electronic system of energy harvesting for a new piezoelectric material

8/10/2019 Electronic System of Energy Harvesting for a new Piezoelectric Material

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POLITECNICO DI TORINO

Facolta di Ingegneria dellInformazioneCorso di Laurea in Ingegneria Elettronica

Tesi di Laurea

Electronic System of EnergyHarvesting for a new Piezoelectric

Composite

Relatori:Prof. Matteo Cocuzza

Dott. Giancarlo CanaveseCandidato:Amedeo Dadduzio

Ottobre 2014


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Acknowledgments

Ringrazio Paolo Motto, Giancarlo Canavese e Valentina Cauda per avermi sapien-

temente guidato nella realizzazione di questo lavoro.Grazie al dottorando Marco Morello, sempre disponibile e pronto a chiarimenti econsigli.Ringrazio ancora mamma, papa e mio fratello Marco. E tutti gli amici.

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Table of contents

Acknowledgments I

1 Introduction 1

1.1 Types of energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.1.1 Photovoltaic Energy Harvesting . . . . . . . . . . . . . . . . 31.1.2 Thermoelectric Energy Harvesting . . . . . . . . . . . . . . . 41.1.3 Kinetic Energy Harvesting . . . . . . . . . . . . . . . . . . . 7

1.2 Energy Requirements of Autonomous Devices . . . . . . . . . . . . . 71.3 Typical System Architecture . . . . . . . . . . . . . . . . . . . . . . . 8

2 Kinetic Energy Harvesting 10

2.1 Introduction to Kinetic Energy Generators . . . . . . . . . . . . . . . 102.2 Kinetic Energy Harvesting Applications . . . . . . . . . . . . . . . . 102.2.1 Human Apllications . . . . . . . . . . . . . . . . . . . . . . . 112.2.2 Industrial Applications . . . . . . . . . . . . . . . . . . . . . 112.2.3 Transport Applications . . . . . . . . . . . . . . . . . . . . . 122.2.4 Structural Applications . . . . . . . . . . . . . . . . . . . . . 14

2.3 Trasduction Mechanism . . . . . . . . . . . . . . . . . . . . . . . . . 152.3.1 Electrostatic Trasduction . . . . . . . . . . . . . . . . . . . . 152.3.2 Electromagnetic Trasduction . . . . . . . . . . . . . . . . . . 172.3.3 Piezoelectric Trasduction . . . . . . . . . . . . . . . . . . . . 18

2.4 Principles of Kinetic Energy Harvesting . . . . . . . . . . . . . . . . 20

2.4.1 Trasfer Function . . . . . . . . . . . . . . . . . . . . . . . . . 212.4.2 Equivalent Circuit . . . . . . . . . . . . . . . . . . . . . . . . 222.4.3 Damping in Kinetic Energy Harvesters . . . . . . . . . . . . . 22

3 Piezoelectricity 24

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243.2 History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243.3 How it Works? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253.4 How are they made? . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

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3.5 Examples of Piezoelectric Materials . . . . . . . . . . . . . . . . . . . 273.5.1 Crystals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.5.2 Ceramics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283.5.3 Polymers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.6 Introduction to Mathematical Model of Piezoelectric Materials . . . . 313.6.1 Mathematical Model . . . . . . . . . . . . . . . . . . . . . . . 33

4 Synthesis and Characterization of Zinc Oxide and Polydimethyl-

Siloxane Composite Material 36

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

4.2 Introduction to Zinc Oxide . . . . . . . . . . . . . . . . . . . . . . . 374.2.1 Variation ofZ nO Morphologies . . . . . . . . . . . . . . . . . 374.3 Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

4.3.1 ZnO microparticle synthesis . . . . . . . . . . . . . . . . . . 394.3.2 Material Characterization . . . . . . . . . . . . . . . . . . . . 404.3.3 Material: Results and Discussion . . . . . . . . . . . . . . . . 404.3.4 Composite Preparation . . . . . . . . . . . . . . . . . . . . . 444.3.5 Composite Characterization . . . . . . . . . . . . . . . . . . . 444.3.6 Composite: Results and Discussion . . . . . . . . . . . . . . . 45

5 Energy Harvesting Circuits 48

5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 485.2 Devices based on AC-DC Rectification . . . . . . . . . . . . . . . . . 48

5.2.1 Circuit Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 495.3 Two-Stage Energy Harvesting Circuit Approach . . . . . . . . . . . . 505.4 Design of the Energy Harveter Circuit . . . . . . . . . . . . . . . . . 52

5.4.1 Designed Circuit Analysis . . . . . . . . . . . . . . . . . . . . 53

6 Circuit Design and Simulations 59

6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 596.2 Design Specification . . . . . . . . . . . . . . . . . . . . . . . . . . . 596.3 Circuit Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

