM-KEH with multiple cantilever-structured coils as shown in Figure 1-2(a), each with a different cantilever length to get different resonant frequencies. The overall frequency response of the output power of this arrayed EM-KEH was effectively broadened as shown in Figure 1-2(b). However, due to the small dimensions of each cantilever, the frequency band located at a high-frequency range of about 3400~4600 Hz which is much larger than common vibrations in the ambient environment (mostly lower than 250 Hz) [START_REF] Roundy | Energy scavenging for wireless sensor nodes with a focus on vibration to electricity conversion[END_REF]. Halim et al. [START_REF] Halim | Design and experiment of a human-limb driven, frequency up-converted electromagnetic energy harvester[END_REF] designed a cylinder non-resonant EM-KEH with two frequency up-converted small generators using spring at the two ends and an inside free-moving ball to harvest energy from low frequency vibrations, as shown in different capacitors to the EM-KEH, but with narrow effective tuning ranges [START_REF] Zhu | General model with experimental validation of electrical resonant frequency tuning of electromagnetic vibration energy harvesters[END_REF]. Other special structure designs of EM-KEHs include a spherical structure with an inside free-rolling magnet by Bowers et al. [START_REF] Bowers | Spherical, rolling magnet generators for passive energy harvesting from human motion[END_REF], as illustrated in Figure 1-2(d),

and using a micro resonant structure with 6 degree-of-freedoms (DOFs) of motions by Liu et al. [START_REF] Liu | A multi-frequency vibration-based MEMS electromagnetic energy harvesting device[END_REF], as shown in Figure 1-2(e), to harvest energy from multi-directional vibrations. It should be noted that the open-circuit voltage and thus the output power of EM-KEHs are usually low due to the constraints in the magnetic field intensity, the turn number of coils, and the working frequency. Moreover, the complicated structure designs and utilization of multiple materials make EM-KEHs not compatible with massive production processes. It is considered that EM generators are irreplaceable in huge power generations, but EM-KEHs are uncompetitive in harvesting small/microscale kinetic energy in comparison with other techniques [START_REF] Roundy | Energy scavenging for wireless sensor nodes with a focus on vibration to electricity conversion[END_REF].

Chapter 1 General background and introduction 5

Piezoelectric KEHs

In crystalline materials with no inversion symmetry, electric potential can be produced under stress, this is called the piezoelectric effect which was first reported by Jacques and Pierre Curie brothers in 1880 [START_REF] Liu | A comprehensive review on piezoelectric energy harvesting technology: Materials, mechanisms, and applications[END_REF], and such materials are termed as piezoelectric (PE) materials. The first well-known application of PE materials is on sonar systems where the inverse PE effect (i.e. the generation of stress by applying electric field) of quartz slice was used to produce ultrasounds. PE materials are usually dielectrics with low conductivity, after depositing with conductive electrodes on their polar directions, they can be used to fabricate KEHs to generate electricity from mechanical stress. Two constitutive equations those describe the PE and reverse PE effects are [START_REF] Roundy | Energy scavenging for wireless sensor nodes with a focus on vibration to electricity conversion[END_REF]:

쮀 /푀 (1-2) 쮀 (1-3)
where δ, σ, and d are tensors of the strain, the stress, and the PE strain coefficients, respectively; Y is the Young's Modulus of the PE material; E and D are vectors of the electric field and the electrical displacement (charge density), respectively.

Two of the PE strain coefficients, d31 and d33, are often used to evaluate the electromechanical coupling intensity of PE materials. Lead zirconated titanate (PZT)

and related inorganic materials with the perovskite crystalline structure are typical piezoelectric materials with high d33 (400~2500 pC/N) [START_REF] Liu | A comprehensive review on piezoelectric energy harvesting technology: Materials, mechanisms, and applications[END_REF][START_REF] Hwang | Self-powered wireless sensor node enabled by an aerosol-deposited pzt flexible energy harvester[END_REF], but also with high stiffness [START_REF] Geisler | Human mechanical energy harvesting systems for smart clothes[END_REF]. Polyvinylidene fluoride (PVDF) as a piezoelectric polymer has low stiffness but a relative lower d33 than piezoelectric ceramics. Nathan S. Shenck and Joseph A. Paradiso [START_REF] Shenck | Energy scavenging with shoe-mounted piezoelectrics[END_REF] designed an energy harvesting shoe using a PZT dimorph under the heel and a flexible PVDF stave under the ball of the foot to scavenge electricity from human walking, as shown in piezoelectric EHs had been developed by MicroGen Systems, Inc. [START_REF] Liu | A comprehensive review on piezoelectric energy harvesting technology: Materials, mechanisms, and applications[END_REF] as shown in For both modes, the ES-KEH output net electric energy that equals the enclosed area of the triangle shape oab in one working cycle. For the constant charge mode, it can be calculated by [START_REF] Meninger | Vibration-to-electric energy conversion[END_REF]:

Electrostatic KEHs

݄ ݎ ݃ ܿ 쮀 1 2 ( 푀 푀 ) ܿ 푀 푀 (1-4).
And for the constant voltage mode, there is [START_REF] Meninger | Vibration-to-electric energy conversion[END_REF]:

݃ ݃ ܿ 쮀 1 2 ( 푀 푀 ) 푀 2 (1-5).
These two modes are two extreme working cycles. In practice, the shape of the which can be realized by a charge pump [START_REF] Roundy | Micro-electrostatic vibration-to-electricity converters[END_REF][START_REF] Xu | Ultrahigh charge density realized by charge pumping at ambient conditions for triboelectric nanogenerators[END_REF][START_REF] Karami | Series-parallel charge pump conditioning circuits for electrostatic kinetic energy harvesting[END_REF] or a Bennet's doubler [START_REF] Karami | Series-parallel charge pump conditioning circuits for electrostatic kinetic energy harvesting[END_REF][START_REF] Ghaffarinejad | Bennet's charge doubler boosting triboelectric kinetic energy harvesters[END_REF][START_REF] Ouanes | Design and test of a bennet's doubler device with mechanical switches for vibrational energy harvesting[END_REF] or a

Cockcroft-Walton voltage multiplier [START_REF] Lefeuvre | Self-biased inductorless interface circuit for electret-free electrostatic energy harvesters[END_REF][START_REF] Wei | Simple and efficient interface circuit for vibration electrostatic energy harvesters[END_REF] circuit, and the teardrop shape (dotted line trace) which can be realized by continuous conditioning circuit or ES-KEHs with electret layer [START_REF] Hinchet | Understanding and modeling of triboelectric-electret nanogenerator[END_REF][START_REF] Zhang | Amplitude-variable output characteristics of triboelectric-electret nanogenerators during multiple working cycles[END_REF]. During the capacitance variation of the ES-KEHs, kinetic energy is converted to electrostatic energy via the Coulomb's force which is more significant than Lorenz's force in micro-scale [START_REF] Mitcheson | Electrostatic microgenerators[END_REF]. In addition, ES-KEHs with variable capacitance structures have good compatibility with MEMS fabrication processes, which is important for batch fabrication with low cost [START_REF] Mitcheson | Electrostatic microgenerators[END_REF][START_REF] Basset | A batch-fabricated and electret-free silicon electrostatic vibration energy harvester[END_REF]. Therefore, ES-KEHs are more suitable than EM-KEHs to be miniaturized and batch-fabricated to harvest micro-vibration energy.

By a simple batch process using only two lithography masks, P. Basset et al. [START_REF] Basset | Electrostatic vibration energy harvester with combined effect of electrical nonlinearities and mechanical impact[END_REF] fabricated a micro ES-KEH with an area of about 1 cm 2 as shown in Besides micro electrostatic KEHs to harvest energy from vibrations, dielectric elastomers (DE) were used to fabricated relative large electrostatic KEHs [START_REF] Chiba | Innovative power generators for energy harvesting using electroactive polymer artificial muscles[END_REF][START_REF] Pelrine | Dielectric elastomers: Generator mode fundamentals and applications[END_REF] to harvest energy from pressure-driven deformations as illustrated in Figure 1-6(c).

However, for those electrostatic KEHs, at least an external initial charge/voltage supply is required to charge the variable capacitor before harvesting energy, as illustrated in Figure 1-6(d), and a switching or continuous conditioning circuit [START_REF] Galayko | Capacitive energy conversion with circuits implementing a rectangular charge-voltage cycle-part 1: Analysis of the electrical domain[END_REF] is usually necessary to control the charge-discharge cycles. Therefore, T. Vu-Cong, T, C.

Jean-Mistral, and A. Sylvestre [START_REF] Vu-Cong | Autonomous dielectric elastomer generator using electret[END_REF][START_REF] Vu-Cong | Electrets substituting external bias voltage in dielectric elastomer generators: Application to human motion[END_REF][START_REF] Jean-Mistral | On the power management and electret hybridization of dielectric elastomer generators[END_REF] used electrets (quasi-permanently charged dielectrics) to substitute the external charge/voltage source, which greatly simplifies the structure and power management circuits of DE-KEHs. Other electrostatic KEHs using electrets will be further introduced in Chapter 2, section 2.4.

Comparisons among different types of KEHs

Among these three common types of KEHs, S.J. Roundy [START_REF] Roundy | Energy scavenging for wireless sensor nodes with a focus on vibration to electricity conversion[END_REF] estimated that the PE-KEHs have the highest practical maximum power density of ~17.7 mJ/cm 3 , the EM-KEHs and ES-KEHs have the same practical maximum power density of ~4 mJ/cm 3 . In practice, there are also other factors (e.g. the dimension, the working frequency, the load circuit) those need to be considered to decide which type of KEHs is more appropriate for specific applications. Several advantages and disadvantages of these three types of KEHs are listed in

Motivations and the outline of this thesis

Chapter 2 Introduction to electrets and electret kinetic energy harvesters

Overview

In this chapter, firstly a brief introduction to the physical fundamentals and charging methods for electrets is given in section 2.2, then a more detailed introduction to electric kinetic energy harvesters (E-KEHs) from the basic principle and research history to the different structure designs, driving modes, and theoretical models is presented in section 2.3~2.5.

Electrets

Physical fundamentals

It is believed that Michael Faraday was the first to outline the basic principles of electrets in 1839 [START_REF] Sessler | Electrets[END_REF], Oliver Heaviside created the word "electret" in 1892 [START_REF] Oliver | Electrical papers[END_REF], and the systematic research into electrets began in 1919 when a Japanese physicist, Mototaro Eguchi, fabricated an electret by cooling and solidifying molten mixture of Carnauba wax and resin with a little beeswax while applying an electric field of about 10 kV•cm -1 to the mixture [START_REF] Eguchi | On dielectric polarisation[END_REF][START_REF] Nalwa | Ferroelectric polymers: Chemistry, physics, and applications[END_REF]. In the book Electret published in 1987 [START_REF] Sessler | Electrets[END_REF], G. M.

Sessler gave a general physical definition of electret as: "An electret is a piece of dielectric material exhibiting a quasi-permanent electrical charge. The term "quasipermanent" means that the time constants characteristic for the decay of the charge are much longer than the time periods over which studies are performed with the electret.". The motioned "electrical charge" could be "real" excess mono-charges on the surface or in the bulk of materials, or polarizations (frozen-in aligned dipoles for polar, or space charges for both polar and non-polar dielectrics) in the bulk, or a composition of them [START_REF] Sessler | Electrets[END_REF][START_REF] Kao | 5 -electrets[END_REF], as illustrated in The charge decay time constant in electret materials is usually expected to be as large as possible. The concerned "time periods" for studies in electrets are usually counted in hours, days, months, and even years [START_REF] Kao | 5 -electrets[END_REF]. Dielectric materials with excellent insulating properties are usually good candidates to make electrets since their extremely low conductivities could lead to a quite large charge decay time constant. For instance, it was estimated that a corona-charged polytetrafluoroethylene (PTFE), which is one of the best insulating polymers with low conductivity of ~10 -22 Ω -1 cm -1 [START_REF] Sessler | Electrets[END_REF], could have of charge stability with a lifetime of a few hundred years in a dry environment [START_REF] Bamji | Superior electrets of polychlorotrifluoroethylene (aclar)[END_REF].

The key issue in studying electret materials is to know how the charge distribution in an electret influence the electric field around it. A general theoretical analysis based on Gauss's law and the Kirchhoff's voltage law was also given by G. M. Sessler [START_REF] Sessler | Electrets[END_REF] as shown in Figure 2-2. A piece of flat electret sheet in the middle with dielectric constant of εr and thickness of df was to be concerned in the model, with assuming that the dielectrics in the Gap 1 with dielectric constant of ε1, thickness of d1, and in the Gap 2 with permittivity of ε2, thickness of d2, cannot be charged, and all lateral dimensions were much greater than the thickness dimension. V0 is the applied or generated voltage across the two electrodes as illustrated in Figure 2-2 when the switch is opencircuited. With such an arrangement, two significant inferences from Sessler's analysis will be introduced as follows.

The first one is that any charge distribution in the electret can be regarded as the electret has "projected" or "effective" surface charge distributions when investigating the induced external electric field around it. Assuming an arbitrary volume charge density ρ(x) located at the vertical coordinate x with setting the bottom of the electret as the coordinate 0 as shown in Figure 2-2, then the corresponding equivalent effect charge density at the bottom and top surfaces of the electret can be calculated by:

1 쮀 1 ( ) () (2-1) 2 쮀 1 () (2-2)
where σ1 and σ2 are the effective surface charge density at the bottom and top surfaces of the electret surfaces respectively. The volume charge density ρ(x) includes the "real" mono-charge density and gradient of the dipole polarization or microscopic charge displacement in the electrets [START_REF] Sessler | Electrets[END_REF]. All the planar charge density in this thesis refers to the effective surface charge density without a specific declaration.

The second one is that the electric field strength in the two gaps and in the electret can be calculated by:

1 쮀 1 ( 1 1 1 2 ( 1 2 ) 1 2 ) (2-3) 2 쮀 1 ( 2 2 2 1 ( 1 2 ) 1 2 ) (2-4) ( ) 쮀 1 ( 1 1 2 1 2 2 2 2 ( 1 () )) (2-5)
where ε0 is the permittivity in the vacuum, 0<x'<df, E1, E2, and E(x'), are the electric field strength in the Gap 1, Gap 2, and in the electret at the vertical coordinate x' respectively, and d0 can be termed as the total effective dielectric thickness defined by:

쮀 1 1 2 2 (2-6).
The first inference simplifies the issues concerning the charge distributions in electrets, and the second inference is helpful for calculating the concerned electric field strengths from a given charge distribution. Note that these equations were obtained with assumptions that the lateral dimensions of the electret and electrodes are the same and much larger than the thickness dimensions, and only the electret in the middle was charged.

Charging methods

The charging method used by Mototaro Eguchi [START_REF] Eguchi | On dielectric polarisation[END_REF] to make the first electret is now called as the thermal charging method. There are several different charging methods to make electrets as listed in Applying an electric field via solid-liquid interfaces Photoelectric effect + applying an electric field High-energy radiation + applying an electric field As can be noticed, most of the charging methods need an applied electric field.

In this thesis, the tribo-charging method will be used to make the so-called "triboelectret" without using any specific applied electric field. The tribo-charging method is based on the triboelectrification (TE) i.e. the charging of two objects due to the physical contact with each other [START_REF] Sessler | Electrets[END_REF][START_REF] Wang | On the origin of contact-electrification[END_REF]. TE is a ubiquitous process that exists everywhere, anywhere, and at any time [START_REF] Wang | On the origin of contact-electrification[END_REF]. Especially, if the TE happens between two objects made with different materials, it is also called as the contact electrification (CE) [START_REF] Sessler | Electrets[END_REF]. It is believed that the electrostatic force caused by the CE-induced charges on dielectrics was discovered by a Greek philosopher Thales as early as 600 B.C. when he found that ambers after rubbed with clothes, could attract light objects such as bits of chaff [START_REF] Kao | 1 -introduction[END_REF]. Other familiar phenomena caused by CE include lightning during thunderstorms, sudden sparks of human bodies.

Though the phenomena caused by CE are so universal, the scientific understanding of the mechanism of CE remains inconclusive, it is likely that different mechanisms may be involved depending on the specific materials and environmental conditions [START_REF] Wang | On the origin of contact-electrification[END_REF][START_REF] Mccarty | Electrostatic self-assembly of polystyrene microspheres by using chemically directed contact electrification[END_REF]. Z. L. Wang and A. C. Wang [START_REF] Wang | On the origin of contact-electrification[END_REF] reviewed recent researches on the CE mechanisms and proposed that the electron transfer due to the overlapping electron cloud under mechanical force/pressure is the dominant mechanism for initiating CE between solids, liquids, and gases, as illustrated in Figure 23. Zou et al. [START_REF] Zou | Quantifying the triboelectric series[END_REF] quantified the tendency of several polymers to gain or lose electrons during the CE process with the liquid mercury and listed them in the triboelectric series which is instructive to choose materials for making tribo-electrets.

Basic principle and early researches of electret kinetic energy harvesters (E-KEHs)

Basic principle

Electret kinetic energy harvester (E-KEH) is one type of electrostatic energy harvester, consisting of at least one insulating electret and at least two conductive electrodes (electrical ground can be one of them). E-KEHs work based on the charge redistribution between the two electrodes through circuit load, under the electrostatic induction effect derived from the Coulomb's force.

Early researches 2.3.2.1 Electret transducers with variable capacitances

The basic working principle of E-KEHs was first applied to electret transducers that convert vibrations/forces into electric signals with the information of the vibrations/forces for sensing. They usually have small dimensions, and the microscale relative displacements, with low-level output electric signals that need preamplifier for further signal processing. Therefore, electret transducers were usually not regarded as energy harvesters despite that they do convert kinetic energy into electricity.

It is believed that the research on electret transducers can be dated back to as early as 1929 when studies on electret microphones were going on in the United States [START_REF] Sessler | Electret transducers: A review[END_REF]. Wax-electrets was used in electret microphones at first with drawbacks such as sensitivity fluctuations and the requirement for complex preamplifier design, then several thermoplastic electret plates and ceramic electret were suggested and attempted to be applied in electret microphones but not practically commercialized [START_REF] Sessler | Electret transducers: A review[END_REF]. Until metalized thin electret foil made with Mylar [START_REF] Sessler | Selfbiased condenser microphone with high capacitance[END_REF][START_REF] Sessler | Electrostatic microphones with electret foil[END_REF] and Teflon [START_REF] Sessler | Electrostatic microphones with foil electret[END_REF] were introduced into electret microphones in 1962 and 1965 by G. M. Sessler and J. E. West at Bell Laboratories, which greatly improved the performance and practicality of electret microphones, then commercialized electret foil microphones were manufactured numerously. Most of the later developed E-KEHs also use the variable capacitance strategy like electret transducers to generate electricity, but with more powerful kinetic energy sources, larger dimensions, and structures that can provide larger capacitance variations to get relative higher electric output.

Chapter 2 Introduction to electrets and electret kinetic energy harvesters 21

Electret generators without variable capacitance

In addition to electret transducers using the variable capacitance strategy, in 1978, Oleg D. Jefimenko and David K. Walker [START_REF] Jefimenko | Electrostatic current generator having a disk electret as an active element[END_REF] proposed a rotating electret generator (EG) consists of two oppositely polarized half-disks electret placed between two pairs of conducting half-disks as shown in Due to its relatively large dimension (disk diameter ~152.4 mm), this EG can output power of ~0.025 W at the rotation speed of 6000 r/min and with a load resistance of 10 MΩ, and it was regarded as the first practical E-KEH by later researchers [START_REF] Tada | Experimental characteristics of electret generator, using polymer film electrets[END_REF][START_REF] Boisseau | Optimization of an electret-based energy harvester[END_REF]. In the article [START_REF] Jefimenko | Electrostatic current generator having a disk electret as an active element[END_REF], Oleg D. Jefimenko and David K. Walker also gave theoretical calculations on the output of the EG and pointed out its characteristics of high internal impedance and facility to provide a high voltage. Later in 1981~1986, Yasufusa Tada in Japan refined and extended the theoretical model of this type of EG using segmented electrets with opposite polarizations/charges [START_REF] Tada | Theoretical characteristics of generalized electret generator, using polymer film electrets[END_REF].

In 1992, Yasufusa Tada published an article in which he reported an EG using Teflon FEP film electret with stable homo-charges [START_REF] Tada | Experimental characteristics of electret generator, using polymer film electrets[END_REF], and the variable capacitance strategy was employed by varying the overlap area between the stator electrode and Chapter 2 Introduction to electrets and electret kinetic energy harvesters 22 the rotating electret film during rotations. After that, there emerged many studies on E-KEH using the variable capacitance strategy, which will be reviewed in the following section 2.4.

Different structures of E-KEHs with variable capacitances

A general introduction to E-KEHs with the parallel-plate configuration

The most common and simple structure of a capacitor is the parallel-plate configuration, which consists of dielectric materials sandwiched between two parallelplate electrodes. For an ideal parallel plate capacitor, the capacitance ignoring the edge effect can be calculated by:

쮀 (2-7),
where C is the capacitance, S is the electrode area, and d0 is the effective dielectric thickness between the two electrodes, as defined by the equation (2-6) but with possible different layers of dielectrics.

For E-KEHs with variable capacitances, the parallel-plate configuration is also often used, with at least one layer of electrets and usually with an air gap as dielectric layers as illustrated in Figure 23456789. Another type of variable electrode distance design is to use cellular/foam/porous electret films that can be easily deformed, with electrodes deposited on both sides as shown in Figure 2-10(f). A brief introduction to cellular electret films will be particularly presented in section 2.4.2.

For the variable permittivity design, besides the electret component, there is another dielectric material that is movable between the gap of the electret and electrodes. When the movable dielectric material is driven by external motions to move, the total or partial capacitance of the E-KEH is changed. The movable dielectric material could be solid as shown in Figure 2-10(g), or liquid as shown in capacitance if regarding the environment around that object as a virtual electric ground [START_REF] Gray | Projected capacitive touch: A practical guide for engineers[END_REF]. The basic definition of capacitance is the ratio of the change in the electric charge (Q) of a system to the corresponding change in its electric potential (V), as expressed by:

쮀 (2-8).
The capacitance can be even considered as a geometrical parameter [START_REF] Basset | Electrostatic kinetic energy harvesting[END_REF].

Therefore, besides the structure designs in Figure 2-10, there are diverse other structures of E-KEH, some of them will be introduced in section 2.4.3.