6.3.1 Piezoelectric Material Model . . . . . . . . . . . . . . . . . . 616.3.2 AC-DC Stage . . . . . . . . . . . . . . . . . . . . . . . . . . . 616.3.3 BOOST Regulator . . . . . . . . . . . . . . . . . . . . . . . . 626.3.4 LDO Regulator . . . . . . . . . . . . . . . . . . . . . . . . . . 64

6.4 Component List . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 656.5 Simulations Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 666.6 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

7 Conclusion 72

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Bibliography 73

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Chapter 1

Introduction

The concept of energy harvesting and its theory.Energy harvesting theory relates to the process of using ambient energy, which isconverted, primarily (but not exclusively) into electrical energy in order to powersmall and autonomous electronic devices. The expressions power harvesting orenergy scavenging are also used to describe the same process. The concept isnot new and has wider applications that are more common such as electrical andthermal power generation for buildings by means of large scale solar panels andwind turbines. Energy harvesting from ambient waste energy for the purpose of

running low-powered electronics has emerged during the last decade as an enablingtechnology for digital and wireless applications. The task of this technology is toprovide remote sources of electric power and/or to recharge storage devices, suchas batteries and capacitors. The concept has ecological ramifications in reducingthe chemical waste produced by replacing batteries and potential monetary gains byreducing maintenance costs. The potential for enabling wireless monitoring appli-cations, such as structural health monitoring, also brings an element of increasingpublic safety. With the previously mentioned potential as motivation, the area of en-ergy harvesting has captivated both academics and industrialists. This has resultedin an explosion of academic research and new products. The evolution of low-power-consuming electronics and the need to provide wireless solutions to sensing problems

have led to an increase of research in energy harvesting.

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1 Introduction

1.1 Types of energy

Figure 1.1. Typical Data for Various Energy Harvesting Sources [1]

In the envirornment there is a various range of different energy domains, whetherinternal or external. Three examples of possible sources for harvesting electricalenergy from a common outdoor environment are investigated in this work: solarenergy (light), thermal energy (heat) and kinetic energy (motion). It is quite difficult

to generalize regarding the typical power levels that are available from these threetypes of energy sources, or which source is most suitable because many subjectsare involved in this study. Neverthless, figure1.1[1] provides a general indication oftypical power levels. It is clear that in terms of power density solar power in outdoorconditions is hard to beat. However, it becomes comparable with the other sourcesif used indoors and is not suitable for embedded applications or dirty environmentswhere the cells can become obscured. In any case the choice of energy source andmethod of implementation is largely governed by the application. There can be afundamental link between the energy source and the design of the harvester. Inthe case of kinetic energy harvesting exploiting vibrations, the source vibrationspectra will vary enormously for different applications. For example, generating

power from human movement requires a totally different solution to the design ofa generator for harvesting machinery vibrations. In every case, clear and precisedata of the energy source is required at the outset. Wireless sensors could be a goodexample of application field. They offer many obvious advantages such as ease ofinstallation, flexibility, suitability for retrofitting and avoidance of the added cost,weight, and unreliability of wired connections. In some scenarios it might not evenbe possible to get access to mains electricity supply. If a sensor node was to beused for monitoring the environment on a glacier or in the desert, the nearest powersocket could be tens of miles away. Batteries would seem to be an obvious source

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1 Introduction

of electrical power, but they have a limited lifetime. For applications requiringseveral hundreds (or even thousands) of sensor nodes scattered over a wide area, itmight not be realistic to expect the batteries to be changed as soon as the sourceis depleted. Furthermore, some applications require the electronics to be embeddedwhere access to replace batteries is inconvenient e.g. implanted medical devices.A solution for powering these applications that exploits the availability of ambientenergy therefore has clear benefits taking in account that energy harvesting devicesshould naturally be designed to operate for the lifetime of the system. It follows abrief review of the main possible sources mentioned before for harvesting electricalenergy.

1.1.1 Photovoltaic Energy Harvesting

Photovoltaic (PV) technologies is the primary power source for any stand-aloneelectronic systems positioned outdoors or in rooms with windows, that uses lightsources. The Sun in outdoor conditions can provide around 100mW/cm2 of opticalpower, a cloudy day will provide around 10 mW/cm2, and around 0.5 mW/cm2

will be incident on most surfaces within a room. The efficency of typical solarcells is in the range of 5 to 20 under standard conditions; they will often be muchless efficient under low illumination levels. The very best devices, typically veryexpensive concentrator cells, are designed to operate under the power of many suns

and are up to 40 efficient. The power density available from solar cells operatingoutdoors can exceed that available with other energy harvesting technologies byseveral orders of magnitude (see Figure1.2). The value is much less for indooroperation; nevertheless, even indoor light energy harvesting can provide sufficientpower densities for low power technologies such as wireless sensor nodes[2, 3, 4].The abundance of optical power that is available for many applications that requiremodest levels of energy assures photovoltaic energy harvesting as a good solution.However, very careful considerations of the nature and frequency of illuminationconditions and the total power usage of the device are required, and the area ofthe solar cell used must be chosen accordingly. Furthermore, devices must haveenergy management and storage systems that ensure that essential features (such

as time keeping or critical monitoring) can be maintained throughout the longestlikely periods of darkness. Solar energy is commonly used within commercial devices,particularly low-power consumable electronics such as calculators. Solar energy isalso often employed for isolated noncritical outdoor systems such as parking meters,weather stations, telephone boxes, and traffic information systems. It is not usedfor alarm systems or any portable high-power systems such as mobile phones orlaptop computers and even less to power electric vehicles. Systems based on solarenergy will nearly always require the end user of the equipment, be it stationaryor portable, to diligently place the device in an appropriate location, and this is

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1 Introduction

often a limiting constraint. The surface area of a photovoltaic module required for adesired power is perhaps the most limiting constraint. The size of an array requiredto power a house would ideally be no more than the area of one side of a roof; thesize required for a laptop should be that of an A4 sheet of paper. Ideally, a single-chip sensing/transceiver system would require a solar cell no greater than its ownarea and ideally we would use the same piece of silicon to provide the base materialfor the solar cell. In many cases applications require device efficiencies higher thanthose currently available at a reasonable cost.

Figure 1.2. Power Densities of Various Energy Harvesting Technologies [1]

1.1.2 Thermoelectric Energy Harvesting

Thermal energy harvesting is related to thermoelectric devices, which are capableof converting heat into electricity. Thermal energy can be found in almost anyenvironment and a vast amount is unused. Typical examples include waste heat fromvehicle exhausts and radiators, geothermal from undergrounds, cooling water of steelplants and other industrial processes, and temperature difference between the surface

and the bottom of oceans. Success in this endeavor will have a wide implication inboth energy supply and environment. Thermoelectric devices can help to improveenergy efficiency and reduce CO2 emissions of fossil fuel systems through wasteheat recovery. They can also be integrated into autonomous systems to enhancethe capability and lifetime of self-power by harvesting thermal energy from theirenvironment, or even charging wireless sensors and mobile devices from human bodyheat. Thermoelectric theory describe the interaction and conversion between heatand electricity in solids, which can be summarized by three thermoelectric effects:the Seebeck effect, the Peltier effect, and the Thomson effect. These three effects

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1 Introduction

are related by the Kelvin relationships. They are the foundation for thermoelectricsand are described in the following sections.[5, 6, 7, 8, 9].

The Seebeck Effect

The Seebeck effect describes a phenomenon that produces a voltage by a tempera-ture gradient. Figure 1.3 shows a circuit that consists of two dissimilar metals orsemiconductors joining together. By applying a temperature difference across twojunctions, a voltageVwill be generated in the circuit

V =abT (1.1)

whereT = (TH-TC) is the temperature difference across the two junctions andis referred to as the Seebeck coefficient. The unit for alpha is V

Kand its value can

be positive or negative depending on the type of conducting charges.

Figure 1.3. The seebeck effect: a voltage generated by the temperature differenceacross the junctions [1]

The Peltier Effect

If we apply a voltage to the circuit as shown in Figure1.3 instead of applying atemperature difference across the junctions in Figure1.4, an electric current thatflows around the circuit will result in heat absorption at one junction and heatdissipation at another due to thermal transport by moving electrons. Consequently,one junction will become cold and the other junction will become hot. Furthermore,if the electric current changes the direction, the heat absorption and dissipation atthe two junctions will be reversed. The amount of heat removed per unit time fromone junction to another junction is given by

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1 Introduction

Q= abI (1.2)

whereIis the electric current in the circuit and ab is referred to as the Peltiercoefficient,

ab=Q

I (atT = 0) (1.3)

Figure 1.4. The peltier effect: heat absorption (or dissipation) at junctions dueto electrical current [1]

The Thomson Effect

Both the Seebeck and Peltier effects can only be observed in a system that consistsof at least two different materials. However, the absorption (or dissipation) of heatalong a single material can occur when the material is subjected to a temperaturedifference and electric current simultaneously as shown in Figure 1.5. The total heatabsorption (or dissipation) is given by:

QT =IT (1.4)

where is referred to as the Thomson coefficient. The unit for the Thomsoneffect is W

A1K

, which is equivalent to VK

.