Cellular/foam/porous piezo-electrets/ferro-electrets

In the cellular electret design represented by the research shown in Figure 2-10(f), when the cellular electret film is pressed or released, the distance between the two electrodes on the top and bottom sides of the electret film changes, it can also be regarded as the effective permittivity of the electret film changes, since it contains the solid matrix (usually polymers) and the gas (usually air) in inner cavities as two different dielectrics, and when the film is deformed, the volume ratio of these two dielectrics will be changed. These cellular electret films can be charged with excess homo positive or negative charges, but are often charged with space charges (macroscopic dipole moments) on the top and bottom sides of inside cavities as illustrated in When a cellular electret film charged with space charges is pressed or released, it performs like a piezoelectric material since the total macroscopic diploe moments of the electret film is changed with the deformation of the film caused by the press or elastic force, so it is called as piezo-electret [START_REF] Gerhard-Multhaupt | Less can be more -holes in polymers lead to a new paradigm of piezoelectric materials for electret transducers[END_REF][START_REF] Altafim | Piezoelectrets from thermo-formed bubble structures of fluoropolymer-electret films[END_REF][START_REF] Wu | Cellular polypropylene piezoelectret for human body energy harvesting and health monitoring[END_REF][START_REF] Kachroudi | Micro-structured pdms piezoelectric enhancement through charging conditions[END_REF]. Since the elastic modulus of the cellular electret films are usually much lower than piezoelectric ceramics, and the effective dipole moment density can be much higher than that in conventional piezoelectric materials, the apparent electromechanical d33 coefficient of piezoelectret can be much higher than conventional piezoelectric ceramics. For instance, a tremendous d33 of 3350 pC/N was obtained in a composite cellular piezo-electret film using PTFE and PDMS [START_REF] Wang | Composite rubber electret with piezoelectric 31 and 33 modes for elastically electromechanical sensors[END_REF], which is much higher than one of the best piezoelectric ceramics PZT with d33 of ~250 to 700 pC/N. The high d33 makes cellular electrets competitive in energy harvesting. Moreover, cellular electret films can also show ferroelectric characteristics via the micro-plasma discharge inside their cavities as shown in Figure 2-11(b), so they were also termed as ferro-electrets [START_REF] Bauer | Ferroelectrets: Soft electroactive foams for transducers[END_REF]. A recent review on cellular polymer ferro-electret and their piezoelectric properties was given by A. Mohebbi [START_REF] Mohebbi | Cellular polymer ferroelectret: A review on their development and their piezoelectric properties[END_REF] for those who are interested.

Triboelectric nanogenerator (TENG) or tribo-electret kinetic energy harvester (TE-KEH) with diverse structure designs

In the article corresponding to Figure 2-10(e), authors didn't particularly precharge the dielectric polymer films but took advantage of the triboelectrification effect to introduce electrostatic charges on these films, making them become triboelectret. E-KEHs using tribo-electret were called as triboelectric generators (TEGs) [START_REF] Fan | Flexible triboelectric generator![END_REF], and later termed as triboelectric nanogenerators (TENGs) to distinguish them from traditional high voltage sources using the triboelectrification effect (such as the Wimshurst machine and the Van de Graaff generator [START_REF] Fan | Transparent triboelectric nanogenerators and self-powered pressure sensors based on micropatterned plastic films[END_REF][START_REF] Wang | Triboelectric nanogenerators as new energy technology for selfpowered systems and as active mechanical and chemical sensors[END_REF]). In this thesis, E-KEHs using tribo-electrets will be termed as TE-KEHs to better express their basic principle and functionality. In recent years, a large and drastically increasing number of researches on TE-KEHs were conducted [START_REF] Cheng | The current development and future outlook of triboelectric nanogenerators: A survey of literature[END_REF], especially by the team of Z. L. Wang who proposed the conception of TE-KEHs [START_REF] Wang | Triboelectric nanogenerators as new energy technology for selfpowered systems and as active mechanical and chemical sensors[END_REF], and pre-charged electrets were also used in several of these researches on TE-KEHs [START_REF] Chen | Au nanocomposite enhanced electret film for triboelectric nanogenerator[END_REF][START_REF] Yang | Electret film-enhanced triboelectric nanogenerator matrix for self-powered instantaneous tactile imaging[END_REF][START_REF] Zhang | An electret film-based triboelectric nanogenerator with largely improved performance via a tapepeeling charging method[END_REF][START_REF] Zhou | Multilayered electret films based triboelectric nanogenerator[END_REF][START_REF] Zhang | Multilayer wavy-structured robust triboelectric nanogenerator for harvesting water wave energy[END_REF][START_REF] Wang | Maximum surface charge density for triboelectric nanogenerators achieved by ionized-air injection: Methodology and theoretical understanding[END_REF] to get higher output power.

Like other E-KEHs, not only the gap-varying structure in In some TE-KEHs, the electrical ground was used as one electrode, the load circuit was connected between one electrode of the TE-KEH and the electrical ground as illustrated in electrode TE-KEHs [START_REF] Yang | A single-electrode based triboelectric nanogenerator as self-powered tracking system[END_REF][START_REF] Zhang | Singleelectrode-based rotating triboelectric nanogenerator for harvesting energy from tires[END_REF]. The electrets in TE-KEHs not only could be planar [START_REF] Zhu | Radial-arrayed rotary electrification for high performance triboelectric generator[END_REF] [ [START_REF] Zhou | Multilayered electret films based triboelectric nanogenerator[END_REF][START_REF] Yang | A single-electrode based triboelectric nanogenerator as self-powered tracking system[END_REF] but also could be flexible [START_REF] Fan | Flexible triboelectric generator![END_REF][START_REF] Matthias | Triboelectretbased aeroelastic flutter energy harvesters[END_REF][START_REF] Bae | Flutter-driven triboelectrification for harvesting wind energy[END_REF][START_REF] Yang | Triboelectric nanogenerator for harvesting wind energy and as self-powered wind vector sensor system[END_REF][START_REF] Zhang | All-in-one selfpowered flexible microsystems based on triboelectric nanogenerators[END_REF], stretchable [START_REF] Wang | A highly stretchable transparent self-powered triboelectric tactile sensor with metallized nanofibers for wearable electronics[END_REF], and shape-adaptive [START_REF] Chen | Shape-adaptive, self-healable triboelectric nanogenerator with enhanced performances by soft solid-solid contact electrification[END_REF][START_REF] Zhu | A shapeadaptive thin-film-based approach for 50% high-efficiency energy generation through micro-grating sliding electrification[END_REF] as shown in The general shape of TE-KEHs could also be curved [START_REF] Ahmed | Selfpowered wireless sensor node enabled by a duck-shaped triboelectric nanogenerator for harvesting water wave energy[END_REF][START_REF] Han | R-shaped hybrid nanogenerator with enhanced piezoelectricity[END_REF] or arch-shaped [START_REF] Wang | Nanoscale triboelectric-effect-enabled energy conversion for sustainably powering portable electronics[END_REF] as shown in to improve the output power of TE-KEHs. A book [START_REF] Wang | Triboelectric nanogenerators[END_REF] and several reviews [START_REF] Wang | Triboelectric nanogenerators as new energy technology for selfpowered systems and as active mechanical and chemical sensors[END_REF][START_REF] Wang | Triboelectric nanogenerators as new energy technology and selfpowered sensors-principles, problems and perspectives[END_REF][START_REF] Zhang | All-in-one selfpowered flexible microsystems based on triboelectric nanogenerators[END_REF][START_REF] Wang | Toward the blue energy dream by triboelectric nanogenerator networks[END_REF][START_REF] Li | Standardization of triboelectric nanogenerators: Progress and perspectives[END_REF][START_REF] Ahmed | Integrated triboelectric nanogenerators in the era of the internet of things[END_REF] on TE-KEHs were published for those who are interested.

Direct motion-driven mode and undirect vibration-driven mode

With For the direct motion-driven mode, the external excitation force to directly drive the movable component of the E-KEH is much larger than the transduction electrostatic force, and the effect of the transduction force on the motion of the kinetic energy source is negligible. For instance, in a water wave-driven buoy-like E-KEH [START_REF] Li | Networks of high performance triboelectric nanogenerators based on liquid-solid interface contact electrification for harvesting low-frequency blue energy[END_REF] shown in The direct motion-driven mode is usually applied to E-KEHs with relatively large dimensions (from a few to tens of centimeters) for harvesting kinetic energy from low-frequency (often less 10 Hz) motions [START_REF] Zi | Harvesting lowfrequency (<5 Hz) irregular mechanical energy: A possible killer application of triboelectric nanogenerator[END_REF][START_REF] Xing | Natural triboelectric nanogenerator based on soles for harvesting low-frequency walking energy[END_REF][START_REF] Zhang | Frequency-multiplication high-output triboelectric nanogenerator for sustainably powering biomedical microsystems[END_REF]. While the undirect vibration-driven mode is usually applied to tiny/micro E-KEHs (dimensions from a few millimeters to a few centimeters), for harvesting kinetic energy from vibrations with low to high frequency (several Hz to 1~2 kHz) [START_REF] Sterken | Power extraction from ambient vibration[END_REF][START_REF] Sterken | A new power mems component with variable capacitance[END_REF][START_REF] Kloub | A micro capacitive vibration energy harvester for low power electronics[END_REF] dependent on the nature frequency of the E-KEH (usually smaller E-KEHs have higher nature frequency).

Different analysis models for E-KEHs with variable capacitances

The compact equivalent electrical model for direct motion-driven E-KEHs

For direct motion-driven E-KEHs, there is no need to solve the equation of motion of the movable component of the E-KEHs if the motion of the external kinetic source is given. Though there are so many different structure designs for E-KEHs as introduced in section 2.4, the parallel-plate configuration is often used to simplify the modeling of KEHs.

where S(t) is the time-varying overlap area of the two electrodes, and d0 is the effective dielectric thickness of the E-KEH. Assuming the electret layer is a rigid body, and the dielectric in the gap between the electret layer and the movable electrode is air, there is:

( ) 쮀 ( ) 쮀 ( ) (2-9)
where df, εr, and d0f are the thickness, dielectric constant, and effective dielectric constant of the electret layer respectively, and z(t) is the time-varying air gap between the electret layer and the movable electrode.

Assuming the electret layer has a homogeneous effective surface charge density of σ, the total net charge of the E-KEH including charges on both electrodes and the electret is 0 (hypothesis of neutrality [START_REF] Basset | Electrostatic kinetic energy harvesting[END_REF]), then the E-KEH can be regarded as a variable capacitance connected in series with a constant voltage source, as illustrated in Where the movable electrode is regarded as a positive electrode. If Cpar is ignorable, according to the Kirchhoff's voltage law, the output voltage of the E-KEH can be calculated as: [START_REF] Roundy | Energy scavenging for wireless sensor nodes with a focus on vibration to electricity conversion[END_REF][START_REF] Dell'anna | State-of-the-art power management circuits for piezoelectric energy harvesters[END_REF][START_REF] Wang | Triboelectric nanogenerators[END_REF][START_REF] Boisseau | Electrostatic conversion for vibration energy harvesting[END_REF][START_REF] Cao | A survey on ambient energy sources and harvesting methods for structural health monitoring applications[END_REF](7)[START_REF] Jordan | Electromagnetic waves and radiating systems[END_REF][START_REF] Brand | Micro energy harvesting[END_REF](10)[START_REF] Zhu | General model with experimental validation of electrical resonant frequency tuning of electromagnetic vibration energy harvesters[END_REF].

( ) 쮀 ( ) ( )
According to the charge conservation, the output current can be calculated as:

( ) 쮀 ( ) (2-12).
The positive direction of the current is marked in Figure 2-17.

If the external circuit load is a resistor R, according to Ohm's law, there is:

( ) 쮀 ( ) (2-13).
Combining (2-9) ~(2-11), there is:

( ) ( ) ( ) 쮀 (2-14).
If the value of Vele and the analytical form of CE-KEH(t) are known, and the initial condition QE-KEH (0) is given, then the first-order linear differential equation [START_REF] Roundy | Energy scavenging for wireless sensor nodes with a focus on vibration to electricity conversion[END_REF][START_REF] Dell'anna | State-of-the-art power management circuits for piezoelectric energy harvesters[END_REF][START_REF] Wang | Triboelectric nanogenerators[END_REF][START_REF] Boisseau | Electrostatic conversion for vibration energy harvesting[END_REF][START_REF] Cao | A survey on ambient energy sources and harvesting methods for structural health monitoring applications[END_REF](7)[START_REF] Jordan | Electromagnetic waves and radiating systems[END_REF][START_REF] Brand | Micro energy harvesting[END_REF](10)[START_REF] Zhu | General model with experimental validation of electrical resonant frequency tuning of electromagnetic vibration energy harvesters[END_REF][START_REF] Sari | An electromagnetic micro power generator for wideband environmental vibrations[END_REF][START_REF] Halim | Design and experiment of a human-limb driven, frequency up-converted electromagnetic energy harvester[END_REF][START_REF] Bowers | Spherical, rolling magnet generators for passive energy harvesting from human motion[END_REF] about the time-varying QE-KEH(t) can be analytically solved as:

( ) 쮀 1 - ( ) 1 - (2-15)
where u and w are intermediate variables for the integration. Then the I(t) and VE-KEH(t) can be obtained from the equations [START_REF] Roundy | Energy scavenging for wireless sensor nodes with a focus on vibration to electricity conversion[END_REF][START_REF] Dell'anna | State-of-the-art power management circuits for piezoelectric energy harvesters[END_REF][START_REF] Wang | Triboelectric nanogenerators[END_REF][START_REF] Boisseau | Electrostatic conversion for vibration energy harvesting[END_REF][START_REF] Cao | A survey on ambient energy sources and harvesting methods for structural health monitoring applications[END_REF](7)[START_REF] Jordan | Electromagnetic waves and radiating systems[END_REF][START_REF] Brand | Micro energy harvesting[END_REF](10)[START_REF] Zhu | General model with experimental validation of electrical resonant frequency tuning of electromagnetic vibration energy harvesters[END_REF][START_REF] Sari | An electromagnetic micro power generator for wideband environmental vibrations[END_REF], [START_REF] Roundy | Energy scavenging for wireless sensor nodes with a focus on vibration to electricity conversion[END_REF][START_REF] Dell'anna | State-of-the-art power management circuits for piezoelectric energy harvesters[END_REF][START_REF] Wang | Triboelectric nanogenerators[END_REF][START_REF] Boisseau | Electrostatic conversion for vibration energy harvesting[END_REF][START_REF] Cao | A survey on ambient energy sources and harvesting methods for structural health monitoring applications[END_REF](7)[START_REF] Jordan | Electromagnetic waves and radiating systems[END_REF][START_REF] Brand | Micro energy harvesting[END_REF](10)[START_REF] Zhu | General model with experimental validation of electrical resonant frequency tuning of electromagnetic vibration energy harvesters[END_REF][START_REF] Sari | An electromagnetic micro power generator for wideband environmental vibrations[END_REF][START_REF] Halim | Design and experiment of a human-limb driven, frequency up-converted electromagnetic energy harvester[END_REF], and [START_REF] Roundy | Energy scavenging for wireless sensor nodes with a focus on vibration to electricity conversion[END_REF][START_REF] Dell'anna | State-of-the-art power management circuits for piezoelectric energy harvesters[END_REF][START_REF] Wang | Triboelectric nanogenerators[END_REF][START_REF] Boisseau | Electrostatic conversion for vibration energy harvesting[END_REF][START_REF] Cao | A survey on ambient energy sources and harvesting methods for structural health monitoring applications[END_REF](7)[START_REF] Jordan | Electromagnetic waves and radiating systems[END_REF][START_REF] Brand | Micro energy harvesting[END_REF](10)[START_REF] Zhu | General model with experimental validation of electrical resonant frequency tuning of electromagnetic vibration energy harvesters[END_REF][START_REF] Sari | An electromagnetic micro power generator for wideband environmental vibrations[END_REF][START_REF] Halim | Design and experiment of a human-limb driven, frequency up-converted electromagnetic energy harvester[END_REF][START_REF] Bowers | Spherical, rolling magnet generators for passive energy harvesting from human motion[END_REF][START_REF] Liu | A multi-frequency vibration-based MEMS electromagnetic energy harvesting device[END_REF].

Chapter 2 Introduction to electrets and electret kinetic energy harvesters 33 Note that this compact equivalent circuit model is only useful when the CE-KEH is time-varying with a known analytical form. For some E-KEHs with time-varying partial capacitances but with a constant CE-KEH, such as the freestanding structure designs illustrated in Figure 23456789101112(e), and (i), this model is not applicable. A detailed equivalent electrical model [START_REF] Basset | Electrostatic kinetic energy harvesting[END_REF][START_REF] Niu | Theory of freestanding triboelectric-layer-based nanogenerators[END_REF] that contains each partial capacitance would be helpful to theoretically analyze the output of the E-KEHs with time-varying partial capacitances but constant CE-KEH.

The electromechanical model for undirect vibration-driven E-KEHs

For micro KEHs to be used in microelectromechanical systems (MEMS), the entire encapsulation is important for the ease of use. One significant encapsulation strategy for KEHs is incorporated with a resonator (passive oscillator [START_REF] Blokhina | Nonlinearity in energy harvesting systems[END_REF]) structure.

One function of the resonator structure is to amplify the relative displacement among different parts of the transduction unit in a KEH from vibration sources with a small amplitude by the phenomenon of resonance [START_REF] Boisseau | Optimization of an electret-based energy harvester[END_REF]. Other possible functions of the resonator structure are to modulate the natural resonance frequency (ωn), bandwidth, and quality factor of the E-KEH for better mechanic-electric coupling [START_REF] Blokhina | Nonlinearity in energy harvesting systems[END_REF].

Moreover, KEHs with a resonator structure only need to be mechanically anchored to one point and thus can simply be fixed to any moving body to generate electricity [START_REF] Williams | Analysis of a micro-electric generator for microsystems[END_REF].

A general 1 degree-of-freedom linear damping model for vibration mechanic analysis

C. B. Williams and R. B. Yates analyzed a micro vibration-electric generator with a resonator structure using a spring-mass-damper model, for all types of mechanic-to-electric energy harvesters with an emphasis on an electromagnetic micro-generator [START_REF] Williams | Analysis of a micro-electric generator for microsystems[END_REF][START_REF] Williams | Analysis of a micro-electric generator for microsystems[END_REF]. They regarded the three possible mechanic-electric transduction mechanisms (electromagnetic, piezoelectric, and electrostatic) just as three approaches to providing the damping force (the Ampere's force for the electromagnetic, the Coulomb's force for the piezoelectric and electrostatic) that fulfills the mechanic-to-electric conversion. And they analyzed the motion equation of the generator with regarding the transduction damping force as a linear (also termed as viscous) damping force, which means the damping force is linearly proportional to the movement velocity with a proportionality coefficient. the generator itself but also on the load circuit, k is the equivalent spring constant of the vibration structure in the generator, y(t) is the displacement of the generator frame caused by external vibrations, x(t) is the displacement of the inertial mass, z(t) is the relative mass-to-frame displacement that equals x(t) -y(t). There is z=0 if there is no external excitation and the mass is at its equilibrium position.

In this model, only the one-dimensional motion of the mass needs to be analyzed if the motion from an external vibration source is given, which makes it become a 1 degree-of-freedom (DOF) vibration problem. And since the transduction damping force is always considered as a linear damping force whatever type the real force is, the model is called a general 1 DOF linear damping model in this thesis.

The differential equations of motion and power transfer of this model according to Newton's second law were listed as follows [START_REF] Williams | Analysis of a micro-electric generator for microsystems[END_REF][START_REF] Williams | Analysis of a micro-electric generator for microsystems[END_REF]:

㔮 쮀 (2-14) 쮀 (2-15),
where p(t) is the instantaneous mechanical power transfer in the mass block. If ignoring all the energy loss from parasitic damping caused by an undesired effect

Chapter 2 Introduction to electrets and electret kinetic energy harvesters 35 such as the air drag and hysteresis loss in the suspension, during steady-state periodic energy conversion working cycles, all the energy transferred to the mass should be converted to electric energy [START_REF] Blokhina | Nonlinearity in energy harvesting systems[END_REF]. The steady-state generated electrical power when the generator frame was excited by a harmonic vibration source, y(t)=Y0cos(ωt), was therefore calculated as [START_REF] Williams | Analysis of a micro-electric generator for microsystems[END_REF][START_REF] Williams | Analysis of a micro-electric generator for microsystems[END_REF][START_REF] Mitcheson | Architectures for vibration-driven micropower generators[END_REF]:

쮀 푀 2 ( ) 3 3 1( ) 2 2 2 2 쮀 3 푀 2 3 1( ) 2 2 2 2 (2-16),
where ωc = ω/ωn, Y0 is the vibration amplitude of the external vibration source, and ζ is the transducer damping ratio of the mechanic-to-electric transduction which is a dimensionless parameter defined as:

쮀 2 㔮 쮀 2 (2-17).
It should be noted that the equation (2-16) was obtained with ignoring parasitic damping, and other practical limitations such as the limitation on the maximum vibration amplitude (Zl) of the inertial mass.

The ζ can be optimized to get the maximum generated power. Without considering the Zl, by finding the extreme point from the equation (2-16), there are [START_REF] Mitcheson | Architectures for vibration-driven micropower generators[END_REF]:

݃ 쮀 2 1 2 (2-18) 푀 쮀 2 푀 2 3 4 2 1 (2-19),
where ζopt is the stationary point on dP/dζ, and Pmax is the corresponding maximum generated power.

The amplitude of the mass-to-frame vibration is related to ζ by [START_REF] Mitcheson | Architectures for vibration-driven micropower generators[END_REF]:

쮀 푀 2 (1 2 ) 2 (2 ) 2
(2-2 ).

If ζopt calculated by the equation (2-18) leads to Z0 > Zl, which means that the optimized ζopt can't be obtained by the generator due to the constraint in its geometric limitation, the ζ should be tuned to as close to ζopt as possible to get the maximum achievable generated power, there are [START_REF] Mitcheson | Architectures for vibration-driven micropower generators[END_REF]:

Chapter 2 Introduction to electrets and electret kinetic energy harvesters

36 ݃ 쮀 1 2 4 ( 푀 ) 2 (1 2 ) 2 (2-2 ) 푀 쮀 푀 2 3 ( 푀 ) 2 ݃ 쮀 푀 2 3 1 2 2 ( 푀 ) 2 4 ( 푀 ) 2 (1 2 ) 2 (2-21)
, where ζoptCZ is the optimal damping ratio of the generator with the constrain of Z0 =Zl, and PmaxCZ is the corresponding maximum generated power by the generator.

When the KEH works at the resonant frequency, which means ωc, there are:

݃ ܿ 쮀 푀 2 (2-22) 푀 ܿ 쮀 1 2 푀 2 3 푀 (2-23)
, where ζoptres is the optimal damping ratio of the generator if it works at the resonant frequency, and Pmaxres is the corresponding maximum generated power by the generator.

If taking the undesired parasitic damping with the damping ratio ζp into consideration, the equations (2- 16) and (2-18) should be modified as [START_REF] Mitcheson | Architectures for vibration-driven micropower generators[END_REF][START_REF] Li | Infrared signal transmission by a laser-micromachined, vibration-induced power generator[END_REF]:

쮀 3 푀 2 3 1( ) 2 2 2( ) 2 (2-24) ݃ 쮀 1 2 1 2 2 4 4 4 2
(2-25).