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1 Introduction

Figure 1.5. The Thomson Effect: heat absorption (or dissipation) by a materialwhen subjected to temperature difference and electrical current

1.1.3 Kinetic Energy Harvesting

The adjective kinetic has its roots in the Greek word kinesis meaning motion. Me-chanical energy can be found almost anywhere so converting mechanical energyfrom ambient vibration into electrical energy is an attractive approach. The sourceof mechanical energy can be a moving human body such as walking, writing with apencil, taking a book offa shelf, or opening a door or a vibrating structure. The pro-

duction of electrical power from kinetic energy sources requires a physical structureto capture the energy and an electrostatic, piezoelectric or electromagnetic mech-anism to convert it to electricity. Large-scale applications, such as those based onthe energy of ocean waves, require low-cost and efficient energy converting devices.Smaller-scale applications, for example, using human activity to power portable de-vices, need to be lightweight and to easily and comfortably integrate with clothingor personal accessories. The answer to improved kinetic energy conversion lies innew materials. A better description of kinetic energy harvesting is given in the nextchapter.

1.2 Energy Requirements of Autonomous DevicesContinuous advance in low-power electronics are making the powering digital devicesfrom ambient energy a distinct and real proposition. The power consumption ofvarious computing platforms is shown in Figure1.6. Aside from systems such asWireless Sensor Networks and Radio Frequency Identification, the multibillion dollarportable electronics market from mobile phones to MP3 players to digital cameraswill be an attractive application for micro and macro-scale energy harvesting whenthe power requirements can be met.

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1 Introduction

Figure 1.6. Hierarchy of computing based on power consumption [1]

The average power consumption of mobile phone is in the order of 1W duringa call and 10mW in standby. Clearly, where energy harvesting is incapable ofdelivering watts of power, it may permit a near indefinite standby lifetime or even

recharge the phone between calls. Advances in low-power electronics are reducingthe energy requirements of other mobile consumer devices including M P3 players(as shown in Figure1.7) that currently consume less than 50mW during playback.There is a clear possibility for energy harvesting to be used to extend the batterylife of these devices significantly or even indefinitely. The possibility of using energyharvesting to recharge the battery in a mobile phone, M P3 player, digital camera,or other mobile device is certainly.

Figure 1.7. The decresing trend of power consumption for the Apple iPod(From:

www.ipodbatteryfaq.com)

1.3 Typical System Architecture

An example of simple block diagram for an energy harvesting system is presented inFigure1.8. This serves to illustrate some of the important design considerations that

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1 Introduction

Figure 1.8. Generalized block diagram of an energy harvesting system

need to be addressed when one considers adopting an energy harvesting strategyto solve a particular problem. The output of an energy harvester takes the formof the electrical variables, voltage, and current. Depending upon the nature of theharvester, the characteristics of these parameters can vary considerably; in particularthe phase, frequency, and amplitude of the AC waveforms and the magnitude ofthe DC level. In order to power an electronic subsystem such as a sensor or amicrocontroller, it is a usual requirement to modify the output of the harvester inorder to supply the desired excitation for the subsystem. For example, a vibrationenergy harvester might produce an AC voltage having a frequency of 50Hz andmagnitude of 1Vand this would need to be converted to, say, a DC voltage of 3V topower a microcontroller. It cannot always be assumed that the output power fromthe energy harvester will be continuous. Take the case of a solar cell and considerthe variability of the incident sunlight that it is exposed to during a typical 24 hperiod. The intensity of the light will change in accordance with overhead cloudcover and the position of the sun in the sky and, of course, at night there will beno output from the harvester at all. In the case of vibration energy harvesting,the power generated will depend upon the characteristics of the source vibrations(such as amplitude and frequency). These source vibrations will often vary and theresulting fluctuations in harvested power could be quite significant, especially inthe case of a tuned resonant generator. It is therefore often necessary to store theenergy on a temporary basis so that it can be delivered in a controlled manner tothe required electronic subsystem. The form of energy storage element might be asupercapacitor or a rechargeable battery. Naturally there are some scenarios wherethe energy supply is constant and there is no need to use a storage component.

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Chapter 2

Kinetic Energy Harvesting

2.1 Introduction to Kinetic Energy Generators

Kinetic energy generators have the task of convert kinetic energy derived from am-bient into electrical energy. This type of energy is typically present within theenvironment as vibrations, random displacements, or forces and can be convertedinto electrical energy using electromagnetic, piezoelectric, or electrostatic mecha-nisms. Goods vibration levels are to be found in numerous applications includingcommon household goods (refrigerators, washing machines, and microwave ovens),industrial plant equipment, moving structures such as automobiles and airplanes,and civil structures such as buildings and bridges [10]. Also human movements canbe investigated as possible source of kinetic energy. Human movement tends to becharacterized by low-frequency, high-amplitude displacements [11, 12]. The amountof electrical energy that is attainable by these approaches is dependent upon thequantity and form of kinetic energy available in the environment and also on theefficiency of both the generator and the power conversion electronics.

2.2 Kinetic Energy Harvesting Applications

Kinetic energy can be harvested from a various range of applications. In this studyare discussed human-, industrial-, transport-, and structural-based applications. So,kinetic generators for various applications will often be very different. It is essen-tial that generators are designed from the outset with a prior knowledge of theapplication and the characteristics of the kinetic energy targeted.

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2 Kinetic Energy Harvesting

2.2.1 Human Apllications

All human movments are characterized by large amplitude displacements at lowfrequencies and by some degree of impact on the heel of the foot during walking.These impacts send shock waves through the human body, but these are rapidlyabsorbed by the joints. The average gait of a walking human of a weight of 68 kgproduces 67W of energy at the heel of the shoe [13]. A study carried out during aEuropean-funded research project, Vibration Energy Scavenging (VIBES), measuredthe vibrations at various locations on the body while walking. The subject takenin account was 1.7m tall, weighed 76kg, and was wearing standard running shoes;measurements were taken at a walking speed of 5km/hfrom the ankle, wrist, chest,

upper arm, and head. The maximum accelerations were found at the ankle inthe direction of walking with a peak acceleration of over 100m/s2 and a frequencyof 1.2Hz. The acceleration in the vertical direction was 20m/s2. At all otherlocations on the body, the frequency remains constant, although the magnitudeof the accelerations in the vertical and walking axes was less than 7 m/s2. Thesefindings are similar to the results published by von Buren et al. [14]. The largeforces generated, for example, heel strikes while walking or during breathing, andangular displacements at the joints also present possibilities for harvesting energy.

Figure 2.1. Example of human application

2.2.2 Industrial Applications

Industrial equipment can be also used as source of energy harvesting. Tipically in-dustrial equipment is powered by mains electricity, so it is common for the frequencyof the supply to be present in the vibration spectra of the machine. Figure2.2 showsthe frequency spectrum of the vibrations found on a U.K. mains-powered air com-pressor. The peak vibration at 50Hz is clearly visible. The level of vibration on

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the plot is shown in units ofg where 1g represents an acceleration of 9.81m/s2; thepeak corresponds to 0.25m/s2. The amplitude of the corresponding displacementsof these vibrations is 2.5m, which is very low compared to those associated withhuman applications.For equipment not powered from the mains, the vibration frequency can vary, inthe range of 20200Hzwith similar vibration amplitudes to those of mains-poweredequipment. These values can be acceptable for the design of a specific-applicationenergy harvesting system.

Figure 2.2. Frequency spectrum of the vibrations found on a U.K. mains-poweredair compressor(VIBES project) [1]

2.2.3 Transport Applications

Transport applications are very different according to the type of vehicle taken in

account. There are many examples such as cars, trains, aircraft, and ships and thevibrations present in each area can often be quite different. In the case of cars, thevibration levels will vary depending upon the location of the generator on the vehicle(i.e., on the wheel or on the chassis), the type of vehicle, the road conditions, andthe speed. Figure2.3 gives some typical data obtained during the VIBES project.It can be seen that anything located away from the wheel or suspension elementsexperiences relatively low levels of vibration at low frequencies. Acceleration levelson the wheel, however, are much greater. In contrast to the results from a vehicle,the frequency spectrum of the vibration measured on a PZL SW-4 helicopter are

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Figure 2.3. Example of vibration data from a range of vehicles(VIBES project)[1]

shown in Figure2.4 [1]. Vibration frequencies on helicopters are governed by boththe rotor speed and number of blades and tend to be relatively consistent. In theexample shown, there is a characteristic frequency at 30Hz, where is present a peakacceleration at 19 m/s2 in this specific location.

Figure 2.4. Frequency spectrum of the vibration measured on a PZL SW-4 heli-copter(VIBES project) [1]

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2.2.4 Structural Applications

Kinetic energy can be available also in buildings and bridges and its quantity can bevariable for different scenarios. For example, vibrations in buildings can be causedby a variety of effects such as seismic activity, subways, road and rail systems,wind, heating, ventilation, air conditioning (HVAC) equipment, elevator/conveyancesystems, and fluid pumping equipment. Hunaidi and Tremblay [15] showed thatvibration levels for these apllications are relatively small, in fact, in a range of1012.5Hzthey obtained a maximum accelertion of 0.1 m/s2 Bridges can exhibitvibrations as a result of the traffic flowing over them. The magnitude and frequency

will depend upon the nature of the structure and the speed, weight, and number ofvehicles traveling over it. Yang et al. [16] tried to measure this data on a bridgeand they found that a 25m long bridge with a single vehicle traveling over it at 20m/s2 exhibits accelerations of 0.035 m/s2 at 2Hz. This can increase to 0.09 m/s2

for 5 vehicles. Williams et al. [17] also explored the feasibility of vibration energyharvesting on bridges. They found the natural frequency for two different concretebridges to be 6Hzand 4.5Hz, with amplitudes of acceleration less than 0.09 m/s2

when an articulated lorry crossed one of the bridges.These values are very low so an efficient energy harvesting circuit must be designedhaving a prior knowledge of the whole system.