A significant undesired parasitic damping will apparently reduce the output electrical power of a KEH, therefore ζp should be as low as possible to get the maximum output power. Note that other practical constraints such as the limitation on the achievable ζ range and on the vibration power source are not considered in this model. And the theoretical generated power is calculated during the steady-state working cycles of the generator. The practical output power of the generator must be lower than the theoretical value due to other possible energy losses due to the charge leakage, operational overhead, electrical losses in the circuit, etc. [START_REF] Mitcheson | Architectures for vibration-driven micropower generators[END_REF]. Nevertheless, this model provides a method to analyze the vibration-driven KEHs from a mechanical point-of-view, which is important to further analyze the electromechanical coupling of KEHs.

A complete electromechanical model for vibration-driven E-KEHs

The general 1 DOF linear damping model was firstly applied on micro electromagnetic generators [START_REF] Williams | Analysis of a micro-electric generator for microsystems[END_REF][START_REF] Williams | Development of an electromagnetic micro-generator[END_REF][START_REF] Amirtharajah | Self-powered signal processing using vibration-based power generation[END_REF], these generators were called as the velocity-damped resonant generator (VDRG) [START_REF] Mitcheson | Architectures for vibration-driven micropower generators[END_REF]. For electrostatic energy harvesters, the Coulomb's force that implement the mechanic-electric energy conversion can't be simply modeled as a linear damping force. Paul D. [START_REF] Boisseau | Optimization of an electret-based energy harvester[END_REF][START_REF] Boisseau | Cantilever-based electret energy harvesters[END_REF] which combined both the theoretical analysis on the mechanic domain [START_REF] Williams | Analysis of a micro-electric generator for microsystems[END_REF][START_REF] Mitcheson | Architectures for vibration-driven micropower generators[END_REF] and the electric domain [START_REF] Jefimenko | Electrostatic current generator having a disk electret as an active element[END_REF][START_REF] Tada | Experimental characteristics of electret generator, using polymer film electrets[END_REF][START_REF] Boland | Micro electret power generator[END_REF]] of E-KEHs as shown in In this complete electromechanical model, the undesired mechanical damping force, which causes the energy loss, was modeled as a linear (viscous) damping force fmec with a damping coefficient of Dm, and the electrostatic force felec between the electret and the counter-electrode was calculated by [START_REF] Basset | Electrostatic kinetic energy harvesting[END_REF]:

쮀 쮀 1 2 ( 2 2 ( ) 2 ( ) ) 쮀 1 2 2 2 ( ) 2 ( ) (2-26)
where x is the deflection of the silicon cantilever at the lateral position of the center of the mass, and We is the electrostatic energy stored in the C(t) calculated by:

쮀 2 2 ( ) 2 ( ) (2-27)
where -Q2(t) is the charge amount on the counter electrode.

Here, the felec is a nonlinear damping force. When the clamped end of the cantilever is excited by an external vibration source y(t), combing the mechanical model illustrated in Correspondingly, the second equation in (2-28) was modified to:

2 쮀 ( ) ( ( ) 푀 ) ( 2 ( 1 ( ) 푀 ( ) ( ) )) (2-29).
From both the simulation results in Simulink and experimental data, Boisseau et al. [START_REF] Boisseau | Cantilever-based electret energy harvesters[END_REF] pointed out that the parasitic capacitance would decrease the harvested power especially when the load resistance is higher than the impedance induced by the parasitic capacitance.

Lumped-parameter equivalent circuit model

Another electromechanical modeling method for undirect-vibration driven E-KEHs is based on the lumped-parameter equivalent circuit model. In 1994, Gary Keith Fedder presented this method in his thesis [START_REF] Fedder | Simulation of microelectromechanical systems[END_REF], in which he proposed an electrical analogy of the mass-spring-damper system to an inductor-capacitor-resistor The mechanical impedance of the mechanic-electric transducer together with the conditioning circuit in the energy harvester was defined as [START_REF] Galayko | A general analytical tool for the design of vibration energy harvesters (VEHs) based on the mechanical impedance concept[END_REF]:

쮀 (2-3 )
where Ψt is the mechanical impedance, F t ω is the complex amplitude of the fundamental harmonic of the complex Fourier series of the electrostatic transduction force, and v is the complex amplitude of the sinusoidal velocity of the moving component of the energy transducer. It was deduced that the energy harvester would harvest the maximal power when the real part of Ψt is maximal in steady states.

Chapter remarks

In

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Chapter 3 Amplitude-variable output characteristics of a contact-separation mode E-KEH during multiple transitory working cycles 44 Chapter 3 Amplitude-variable output characteristics of a contact-separation mode E-KEH during multiple transitory working cycles

Introduction

The analytical solution of the compact equivalent electrical model for the direct motion-driven parallel-plate E-KEHs has been introduced in section 2.5.1. In this chapter, the general analytical solution of the detailed equivalent electrical model for a direct motion-driven contact-separation (CS) mode (which means a gap-varying mode with a minimum air gap of 0) parallel-plate E-KEH is given in section 3.2. Then simulations of the output voltage/current/power of the E-KEH based on this model are presented in section 3.3. Most previous theoretical researches on E-KEHs focused on the steady-state output of E-KEHs driven by harmonic motions [START_REF] Hinchet | Understanding and modeling of triboelectric-electret nanogenerator[END_REF][START_REF] Niu | Theoretical investigation and structural optimization of single-electrode triboelectric nanogenerators[END_REF][START_REF] Dharmasena | Triboelectric nanogenerators: Providing a fundamental framework[END_REF].

Though some researchers already obtained asymmetric and amplitude-variable simulation results of output voltage [START_REF] Geisler | Human mechanical energy harvesting systems for smart clothes[END_REF][START_REF] Hinchet | Understanding and modeling of triboelectric-electret nanogenerator[END_REF] or current [START_REF] Dharmasena | Triboelectric nanogenerators: Providing a fundamental framework[END_REF] of E-KEHs, the detailed cause of these characteristics need to be further discussed, which could be helpful for optimizing the performance of E-KEHs. In section 3.3, the reason for the asymmetric and amplitude-variable output characteristics of the E-KEH, and their dependence on the load resistance are discussed based on the simulated results. The output power of the E-KEH with different load resistances and initial conditions are analyzed using the QV cycle analysis method. At last, in section 3.4, the asymmetric and amplitudevariable output voltage of an E-KEH made with PTFE film is verified by both experimental and simulated data.

Analytical solution of the detailed equivalent electrical model for a contact-separation mode E-EKH

The analytical solution with arbitrary initial conditions

A simplified CS mode E-KEH with three rigid-body components (one electret film layer and two electrodes) is taken as the research object of this chapter. The structure of the E-KEH is illustrated in Figure 3-1(a), and the cross-section sketch of the E-KEH is shown in Figure 3-1(b). In the sketch, σ is the effective homogenous Chapter 3 Amplitude-variable output characteristics of a contact-separation mode E-KEH during multiple transitory working cycles 45 surface charge density on the top side of the electret film, S is the area of the electret film, εr and df is the dielectric constant and the thickness of the electret film respectively, z(t) is the time-varying air gap distance, Q(t) is the time-dependent charge amount on the back electrode (the polarity of Q(t) is opposite with σ), and R is the load resistance in the external circuit. Using the hypothesis of neutrality [START_REF] Basset | Electrostatic kinetic energy harvesting[END_REF] to the E-KEH, the charge amount on the top electrode is -σS-Q(t). The electret film was regarded as a perfect electret without charge decay, which means σ was considered as a constant. The planar dimensions of the electret film and the two electrodes are the same, which are assumed to be much larger than df and the maximum z(t), which means the fringe effect of the electric field is always negligible.

쮀 쮀 (3-1) ݎ푀 쮀 (3-2)
where d0f is the effective dielectric thickness of the electret film defined as df/εr [START_REF] Niu | Theoretical study of contact-mode triboelectric nanogenerators as an effective power source[END_REF].

With the relative approaching and separating movement between the top electrode and the electret film, Cgap(t) changes with z(t) while Cf keeps unchanged.

According to the Gauss' law, the back electrode holds an electric potential of Q(t)/Cf, while the top electrode holds an electric potential of (-σS-Q (t))/Cgap (t), both Chapter 3 Amplitude-variable output characteristics of a contact-separation mode E-KEH during multiple transitory working cycles 46 taking the top surface of the electret film as the reference. The potential difference between these two electrodes is the output voltage VE-KEH(t) of the E-KEH. If regarding the top electrode as the positive electrode, there is:

쮀 ݎ푀 (3-3)
The VE-KEH(t) leads to the charge-transfer between the top and back electrodes, which give rise to an output current I(t) in the circuit. According to charge conservation, there is:

쮀 (3-4)
On the other hand, applying Ohm's law to the load resistance, there is:

쮀 (3-5). Substitute (3-1) ~(3-4) to (3-5), there is 쮀 (3-6).
It's easy to prove that the differential equation [START_REF] Dell'anna | State-of-the-art power management circuits for piezoelectric energy harvesters[END_REF][START_REF] Wang | Triboelectric nanogenerators[END_REF][START_REF] Boisseau | Electrostatic conversion for vibration energy harvesting[END_REF][START_REF] Cao | A survey on ambient energy sources and harvesting methods for structural health monitoring applications[END_REF] is equivalent to the equation

( ) 쮀 ( ) (3-7).
Note that the total capacitance CE-KEH(t) of the E-KEH equals the series connection of Cf and Cgap (t), which is:

( ) 쮀 ݎ푀 ݎ푀 쮀 ( ) (3-8).
Therefore, both the compact and detailed electrical models are applicable to the CS mode E-KEH. The compact model is more concise, while the detailed model is more intuitive.

For the first-order linear differential equation

(3-6) about Q(t), if Q(0) is given,
and z(t) has a known analytical form, it can be analytically solved as:

쮀 ( ( ) ) ( ( ) ) (3-9)
where u and w are intermediate variables for the integration.

Chapter 3 Amplitude-variable output characteristics of a contact-separation mode E-KEH during multiple transitory working cycles 47 I(t) can be derived from [START_REF] Dell'anna | State-of-the-art power management circuits for piezoelectric energy harvesters[END_REF][START_REF] Wang | Triboelectric nanogenerators[END_REF] and (3-9) as:

쮀 ( ( ) ) ( ( ) ) (3-1 ).
Then VE-KEH(t) can be easily obtained from [START_REF] Dell'anna | State-of-the-art power management circuits for piezoelectric energy harvesters[END_REF][START_REF] Wang | Triboelectric nanogenerators[END_REF][START_REF] Boisseau | Electrostatic conversion for vibration energy harvesting[END_REF] and (3-10), and the output power P(t) of the E-KEH to the load resistance can be calculated by the Joule's law as:

( ) 쮀 2 ( ) (3-11).

The initial electric equilibrium assumption

The equation [START_REF] Dell'anna | State-of-the-art power management circuits for piezoelectric energy harvesters[END_REF][START_REF] Wang | Triboelectric nanogenerators[END_REF][START_REF] Boisseau | Electrostatic conversion for vibration energy harvesting[END_REF][START_REF] Cao | A survey on ambient energy sources and harvesting methods for structural health monitoring applications[END_REF](7)[START_REF] Jordan | Electromagnetic waves and radiating systems[END_REF][START_REF] Brand | Micro energy harvesting[END_REF] gives the analytical solution of Q(t) without specifying Q(0). Now assuming the E-KEH starts working from the electric equilibrium state, which means VE-KEH(0) = 0, according to the equations (3-1) ~(3-3), there are:

ݎ푀 쮀 (3-12) 쮀 (3-13).
With this assumption, the initial condition Q(0) can be easily obtained from the equation (3-13) once z(0) is given.

For instance, for the most used case [START_REF] Yang | A fully verified theoretical analysis of contactmode triboelectric nanogenerators as a wearable power source[END_REF][START_REF] Niu | Theoretical study of contact-mode triboelectric nanogenerators as an effective power source[END_REF][START_REF] Niu | Theoretical systems of triboelectric nanogenerators[END_REF] z(0) = 0, the initial condition is Q(0) = 0, the equation (3-9) becomes:

쮀 ( ) ( ) (3-14).
For another case z(0) = zmax, where zmax is the maximum air gap during the working of the E-KEH, there are:

쮀 푀 푀 쮀 푀 (3-15) 쮀 푀 ( ( ) ) ( ( )
) [START_REF] Dell'anna | State-of-the-art power management circuits for piezoelectric energy harvesters[END_REF][START_REF] Wang | Triboelectric nanogenerators[END_REF][START_REF] Boisseau | Electrostatic conversion for vibration energy harvesting[END_REF][START_REF] Cao | A survey on ambient energy sources and harvesting methods for structural health monitoring applications[END_REF](7)[START_REF] Jordan | Electromagnetic waves and radiating systems[END_REF][START_REF] Brand | Micro energy harvesting[END_REF](10)[START_REF] Zhu | General model with experimental validation of electrical resonant frequency tuning of electromagnetic vibration energy harvesters[END_REF][START_REF] Sari | An electromagnetic micro power generator for wideband environmental vibrations[END_REF][START_REF] Halim | Design and experiment of a human-limb driven, frequency up-converted electromagnetic energy harvester[END_REF][START_REF] Bowers | Spherical, rolling magnet generators for passive energy harvesting from human motion[END_REF][START_REF] Liu | A multi-frequency vibration-based MEMS electromagnetic energy harvesting device[END_REF][START_REF] Liu | A comprehensive review on piezoelectric energy harvesting technology: Materials, mechanisms, and applications[END_REF].

The simulation results in section 3.3 are mainly based on these two cases together with this initial electric equilibrium assumption.

Chapter 3 Amplitude-variable output characteristics of a contact-separation mode E-KEH during multiple transitory working cycles 48

The short-circuit current and the open-circuit voltage

The short-circuit current and the open-circuit voltage of E-KEHs are two of the most widely used indicators to evaluate the performance of E-KEHs.

In the short-circuit condition, there always is VE-KEH(t) = 0, which means the top and back electrodes of the CS mode E-KEH are always at the electrical equilibrium state. If using Qeq(t) instead of Q(t) to represent the charge amount on the back electrode in the short-circuit condition for distinction, according to the equation (3-3), there is:

쮀 (3-17).
The short-circuit current is:

쮀 쮀 ( ) 2 (3-18)
where v(t) is the relative movement velocity of the top electrode with respect to the electret film, which can be obtained by:

쮀 (3-19).
In the open-circuit condition, there always is

Q(t) = Q(0), I(t) = 0,

Simulation results and discussion

Parameters for the simulation

Based on section 3.2, the Q(t), I(t), VE-KEH(t), and P(t) of the CS mode E-KEH can be simulated when the driving motions and parameter values are given, by using a symbolic differential equation solver "dsolve" in MATLAB to solve the equation [START_REF] Dell'anna | State-of-the-art power management circuits for piezoelectric energy harvesters[END_REF][START_REF] Wang | Triboelectric nanogenerators[END_REF][START_REF] Boisseau | Electrostatic conversion for vibration energy harvesting[END_REF][START_REF] Cao | A survey on ambient energy sources and harvesting methods for structural health monitoring applications[END_REF]. In previous researches, mainly two types of movements were studied for the CS mode E-KEHs. One is a single separation process with a given average velocity [START_REF] Niu | Theoretical study of contact-mode triboelectric nanogenerators as an effective power source[END_REF],

the other one is regular harmonic movements [START_REF] Hinchet | Understanding and modeling of triboelectric-electret nanogenerator[END_REF][START_REF] Shao | 3D mathematical model of contactseparation and single-electrode mode triboelectric nanogenerators[END_REF]. Here, a piecewise acceleration-uniform motion-deceleration cyclic movement, which can be realized by a linear motor system in our laboratory, was used to simulate the output of E-KEH.

Chapter 3 Amplitude-variable output characteristics of a contact-separation mode E-KEH during multiple transitory working cycles 49 For comparison with other research, the same geometrical (thickness and area of electret film), material parameters (permittivity and surface charge density), and movement speed during the uniform motion with references [START_REF] Hinchet | Understanding and modeling of triboelectric-electret nanogenerator[END_REF][START_REF] Niu | Theoretical study of contact-mode triboelectric nanogenerators as an effective power source[END_REF] were used, except that both large acceleration and deceleration of ±100 m/s 2 were used to make the movement reciprocating and cyclic. The detailed parameter values are listed in At first, the case z(0) = 0 was considered. The z(t) was described by the following periodic piecewise function:

쮀 푀 1 2 2 1 1 2 2푀 1 1 1 1 2 푀 푀 2 3 2 2 2 3 푀 푀 3 3 2 2 3 4 푀 2 2 2푀 3 2 4 4 5 푀 4 2 2 5
(3-21)

Chapter 3 Amplitude-variable output characteristics of a contact-separation mode E-KEH during multiple transitory working cycles

50 with 1 쮀 1 푀 1 2 쮀 푀 1 1 2푀 1 1 2푀 2 3 쮀 푀 1 1 2푀 1 1 2푀 2 4 쮀 푀 1 1 2푀 1 1 2푀 2 2 푀 3 5 쮀 푀 1 1 2푀 1 1 2푀 2 푀 2 2 2푀 3 2 2푀 4 쮀 푀 1 1 2푀 1 1 2푀 2 푀 2 2 2푀 3 2 2푀 4 (3-22)

Charge-transfer process

For the case z(0) = 0, Q(0) = 0, Figure 3 Firstly, by comparing the Q(t) and the short-circuit equilibrium charge Qeq(t), it can be found that positive charges will transfer to the back electrode when Q(t)<Qeq(t), generating positive current. And when Q(t)>Qeq(t), positive charges will transfer in an opposite direction, generating negative current. The vertical dash-dot lines in Fig. 2(a)~(c) mark the moment when Q(t)=Qeq(t) and meanwhile I(t)=0. It can be summarized that the difference between Q(t) and Qeq(t) leads to the charge-transfer between the two electrodes in a direction that can reduce this difference.

Secondly, the first positive current peak (Ipp1) has an obviously larger amplitude than other current peaks. For example in And the asymmetric output characteristic becomes more obvious when R is larger since a larger R leads to larger τ that heavily retards the charge-transfer process.

Chapter 3 Amplitude-variable output characteristics of a contact-separation mode E-KEH during multiple transitory working cycles 53 In Figure 34, all Q(t) simulated with different load resistances show smaller variation range than Qeq(t) in each charge-transfer cycle, and a larger R leads to a smaller variation range, meaning fewer charge is transferred in each cycle due to the larger resistance. With the resistance of 1 MΩ, 10 MΩ, and 100 MΩ, Q(t) is limited in a stable range after three charge-transfer cycles. Taking the charge-transfer process with R of 100 MΩ as an example shown in Figure 34, the amplitude of Q(t) varies from the first to the third charge-transfer cycles and then is limited between steady upper and lower limiting values marked by the red and black dash lines, respectively. This is because Qtrp is larger than Qtrn in the first and second chargetransfer cycles and becomes the same with Qtrn in the third cycle as shown in the inset of Figure 34. While with the resistance of 1 GΩ and 10 GΩ, the amplitude of Q(t) keeps a growing trend in 10 motion cycles.

Amplitude-variable output current/voltage/power

In Figure 34, larger Resistance leads to a lower amplitude of I(t), which is in accordance with the literature [START_REF] Niu | Theoretical study of contact-mode triboelectric nanogenerators as an effective power source[END_REF][START_REF] Niu | Theoretical systems of triboelectric nanogenerators[END_REF]. This makes the current peaks and the Chapter 3 Amplitude-variable output characteristics of a contact-separation mode E-KEH during multiple transitory working cycles 54 variations in the amplitude of I(t) with larger resistances unobservable in Figure 34). On the contrary, the amplitude of VE-KEH(t) is higher with larger Resistance, making the variation in the amplitude of VE-KEH(t) prominent as shown in Figure 34 9.87×10 -3 9.57×10 -2 9.57×10 -1 9.57×10 -3 9.57×10 -2 9.57×10 -1

All adjusted coefficients of determination of these fittings are 1, indicating perfect fittings. Standard errors of these parameters in fitting are given in Table 3-3. 3.70×10 -3 4.95×10 -2 2.89×10 -1 1.21×10 -7 8.87×10 -7 5.84×10 -6 t0 (s) 0 0 0 0 0 0 Va (V) 1.08×10 -2 4.49×10 -2 2.88×10 -1 3.32×10 -7 8.02×10 -7 5.82×10 -6 τd (s)

Table 3-3 Standard errors (SE) of the corresponding parameters in

1.09×10 -6 1.15×10 -5 2.84×10 -4 3.57×10 -9 6.02×10 -9 1.62×10 -7

Chapter 3 Amplitude-variable output characteristics of a contact-separation mode E-KEH during multiple transitory working cycles 55

The time-dependent part in the equation has the same exponential form as the discharging curve equation of a resistor-capacitor (RC) circuit. In analogy with the RC circuit discharging process, we define the parameter τd as the time constant of this variation. From Table 3-2, τd is almost directly proportional to the resistance value R especially for the large R of 1 GΩ and 10 GΩ, meaning that it takes a longer time for the E-KEH to give steady output with larger R than with smaller R.

From the equation , it can be inferred that the Vpp or Vpp value will gradually approach the corresponding Vs value when the time is long enough. By using the equation and parameter values in Table 3- In the first movement cycle, the peak P(t) increases from ~1.29 mW to ~2.30 mW if R increases from 1 MΩ to 100 MΩ, then decreases to ~0.125 mW if R further increases to 10 GΩ. However, in the followed motion cycles, P(t) peak values are much lower than those in the first cycle, especially for P(t) with R of 10 MΩ and 100 MΩ. This can also be noticed in Though the output energy with R of 100 MΩ after the first motion cycle is much higher than those with other resistances, in the followed cycles little energy is output with R of 100 MΩ and the total energy is overpassed by that with R of 1 GΩ after several cycles. The average output power (AvgP) of the E-KEH in each motion cycle can be calculated by:

ݎ ( ) 쮀 ( 1)ͳ ͳ ( ) (3-25)
where c is the motion cycle number and T is the period of one movement cycle.

Chapter 3 Amplitude-variable output characteristics of a contact-separation mode E-KEH during multiple transitory working cycles

Simulations with another initial condition

Then the case z(0) = zmax i.e. the initial condition Q(0) = Qmax was considered (will be called the second initial condition for convenience), using the same parameter values in Table 3- 9.56×10 -3 9.57×10 -2 9.58×10 -1 9.55×10 -3 9.57×10 -2 9.57×10 -1

Chapter 3 Amplitude-variable output characteristics of a contact-separation mode E-KEH during multiple transitory working cycles 60 2.42×10 -5 5.99×10 -4 0.01029 6.90×10 -6 1.24×10 -5 5.52×10 -5 t0 (s) 0 0 0 0 0 0 Va (V) 7.06×10 -5 5.44×10 -4 1.03×10 -2 2.02×10 -5 1.12×10 -5 5.51×10 -5 τd (s) 7.80×10 -7 4.40×10 -6 2.85×10 -4 2.29×10 -6 2.29×10 -6 4.32×10 -5 Vs values in Chapter 3 Amplitude-variable output characteristics of a contact-separation mode E-KEH during multiple transitory working cycles 62

Table 3-5 Standard errors (SE) of the corresponding parameters in

QV cycle analysis

The output energy of the E-KEH can be explicitly evaluated from the chargevoltage (QV) diagram. The area of the QV loop equals the output energy of the E-KEH per charge-transfer cycle [START_REF] Galayko | Capacitive energy conversion with circuits implementing a rectangular charge-voltage cycle-part 1: Analysis of the electrical domain[END_REF][START_REF] Galayko | Tools for analytical and numerical analysis of electrostatic vibration energy harvesters: Application to a continuous mode conditioning circuit[END_REF].

Experimental and simulation verifications

Experimental Methods

To verify the simulated amplitude-variable characteristics, a TE-KEH with a piece of ~4 cm × 4 cm rectangular 100 μm-thick skived PTFE film as the electret layer was made and tested. The PTFE film was cleaned by deionized water and ethanol using an ultrasonic cleaner at first. After fully dried, a piece of conductive and adhesive copper tape (3M, type 1181) was pasted on one side of the PTFE film to form the back electrode. Then the PTFE film with the back electrode was attached to the sliding block of a linear motor (Afag Electro slide ES20-100 with LinMot servo drive) by double-sided adhesive tapes, and a piece of Al foil was attached to a fixed plate faced with the PTFE film as shown in Figure 345678910111213141516. Motion parameters (zmax, v1, v2, a1, a2, a3, and a4) of the sliding block of the linear motor were set in the control software (LinMot-Talk 6.0) as values listed in Table 3-

Chapter 3 Amplitude-variable output characteristics of a contact-separation mode E-KEH during multiple transitory working cycles

Estimations of parameter values for corresponding simulations

To do corresponding simulations with the experiments, the effective motion parameter values and the charge density need to be redetermined. From the data in almost still for ~0.011s when it moved to the position of z=0, and it moved at a rather low velocity for ~0.011s when it got close to the position of z=0.7 mm. To simplify the simulation, the movement velocity during these two durations of 0.011 s was set as 0, and these two durations were called as the wait time tw1 and tw2.

To estimate the charge density on the PTFE film, the transfer charge amount of the TE-KEH was measured, with setting the zmax as 10 mm and the wait time as 5 s at both limiting positions of z=0 and z=zmax. With such a large zmax and wait time, it's reasonable to assume that the maximum short-circuit transferred charge amount approximates to the charge amount on the PTFE film [START_REF] Wang | Maximum surface charge density for triboelectric nanogenerators achieved by ionized-air injection: Methodology and theoretical understanding[END_REF][START_REF] Zi | Standards and figure-ofmerits for quantifying the performance of triboelectric nanogenerators[END_REF]. From the results shown in Figure 3-20, the polarity of charges on the PTFE film was confirmed to be negative since positive charges were transferred from the top electrode to the back electrode during the gap enlarging process, and in the opposite direction during the gap closing process. And the effective surface charge density on the PTFE film was estimated to be -50 μC/m 2 according to the measured maximum transferred charge amount of ~80 nC for the PTFE film with the area of ~16 cm 2 . All the parameter values for corresponding simulations are listed in Table 3-6. 4 and the initial condition z(0)= zmax.

Chapter 3 Amplitude-variable output characteristics of a contact-separation mode E-KEH during multiple transitory working cycles

The corresponding simulated z(t), v(t), and CTE-KEH(t) curves are shown in

(t), v(t), and (b) CTE-KEH (t) curves using parameter values in Table 3-6 and the initial condition that z(0)=0 and Q(0)=0. (c) Simulated z(t), v(t), and (d) CTE-KEH (t) data using parameter values listed in Table

Results and discussion

The measured output voltages of the TE-KEH with the load resistance of 10 MΩ, 100 MΩ, and 1.1 GΩ are plotted in

Chapter conclusion

In this chapter, at first, the analytical solution of the CS mode E-KEH with a resistive load was given based on the detailed equivalent electrical model. Then symbolic computations in MATLAB were used to calculate the charge-transfer process and output current/voltage/power of an E-KEH driven by a piecewise periodic reciprocating movement with acceleration/deceleration processes, with different load resistances.

It was found that the amplitudes of the output voltage/current of the E-KEH varied over time in an exponential form and finally got to steady ranges, which was caused by the lag between the charge-transfer cycle and the driving motion cycle. This lag also led to the asymmetric between the output positive and negative current/voltage peaks. And the time for the E-KEH to get steady output is positively correlated to the load resistance.

Chapter 3 Amplitude-variable output characteristics of a contact-separation mode E-KEH during multiple transitory working cycles 71 It was also found, with the first initial condition that the E-KEH started working from the contact position, the variation range of the output voltage peaks was much larger than that the E-KEH started working from the fully-separated position (the second initial condition) with the same load resistance, and the optimum load resistance in latter motion cycles could be very different from that in the first cycle.

By comparing QV diagrams of the E-KEH simulated from the two initial conditions, it was found that the E-KEH would finally output the same steady QV cycle with the same load resistance after long enough time if the periodic driving motion was kept the same.

At last, the influences of the load resistance and the initial condition on the amplitude-variable output voltage of a TE-KEH made with PTFE film were confirmed by both experiments and simulations.

Chapter 4 Optimizing the output power of the contactseparation mode TE-KEH

Introduction

It has been demonstrated that if the time constant of the RC circuit formed by E-KEHs with load resistance is too large, the charge-transfer cycle may fall behind the periodic motion cycle a lot, resulting in the incomplete charge-transfer and consequently dramatical decay in the output power of E-KEHs during continuous multiple working cycles. It's clear that the maximum time constant is obtained when the capacitance of E-KEHs is maximum, which corresponding to the contact state (air gap is 0) for the CS mode E-KEHs. Therefore, prolonging the contact time (wait time at the contact state) could possibly help to complete the charge-transfer process and improve the output power and efficiency of contact-separation (CS) mode E-KEHs with large load resistances.

In this chapter, at first, the strategy of improving the output power and efficiency of a CS mode TE-KEH by the optimization of the contact time is verified by both experimental and simulation results. The theoretical maximum output energy per working cycle of the TE-KEH is deduced. Then several usually unfavorable factors that would reduce the effective output energy per working cycle of the TE-KEH are discussed. At last, the tribo-charging method and the optimization of the maximum air gap are also used to further improve the output power of the TE-KEH.

Optimization of the contact time

Experimental results

The TE-KEH was made with a 4 cm × 4 cm sized 55 μm-thick PTFE film, with conductive copper tape (3M 1181-50. These experimental results verify that appropriate contact time is beneficial for improving the output power and the mechanic-electric conversion efficiency of the TE-KEH. To further investigate this strategy, corresponding simulations in MATLAB were conducted and discussed in section 4.2.2.

Chapter 4 Optimizing the output power of the contact-separation mode TE-KEH 76

Simulation results

The similar simulation method with that in Chapter 3 was used, except that a finite differential equation solver "ode45" instead of the symbolic differential equation solver "dsolve" was used for a faster calculation speed. The geometric parameter values were set same with the TE-KEH in the experiment, the surface charge density was estimated from the maximum transferred charge amount in Figure 4-4 The simulated z(t) and v(t) curves with different contact times are shown in The simulated maximum AvgP is ~186 μW, which is close to the experimental value of ~197 μW in Figure 4-3(b). However, the optimum contact time of around 0.092s (corresponding to the motion frequency of ~4.75 Hz) is quite different from the experimental result of around 0.052s (corresponding to the motion frequency of ~6.4 Hz). There are several possible causes for this, such as the slight difference between the actual and the simulated motion curves, the influence of the surface morphology of the electret film and the electrodes, the influence of parasitic capacitance. Several of these possible causes will be discussed in section 4.4.1.

The maximum theoretical output energy per working cycle of the TE-KEHs with switch controlling

Parallel-connected switch-controlled working cycles

The output energy of the TE-KEH per working cycle increase with the contact time as shown in Figure 4-9. There must be a limit of the output energy of the TE-KEH with given maximum air gap and surface charge density. To calculate the maximum theoretical output energy per working cycle of the TE-KEHs, Zi et al. [START_REF] Zi | Standards and figure-ofmerits for quantifying the performance of triboelectric nanogenerators[END_REF] proposed the concept of the 'cycles for maximized energy output' (CMEO). They defined the CMEO by four working steps as shown in Figure 4-12, using a lateralsliding (LS) mode TE-KEH (termed as TENG in their article) as an example. The TE-KEH was connected in parallel to a switch. In step 1 of the CMEO, the switch was open-circuited while the relative displacement between the tribo-electret layer and the top electrode increased from 0 to the maximum value of xmax; in step 2, the switch was closed to enable the complete charge-transfer between the two electrodes; then in step 3, the switch was open-circuited again while the relative displacement decreased from xmax to 0; at last in step 4, the switch was closed again to enable the complete chargetransfer in the opposite direction with that in step 2, making the QV curve go back to the beginning state in step 1 and become a closed loop. Chapter 4 Optimizing the output power of the contact-separation mode TE-KEH 81 They declared that the TE-KEH could output the maximum energy per cycle in such a working cycle with load resistors. However, it should be noticed that the load resistance was short-circuited by the closed switch in step 2 and step 4 of the cycle, which means most of the electric energy was not consumed by the load resistance but was dissipated by the switch during these two steps. Therefore, we propose a seriesconnected switch-controlled CMEO, taking a CS mode TE-KEH as an example.

Series-connected switch-controlled working cycles

As illustrated in Figure 4-13, for the series-connected switch-controlled CMEO, the switch is connected in series with the load resistance (here is the oscilloscope with a 100 MΩ probe). The working process also consists of four steps. In step (i), the top electrode fully contacts with the electret film while keeping the switch closed for long enough time to have an initial electric equilibrium state, then the switch is disconnected, and the top electrode moves away from the electret film; in step (ii), the top electrode keeps still after arriving the maximum distance with gap of zmax, then the switch is closed and kept closed for long enough time to complete the charge-transfer (which means the electric equilibrium state is re-established, i.e. VE-KEH = 0) between the top and back electrodes through the load resistance, the TE-KEH outputs a voltage pulse with the peak value of Voc, max during this process; next, in step (iii), the switch is turned off and Chapter 4 Optimizing the output power of the contact-separation mode TE-KEH 82 kept open-circuited, and the top electrode moves towards the electret film; finally in step (iv), the top electrode keeps contact with the electret film, the switch is closed and kept short-circuited for long enough time to complete the charge-transfer, the TE-KEH outputs an opposite voltage pulse with peak value of -V'max and goes back to the initial electric equilibrium state in step (i).

In this series-connected switch-controlled CMEO, the TE-KEH output the same maximum energy per cycle with the same maximum air gap whatever the load resistance is, as illustrated in the minimum value CTE-KEH, min, and the charge-transfer between the two electrodes leads to the decrease of VE-KEH from Voc, max to 0 and the increase of charge amount on the back electrode from 0 to Qmax; in step (iii), the voltage decrease from 0 to -V'max without charge-transfer; finally in step (iv), the top electrode contacts with the electret film and keeps still, the total capacitance of the TE-KEH gets the maximum value CTE-KEH, max which equals the capacitance of the electret film Cf, the charge-transfer between the two electrodes leads to the increase of VE-KEH from -V' max to 0 and the decrease of charge amount on the back electrode from Qmax to 0. This QV cycle is the same with the CMEO with infinite load resistance proposed by Zi et al [START_REF] Zi | Standards and figure-ofmerits for quantifying the performance of triboelectric nanogenerators[END_REF], but it can be reached with any load resistance if the TE-KEH follows the series-connected switch-controlled CMEO, and the electric energy during the charge-transfer process is all consumed by the load resistance. Note that the required time for complete charge-transfers in step (ii) and (iv) is dependent on the time constant of the total circuit which is related to the load resistance.

From Figure 4-14, it is easy to calculate the area of this QV cycle as:

푀 쮀 1 2 푀 ݃ , 푀 푀 (4-1).
Qmax is the maximum transferred charge amount between the two electrodes, which can be calculated by:

푀 쮀 ݎ푀 ( 푀 ) (4-2)
with Qf is the effective surface charge amount on the top side of the electret film, Cf is the capacitance between the top side of the electret film and the back electrode, and Cgap(zmax) is the capacitance between the top electrode and the top side of the electret film when the air gap reaches the maximum value of zmax.

The Voc, max and V' max can be calculated by:

݃ , 푀 쮀 ݎ푀 ( 푀 ) (4-3)
푀 쮀 푀 쮀 ݎ푀 ( 푀 ) (4-4).
Combing equations (4-1) ~(4-4), there is:

푀 쮀 2 ( 2 2 ݎ푀 ( 푀 )) 2 ݎ푀 ( 푀 )( ݎ푀 ( 푀 )) 2 (4-5).
It can be noticed that Wmax is only related to Qf, Cf, and Cgap(zmax). Further, if the fringe and parasitic capacitance are ignorable, and all the components of the TE-KEH are regarded as ideal rigid bodies, with replacing the Qf by the product of the effective surface charge density σ and area S of the electret film, equations (4-2) ~(4-5) can be rewritten as:

푀 쮀 푀 / 푀 (4-6) ݃ , 푀 쮀 푀 (4-7) 푀 쮀 푀 쮀 / / 푀 (4-8) 푀 쮀 2 푀 2 2 ( / 푀 ) (4-9)
Chapter 4 Optimizing the output power of the contact-separation mode TE-KEH 84From equation (4-9), Wmax is proportional to the square of σ, and it is also correlated to S, zmax, and df which are geometric parameters of the TE-KEH, and εr which is a material's property of the electret. This equation provides a general guide on how these parameters influence the theoretical limitation of the output energy of the contact-separation mode TE-KEH in one working cycle, which however can't be used to estimate the output power of the TE-KEH since it doesn't contain the information on the period of such a working cycle.

Several usually unfavorable factors that would reduce the practical output energy per working cycle of the TE-KEH

The microscale incomplete surface contact

In the series-connected switch-controlled CMEO illustrated in Figure 4-13, the step (ii) and (iv) can be regarded as the discharging process of an RC circuit. The voltage across the capacitor varies with time in an exponential during this process, with the time constant that equals the product of the load resistance R and the capacitance C, where C is the CTE-KEH, min in step (ii), and is CTE-KEH, max which equals Cf in step (iv). Therefore, the value of CTE-KEH, min and CTE-KEH, max can be evaluated by fitting the measured output voltage curves of the TE-KEH. However, if using the formula (2-7) for calculating the capacitance of an ideal parallel-plate capacitor, the calculated Cf is ~541 pF, which is more than two times of the fitted CTE-KEH, max result in The copper conductive tape as the back electrode may also have some microbubbles between the adhesive matrix and the copper substrate as shown in Hz is about 2.17 that is in agreement with the reported value of 2.1~2.2 [START_REF] Ebnesajjad | Fluoroplastics, volume 2: Melt processible fluoropolymers-the definitive user's guide and data book[END_REF], while for other samples, measured εr at 1 Hz is between 1.25~1.30 which is quite lower than the reported value.

The lower effective εr value would lead to lower output energy per working cycle of the TE-KEH than the maximum possible value according to the equation [START_REF] Boisseau | Electrostatic conversion for vibration energy harvesting[END_REF][START_REF] Cao | A survey on ambient energy sources and harvesting methods for structural health monitoring applications[END_REF](7)[START_REF] Jordan | Electromagnetic waves and radiating systems[END_REF][START_REF] Brand | Micro energy harvesting[END_REF].

And it may be responsible for that the optimum contact time from simulation results in section 4.

The electric breakdown

The positive output voltage peak curves in step (ii) of the series switchcontrolled CMEO of the same TE-KEH were also fitted to evaluate the CTE-KEH, min, as shown in As can be imagined, the open-circuited pushbutton switch can be regarded as a capacitance before it was fully closed since there was an Chapter 4 Optimizing the output power of the contact-separation mode TE-KEH 88 air gap between the two electrodes of it. When the switch was pushing from the opencircuited state to the short-circuited state, the capacitance formed by the switch increased with the air gap between its two electrodes decreasing, the capacitance of the total circuit also increased since the TE-KEH was connected in series with the switch, and the two electrodes kept holding a high voltage generated by the TE-KEH, then when the air gap between the two electrodes of the switch decreased to a certain value, air breakdown might occur according to the Paschen's law [START_REF] Wang | Maximum surface charge density for triboelectric nanogenerators achieved by ionized-air injection: Methodology and theoretical understanding[END_REF], some chargetransfer between the two electrodes would happen through the conductive path formed by the air gap breakdown though the switch was not fully closed yet, until the voltage was decreased below the threshold value for the electric breakdown, then the second charge-transfer process would occur when the switch was fully closed to complete the charge-transfer between the two electrodes of the TE-KEH. That's why there were two positive voltage peaks in one working cycle of the TE-KEH, and the first positive voltage peak corresponded to a smaller capacitance than the second one.

If the electric breakdown occurred between the top electrode of the TE-KEH with the PTFE surface during their separation process, C1 would be larger than C2 since the CTE-KEH kept decreasing during the separation process. This electric breakdown of the switch would also lead to lower output energy per working cycle of the TE-KEH than the maximum possible value since part of the electric energy was consumed by the air breakdown process.

Besides the electric breakdown of the switch, if the surface charge density of the electret film is too high, air breakdown may also occur between the top electrode and the electret film, which will reduce the effective surface charge density of the electret film and thus reduce the output power of E-KEHs. This may be happed to electrets pre-charged by other charging methods such as ion injections [START_REF] Wang | Maximum surface charge density for triboelectric nanogenerators achieved by ionized-air injection: Methodology and theoretical understanding[END_REF]. For the tribocharging method, the maximum triboelectric charge density of the electret is also limited by the air breakdown effect. The threshold of the air breakdown voltage is related to the air pressure according to the Paschen's law. Therefore, Wang et al. [START_REF] Wang | Achieving ultrahigh triboelectric charge density for efficient energy harvesting[END_REF] greatly improved the effective maximum triboelectric charge density on the electret film of a TE-KEH to remarkable 1003μC/m 2 by placing it in a vacuum chamber with extremely low air pressure which can shift the Paschen's curve and with the help of a doped ferroelectric barium titanate (BT) substrate layer. Quite recently, X. Xia, J.J. Fu, Chapter 4 Optimizing the output power of the contact-separation mode TE-KEH 89 and Y.L. Zi [START_REF] Xia | A universal standardized method for output capability assessment of nanogenerators[END_REF] proposed a method to assess the output capability of TE-KEHs with taking the constrain of the triboelectric charge density by the air breakdown effect.

Though the air breakdown will constrain the triboelectric charge density and output power of TE-KEHs in most cases, on the contrary, it can also be used to improve the triboelectric charge density and output performance of TE-EKHs with the special design. Also quite recently, D. Liu et al. [START_REF] Liu | A constant current triboelectric nanogenerator arising from electrostatic breakdown[END_REF] designed a special electrode structure to take advantage of the air breakdown to attain a quite high triboelectric charge density of 430μC/m 2 on the PTFE film in a TE-KEH and to acquire constant direct current (DC) from the TE-KEH without using rectification and energy storage units, which greatly simplifies the power managements of TE-KEHs.

The parasitic capacitance and the fringe capacitance

The parasitic capacitance means unavoidable and usually undesired capacitance in electric circuits that simply comes from the proximity of different components in the circuits or surrounding objects [163]. For E-KEHs, parasitic capacitance in the electric circuit was usually modeled as a constant capacitor (Cp) connected in parallel with the E-KEHs as introduced in section 2.3.5.3. The Cp would reduce the effective output energy per working cycle of the E-KEHs to the desired electric load, especially with large resistive loads [START_REF] Boisseau | Cantilever-based electret energy harvesters[END_REF][START_REF] Dai | Simulation and structure optimization of triboelectric nanogenerators considering the effects of parasitic capacitance[END_REF], since part of the output current will be shunted to the bypass formed by Cp. [START_REF] Boisseau | Optimization of an electret-based energy harvester[END_REF][START_REF] Boisseau | Cantilever-based electret energy harvesters[END_REF]. The fringe capacitance can be analytically calculated using different models [START_REF] Zi | Standards and figure-ofmerits for quantifying the performance of triboelectric nanogenerators[END_REF][START_REF] Fang | Computation of capacitance and electrostatic forces for the electrostatically driving actuators considering fringe effects[END_REF][START_REF] Shah | Modelling and analysis of fringing and metal thickness effects in mems parallel plate capacitors[END_REF][START_REF] Feng | Improved capacitance model involving fringing effects for electret-based rotational energy harvesting devices[END_REF] or numerically simulated using the finite element method [START_REF] Boisseau | Optimization of an electret-based energy harvester[END_REF][START_REF] Zi | Standards and figure-ofmerits for quantifying the performance of triboelectric nanogenerators[END_REF][START_REF] Boisseau | Cantilever-based electret energy harvesters[END_REF], and its value is positively related to the ratio between the lateral dimension and the plate distance of the parallel-plate capacitor. For miniature E-KEHs with relatively large lateral dimensions and small air gaps, the influence of the fringe capacitance on the output energy of the E-KEHs can be ignorable in most cases in comparison with the impact from the parasitic capacitance.

The ignored parasitic capacitance and fringe capacitance could be one reason that leads to lower output voltage peaks of the TE-KEH form experimental results than those in form experimental results in section 3.4.3.

Other optimizations

Tribo-charging

With the optimum contact time, the output power of the TE-KEH could be further improved by tribo-charging the PTFE film with a higher surface charge density. Since PTFE is the most known tribo-negative material [START_REF] Zhang | Theoretical comparison, equivalent transformation, and conjunction operations of electromagnetic induction generator and triboelectric nanogenerator for harvesting mechanical energy[END_REF], it's facile to tribo-charge it with negative charges by rubbing it with other objects.

Optimization of the maximum air gap

The maximum air gap zmax is another significant parameter that influences the performance of the TE-KEH. electret layer. Thirdly, the influences of the microscale incomplete surface contact, the electric breakdown, the parasitic and the fringe capacitance on the output energy of TE-KEHs were discussed. At last, by the tribo-charging method and the optimization of the maximum air gap, the average output power of the same CS mode parallel-plate TE-KEH made with PTFE film to the load resistance of 100 MΩ was further improved to ~503 μW (corresponding to a power density of ~31.4 μW/cm 2 ), with a ~100 μC/m 2 effective surface charge density on the PTFE film, an optimum maximum air gap of ~0.87 mm, and a driving motion with frequency of ~8.62 Hz.