Figure 2.5. Sketch of a building affected by seismic activity.

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2.3 Trasduction Mechanism

Some form of transduction mechanism is obviously required to convert the kineticenergy into electrical energy. The trasduction mechanisms are piezoelectric, elec-tromagnetic and electrostatic. [18] These mechanisms have to be incorporated intothe mechanical system that has been designed to maximize the energy coupledfrom the application environmental to the transducer. The transducer can generateelectricity from mechanical strain or the relative displacement present within thesystem, depending upon the type of transducer. The use of active materials such aspiezoelectrics is an obvious example that enables the strain to be directly converted

into electrical energy. Electromagnetic and electrostatic transduction exploits therelative velocity or displacement that occurs within a generator. Each transduc-tion mechanism has different characteristics such as damping effects, ease of use,scalability, and effectiveness. The suitability of each mechanism for any particularapplication depends largely on the practical constraints applied. Assuming no sizeconstraints, electromagnetic harvesting will be the most efficient because the coilcan be large, with a high number of turns and low coil resistance (larger diameterwire) providing very high potential coupling factors. The efficiency of piezoelectricgenerators is fundamentally limited by the piezoelectric properties of the material.The efficiency of electrostatic generators is reduced by technical challenges relatingto charging the electrodes, the separation distances, and the amplitudes of displace-

ment.

2.3.1 Electrostatic Trasduction

The basis of electrostatic generator is the variable capacitor. The variable ca-pacitance structure is driven by mechanical vibrations. The capacitance variesbetween maximum and minimum values. If the charge on the capacitor is con-strained, charge will move from the capacitor to a storage device or to the load asthe capacitance decreases. Thus, mechanical energy is converted to electrical en-ergy. Electrostatic generators can be classified into three types, i.e. in-plane overlap(Figure2.6) which varies the overlap area between electrode fingers, in-plane gap

closing (Figure2.6) which varies the gap between electrode fingers and out-of-planegap closing (Figure2.6) which varies the gap between two large electrode plates [19].

These three types can be operated either in charge-constrained or voltage-constrainedcycles. Generally, generators working in voltage-constrained cycles provide moreenergy than generators in charge-constrained cycles. However, by incorporatinga capacitor in parallel with the energy harvesting capacitor, the energy from thecharge-constrained system can approach that of the voltage-constrained system asthe parallel capacitance approaches infinity. This parallel capacitor effectively con-strains the voltage on the energy harvesting capacitor [20]. A simplified circuit for

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Figure 2.6. Electrostatic generators:(a)in-plane overlap;(b)in-plane gap clos-ing;(c)out of plane gap closing [18]

an electrostatic generator using charge-constrained conversion is shown in Figure2.7.

Vin is a pre-charged reservoir, which could be a capacitor or a rechargeable battery.

Figure 2.7. Circuit representation for an electrostatic generator [18]

Cv is a variable capacitor, which is one of the three types mentioned above. Cpar isthe parasitic capacitance associated with the variable capacitor structure and anyinterconnections, which limits the maximum voltage. CL is the storage capacitor orany kind of load.

Vmax=Cmax+ Cpar

Cmin+ CparVin (2.1)

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An electrostatic generator can be easily realized in MEMS version. Since thefabrication process of electrostatic generators is similar to that of VLSI, electro-static generators can be assembled with VLSI without difficulties. Unfortunately,electrostatic generators require an initial polarizing voltage or charge. The out-put impedance of the devices is often very high, which makes them less suitableas a power supply. However, they can be used to charge a battery, in which case,electrostatic generators can use electrets to provide the initial charge.

2.3.2 Electromagnetic Trasduction

Electromagnetic induction was discovered by Michael Faraday in 1831. Faradays lawof electromagnetic induction states that an electrical current will be induced in anyclosed circuit when the magnetic flux through a surface bounded by the conductorchanges. This applies whether the field itself changes in strength or the conductoris moved through it. In an electromagnetic generator, permanent magnets are usedto produce strong magnetic field and a coil is used as the conductor. Either thepermanent magnet or the coil is fixed to the frame while the other is attached tothe inertial mass. The relative displacement caused by the vibration makes thetransduction mechanism work and generate electrical energy. The induced voltage,also known as electromotive force (e.m.f), across the coil is proportional to thestrength of the magnetic field, the velocity of the relative motion and the number

of turns of the coil. An electromagnetic generator is characterized by high outputcurrent level at the expense of low voltages. Figure2.8 [18] shows two commonlyseen examples of electromagnetic generators.

Figure 2.8. Two examples of electromagnetic generators[18]

Electromagnetic generators perform better in macroscale than in microscale [21].Particularly, generators integrated with MEMS with electroplated coils and magnetsmay not be able to produce useful power levels due to poor electromagnetic coupling.A simplified circuit for an electromagnetic generator is showed below[18].

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Figure 2.9. Circuit representation for an electromagnetic generator.[18]

2.3.3 Piezoelectric Trasduction

Piezoelectric materials have been used for many years to convert mechanical energyinto electrical energy. Piezoelectrics contain dipoles, which cause the material tobecome electrically polarized when subjected to mechanical force. The degree ofpolarization is proportional to the applied strain. Conversely, an applied electricfield causes the dipoles to rotate, which results in the material deforming. Piezo-electric materials are therefore used in a variety of commercial sensors and actuatorsand are also a candidate for kinetic energy-harvesting applications. The piezoelec-tric effect is found in single crystal materials (e.g., quartz), ceramics (known as

piezo-ceramics) [e.g., lead zirconate titanate (PZT)], thin-film materials (e.g., sput-tered zinc oxide), screen printable thick films based upon piezoceramic powders,and polymer materials such as polyvinylidene fluoride (PVDF). Such materials haveanisotropic piezoelectric behavior. This means that the properties of the materialdiffer depending upon the direction of the strain and the orientation of the polar-ization (and therefore the position of the electrodes). The piezoelectric propertiesof a material are characterized by a series of constants shown in Figure2.10. These

Figure 2.10. Piezoelectric Material Properties. [1]

are listed with their respective axis notations to fully describe the anisotropy. Forexample, the 3 direction refers to piezoelectric materials that have been polarized

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along their thickness (i.e., having electrodes on the top and bottom surfaces). If amechanical strain is applied in the same direction, the constants are denoted withthe subscript 33 (e.g., d33). If the strain is applied perpendicular to the directionof polarization (e.g., the 1 direction), the constants are denoted with the subscript31 (e.g., d31). These are illustrated in Figure2.11, but for a more complete de-scription, refer to the IEEE standards [22]. In a majority of scenarios, piezoelectric

Figure 2.11. Piezoelectric costants in typical energy-harvesting modes [1]

harvesters operate in the lateral 31 mode. This is because the piezoelectric elementis often bonded to the surface of a mechanical spring element that converts vertical

displacements into a lateral strain across the piezoelectric element. Some designscan operate in the compressive 33 mode and these have the advantage of exploitingthe 33 constants, which are typically greater than the 31 equivalents. Compressivestrains, however, are typically much lower than the lateral strains occurring whenthe piezoelectric is bonded onto a flexing structure. The piezoelectric constants forquartz, soft and hard lead zirconate titanate piezoceramics (PZT-5H and PZT-5A,respectively), barium titanate (BaTiO3), and polyvinylidene fluoride (PVDF) aregiven in Figure2.12. These properties typically vary with age, stress, and temper-ature. The aging rate tends to be logarithmic with time and is dependent on theformation/deposition method and material type. Stressing the material further in-creases the aging process. Soft piezoceramics (e.g., PZT-5H) are more susceptible to

stress-induced changes than the harder compositions such as PZT-5A. Temperatureis also a limiting factor with piezoceramics due to the effect of crystal structurechanges above the Curie point. Above this limit, the piezoelectric material willlose it piezoelectric properties, effectively becoming depolarized. The applicationof stress can also lower the Curie temperature and therefore the maximum practi-cal operating temperature will typically be reduced. Over the last decade, severalarticles have appeared on the use of these transduction mechanisms for low powergeneration from ambient vibrations. Two of the review articles covering the ex-perimental research on all transduction mechanisms are given by Beeby et al. [23]

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Figure 2.12. Coefficients of Common Piezoelectric Materials. [1]

and Cook-Chennault et al. [24]. Comparing the number of publications that haveappeared using each of these three transduction alternatives, it can be seen thatpiezoelectric transduction has received the greatest attention, especially in the lastten years.