Chapter 5 Tape-peeling tribo-charged FEP film-based TE-KEHs

Introduction

Higher effective surface charge density on the electret layer can significantly improve the output power of TE-KEHs [START_REF] Boisseau | Electrostatic conversion for vibration energy harvesting[END_REF][START_REF] Xu | Ultrahigh charge density realized by charge pumping at ambient conditions for triboelectric nanogenerators[END_REF][START_REF] Boisseau | Optimization of an electret-based energy harvester[END_REF][START_REF] Wang | Maximum surface charge density for triboelectric nanogenerators achieved by ionized-air injection: Methodology and theoretical understanding[END_REF][START_REF] Li | Significant enhancement of triboelectric charge density by fluorinated surface modification in nanoscale for converting mechanical energy[END_REF]. For most charging techniques, high voltage sources and other assorted apparatuses are usually indispensable [START_REF] Arakawa | Micro seismic power generator using electret polymer film[END_REF][START_REF] Sterken | Harvesting energy from vibrations by a micromachined electret generator[END_REF][START_REF] Suzuki | Development of a high-performance fluorpolymer electret mixed with nano-particles and its application to vibration energy harvesting[END_REF][START_REF] Xiao | A flexible electret membrane with persistent electrostatic effect and resistance to harsh environment for energy harvesting[END_REF][START_REF] Chen | A micro-oscillation-driven energy harvester based on a flexible bipolar electret membrane with high output power[END_REF][START_REF] Zhang | Audio and ultrasonic responses of laminated fluoroethylenepropylene and porous polytetrafluoroethylene films with different charge distributions[END_REF]. Triboelectrification, which is the charge-transfer phenomenon between two surfaces or fluid/solid interfaces after contact and separation [START_REF] Baytekin | The mosaic of surface charge in contact electrification[END_REF][START_REF] Li | A nanowire based triboelectric nanogenerator for harvesting water wave energy and its applications[END_REF][START_REF] Budakian | Picosecond discharges and stick-slip friction at a moving meniscus of mercury on glass[END_REF], can be used as a facile method to charge dielectrics to get electrets without any equipment [START_REF] Sessler | Electrets[END_REF][START_REF] Wei | Surface-charge engineering for highperformance triboelectric nanogenerator based on identical electrification materials[END_REF]. Nevertheless, the triboelectric charge density cannot be directly controlled or varied without changing the materials employed [START_REF] Wang | Maximum surface charge density for triboelectric nanogenerators achieved by ionized-air injection: Methodology and theoretical understanding[END_REF].

In this chapter, a novel facile tape-peeling tribo-charging method is used to charge the fluorinated ethylene propylene (FEP) film. Firstly, the surface potential of the FEP film and corresponding output voltage and current of TE-KEHs made with the FEP film after different counts of tape-peeling treatment are measured. Secondly, the surface potential mapping technique is used to analyze the impact of the tapepeeling treatment on the potential distribution of the FEP film. At last, harvesting kinetic energy from wind and human motions with a prototype of this type of TE-KEH is demonstrated, with an apparent ~692% improvement in the output power by the tape-peeling charging method.

Material properties

Fluorinated ethylene propylene (FEP) is a copolymer of hexafluoropropylene and tetrafluoroethylene. It is the first thermoplastic processing fluoropolymer (due to its low viscosity in comparison with previous fluoropolymers) invented in 1960, with excellent chemical inertness, thermostability, a melting temperature of around 260~275°C, a low dielectric constant (εr=2.1 at 23 ℃, 10 2 ~10 6 Hz) and dielectric loss (0.00006~0.0005 at 23 ℃, 10 2 ~10 6 Hz), extremely low conductivity (~10 -22 Ω -1 cm -1 ), and high dielectric strength (~19.7 kV/mm) [START_REF] Sessler | Electrets[END_REF][START_REF] Ebnesajjad | Fluoroplastics, volume 2: Melt processible fluoropolymers-the definitive user's guide and data book[END_REF]. The FEP film used in our Figure 5-2 shows the chemical formula of FEP. As an all fluorinated polymer, its molecular link is full of the most electronegative functional group -F [START_REF] Wang | Maximum surface charge density for triboelectric nanogenerators achieved by ionized-air injection: Methodology and theoretical understanding[END_REF], which makes it one of the most triboelectrically negative materials in the triboelectric series [START_REF] Zi | Standards and figure-ofmerits for quantifying the performance of triboelectric nanogenerators[END_REF]. This excellent electronegative property together with its outstanding insulating property makes it a good candidate for tribo-charged electrets. The infrared transmission spectrum of the FEP film was measured by a Fouriertransform infrared spectroscopy (FT-IR) spectrometer (type Perkin Elmer Spectrum Two with a Universal Attenuated Total Reflection (type UATR Two) accessory), with a resolution of 4 cm -1 . Before the FT-IR test, the FEP film was cleaned by deionized water and ethanol successively using an ultrasonic cleaner. Measured FT-IR spectrum is shown in Figure 5-3. the absorption band peaked at the wavenumber (1/wavelength) of 1202 cm -1 and 1147 cm -1 can be assigned to the CF2 stretching vibrations, peaked at 982 cm -1 to the CF3 stretching vibration, peaked at 638 cm -1 to the C-C-F bending vibration, and peaked at 554 cm -1 and 509 cm -1 to the CF2 bending vibration [START_REF] Jung | Validation of ATR FT-IR to identify polymers of plastic marine debris, including those ingested by marine organisms[END_REF][START_REF] Kostromina | X-ray study of structural parameters of some tetrafluoroethylene copolymers[END_REF]. The FT-IR spectrum of the FEP film is in good accordance with its chemical structure.

Methods

Structure and test set-up of the energy harvester

The FEP film-based TE-KEH consists of two parts: one is a piece of FEP film with one side metalized, the other is a metal electrode. To fabricate the TE-KEH, a piece of rectangular FEP film with a size of ~4 × 4 cm 2 was cleaned by deionized water and ethanol using an ultrasonic cleaner at first. Then silver paint was coated on one side of the cleaned and dried FEP film as a back electrode, with margins of ~2 mm in each edge of the film to prevent possible short circuit with the other metal electrode (a piece of aluminum foil with the same size of the FEP film). A copper wire was fixed to the back electrode as a conductive export wire.

The processed FEP film was attached to the sliding block of the linear motor by double-sided adhesive tapes, and the Al foil was attached to a fixed plate faced with the FEP film. All the test set-up on the linear motor system is the same as in section 3.4.1.

Tape-peeling charging process

The FEP film was innovatively charged by an adhesive tape-peeling triboelectrification method.

Results and discussion

Improving the performance of the TE-KEH by the tape-peeling charging method

The improvement in the output voltage and current of the TE-KEH by this tapepeeling charging method for the FEP film is presented in The recorded current waveform was not so regular as the voltage. This is because the external circuit resistance was negligible during the current measurement, resulting in a quite transient charge-transfer process between the two electrodes.

Meanwhile, the data sampling rate of the electrometer system we used (Keithley 6514 with IEEE 488 cable) is not high enough (the shortest time interval between two data points is ~18ms). Therefore, only one data point could be acquired in one current peak as shown in Figure 5-7(a), which is far from enough to record the full waveform of current peaks. While the oscilloscope for the voltage measurement has a much higher data sampling rate (the time interval between two data points in the was set as 0.2ms), which is enough to record the shape of the full voltage waveform as shown in meaning that the FEP film originally has negative charges which may be obtained during its fabrication and processing. With increasing tape-peeling treatment count from 0 to 5, the surface potential maintained negative with the absolute value Chapter 5 Tape-peeling tribo-charged FEP film-based TE-KEHs 102 gradually increasing, meaning that more negative charges were obtained by the FEP film. However, in the fifth treatment, it took three tape-peeling processes to have such an apparent increase in the surface potential, and after the sixth treatment, the absolute surface potential value even decreases a little. Additionally, the surface potential of the FEP film almost kept unchanged before and after the linear motor test with the treatment count from 0 to 4, revealing the temporal stability of negative charges on the FEP film. While with the treatment count of 5 and 6, the surface potential shows a more apparent decrease after the linear motor test. Possible micro-scale air breakdown [START_REF] Sessler | Electrets[END_REF] may be responsible for the decrease of surface potential after the sixth treatment. The short-circuit transferred charge amount measured by the Keithley 6514 electrometer from another TE-KEH made with a ~4 cm × 4 cm sized FEP film was shown in Figure 56789. In these measurements, the minimum and maximum air gap, the moving speed and acceleration/deceleration were kept the same as listed in Table 5-1, but the wait time at both limit positions was set as ~2s. The transferred charge amount between the two electrodes of the TE-KEH was increased with the tapepeeling treatment count. After three times of tape-peeling treatment, the transferred charge amount in each half working cycle of the TE-KEH was increased from ~19nC to ~53nC, corresponding to an improvement of ~180%. The stability of the charge- The output voltage of this TE-KEH was also increased with the tape-peeling charging count correspondingly as shown in Figure 56789). For these measurements, the maximum air gap was set as ~20 mm, and the wait time was set as ~0.22s, with other movement parameters unchanged as listed in Table 5-1. The period of such a motion cycle was ~0.65s. After three times of tape-peeling treatment, the positive voltage peak value was increased from about 69 V to about 159 V, and the negative one was increased from about -120 V to about -365 V. The stability of the output voltage of the TE-KEH after the third tape-peelings was then verified in a relatively long-time test. In this test, the maximum air gap was set as ~5 mm, and the wait time was set as ~0.22s, with other movement parameters unchanged, corresponding to a reciprocating movement frequency of ~2 Hz. Like the transferred charge amount, the output voltage of the TE-KEH also kept stable peak values as shown in Figure 56789.

Surface potential mapping

To further investigate the tape-peeling tribo-charging effect, the surface potential mapping technique was used. To get a surface potential mapping, the probe of a noncontacting Trek 341B electrostatic voltmeter was fixed on a pneumatic displacement system as shown in It can be noticed that the general shape of the potential distribution after the test is similar to that before the test, but the general color tone of the map has a slight shift to the more negative direction. Next, the FEP film was tribo-charged by 5 tapepeeling treatments, then its surface potential distribution was mapped again as presented in These surface potential mapping results confirm that the tape-peeling tribocharging is an effective method to charge the FEP film with negative charges to get higher output voltage from the FEP film-based TE-KEH. The contact electrification Chapter 5 Tape-peeling tribo-charged FEP film-based TE-KEHs 107 between the FEP film and Al foil could also charge the FEP film with negative charges, but the tape-peeling method has a greater influence on the surface potential distribution of the FEP film, which may be due to that the adhesive tape has better microscale contact with the FEP film than the Al foil.

Demonstration of harvesting energy from wind and human motions

To be more practical, the TE-KEH should be able to harvest energy from motions in the environment. Since the 100 μm-thick FEP film is very flexible, it can be driven by the wind to flutter, making the FEP film-based TE-KEH be able to generate electricity from the wind. To fabricate the wind-driven TE-KEH, one side of the FEP film was metalized with silver paint, also with margins of ~2 mm in each edge, an Al foil was pasted on an acrylic plate, and then the FEP film was fixed upon the Al foil at one corner by a metal clamp, with non-metalized side faced with the Al foil. The FEP film contacted with the Al foil except that there was a slit of ~3mm between the FEP film and the Al From (I) to (IV), the output voltage showed a gradually increasing trend. The surface potential of the FEP film before each test from (I) to (IV) was measured and presented in Figure 5-13(c), which also had an increasing trend. These results reveal that the charge amount on the FEP surface can be improved not only by the tape-peeling treatment but also by the triboelectrification between the FEP film and the Al foil during the wind blowing process. the two charging curves of the 10 μF Cs during the 30s working processes of the wind-driven TE-KEH between test (I) and (V), and between test (III) and (IV) are presented. Before the tape-peeling treatment, the Cs was charged from 0V to a voltage of ~3.9 V in 30 s ((II) to (II)), corresponding to an average charging power of ~2.5 μW; after the FEP film was treated by the tape-peeling process, the Cs was charged Chapter 5 Tape-peeling tribo-charged FEP film-based TE-KEHs 109 from 0V to 10.9 V in 30 s ((III) to (IV)), corresponding to an ~692% improvement in the average charging power to ~19.8 μW, which is enough to drive a sensor unit or other low power dissipation electronics [START_REF] Mitcheson | Energy harvesting from human and machine motion for wireless electronic devices[END_REF][START_REF] Byun | Potential role of motion for enhancing maximum output energy of triboelectric nanogenerator[END_REF]. It is worthy to be noted that these average charging powers are calculated based on the energy stored in Cs. The highimpedance probe of the oscilloscope and the rectifier bridge also consume some power, so the actual average output power of the TE-KEH should higher than these Cs charging powers.

The energy loss during the rectification might be caused by the reverse current leakage of the diodes in the rectifier bridge. Sinusoidal voltage waves from a signal generator before and after rectification by the rectifier bridge is given in

Chapter conclusion

In this chapter, the chemical formula of the FEP film was confirmed by the FT-IR spectrum. An adhesive tape-peeling tribo-charging method was used to charge the FEP electret film used for TE-KEHs. The composition of the adhesive on the tape was identified to be butyl polyacrylate by the Raman spectrum analysis.

The surface potential of a ~4 × 4 cm 2 FEP film was improved from about -360V to about -2850V after several tape-peeling treatments. The positive out voltage peak of the TE-KEH comprised of the FEP film was correspondingly improved from 41 V to 195 V, negative peak improved from -83 V to -363 V, positive peak current density improved from 1.5 mA/m 2 to 7.3 mA/m 2 , and negative peak current density improved from -1.3 mA/m 2 to -5.3 mA/m 2 , in tests with the relative mechanical motion of the TE-KEH controlled by a linear motor system. The transferred charge amount of a TE-KEH made with another ~4 × 4 cm 2 FEP film were also apparently improved from ~19nC to ~53nC after several tape-peeling treatments, with corresponding positive voltage peak value increased from about 69 V to about 159 V, and the negative voltage peak value increased from about -120 V to about -365 V. The surface potential mapping of the FEP film confirmed that tape-peeling tribo-charging method could effectively charge the FEP film with negative charges, and it had more apparent influence on the surface potential distribution of the FEP film than the triboelectrification between the FEP film and Al foil during the linear motor test.

Moreover, a TE-KEH made with an 8 × 8 cm 2 FEP film was driven by the wind from a hairdryer with a wind speed of ~18m/s to charge a 10μF capacitor for energy harvesting and storage demonstration. Before the tape-peeling treatment, the winddriven TE-KEH can charge the 10μF capacitor from 0 to 3.9 V in 30 s, corresponding to an average charging power of ~2.5μW; after the tape-peeling treatment, the same capacitor was charged by the TE-KEH from 0V to 10.9 V in 30 s, corresponding to an ~692% improvement in the average charging power to ~19.8μW. In addition, when the FEP film was slightly waved by hand, the TE-KEH was able to light up 42 LEDs. These demonstrations revealed potential applications of this miniature TE-KEH Secondly, the optimization of the contact time to improve the output power and efficiency of a CS mode TE-KEH with large resistive load was proved to be effective with both experimental and simulation results, the maximum theoretical output energy per working cycle of the TE-KEH with resistive loads was deduced from a seriesconnected switch-controlled working cycle, and the tribo-charging method and the optimization of the maximum air gap were also used to improve the output power of the TE-KEH. With these optimizations, the average output power of the CS mode TE-KEH made with a 4 cm × 4 cm sized 55 μm-thick PTFE film to the load resistance of 100 MΩ was improved from ~150 μW to ~503 μW, under a driving motion with frequency of ~8.62 Hz and with a maximum air gap of ~0.87 mm.

Thirdly, via a novel tape-peeling tribo-charging method, the output voltage and current of 4 cm × 4 cm sized TE-KEH made with 100 μm-thick FEP film was apparently increased, and the average output power of a wind-driven flexible TE-KEH prototype made with 8 cm × 8 cm sized and 100 μm-thick FEP film to charge a 10μF capacitor was improved from ~2.5 μW to ~19.8 μW. The capability of this TE-KEH prototype to harvest energy from low-frequency human motions was also demonstrated.

It is noteworthy though all these results are based on the CS mode TE-KEHs, they are also applicable to other types of E-KEHs with variable capacitance structures since they have the same basic working principle as will be discussed in section 6.2.1.

Chapter 6 General conclusions and perspectives 114 6.2 Remarks and perspectives

Remarks on simulations and power managements of E-KEHs

The effectiveness of the contact time optimization strategy to optimize the output power of the gap-varying E-KEHs with large load resistances had been demonstrated.

In practice, there are several methods to implement this strategy, such as put the top electrode or the electret film with the back electrode on soft substrate, or use deformable low-modulus electret materials, which could prolong the effective contact time by the deformation of the substrate or electret film at the contact state. This strategy could also be applicable to other types of E-KEHs when the total electrical circuit has a relatively large time constant in comparison with the cycle period of the driving motions. However, the limitation of this strategy is that the output power of the E-KEHs is calculated by Joule's law applying to pure resistive loads. The power consumed by resistive loads can only be converted into heat, which is not practical in many applications.

For E-KEHs with complex load circuits, the analytical modeling and simulations could be complicated. Graphical modeling tools for electrical circuits, such as the SPICE and Simulink, would be very helpful to simulate the output of E-KEHs with complex load circuits and to design the power management unit for E-KEHs. A mechanic-electric coupling Simulink model for an undirect vibration-driven E-KEH with a cantilever structure had been developed by S. Boisseau, G. Despesse, and A. Sylvestre, as introduced in section 2.3.5.2. For direct motion-driven E-KEHs, modeling and simulations based on SPICE software had been demonstrated by Niu et al. [START_REF] Niu | Simulation method for optimizing the performance of an integrated triboelectric nanogenerator energy harvesting system[END_REF] and R. Hinchet et al. [START_REF] Hinchet | Understanding and modeling of triboelectric-electret nanogenerator[END_REF]. More broadly speaking, the utilization of SPICE software and Simulink for simulations of microelectromechanical systems was demonstrated by Gary Keith Fedder in 1994 [START_REF] Fedder | Simulation of microelectromechanical systems[END_REF] based on the lumped-parameter modeling, as introduced in section 2.3.5.3. Therefore, besides the analytical modeling in this thesis, a Simulink model for the direct motion-driven E-KEH was also established as shown in Figure 6-1, with a series-connected LRC load in the circuit, which however will not be discussed in detail in this thesis. If the information for all these three aspects is totally known, the simulation of E-KEHs would become just the electrical circuit simulation problem whatever the structure of the E-KEH is.

The time-varying capacitance can be recorded with an LCR meter with enough sampling speed or measured with a two-channel voltage recorder together with an alternative current (AC) voltage source with enough frequency range in comparison with the expected driving motion frequency [START_REF] Hinchet | Understanding and modeling of triboelectric-electret nanogenerator[END_REF][START_REF] Lu | A batch-fabricated electret-biased wideband mems vibration energy harvester with frequency-up conversion behavior powering a uhf wireless sensor node[END_REF][START_REF] Lu | A flexible electrostatic kinetic energy harvester based on electret films of electrospun nanofibers[END_REF].

The effective surface charge density or surface potential of the electret film can be measured by the method we used (termed as the dynamic capacitor method [START_REF] Sessler | Electrets[END_REF]), or by other methods such as the dissectible capacitor method, the capacitive probe method, the compensation method, the thermal-pulse method, and the polarization and depolarization current method. These methods were reviewed in the book Electrets by G. M. Sessler et al [START_REF] Sessler | Electrets[END_REF]. Nowadays, the most widely used surface potential measurement method is the compensation method with the help of commercialized electrostatic voltmeters [START_REF] Hinchet | Understanding and modeling of triboelectric-electret nanogenerator[END_REF][START_REF] Vu-Cong | Electrets substituting external bias voltage in dielectric elastomer generators: Application to human motion[END_REF][START_REF] Zhou | Multilayered electret films based triboelectric nanogenerator[END_REF].

The configuration of the load circuit depends on the specific application scenario of E-KEHs. Not only the power-consuming circuit but also the circuit of possible power management unit for E-KEHs in practical applications should be taken into consideration. The configuration of the load circuit has a significant influence on the effective output power of E-KEHs, that's why power management units to modulate Chapter 6 General conclusions and perspectives 116 the output characteristics of E-KEHs are important and sometimes necessary. Typical power management units for E-KEHs include full-wave [START_REF] Xu | Coupled triboelectric nanogenerator networks for efficient water wave energy harvesting[END_REF][START_REF] Niu | Simulation method for optimizing the performance of an integrated triboelectric nanogenerator energy harvesting system[END_REF][START_REF] Niu | Optimization of triboelectric nanogenerator charging systems for efficient energy harvesting and storage[END_REF][START_REF] Niu | A universal self-charging system driven by random biomechanical energy for sustainable operation of mobile electronics[END_REF][START_REF] Jin | Self-powered wireless smart sensor based on maglev porous nanogenerator for train monitoring system[END_REF] or halfwave [START_REF] Ghaffarinejad | Superior performance of half-wave to full-wave rectifier as a power conditioning circuit for triboelectric nanogenerators: Application to contact-separation and sliding mode teng[END_REF][START_REF] Ghaffarinejad | A conditioning circuit with exponential enhancement of output energy for triboelectric nanogenerator[END_REF] rectifying circuits with energy storage or buffer capacitors and with possible transformer [START_REF] Cheng | High efficiency power management and charge boosting strategy for a triboelectric nanogenerator[END_REF] or voltage comparator [START_REF] Xi | Universal power management strategy for triboelectric nanogenerator[END_REF], charge pump or voltage multiplier or bennet's doubler circuits [START_REF] Jean-Mistral | On the power management and electret hybridization of dielectric elastomer generators[END_REF][START_REF] Ghaffarinejad | A conditioning circuit with exponential enhancement of output energy for triboelectric nanogenerator[END_REF] as introduced in section 1.2.3, and integrated commercial power management circuits [START_REF] Ahmed | Integrated triboelectric nanogenerators in the era of the internet of things[END_REF][START_REF] Chen | A novel triboelectric nanogenerator based on electrospun polyvinylidene fluoride nanofibers for effective acoustic energy harvesting and self-powered multifunctional sensing[END_REF].

Future work

E-KEHs are quite application-specific devices. In practical energy harvesting cases, E-KEHs should be designed according to the driving motion characteristics including the motion amplitude and frequency distribution, the circuit characteristics including the power demand of the electric load, and other specific considerations such as the cost, the eco-friendly, the fabrication technique, the matching power management circuit, and the expected service life-time, as illustrated in Figure 6-2.

Though the basic working principle of E-KEHs is easy to understand, and prototypes of E-KEHs are facile to fabricate and investigate in labs, the successful design, fabrication, and widespread applications of E-KEHs need cooperation of experts from multiple disciplines [START_REF] Li | Standardization of triboelectric nanogenerators: Progress and perspectives[END_REF][START_REF] Ahmed | Environmental life cycle assessment and techno-economic analysis of triboelectric nanogenerators[END_REF]. In the future, with specifying the application scenario, the following works related to this thesis could be interesting to construct systems powered by E-KEHs with high efficiencies:

1. Data acquisition and analysis of the motion/vibration amplitude and frequency spectra in the aimed application environment of the E-KEHspowered systems.

Figure 1 -

 1 1 shows the comparison of advantages and disadvantages in using batteries and energy harvesters (EHs) in such systems.

Figure 1 - 1

 11 Figure 1-1 Comparison between the battery and energy harvesters in powering IoT or WSN node and implantable devices.

Figure 1 - 2 (

 12 b), with a flat peak-to-peak open-circuit voltage around 2.4 V in the excitation frequency range of 14~25 Hz. Besides these two designs, Zhu et al. proposed a method of tuning the electrical resonant frequency of the EM-KEH with loading

Figure 1 - 2

 12 Figure 1-2 Diverse miniature EM-KEHs. (a) An arrayed multiple cantilever EM-KEH with its frequency response shown in (b) [12]. (c) An EM-KEH with the inside free-moving ball for energy harvesting from low-frequency vibrations [13]. (d) A spherical EM-KEH with inside free-rolling magnet ball for harvesting energy from irregular human motions [14]. (e) A resonant EM-KEH with 6 degree-of-freedom for harvesting energy from vibrations of multiple directions [15].

Figure 1 - 3 (

 13 a). Liu et al. [20] designed a PZT-based EH with two cantilever structures with different resonant frequencies to broaden the operation frequency range and increases the output voltage and power, as shown in Figure 1-3(b). Wurtzite aluminum nitride (AlN) is another usually used piezoelectric ceramic. Self-powered wireless sensor models based on MEMS AlN

Figure 1 -

 1 Figure 1-3(c).

Figure 1 - 3

 13 Figure 1-3 Diverse miniature PE-KEHs. (a) A piezoelectric EH mounted in a shoe to harvest energy from human walking [19]. (a) A piezoelectric EH based on two cantilever structures with different resonant frequencies. [20] (c) An AlNbased EH model for self-powered wireless sensors [16]. (d) The piezoelectric effect on a single ZnO nanowire [21]. (e) A self-powered wireless sensor system based on ZnO nanowire arrays [22]. (f) Near-filed electrospinning PVDF nanowires with intrinsic high piezoelectric coefficients [23].

Figure 1 - 4 (

 14 Figure 1-4(b), the capacitor is firstly pre-charged to a constant voltage value when C is at the maximum value (o→a), then discharge occurs with C decreasing and the voltage keeps constant (a→b), finally C goes back to the maximum value to start the next cycle.

Figure 1 - 4

 14 Figure 1-4 Illustrations of (a) the constant charge and (b) the constant voltage working modes of a variable capacitor electrostatic EH with corresponding QV diagrams, reproduced from [25].

8 [ 27 ]

 827 QV diagram can be modulated by external conditioning circuits. To implement the constant voltage or charge mode in an ES-KEH, at least two synchronized switches with the switching on-off period same with the variation period of C are necessary Chapter 1 General background and introduction . There are other shapes of the QV cycle of ES-KEHs that can be implemented by simpler conditioning circuits. As illustrated in Figure 1-5(a), besides the triangle QV cycle shapes for the constant-charge (trace OCB) and constant-voltage (trace OAB), other common shapes of QV cycle of ES-KEH includes the rectangle (trace DFBE)

Figure 1 - 5 (

 15 b) illustrated successive QV cycles from the first triangle shape to a series of trapezoidal shapes, which can be obtained from an ES-KEH with a pre-charged large reservoir capacitor as the voltage source and with an idealized pre-charged charge pump circuit[START_REF] Galayko | Capacitive energy conversion with circuits implementing a rectangular charge-voltage cycle-part 1: Analysis of the electrical domain[END_REF].

Figure 1 - 5 (

 15 Figure 1-5 (a) Common shapes of the QV cycle of ES-KEHs. (b) Illustration of successive QV cycles from an ES-KEH with an idealized pre-charged charge pump circuit. [27]

Figure 1 - 6 (

 16 a). The micro interdigit variable capacitance structure of another micro ES-KEH with an overall size of 1 cm × 1.5 cm × 200 µm by Bogdan Vysotskyi et al. [39] is presented in Figure 1-6(a).

Figure 1 - 6 (

 16 Figure 1-6 (a) A batch-fabricated micro ES-KEH [38]. (b) Photograph of a micro ES-KEH showing the micro comb variable capacitance structure [39]. (c) Scheme of an ES-KEH using dielectric elastomer [40]. (d) A circuit provides an initial charge to the variable capacitor in an ES-KEH [41]. (e) A dielectric elastomer ES-KEH using electret as the biasing voltage source [42].

  ES-KEHs using electrets, especially the tribo-charging electrets (tribo-electrets), are the research objects of this thesis. The motivations include understanding the basic working principle of electret-KEHs (E-KEHs) by analytical modeling and numerical simulations, optimizing the output power of tribo-electret KEHs (TE-KEHs) based on the simulation results and experiments, and developing a facile and effective tribocharging method to charge the electrets.The general outline of this thesis is as follows. In Chapter 1, the general background and brief introductions and comparisons of three common types of KEHs have been presented. In Chapter 2, physical fundamentals and charging methods for electrets are briefly introduced, and an introduction to the basic principle, early researches, structure designs, and the physical models of E-KEHs is given. In Chapter 3, the analytical solution of a detailed equivalent circuit model for contactseparation (CS) mode E-KEHs is given, then the amplitude-variable output characteristics of a CS mode E-KEH during transitory working cycles with different load resistances and initial conditions are studied, the reason for these characteristics are analyzed based on both simulation and experimental results. In Chapter 4, several optimization methods are used to improve the output power of a CS mode TE-KEH, Chapter 1 General background and introduction 11 the maximum theoretical output energy or the TE-KEH is deduced, and several usually unfavorable factors that would reduce the effective output energy per working cycle of TE-KEHs are discussed. In Chapter 5, a novel tape-peeling tribo-charging method is used to charge FEP electret films, the output voltage and current of TE-KEHs based on the FEP films are apparently improved by the tribo-charging method, and the prototype of a flexible FEP-film based TE-KEH is demonstrated to harvest energy from wind and gentle human motions. In Chapter 6, remarks on simulations and power managements of E-KEHs are given, and perspectives on future work related to this thesis are presented.

Figure 2

 2

Figure 2 - 1

 21 Figure 2-1 Different types of electrical charges in electrets.

Figure 2 - 2

 22 Figure 2-2 The cross-section view of the general arrangement of a piece of electret with two dielectric gaps and two nearby metal electrodes analyzed by G. M. Sessler [46].

Figure 2 - 3

 23 Figure 2-3 An electron-cloud-potential-well model proposed for explaining the contact electrification [53].

Figure 2 - 4

 24 Figure 2-4 Schematic of the electrostatic induction effect on isolated conductive objects [57].

Figure 2 - 5

 25 Figure 2-5 Schematic diagram for the basic working principle of an E-KEH.

Figure 2 - 6

 26 Figure 2-6 Cutaway drawing of a typical foil-electret microphone (top), the photograph of a commercial foil-electret microphone (bottom left), and corresponding schematic circuit diagram (bottom right) [58].

Figure 2 -

 2 Figure 2-7 (a) A perspective view of the respiration monitoring apparatus positioned relative to a patient in bed with a force transducer. (b) A perspective view of the force transducer. (c) A cross-section view of an alternate embodiment of an electret force transducer. (d) An electrical schematic diagram showing a circuit with an amplifier unit for the force transducer to energize both a visual and an audible alarm to indicate cessation of respiration of the patient. Reproduced from the referenced patent [62].

Figure 2 - 8 .

 28 In this EG, the charge-transfer between the two pairs of conducting half-disks was caused by the variation of the induced charge displacement on the two pairs of electrodes during the rotation of the two oppositely charged electrets disks, not by the variation of the capacitance. As marked by the red dashed oval in Figure 2-8(b), the left conducting half-disk on one side of the EG was electrically connected with the right conducting half-disk on the other side to form an electrode, and other two conducting half-disks were electrically connected to form the other electrode of the EG.

Figure 2 -

 2 Figure 2-8 (a) The photograph and (b) the exploded view of the electret generator with two oppositely charged electret plates and the half-disk structure proposed by Oleg D. Jefimenko and David K. Walker [63].

Figure 2 - 9

 29 Figure 2-9 Illustration of the parallel-plate configuration of an E-KEH.

Figure 2 -

 2 Figure 2-10(b). Otherwise, the two electrodes can be both fixed with the electret component, and a third conductive electrode (metal rotor) can do relative movement to change the overlap area of the third electrode with one fixed electrode in comparison with the other one, as shown in top of Figure 2-10(c), or the two electrodes are fixed but the electret component is movable to change the overlap area of the electret with one fixed electrode in comparison with the other one, as shown in bottom of Figure 2-10(c).

Figure 2 -

 2 Figure 2-10 Different types of variable capacitance E-KEHs with representative material and structure designs. (a) Relative rotation design from [64]. (b) Relative sliding design from [67]. (c) Relative sliding design from [68]. (d) Gapvarying design from [69]. (e) Gap-varying design from [70]. (f) Cellular electret design from [71]. (g) The design with movable solid dielectrics from [69]. (h) The design with movable liquid dielectrics from [72].

Figure 2 -

 2 Figure 2-10(h). Like the design in Figure 2-10(c), the variable permittivity design could also have both fixed electrodes. Since the electrodes of E-KEH need to output electricity to external circuit load, these designs with fixed both electrodes can greatly simplify the electric connection to external circuit load and reduce the damage risks to the electrodes and electric connectors, which is significant for developing E-KEHs with long life-times.

Figure 2 -

 2 11(a).

Figure 2 -

 2 Figure 2-11 Illustrations of (a) the analogy between the microscopic dipole moment in ferroelectrics (left) and the macroscopic dipole moment (right) in ferro-electrets, and (b) the ferroelectric-like characteristics of ferro-electrets obtained via the micro-plasma discharge inside the cavities, from [75].

Figure 2 -

 2 10(e) but also other types of structure designs were used in TE-KEHs for different working modes as illustrated in Figure 2-12. Among these diverse designs, the free-standing relative sliding modes in Figure 2-12(c) and (i), and the free-standing gap-varying modes in Figure 2-12(e) have fixed both electrodes, and the electret is free-standing and movable.

Figure 2 -

 2 Figure 2-12 Basic structure designs and working modes of TE-KEHs. On the left: illustrations of TE-KEHs with (a) the gap-varying, (b) the relative sliding, (c) the freestanding relative sliding, (d) the single-electrode gap-varying, and (e) the freestanding gap-varying designs, with virtual capacitances illustrated, from [91]. On the right, illustrations of TE-KEHs working under the (f) vertical contactseparation mode, (g) in-plane sliding mode, (h) single-electrode mode, and (i)

Figure 2 -

 2 12(h) andFigure 2-13(a), they were regarded as single-

Figure 2 -

 2 13(b) and (c), or fiber-shaped that can be woven into cloth to harvest human body motion energy [103] as shown in Figure 2-13(d).

Figure 2 -

 2 13(e), cylindrical[START_REF] Bai | Cylindrical rotating triboelectric nanogenerator[END_REF] as shown in Figure2-13(f), tubular[108][START_REF] Pan | Liquid-fep-based u-tube triboelectric nanogenerator for harvesting 126 water-wave energy[END_REF][START_REF] Su | Triboelectric sensor for self-powered tracking of object motion inside tubing[END_REF] as shown in Figure2-13(g), polyhedral[START_REF] Zhang | Multilayer wavy-structured robust triboelectric nanogenerator for harvesting water wave energy[END_REF] or spherical[START_REF] Wang | Triboelectric nanogenerator based on fully enclosed rolling spherical structure for harvesting low-frequency water wave energy[END_REF][START_REF] Xu | Coupled triboelectric nanogenerator networks for efficient water wave energy harvesting[END_REF] as shown in Figure2-13(h). Moreover, to get more power from environmental kinetic energy sources, the integration of multiple TE-KEHs is important, which could be distributed[START_REF] Xu | Coupled triboelectric nanogenerator networks for efficient water wave energy harvesting[END_REF][START_REF] Chen | Networks of triboelectric nanogenerators for harvesting water wave energy: A potential approach toward blue energy[END_REF][START_REF] Wang | Toward the blue energy dream by triboelectric nanogenerator networks[END_REF][START_REF] Li | Networks of high performance triboelectric nanogenerators based on liquid-solid interface contact electrification for harvesting low-frequency blue energy[END_REF][START_REF] Wang | Catch wave power in floating nets[END_REF] as shown in Figure2-13(i), or stacked in multi-layer[START_REF] Seol | Vertically stacked thin triboelectric nanogenerator for wind energy harvesting[END_REF][START_REF] Du | A three dimensional multi-layered sliding triboelectric nanogenerator[END_REF][START_REF] Bai | Integrated multilayered triboelectric nanogenerator for harvesting biomechanical energy from human motions[END_REF] as shown in Figure2-13(j).

Figure 2 -

 2 Figure 2-13 Diverse structure and integration designs of TE-KEHs. (a) Sliding mode single-electrode structure [93]. (b) With flexible electret film for harvesting wind energy by fluttering [98]. (c) With shape-adaptive electret film [101]. (d) With electret fibers that can be woven [103]. (e) Arch-shaped TE-EKH [106]. (f) Cylindrical TE-EKH [107]. (g) Tubular TE-KEH [110]. (h) Spherical TE-KEH

Figure 2 -Figure 2 -

 22 Figure 2-14 (a) A U-tube shaped TE-KEH filled with liquid dielectrics [109]. (b) A TE-KEH with liquid metal as an electrode [120]. (c) A TE-KEH using the electret of mesoporous PDMS film impregnated with gold nanoparticles [121].

  different structures, E-KEHs can be driven by external kinetic sources by basically two different modes, one is the direct motion-driven mode which means the motion of the movable component of the E-KEH is directly determined by the motion Chapter 2 Introduction to electrets and electret kinetic energy harvesters 29 of the external kinetic source, while the other one is the undirect vibration-driven mode which means the motion of the movable component of the E-KEHs is determined by both the motion of the external kinetic source and the mechanical properties of the E-KEH itself.

Figure 2 -

 2 Figure 2-15 Different driven modes of E-KEHs. (a) An E-KEH with the entire structure driven by water wave motion [115]. (b) A wind-driven E-KEH with a rotating part and a stator part [130]. (c) The scheme of a KEH with a mechanical resonator structure for transferring energy from the vibration source to the electromechanical transducer [74]. (d) A micro vibration-driven E-KEH with the mechanical resonator structure, using the variable overlap area and electrode distance combined design [131]. (e) A micro vibration-driven E-KEH with the mechanical resonator structure, using the gap-varying design [132].

Figure 2 -

 2 15(a), external water can be part of the E-KEH as movable dielectrics (on the left), or a direct motion source to shake the E-KEH and lead to the waggle of the inner liquid dielectrics, and the electrostatic force is considered to have no effect on the water flow. This buoy-like E-KEH can be entirely placed on the sea to harvest kinetic energy from waves. While for most of the direct motion-driven E-KEHs, there are at least two solid components with one fixed and the other one movable. For instance, in a wind-driven rotary E-KEH[START_REF] Xie | Rotary triboelectric nanogenerator based on a hybridized mechanism for harvesting wind energy[END_REF] shown in Figure2-15(b), there are aluminum sheets as stator electrodes and one side metalized PTFE electret film on a rotary shaft driven by the wind as the rotor blade. A small part of the kinetic energy from wind can be converted to electricity via the wind-driven relative movement between the stator and the rotor of the E-KEH.For vibration-driven E-KEHs that usually contain a mechanical resonator structure modeled by a spring-mass-damper system as shown in Figure 2-15(c), the external excitation force act on the variable capacitor through the resonator structure, and the transduction force is considered to act as a damper in the resonator model. Vibration-driven E-KEHs can be entirely attached to the vibration source, and the relative movement between different parts of the electromechanical transduction unit was provided by the resonator structure excited by the vibration source. The variable capacitance design in vibration-driven E-KEHs can be a combined design of variable overlap area and variable electrode distance as shown in Figure 2-15(d), can also be a gap-varying design as shown in Figure 2-15(e).

Figure 2 -

 2 Figure 2-16 Parallel-plate configurations of E-KEHs.

Figure 2 - 17 .Figure 2 -

 2172 Figure 2-17 The compact equivalent electrical model of an E-KEH with a timevarying total capacitance.

Figure 2 -Figure 2 - 18 .

 2218 Figure 2-18 Schematic diagram of the micro-electric generator with a seismic mass, from [142].

Figure 2 -

 2 19(a), based on a microstructured E-KEH proposed by Yoshihiko Sakane, et al. [148], and a cantilever-based E-KEH [146] fabricated by themselves. The active energy transduction component of the cantilever-based E-KEH is a oneside metalized electret film facing a counter electrode as shown in Figure 2-19(b). In their experiments, the electret film is a piece of corona-charged Teflon FEP film with the rear side evaporated with a layer of alumina as the electrode, and the counter electrode is a silicon cantilever with a mass on the free end as shown in Figure 2-19(c). An equivalent electric circuit was used analyze the electric output of the E-KEH as shown in Figure 2-19(d), in which the charged electret film was regarded as a constant voltage source V and the total capacitance between the two electrodes was considered as a time-varying capacitor C(t).

Figure 2 -

 2 Figure 2-19 The complete electromechanical model for the undirect vibration driven cantilever-based E-KEH, from [146]. (a) The mass-spring-damper mechanical model concerning both the undesired mechanical friction force fmec and the transduction electrostatic force felec. (b) The cross-section scheme of the energy conversion component and (c) the entire structure of the cantilever-based E-KEH. (d) The equivalent circuit model of the E-KEH.

Figure 2 -Figure 2 -

 22 Figure 2-19(d), there is:

Figure 2 -

 2 Figure 2-20 The equivalent circuit model of the E-KEH taking the effect of the parasitic capacitance into consideration [146].

Chapter 2

 2 Introduction to electrets and electret kinetic energy harvesters 40 (LCR) circuit, as illustrated in Figure 2-21, and he also gave the time-varying capacitor model in SPICE software as shown in Figure 2-22.

Figure 2 -

 2 Figure 2-21 Electrical analogy to a mechanical system [149]. (a) A mechanical mass-spring-damper system. (b) The equivalent LCR circuit.

Figure 2 -

 2 Figure 2-22 The time-varying capacitor model in SPICE [149]. (a) Circuit instance. (b) Sub-circuit.

Figure 2 -

 2 Figure 2-23 Equivalent electrical representation of the mechanical domain of the vibration energy harvester [152].

  summary, E-KEHs are quite application-specific power sources. Many different structure designs for E-KEHs are introduced in this chapter, most of them are based on the variable capacitance principle. The variable capacitance of E-KEHs can be the total or partial capacitances of the E-KEHs. Driving modes of E-KEHs are divided into two categories: the direct motion-driven mode and the undirect vibrationdriven mode. Several different analytical models to analyze the output of E-KEHs are also introduced.

Figure 3 -

 3 Figure 3-1 (a) The schematic of the CS mode E-KEH. (b) The cross-section structure of the E-KEH. (b) The detailed equivalent electrical model of the E-KEH.

Figure 3 -

 3 Figure 3-1(c) shows the detailed equivalent electrical model of the E-KEH, where Cgap (t) represents the variable capacitance formed by the air gap between the top electrode and the top surface of the electret film, which is variable with the variation of z(t), Cf represents the capacitance between the back electrode and the top surface of the electret film. The value of Cf and Cgap (t) ignoring the fringe capacitance can be calculated by:

( 2 - 14 )

 214 based on the compact equivalent electrical model with the help of the equations (2-8) ~(2-10) and the following substitution:

  according to the equations (3-1) ~(3-3), the open-circuit voltage of the CS mode E-KEH is:

Figure 3 -

 3 Figure 3-2 (a) Simulated z(t), v(t), and (b) CE-KEH(t), in the case z(0) = 0.

Figure 3 -

 3 2(a) shows the simulated z(t) and v(t) during one movement cycle, with the period (T) of 0.022s.

Figure 3 -

 3 Figure 3-2(b) shows the corresponding CE-KEH(t) calculated by the equation (3-8) during three motion cycles.

  -3 shows corresponding simulated charge-transfer processes between the two electrodes of the E-KEH in the first three motion cycles with load resistances of 1 MΩ, 100 MΩ, and 1 GΩ respectively. Many information can be obtained from this figure.

Chapter 3 51 Figure 3 - 3

 35133 Figure 3-3 Charge-transfer processes of the E-KEH simulated with the load resistances of (a) 1 MΩ, (b) 100 MΩ, and (c) 1 GΩ, using z(0)=0 and Q(0)=0, in the first three motion cycles.

Figure 3 - 3 (

 33 a), Ipp1 is ~36 μA, while the first negative current peak (Inp1) is ~-18.6 μA, and the second positive current peak (Ipp2) is ~24.5 μA. This can be explained by the characteristics of the charging and discharging processes of the RC series circuit. For an RC series circuit, the charge or Chapter 3 Amplitude-variable output characteristics of a contact-separation mode E-KEH during multiple transitory working cycles 52 discharge time of the capacitor depends on the time constant (τ=R×C) of the circuit.With a larger τ, the charge or discharge takes a longer time. For instance, in Figure3-3(b), at t=0, Q(t), Qeq(t), and |∆Q| (the difference between Q(t) and Qeq(t)) are 0, the CE-KEH value is at the maximum value Cmax. Then CE-KEH decreases but is still high, the z(t)-dependent Qeq(t) increases fast but the Q(t) increases slower because of large τ with high CE-KEH, making |∆Q| increase. With CE-KEH further decreasing, τ decreases a lot so that the charge can transfer faster, and |∆Q| is gradually reduced to 0 at the time marked by the first vertical dash-dot line. After that, both Qeq(t) and Q(t) decrease but CE-KEH increases dramatically, resulting in an increasing τ and |∆Q|. When a whole motion cycle ends, Qeq(t) decreases to 0 but Q(t) is still much larger than 0. Then Qeq(t) starts to increase again in the second movement cycle, τ starts to decrease, meanwhile Q(t) keeps decreasing until the moment that |∆Q| becomes 0 again as marked by the second vertical dash-dot line. Then the second charge-transfer cycle begins. The charge-transfer cycle (including an entire positive and an entire negative current peaks) falls behind the movement cycle, resulting in that transferred charge amount in the first positive current peak (Qtrp1) is larger than that in the first negative current peak (Qtrn1) and in following current peaks (Qtrp2, Qtrn2, Qtrp3…), making the first current peak higher than the others. In Fig.2(b), Ipp1 is ~4.8 μA, Inp1 is ~-0.35 μA, and Ipp2 is ~0.77 μA. At last, in Figure 3-3(a), the positive current peaks have a larger amplitude of ~24.5 μA than that of negative peaks of 18.6 μA in latter charge-transfer cycles even with the same transferred charge amount (Qtrp2 = Qtrn2 = Qtrp3 =…). And in Figure 3-3(b) and (c), not only the amplitude and the transferred charge amount Qtrp of the positive current peaks (Ipp) are apparently larger than those of the negative ones (Inp and Qtrn), but also the time duration of the positive current peak (tdpp) is apparently longer than the negative one (tdnp) in each charge-transfer cycle. Though the movement profile is symmetric in both approaching and separating directions. Moreover, it can be noticed from Figure 3-3(b) and (c) that Ipp and tdpp gradually decrease from the first to the third charge-transfer cycle, meanwhile the amplitude of Inp and tdnp gradually increase. This asymmetric output characteristic of the E-KEH is also attributed to the lag between the charge-transfer cycle and the movement cycle.

Figure 3 - 4

 34 Figure 3-4 Output characteristics of the E-KEH simulated with the different load resistances during the first 10 motion cycles, using the initial condition z(0)=0 and Q(0)=0. (a) Time-dependent Q(t), (b) I(t), and (c) VE-KEH(t) of the E-KEH. (d) The variation in the amplitude of Q(t), the inset shows the variation in transferred charge amounts in two directions (Qtrp and Qtrn). (e) Positive (Vpp) and (f) negative (Vnp) output voltage peak values with fitted curves.

Figure 3 -

 3 Figure 3-4(a)~(c) shows the simulated Qeq(t), Q(t), Ieq(t), I(t), and VE-KEH(t) of the E-KEH with different load resistances in the first 10 motion cycles, and with the first initial condition i.e. z(0)=0 and Q(0)=0.

  ). With the resistance of 1 MΩ, 10 MΩ, and 100 MΩ, the positive voltage peak value (Vpp) and the negative voltage peak value (Vnp) vary to steady ranges in three cycles. With the resistance of 1 GΩ and 10 GΩ, Vpp shows an apparent decreasing trend during all the ten cycles. All positive (Vpp) and negative (Vnp) output voltage peak values with resistances of 100 MΩ, 1 GΩ, and 10 GΩ from the first the tenth cycles are plotted in Figure 3-4(e) and (f) respectively. Vpp and Vnp values vary with time perfectly in accordance with the following equation: ( ) 쮀 ܿ 푀 ( ( )/ ) (3-23), where t0 is the time when the first corresponding voltage peak value (Vpp1 for Vpp values, and Vnp1 for Vnp values) appears, τd is a fitting parameter with the same unit of time, Vs and Va are two other fitting parameters with the same unit of voltage. These parameter values are given inTable 3-2.

2 ,

 2 Vpp and Vnp values in 6 seconds were fitted and shown in Figure 3-5(a). Though the first Vpp and Vnp values with 100 MΩ, 1 GΩ, and 10 GΩ are so different as shown in Figure 3-4(e) and (f), after 6 seconds, their difference becomes very small since the Vs values with 100 MΩ, 1 GΩ, and 10 GΩ are very close, as given in Table 3-2. The parameter Va determines the difference between the Vpp1 or Vnp1 and the corresponding Vs, which reveals the rangeability of Vpp or Vnp. In Table 3-2, Va is larger with larger resistance for both Vpp and Vnp, meaning that the rangeability of Vpp or Vnp is larger with larger Resistance as can be seen from Figure 3-5 (a).

Figure 3 -

 3 Figure 3-5 (a) Fitted variation trend of Vpp and Vnp in 6s. (b) Vpp1 and Vpp10 values with different load resistances. (c) Vnp1 and Vnp10 values with different load resistances.

Figure 3 -

 3 Figure 3-5 (b) and (c). Both Vpp1 and Vpp10 increase with R and saturate at a value of ~1130 V when R is high enough, while the absolute values of Vnp1, and Vnp10 increase with R from 1 MΩ to 100 MΩ and then decrease with increasing R.

Figure 3 - 6 ( 56 Figure 3 - 6

 365636 Figure 3-6(a) shows the simulated instantaneous output power P(t) of the E-KEH with different load resistances in the first 10 motion cycles.

Figure 3 - 6 (

 36 b) that presents the accumulated output energy W(t) of the E-KEH to different load resistance based on the following equation:

Figure 3 -

 3 Figure 3-7 (a) Average output power per motion cycle (AvgP) of the E-KEH. (b) The first P(t) peak value, and the AvgP in the first and tenth motion cycles of the E-KEH with different load resistances.

1 .

 1 The z(t) and v(t) profiles are shifted half period from the case z(0) = 0, as plotted in Figure3-8.

Figure 3 - 8 58 Figure 3 - 9 3 - 3 .

 38583933 Figure 3-8 Simulated z(t) and v(t) curves in the first motion cycle with z(0) = zmax.

Figure 3 - 9 ( 3 - 3 .

 3933 Figure 3-9(b) and (c), the amplitude of Inp is higher than that of Ipp, but their difference is also smaller than that in Figure 3-3(b) and (c). This is also due to variations of CE-KEH and |∆Q|. For instance, in Figure 3-9(b), in the time duration of the first negative current peak (tdnp1), both the maximum |∆Q| and CE-KEH are much larger than those in the time duration of the first positive current peak (tdpp1). So even though the transferred charge amount in the time duration of tdnp1 is larger, it takes a

Figure 3 -

 3 Figure 3-10(a)~(c) shows the simulated Q(t), I(t) and VE-KEH(t) of the E-KEH with different load resistances in the first 10 motion cycles using the second initial condition. Variations in the amplitude of Q(t) and I(t) with large R are not easy to observe in Figure 3-10(a) and (b), but the variation in the amplitude of VE-KEH(t) can be clearly noticed in Figure 3-10(c). In comparison with Figure 3-4(c), it's similar that the amplitude of VE-KEH(t) varies at first and then goes to near-stable ranges in three cycles with R of 1 MΩ, 10 MΩ, and 100 MΩ, and it keeps varying even after ten cycles with larger R of 1 GΩ and 10 GΩ.

Figure 3 -

 3 Figure 3-10 Simulated output characteristics of the E-KEH with different load resistances during the first 10 motion cycles, using the second initial condition (z(0) = zmax and Q(0) = Qmax). (a) Q(t), (b) I(t), and (c) VE-KEH(t) of the E-KEH with different load resistances.

Figure 3 -

 3 10(c) are smaller than those in Figure 3-4(c) with the same R. And the time constant τd values in Table 3-4 are almost the same with those corresponding inTable 3-2.

Figure 3 -

 3 Figure 3-11 (a) VE-KEH(t) of the E-KEH with the load resistance of 1GΩ during 25 motion cycles, with the variation trend of the amplitude of VE-KEH(t) marked by fitting curves. (e) Positive (Vpp) and (f) negative (Vnp) voltage peak values of the E-KEH with different load resistances in the first and tenth motion cycles and their final steady-state values.

Figure 3 - 4 .

 34 Figure 3-11(a) shows VE-KEH(t) in the first 25 motion cycles of the E-KEH with R of 1 GΩ as an example. The amplitude of positive voltage peaks shows an apparent increasing trend and then approaches a steady value, while the amplitude of negative voltage peaks slightly decreases and then approaches to a steady value. And the variation of VE-KEH(t) is limited between the fitting lines for Vpp and Vnp using the values of parameters given inTable 3-4.

Figure 3 -

 3 Figure 3-12 Simulated output power and accumulated output energy of the E-KEH with different load resistances during the first 10 motion cycles, using the second initial condition. (a) Instantaneous output power (P(t)), (b) the accumulated output energy (W(t)), and (c) average output power per motion cycle (AvgP(c)) of the E-KEH. (d) The first P(t) peak value, and the AvgP of the E-KEH in the first and tenth motion cycles with different load resistances.

Figure 3 - 3 - 6 and

 336 Figure 3-12(a)~(c) presents the output power, accumulated output energy, and average power per motion cycle of the E-KEH in the first 10 motion cycles, using the second initial condition. The influences of R on the output power and average power is shown in Figure 3-12(d). In all motion cycles, smaller R leads to both higher peak power and average power, which is quite different from the result shown in Figure 3-6 and Figure 3-7. The peak values of the P(t) and the AvgP in the first motion cycle with different R are lower than those in Figure 3-7(b). More similarities and differences in the simulated output energy and power of the E-KEH from these two initial conditions are discussed in section 3.3.5.

Figure 3 -

 3 Figure 3-13 QV diagrams of the E-KEH simulated with (a) the first initial condition (z(0)=0 and Q(0)=0) and (b) the second initial condition (z(0)= zmax and Q(0)=Qmax), with different load resistances. (c) The influence of the load resistance on the output average power per motion cycle of the E-KEH simulated with the second initial condition.

Figure 3 -

 3 Figure 3-13(a) and (b) show the QV diagrams of the E-KEH during no less than 10 motion cycles simulated with the first and the second initial conditions respectively. In Figure 3-13(a), with relatively small R as 1 MΩ, 10 MΩ, and 100 MΩ, the QV curve shows a large span arc-shaped line in the first charge-transfer cycle and then becomes a closed-loop after less than 3 motion cycles, while for the results with large R as 1 GΩ, and 10 GΩ, the QV curve keeps unclosed with a damped variation trend in simulated 30 motion cycles. In Figure 3-13(b), with R of 1 MΩ, 10 MΩ, and 100 MΩ, there is no arch-shaped line and the QV line becomes a closed teardrop-shaped loop after less than 3 motion cycles, which is typical for E-KEH with the continuous conditioning circuit [27, 35], while with larger R as 1 GΩ, and 10 GΩ, the QV line keeps unclosed with a growing variation trend in simulated 25 motion cycles. The area of the closed QV cycle with R of 1 MΩ in Figure 3-13(b) is the largest as ~0.99 μJ per cycle, which is also in accordance with Figure 3-12(b)~(d). To get the more accurate optimum load resistance (Ropt) for the E-KEH to output the maximum steady AvgP, the AvgP in the third motion cycle of the E-KEH with R from 0.5 MΩ to 2 MΩ were calculated with the second initial condition and shown in Figure 3-13(c). The AvgP increases and then decreases with increasing R and gets the maximum value of ~45.27 μW with R of 1.2 MΩ among all the calculated data.

Chapter 3 63 Figure 3 -

 3633 Figure 3-14 Simulated QV diagrams of the E-KEH with the first and second initial conditions, with load resistances of (a) 1 MΩ, (b) 100 MΩ, and (c) 1 GΩ, respectively. (d) The overlapped QV cycle with 1 GΩ load resistance at the 100 th working cycle of the E-KEH that starts working from the first (from 0) and the second (from zmax) initial conditions respectively.

Figure 3 -

 3 14(a) and (b) present the results of the first 10 motion cycles from the first initial condition (from 0) and from the second initial condition (from zmax). The QV cycles from the two different initial conditions become overlapped after the first cycle with R of 1 MΩ, and it takes about three cycles for those with R of 100 MΩ to become fully overlapped. In Figure 3-14(c) with the data of the first 100 motion cycles from the first and second initial conditions.

Figure 3 -

 3 14(d) clearly shows that the 100 th QV cycles of the E-KEH with R of 1 GΩ starting from these two initial conditions overlap with each other.

Figure 3 -

 3 Figure 3-15 (a) Overlapped QV cycles of the E-KEH starts working from z(0)=zmax and from z(0)=zmax/2, with R of 1 MΩ and Q(0)=Qeq(0). (b) z(t) and v(t) profiles using the initial condition z(0)=zmax/2, and v(0)=v1.

Figure 3 -

 3 Figure 3-16 (a) Photograph of the PTFE film-based TE-KEH mounted on the sliding rail of the linear motor. (b) Photograph of the linear motor system together with electrical measuring equipment.

1 .

 1 However, the recorded values of these parameters by the software were different from set values.

Figure 3 -

 3 17(a) and (b) show z(t) and v(t) data recorded by the control software of the linear motor. These differences may be caused by the uncontrollable impact or vibrations, or the neglected deformations of the components and substrates of the TE-KEH during movements of the sliding block in such a short distance and with high acceleration/deceleration. Chapter 3 Amplitude-variable output characteristics of a contact-separation mode E-KEH during multiple transitory working cycles 66

Figure 3 -

 3 Figure 3-17 (a) z(t) and (b) v(t) data recorded by the linear motor system during the measurement of the TE-KEH starts working from z(0)=zmax and z(0)=0 respectively.

Figure 3 -

 3 Figure 3-17(a) and (b), the actual zmax was estimated at 0.7 mm, v1 and v2 were estimated at 0.14 m/s and -0.17 m/s respectively. The acceleration and deceleration of the slider block were estimated according to the linear fitting results of the v(t) data as shown in Figure 3-18 and Figure 3-19.

Figure 3 - 67 Figure 3 -

 3673 Figure 3-18 Recorded v(t) data with linear fitting for (a) a1, (b) a2, (c) a3, and (d) a4 with the motion starting from the fully-separated position.

Figure 3 -

 3 Figure 3-20 The measured short-circuit transferred charge amount data of the TE-KEH that starts working from the two different positions.

Figure 3

 3

Figure 3 -

 3 Figure 3-21 (a) Simulated z(t), v(t), and (b) CTE-KEH (t) curves using parameter values in Table 3-6 and the initial condition that z(0)=0 and Q(0)=0. (c) Simulated z(t), v(t), and (d) CTE-KEH (t) data using parameter values listed in Table4and the initial condition z(0)= zmax.

Figure 3 -

 3 22(a)~(c). And the simulated output voltages of the TE-KEH with corresponding load resistances are presented in Figure 3-22(d)~(f). With R of 10 MΩ, both the simulated and measured output voltages have no apparent variation in the peak amplitude for both initial conditions. With R of 100 MΩ, the first positive voltage peak (Vpp1) of both the simulated and measured data using the first initial condition (z(0) = 0) has a much larger amplitude than other voltage peaks. And with R of 1.1 GΩ, apparent variations in the amplitude of voltage peaks appear both in the experimental and simulated data during several motion cycles, especially for the result using the first initial condition, and then the amplitude of voltage peaks becomes almost the same for both initial conditions. These results confirm the presence of variations in the amplitude of output voltages of the TE-KEH with large load resistances and reveal the influence of the initial condition and the load resistance on the amplitude-variable output voltage of the TE-KEH.

Figure 3 -

 3 Figure 3-22 (a), (b), and (c) Measured output voltage of the TE-KEH with load resistances of 10 MΩ, 100 MΩ, and 1.1 GΩ respectively. (d), (e), and (f) Simulated output voltage of the TE-KEH with load resistances of 10 MΩ, 100 MΩ, and 1.1 GΩ respectively.

  8) as the back electrode and aluminum foil as the top electrode. The structure of the TE-KEH and the measurement equipment are the same as those introduced in section 3.4.1. The output voltages of a TE-KEH driven by periodical linear motions with the same maximum air gap, same motion velocity, and same acceleration/deceleration profiles but different contact times were measured. All measurements were started from the contact state (z(0)=0), and the top Chapter 4 Optimizing the output power of the contact-separation mode TE-KEH 73 and back electrodes were short-circuited before each measurement to ensure the initial electrostatic equilibrium. The recorded time-dependent air gap z(t) and relative motion velocity v(t) between the top electrode and the PTFE film are shown in Figure 4-1. The maximum air gap zmax is ~1.82 mm, the maximum movement velocity is about ±0.064 m/s, the acceleration/deceleration are listed in Table 4-1. With different contact times, the shape of the z(t) and v(t) profiles almost kept unchanged, excluding possible influences of zmax and the maximum velocity and acceleration/deceleration on the output of power of the TE-KEH.

Figure 4 - 1

 41 Figure 4-1 The time-dependent (a) air gap and (b) motion velocity profiles with different contact times, recorded by the linear motor system in experiments.

Figure 4 - 2

 42 Figure 4-2 The output voltages of the TE-KEH with the contact time of (a) 12 ms; (b) 17 ms; (c) 22 ms; (d) 32 ms; (e) 42 ms; (f) 52 ms; (g) 62 ms; (h) 72 ms; and (i) 112 ms, respectively.

Figure 4 -

 4 Figure 4-3 (a) The instantaneous output power and (b) the average output power of the TE-KEH with different contact times which also led to different driving motion frequencies.

Figure 4 - 4

 44 Figure 4-4 The transferred charge amount of the TE-KEH (a) before and (b) after all the output voltage measurements.

4 - 1 .

 41 , and the driving motion parameter values (zmax, v1, v2, a1, a2, a3, and a4) were estimated from recorded data in Figure All parameter values used in the simulations are listed inTable 4-1.

Figure 4 - 5 .

 45 Figure 4-5. The corresponding Q(t), VE-KEH(t), P(t), and QV curves of the TE-KEH are shown in Figure 4-6, Figure 4-7, Figure 4-8, and Figure 4-9, respectively.

Figure 4 - 5

 45 Figure 4-5 Simulated (a) z(t) and (b) v(t) curves with different contact times, using parameter values inTable 4-1.

Figure 4 - 6

 46 Figure 4-6 Simulated Q(t) curves of the TE-KEH with different contact time.

Figure 4 -

 4 Figure 4-7 Simulated VE-KEH(t) curves of the TE-KEH with different contact time.

Figure 4 - 8

 48 Figure 4-8 Simulated P(t) curves with different contact time.

Figure 4 - 9 Figure 4 -

 494 Figure 4-9 Simulated QV curves of the TE-KEH with different contact times.

Figure 4 -

 4 Figure 4-10 The average output power per motion cycle of the TE-KEH from the first to the fifth cycle.

Figure 4 -

 4 Figure 4-11 to clearly show the influence of the contact time on AvgP of the TE-KEH. Like the experimental results presented in Figure 4-3, the AvgP first increases and then decreases with the contact time.

Figure 4 -

 4 Figure 4-11 Simulated average output power (AvgP) of the TE-KEH in the fifth working cycle with different contact times.

Figure 4 -

 4 Figure 4-12 The CMEO of a lateral sliding mode TE-KEH defined by Zi et al. [91]. (a) Schematic diagram of the LS-mode TE-KEH with the displacement x=0 and x=xmax. (b) QV curve of the TE-KEH during the CMEO with the load resistance R=100MΩ.

Figure 4 -

 4 Figure 4-13 Illustration of four working steps of the series-connected switchcontrolled CMEO of a CS mode TE-KEH.

Figure 4

 4

Figure 4 -

 4 Figure 4-14 The maximum possible QV cycle of the TE-KEH.

A

  pushbutton switch was used to implement the switch-controlled CMEO working cycle on the same TE-KEH made with the 4 cm × 4 cm sized 55 μm-thick PTFE film. Three fitted discharging voltage curves in the step (iv) of the CMEO cycle are given in Figure 4-15. The experimental data were measured with the oscilloscope using a probe with 10 MΩ input impedance. From the fitted results, CTE-KEH, max is around 246 pF.

Figure 4 -

 4 Figure 4-15 Three fitted output voltage curves of the TE-KEH at the contact state.

Figure 4 - 15 .

 415 If taking the fringe or parasitic capacitance into consideration, the calculated Cf would be larger. Therefore, this difference between the calculated Cf and the fitted CTE-KEH, max must come from other reasons. The microscale surface morphologies of the electrodes and the electret film were considered. By using the scanning electron microscope (SEM, JEOL JSM-6010PLUS/LV), the microscale surface morphologies of the top electrode (Al foil) and the PTFE film were observed and presented in Figure 4-16. There are apparent micro scratches on both of Al foil and the skived PTFE film, which might be formed during their fabrication processes.

Figure 4 -

 4 Figure 4-16 SEM images of the Al foil and the PTFE film.

Figure 4

 4 Figure 4-17.

Figure 4 -

 4 Figure 4-17 SEM images of the adhesive side of the copper tape.

Figure 4 -

 4 Figure 4-18 (a) The schematic showing how the micro scratch and bubble introduced micro air gap capacitors influence the CTE-KEH, max. (b) Frequencydependent dielectric constant spectra of the PTFE film with different electrodes.

Figure 4 -

 4 Figure 4-18(b). All the sample is 1 cm × 1 cm sized 55 μm-thick PTFE film. Double Au film means that both faces of the sample were deposited with a thin layer of gold films by plasma sputtering, double Al foil means that both faces of the sample were attached with Al foil, double Cu tape means that both faces of the sample were attached with the adhesive copper tapes, and one-Al-one-Cu tape means that one face of the sample was attached with the copper tape and the other one with Al foil which is the same with the TE-KEH structure. For the sample with sputtered Au films which could have good contact with the PTFE film, the measured dielectric constant εr at 1

  2.2 is about 1.77 times of the optimum contact time from experimental Chapter 4 Optimizing the output power of the contact-separation mode TE-KEH 87 results in section 4.2.1, since the εr of the PTFE film measured with good surface contact (double Au film) is about 1.67~1.73 times of the effective εr value of the PTFE film with incomplete surface contact. It may also be one reason that leads to lower output voltage peak values of the TE-KEH form experimental results than those in form experimental results in section 3.4.3.

Figure 4 -

 4 19(a)~(c).There were two positive voltage peaks correspond to one negative voltage peak, which implied the occurrence of an electric breakdown in the circuit.

Figure 4 -

 4 Figure 4-19 (a), (b), and (c) are three fitted output voltage curves of the TE-KEH at the separation state. (d) The illustration shows the electric breakdown that happens at the open-circuited switch.

Figure 4 -

 4 Figure 4-20 Illustration of curved electric field lines around the plate edges of a parallel-plate capacitance [165].

Figure 4 - 21 shows

 421 the transferred charge amount, output voltage, and output power of the TE-KEH before and after tribo-charging the PTFE film by rubbing its surface with a nitrile glove.

Figure 4 -

 4 Figure 4-21 Improved (a) transferred charge amount, (b) output voltage and (c) output power of the TE-KEH by tribo-charging the PTFE film. (d) The timedependent air gap profiles recorded by the linear motor system.

Figure 4 -

 4 Figure 4-22 (a) The output power of the TE-KEH in 20 seconds, before and after tribo-charging. (b) The accumulated output energy of the TE-KEH in ~10 seconds, which clearly shows the improvement of the average output power of the TE-KEH by tribo-charging.

Figure 4 -

 4 Figure 4-22(a) shows the instantaneous output power of the TE-KEH in 20 seconds. By integrating the instantaneous output power with time, the accumulated output energy and average output power (AvgP) of the TE-KEH were obtained and shown in Figure 4-22(b). The AvgP of the TE-KEH in the first 10 seconds of measurements was improved from ~224 μW (power density of ~14 μW/cm 2 ) before the tribo-charging to ~405 μW (power density of ~25.3 μW/cm 2 ) after the tribocharging.

Figure 4 -

 4 23(a) shows z(t) profiles recorded by the linear motor systems when testing the TE-KEH with different zmax values, using the same optimized contact time of ~52ms, and other movement parameters (peak motion velocity, acceleration/deceleration) were set the same in the linear motor control Chapter 4 Optimizing the output power of the contact-separation mode TE-KEH 92 system. Corresponding output voltage and output power of the TE-KEH are plotted in

Figure 4 -

 4 Figure 4-23(b) and (c). With the zmax of 1.87 mm, 1.37mm, and 0.87 mm, the peak output voltage and power values were close to each other, while with the zmax of 0.3mm, the peak output voltage and power values were apparently lower than others.

Figure 4 -

 4 Figure 4-23 (a) z-t profiles with different zmax values, and corresponding (b) output voltage and (c) power of the TE-KEH measured with the oscilloscope using a 100 MΩ probe.

Figure 4 -

 4 Figure 4-24 (a) The accumulated output energy of the TE-KEH in the first 10 seconds with zmax. (b) The average output power of the TE-KEH in ~10 seconds and the corresponding mechanical motion frequency with different zmax. (c) The recorded v(t) curves with different zmax. (d) The experimental and theoretical dependence of the maximum transferred charge amount Qmax on zmax.

Chapter 5

 5 Tape-peeling tribo-charged FEP film-based TE-KEHs 97 experiments is 100 μm-thick NEOFLON FEP film produced by Daikin ® and bought from Suzhou Guanghui Technology Co. Ltd. It is a flexible and highly transparent film as shown in Figure 5-1.

Figure 5 - 1

 51 Figure 5-1 Photograph of a piece of the 100 μm-thick FEP film, with outlines marked by the dash red lines.

Figure 5 - 2

 52 Figure 5-2 The chemical formula of FEP.

Figure 5 - 3

 53 Figure 5-3 The infrared transmission spectrum of the FEP film.

Figure 5 - 4

 54 illustrates the process of this method. Briefly, one piece of adhesive tape (Lyreco, polypropylene substrate with an acrylic adhesive) was firstly pasted on the naked side of the processed FEP film, then triboelectrification occurs when the tape was peeled off, making the FEP film negatively charged, and the acrylic adhesive on the sticky side of tape positively charged. The contact between the adhesive and the FEP film could be tight due to the strong van der Waals interaction[181,[START_REF] Gay | Theory of tackiness[END_REF], and this triboelectrification can change the surface charge density of the FEP film obviously.

Figure 5 - 4

 54 Figure 5-4 The schematic of charging the FEP film with tape.

Figure 5 - 5

 55 Figure 5-5 The Raman spectrum of the adhesive measured from the tape we used (black line), and the Raman spectrum of the butyl polyacrylate in the database provided by the Bio-Rad Laboratories, Inc (red line). Inset is the chemical constitution of the butyl polyacrylate.

Figure 5 - 6 . 5 - 1 .Table 5 - 1

 565151 All the resultswere measured with the minimum air gap set as 0 (which means a direct contact) and the maximum air gap set as ~20 mm, the maximum moving speed of the sliding block set as ±0.2 m/s and the acceleration/deceleration set as ±10 m/s 2 in both backward and Chapter 5 Tape-peeling tribo-charged FEP film-based TE-KEHs 100 forward directions. And in each motion cycle, the wait time of the sliding block at the contact position (the contact time) and at the maximum air gap position were both set as ~0.1s for complete charge-transfer. These motion parameters are listed in Table The period of such a motion cycle is ~0.45s, corresponding to a frequency of ~2.2 Hz. Linear motor motion parameters for measuring the output of the FEP film-based TE-KEH Parameter Value Minimum air gap Maximum air gap Maximum moving speed Acceleration and deceleration at both directions Wait time at the two limiting positions 0 ~20 mm ±0.2 m/s ±10 m/s 2 ~0.1s With increasing tape-peeling treatment count from 0 to 5, the output voltage of the TE-KEH gradually increased and then decreased a little after the sixth treatment as shown in Figure 5-6(a). The short-circuit current density (the current divided by the area of the FEP film) had the same trend as shown in Figure 5-6(b).

Figure 5 - 6

 56 Figure 5-6 Increasing (a) output voltages and (b) current densities of the TE-KEH with the FEP film treated by the tape with increasing counts (from left to right: 0~5 counts). (b) Increasing current densities of the TE-KEH with increasing the treatment count.

Figure 5 -

 5 7(b). Nevertheless, a general variation trend of the current density with the treatment count can still be clearly noticed in Figure 5-6(b). It is noteworthy that for the treatment count from 1 to 4, each treatment count is corresponding to one tapepealing process, while for the fifth and sixth treatments, three tape-peeling processes were performed to have an observable increase in the surface potential of the FEP film which is monitored with a USSVM2 surface voltmeter (a type of electric field meter, bought from the ALPHALAB Inc. in the U.S.A.) as shown in Figure 5-8(a).

Figure 5 -

 5 Figure 5-7 (a) Recorded data points in one positive and one negative shortcircuit current peaks. (b) Recorded data points in one positive and one negative voltage peaks.

Figure 5 -

 5 Figure 5-8 (a) Photograph of the surface voltmeter with the probe fixed. (b) The increasing surface potential of the FEP film with tape-peeling treatment counts, before and after the linear motor test. (c) Statistic results of the positive and negative output voltage peak values of the TE-KEH. (d) Statistic results of the positive and negative short-circuit current density peak values of the TE-KEH.

Figure 5 -

 5 Figure 5-9 (a) Increasing short-circuit transferred charge amount of the TE-KEH by the tape-peeling charging method. (b) The stability of the transferred charge amount of the TE-KEH. (c) Increasing the output voltage of the TE-KEH by the tape-peeling charging method. and output voltage (d) The stability of output voltage of the TE-KEH.

Chapter 5

 5 Tape-peeling tribo-charged FEP film-based TE-KEHs 104 transfer amount of the TE-KEH after the third tape-peelings was verified in a relatively long-time test. In this test, the maximum air gap was set as ~2 mm, and the wait time was set as ~0.42s to shorten the period of one motion cycle for measuring more working cycles of the TE-KEH during the test, with other movement parameters unchanged. The period of such a motion cycle was ~0.94s. In more than 1140s, the transferred charge amount had no obvious change as shown in Figure 5-9(b), revealing the stability of the tape-peeling introduced electrostatic charges on the FEP electret film.

Figure 5 -

 5 10, the FEP film was placed on a sample plate beneath the probe. The probe scanned the area of the FEP film by the stepping movement of the probe and the sample plate in two perpendicular directions to record the surface potential distribution of the FEP film. The scanning process and the data record were controlled by customized LABVIEW-based programs installed on a computer. The Trek 341B electrostatic voltmeter can precisely measure the very localized surface potential of the FEP film based on the field-nulling technique, regardless of the probeto-surface distance. We set the spatial resolution of the probe scanning as 1 mm, Chapter 5 Tape-peeling tribo-charged FEP film-based TE-KEHs 105 which means that the Trek 341B recorded one surface potential value per millimeter at both scanning directions.

Figure 5 -

 5 Figure 5-10 (a)Photograph of the Trek 341B electrostatic voltmeter. (b) Photograph of the pneumatic displacement system.

Figure 5 -

 5 Figure 5-11 (a) The surface potential mapping of the ~4 cm × 4 cm sized FEP film before any test and treatment. (b) The output voltage of the FEP film-based TE-KEH. (c) and (d) Surface potential mapping of the FEP film after the linear motor and after the tape-peeling treatments. (e) The output voltage of the TE-KEH after the FEP film was charged by the tape-peeling method. (f) Surface potential mapping of the FEP film after all the tests.

Figure 5 -

 5 Figure 5-11(a) is the surface potential mapping of a ~4 cm × 4 cm sized FEP film with backside metalized by silver paint before any test and without tape-peeling treatment. Then the FEP film was mounted onto the linear motor system to measure the output voltage of the FEP film-based TE-KEH. The measured output voltage was plotted in Figure 5-11(b). The time-varying air gap and movement velocity curves

Figure 5 -

 5 11(d). The surface distribution was apparently changed to a more negative state by the tape-peeling treatments. After that, the output voltage of the TE-KEH based on this FEP film was measured again and shown in Figure 5-11(e). It's clear that the output voltage of the TE-KEH was increased by the tapepeeling treatment by comparing Figure 5-11(b) and (e). Finally, the surface potential distribution of the FEP film was mapped again as presented in Figure 5-11(f). The general shape of potential distribution in Figure 5-11(d) and (f) also kept similar. The average surface potentials of the FEP film corresponding to the maps in Figure 5-11(a), (c), (d), and (f) are plotted in Figure 5-12(b). The absolute average surface potential of the FEP film was slightly increased after the first linear motor test, then had a more obvious increase by tape-peeling, finally kept almost unchanged after the second linear motor test.

Figure 5 -

 5 Figure 5-12 (a) The time-dependent movement velocity of the sliding block and the time-dependent air gap during the linear motor test. (b) The average surface potential values corresponding to the mapping images in Figure 3-15.

Figure 5 -

 5 13(a) shows the photograph of the winddriven TE-KEH made with a ~8 cm × 8 cm sized FEP film and the diagram illustrating its working process.

Figure 5 -

 5 Figure 5-13 (a) The wind-driven TE-KEH made with an ~8 cm × 8 cm sized FEP film. (b) Output voltages of the TE-KEH with FEP film holding different surface potentials. (c) Measured surface potentials of the FEP film corresponding to the output voltages in (b). (d) The circuit diagram of the TE-KEH driven by the wind to charge a capacitor. (e) Charging curves of the capacitor charged by the TE-KEH before and after tape treatment.

Chapter 5

 5 Tape-peeling tribo-charged FEP film-based TE-KEHs 108 foil at the fixed corner. The TE-KEH was driven by the wind from a hairdryer for demonstration, with a wind speed of ~18m/s. The wind blew through the slit between the FEP film and the Al foil, making the FEP film flutter irregularly and flap the Al foil continuously. The flutter of the FEP film made the capacitance between the FEP film and the Al foil variable with time and consequently generated a time-variable potential difference between the Al foil and the back electrode of the FEP film which was measured by the oscilloscope with the 100 MΩ high-impedance probe.

Figure 5 -

 5 Figure 5-13(b) presents the measured output voltages of the wind-driven TE-KEH. The four parts (I), (II), (III), and (IV) were measured in sequence. Among them, (I) was measured without any treatment to the surface of the FEP film, (II) was measured after the TE-KEH kept driven by wind for 30 s to charge a commercial aluminum electrolytic capacitor 10 μF capacitor through a full-wave rectifier (diagram of the electric circuit shown in Figure 5-13(d)), (III) was measured after the FEP film was treated twice by the tape-peeling process, and (IV) was measured after the TE-KEH kept working under wind blowing for another 30s to charge the 10 μF capacitor again. For each part, the output voltage obviously appeared when the wind began and disappeared when the wind stopped. Because the flutter of the FEP film was irregular, the measured voltage peak values are also irregular in each part.

Figure 5 -

 5 Figure 5-13(d) is the circuit diagram of the TE-KEH driven by the wind to charge a capacitor for energy storage (Cs). A rectifier bridge comprising four high voltage rectifier diodes (type IN4007) was used to convert generated irregular AC voltage output to DC output, which is essential for charging the Cs. In Figure 5-13(e),

Figure 5 -

 5 14(a) and (b) to show the voltage drop caused by rectifying.

Figure 5 -

 5 photograph Figure 5-14(d), 42 light-emitting diodes (LEDs) were directly lighted up by the TE-KEH with a rectifier bridge when the FEP film was slightly and slowly swung by hand.

Figure 5 -

 5 Figure 5-14 A 50 Hz sinusoidal voltage signal (a) before and (b) after rectification. (c) The output voltage of the wind-driven TE-KEH before and after

Chapter 5 Chapter 6 General conclusions and perspectives 6 . 1

 5661 Tape-peeling tribo-charged FEP film-based TE-KEHs 111 prototype in harvesting energy from irregular mechanical motions to power low power-consuming electronics. General conclusions Firstly, the reason for the amplitude-variable output characteristics of contactseparation (CS) mode electret kinetic energy harvesters (E-KEHs) with load resistances during transitory working cycles is attributed to the lag of the chargetransfer cycle to the driving motion cycle, based on simulated and experimental output data of a CS mode tribo-electret KEH (TE-KEH) made with PTFE film with different load resistances and initial working conditions.

Figure 6 - 1

 61 Figure 6-1 The Simulink model for E-KEHs with a series-connected LRC load.

Figure 6 - 2

 62 Figure 6-2 Comprehensive considerations on the design, fabrication, and application of E-KEHs.

Chapter 6 2 . 4 . 5 .

 6245 General conclusions and perspectives117 To design the specific geometric structure of E-KEHs according to features of the motion/vibration source in the environment and the power demand of the system. 3. Preparation of electret layers using amorphous fluoropolymer resins with high and stable effective surface charge density by multiple charging methods. Measurement of the time-varying capacitance of the E-KEHs working in the application environment, and the impedance spectra of the electric load of the system. To simulate the output of the E-KEHs based on the measured time-varying capacitance data, the effective surface charge density of the electret layers, and the impedance spectra of the electric load. To design or choose appropriate power management units with the help of the simulation method and verify their effectiveness by measured data. Ces caractéristiques de sortie à amplitude variable sont attribuées au fait du décalage du cycle de transfert de charge par rapport au cycle de mouvement d'excitation. Les influences de la condition initiale et de la résistance de charge sur la variation des pics de tension de sortie d'un tribo-électret REC (TE-REC) en mode CS réalisé avec un film électret en polytétrafluoroéthylène (PTFE) one été étudiées en détail et puis vérifiées à la fois par simulations et expériences. Dans le quatrième chapitre, une méthode d'optimisation du temps de contact est utilisée pour améliorer la puissance de sortie et l'efficacité du TE-REC en mode CS avec une résistance de charge de 100 MΩ. L'énergie théorique maximale convertie par cycle de travail du TE-REC est ainsi analysée. Les influences de plusieurs facteurs défavorables qui généralement réduiraient la conversion d'énergie par cycle de travail du TE-REC sont étudiées. L'optimisation de l'intervalle maximale d'air et la méthode tribo-charge sont également utilisées pour améliorer la puissance moyenne sortie du TE-REC avec un film polymère de 4 cm × 4 cm, de ~150 μW à ~503 μW. Dans le cinquième chapitre, une méthode innovante et facile a été développée pour charger le film polymère électret en éthylène propylène fluoré (FEP) par pelage de ruban adhésif, au lieu d'utiliser de source de haute tension électrique. La distribution du potentiel de la surface du film de FEP est fortement modifiée après plusieurs pelages. Par conséquence, la tension et le courant de sortie des TE-REC fabriqués avec le film FEP traité sont beaucoup améliorés. Pour un TE-REC flexible d'une surface de 64 cm 2 soufflé par du vent, une amélioration évidente d'environ 692% de la puissance de sortie, correspondant 2,5 μW à environ 19,8 μW, a été obtenue par cette méthode. Enfin, dans le sixième chapitre, les conclusions générales de cette thèse, ainsi quelques remarques sur la simulation et la gestion de puissance des E-RECs, sont présentées. Certaines perspectives s'ouvrant sur les futurs travaux intéressants sont également introduites.

Table 1 -1.Table 1 -1 Estimated power densities of several energy sources [2, 6].

 11

	Energy sources	Estimated Power density (μW/cm 3 ) Harvesting method
	Solar (outdoors) Solar (indoors)	150~15000 6~100	Photovoltaic
	Human walking	~330	Kinetic energy harvesters
	Vibrations (human motion)	~4	(Electromagnetic,
	Vibrations (machine)	~800	Piezoelectric, Electrostatic)
	Daily temperature variation ~10	Pyroelectric
	10 ℃ temperature gradient ~15	Thermoelectric

Table 1 -2.

 1

	Chapter 1 General background and introduction

Table 1 -2 Comparison of advantages and disadvantages of the three types of KEHs.

 1

	Type	Advantages		Disadvantages
	Electromagnetic High efficiency; Large	Low output voltage for miniature
		Reliability;		Low	devices; Heavy magnets; Difficult
		mechanical	damping;	to batch-fabricate miniature devices
		Small	Resistive
		impedance
	Piezoelectric	High energy density;	Low efficiency; Pulsed output;
		Moderate output voltage;	High capacitive impedance; Need
		Easy to scale down by	relatively large forces to deform
		using nanomaterials		piezoelectric materials;
	Electrostatic	High efficiency and open-	Need pre-charge or biasing voltage;
		circuit	voltage	for	High capacitive impedance; Low
		miniature devices; Low	output	current;	Risks	of
		weight; Compatible with	electrostatic	adherence	and
		microfabrication		discharge

Table 2 -1.

 2

Table 2 -1 Different charging methods for making electrets [46, 52].

 2

	Charging methods	Brief procedure
	Thermal charging	Heating and cooling in a constant electric field
	Tribo-charging	Contact or friction on metallic or dielectric objects
	Corona-charging	Corona discharge + electric field + possibly heating
	Electron or ion injections Injecting monoenergetic charged particle beams
	Liquid contact charging
	Photo-charging
	Radiation charging

Table 3 -1.Table 3 -1 Parameter values used in simulating the output of E-KEH for comparisons with the literature [35, 155]

 33

	Parameter

Table 3 -2 Parameter values in fitting Vpp and Vnp with the first initial condition

 3

				Load resistance R
	Parameter	100 MΩ 1 GΩ	10 GΩ	100 MΩ	1 GΩ	10 GΩ
		Fitting parameters for Vpp	Fitting parameters for Vnp
	Vs (V)	35.65	38.70	38.75	-38.36	-38.69	-38.70
	t0 (s)	7.55×10 -3 1.08×10 -2 1.10×10 -2 2.20×10 -2 2.20×10 -2 2.20×10 -2
	Va (V)	444.00	974.70	1079.00	3.86	30.75	37.82
	τd (s)

Table 3 -2

 3

	Parameter	SE of fitting parameters for Vpp 100 MΩ 1 GΩ 10 GΩ	SE of fitting parameters for Vnp 100 MΩ 1 GΩ 10 GΩ
	Vs (V)

Table 3 -

 3 4, with corresponding Standard errors given in

Table 3 -5.Table 3 -4 Parameter values used in fitting Vpp and Vnp with the second initial condition (z(0) = zmax and Q(0) = Qmax).

 33

				Load resistance R
	Parameter	100 MΩ 1 GΩ	10 GΩ	100 MΩ 1 GΩ	10 GΩ
		Fitting parameters for Vpp	Fitting parameters for Vnp
	Vs (V)	35.66	38.66	38.71	-38.36	-38.69	-38.70
	t0 (s)	2.1×10 -2 2.2×10 -2	2.2×10 -2	1.1×10 -2	1.1×10 -2	1.1×10 -2
	Va (V)	-3.743	-30.73	-37.83	-0.3658	-1.221	-1.357
	τd (s)

Table 3 -4

 3

	Parameters	SE of fitting parameters for Vpp 100 MΩ 1 GΩ 10 GΩ	SE of fitting parameters for Vnp 100 MΩ 1 GΩ 10 GΩ
	Vs (V)

Table 3 -

 3 4 are almost the same as those in Table 3-2, meaning that stable peak values of VE-KEH(t) with these two different initial conditions will finally be the same. Va values in Table 3-4 are all negative, meaning that the amplitude of the positive voltage peaks (|Vpp|) gradually increases but that of negative voltage peak

(|Vnp|) decreases with the cycle number. Each |Va| is smaller than the corresponding one in Table

3

-2, reflecting the fact that variation ranges of VE-KEH(t) in

Table 3 -6 Parameter values in simulating the output of TE-KEH corresponding to the experimental verification.

 3

	Parameter

Table 4 -1 Parameter values used in simulating the output of the TE-KEH with different contact times.

 4

	Parameter

This page is intentionally left blankChapter 5 Tape-peeling tribo-charged FEP film-based TE-KEHs

Acknowledgements

First, I would like to express my sincere gratitude to my supervisor Prof. Jinbo Bai for giving me the opportunity to do this research and for his guidance always with patience and encouragement during my doctoral study. Special gratitude is also given to my co-supervisors Dr. Delong He and Prof. Philippe Molinié. They gave me many

This dependence trend of the AvgP on zmax maybe a consequence of the combination of several factors. At first, the frequency of the mechanical movement monotonically decreased with increasing zmax as shown in Figure 4-24(b), this could lead to the decrease of the AvgP with increasing zmax since less working cycles were carried out by the TE-KEH within a certain period of time. Secondly, with the minimum zmax of 0.3 mm, although the movement frequency was the highest, the peak velocity of the motion became the lowest as shown in Figure 4-24(c), because the movement velocity couldn't be accelerated to the same peak value in such a short distance with the same acceleration value (the slope in the velocity curves) with larger zmax, this could be one reason that led to the lower AvgP with the minimum zmax than others. Thirdly, according to the equation [START_REF] Dell'anna | State-of-the-art power management circuits for piezoelectric energy harvesters[END_REF][START_REF] Wang | Triboelectric nanogenerators[END_REF][START_REF] Boisseau | Electrostatic conversion for vibration energy harvesting[END_REF][START_REF] Cao | A survey on ambient energy sources and harvesting methods for structural health monitoring applications[END_REF](7)[START_REF] Jordan | Electromagnetic waves and radiating systems[END_REF][START_REF] Brand | Micro energy harvesting[END_REF](10)[START_REF] Zhu | General model with experimental validation of electrical resonant frequency tuning of electromagnetic vibration energy harvesters[END_REF][START_REF] Sari | An electromagnetic micro power generator for wideband environmental vibrations[END_REF][START_REF] Halim | Design and experiment of a human-limb driven, frequency up-converted electromagnetic energy harvester[END_REF][START_REF] Bowers | Spherical, rolling magnet generators for passive energy harvesting from human motion[END_REF][START_REF] Liu | A multi-frequency vibration-based MEMS electromagnetic energy harvesting device[END_REF], the maximum transferred charge amount Qmax is dependent on zmax. Figure 4-24(d) shows the theoretically calculated Qmax-zmax curve by the equation [START_REF] Dell'anna | State-of-the-art power management circuits for piezoelectric energy harvesters[END_REF][START_REF] Wang | Triboelectric nanogenerators[END_REF][START_REF] Boisseau | Electrostatic conversion for vibration energy harvesting[END_REF][START_REF] Cao | A survey on ambient energy sources and harvesting methods for structural health monitoring applications[END_REF](7)[START_REF] Jordan | Electromagnetic waves and radiating systems[END_REF][START_REF] Brand | Micro energy harvesting[END_REF](10)[START_REF] Zhu | General model with experimental validation of electrical resonant frequency tuning of electromagnetic vibration energy harvesters[END_REF][START_REF] Sari | An electromagnetic micro power generator for wideband environmental vibrations[END_REF][START_REF] Halim | Design and experiment of a human-limb driven, frequency up-converted electromagnetic energy harvester[END_REF][START_REF] Bowers | Spherical, rolling magnet generators for passive energy harvesting from human motion[END_REF][START_REF] Liu | A multi-frequency vibration-based MEMS electromagnetic energy harvesting device[END_REF] and experimentally measured data, using the measured Qmax value with zmax = 20 mm to calibrate the measured and calculated total charge amount. It can be noticed that Qmax with zmax = 0.3 mm was apparently lower than others, which could also be a significant reason that led to the lower AvgP with the zmax of 0.3 mm than others. With increasing zmax from 0, Qmax increased dramatically with small zmax and then increased quite gently and approached almost flat with large zmax, which is in correspondence with other literature that most of the power of the CS mode TE-KEH is generated at small gap [START_REF] Hinchet | Understanding and modeling of triboelectric-electret nanogenerator[END_REF].

Chapter Conclusion

In this chapter, firstly, by increasing the contact time from ~12ms to ~52ms, the average output power of a contact-separation (CS) mode parallel-plate TE-KEH made with a 4 cm × 4 cm sized 55 μm-thick PTFE film to the load resistance of 100 MΩ was improved from ~150 μW to ~197 μW, with the corresponding frequency of the driving motion with the same maximum air gap was decreased from ~8.6 Hz to ~6.4 Hz, which means the energy conversion efficiency of the TE-KEH was also increased. This optimizing strategy to improve the output power of the was also verified by corresponding simulations results. Secondly, a series-connected switch-controlled working cycle was analyzed to obtain the dependence of the maximum theoretical output energy per working cycle of TE-KEHs on the geometrical parameters of TE-KEHs and on the effective surface charge density and dielectric constant of the

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