2.4 Principles of Kinetic Energy HarvestingInertial-based kinetic energy harvesters are modelled as second-order, spring-masssystems. The generic model of kinetic energy harvesters was first developed byWilliams and Yates [25]. Figure2.13 shows a generic model of such a generator, whichconsists of a seismic mass, m, and a spring with the spring constant ofk. Whenthe generator vibrates, the mass moves out of phase with the generator housing.There is a relative movement between the mass and the housing. This displacementis sinusoidal in amplitude and can drive a suitable transducer to generate electricalenergy. b is the damping coefficient that consists of mechanically induced damping(parasitic damping) coefficient bm and electrically induced damping coefficient be,

i.e. b = bm+ be.y(t) is the displacement of the generator housing and z(t) is therelative motion of the mass with respect to the housing. For a sinusoidal excitation,y(t) can be written asy(t) =Y sint, whereYis the amplitude of vibration and isthe angular frequency of vibration. The transduction mechanism itself can generateelectricity by exploiting the mechanical strain or relative displacement occurringwithin the system. The strain effect utilizes the deformation within the mechanicalsystem and typically employs active materials (e.g. piezoelectric). In the case ofrelative displacement, either the velocity or position can be coupled to a transductionmechanism. Velocity is typically associated with electromagnetic transduction while

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Figure 2.13. Generic Model of Kinetic Energy Harvester. [18]

relative position is associated with electrostatic transduction. Each transductionmechanism exhibits different damping characteristics and this should be taken intoconsideration while modelling the generators. Thermomechanical system can beincreased in complexity, for example, by including a hydraulic system to magnifyamplitudes or forces, or couple linear displacements into rotary generators.

2.4.1 Trasfer Function

For the analysis, it is assumed that the mass of the vibration source is much greaterthan the mass of seismic mass in the generator and the vibration source is unaffectedby the movement of the generator. Then the differential equation of the movementof the mass with respect to the generator housing from the dynamic forces on themass can be derived as follows:

md2z(t)

dt2

+ bdz(t)

dt

=

md2y(t)

dt2

(2.2)

which can be written in the form after the Laplace transform as

ms2z(s) + bsz(s) + ksz(s) = ma(s) (2.3)where a(s) is the Laplace expression of the acceleration of the vibration, a(t),

which is given by

a(t) =d2y(t)

dt2 (2.4)

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Thus, the transfer function of a vibration-based micro-generator is

z(s)

a(s)=

1

s2 + bm

s + km

= 1

s2 + tQ

s +2r(2.5)

whereQ = b is the quality factor and r= k

mis the resonant frequency.

2.4.2 Equivalent Circuit

An equivalent electrical circuit for a kinetic energy harvester can be found from Eq.2.5, which, when rearranged, gives

ma(s) =sZ(s)

ms + b +k

s

(2.6)

Equation (2.6) can be rewritten as

I(s) =E(s)

sC+ 1

R+

1

sL

(2.7)

where I(s) = ma(s), E(s) = sZ(s), C = m, R = 1b

, L = 1k

. Based on previousequation an equivalent electrical circuit can be built as shown in Fig2.14.

Figure 2.14. Equivalent Circuit of a Kinetic Energy Harvester. [18]

2.4.3 Damping in Kinetic Energy Harvesters

As mentioned above, damping in kinetic energy harvesters consists of mechanicallyinduced damping (parasitic damping) and electrically induced damping. The overalldamping factor of the system, T, is given by

T = b

2mr=

bm+ be2mr

=m+e (2.8)

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where m = bm2mr

is the mechanically induced damping factor and e = be2mr

isthe electrically induced damping factor. Total quality factor (Q-factor) is a functionof damping factor. The total Q-factor is given by

QT = 1

2T(2.9)

This is the Q-factor when the generator is connected to the optimum load. Therelation between total quality factor and the electrical and mechanical damping isgiven by

1

QT =

1

QOC +

1

Qe (2.10)

where QOC = 12m

is the open circuit Q-factor which reflects the mechanical

damping. Qe, which equals 12e

, reflects performance of the transduction mechanism.It cannot be measured directly, but can be calculated using above equation once QTandQOC are measured.

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Chapter 3

Piezoelectricity

3.1 Introduction

Nowadays, most of the research in the energy field is to develop sources of energyfor future. With oil resources being over tapped and eventually bound to end, it istime to find renewable sources of energy for the future. Piezoelectric materials arebeing more and more studied as they turn out to be very unusual materials withvery specific and interesting properties. In fact, these materials have the abilityto produce electrical energy from mechanical energy, for example they can convert

mechanical behavior like vibrations into electricity. Such devices are commonlyreferred to as energy harvesters and can be used in applications where outside poweris unavailable and batteries are not a feasible option. While recent experiments haveshown that these materials could be used as power generators, the amount of energyproduced is still very low, hence to optimize them.

3.2 History

The piezoelectric effect was discovered in 1880 by the bothers Pierre and JacquesCurie. They combined what they knew about pyroelectricity and about structures

of crystals to demonstrate the effect with tourmaline, quartz, topaz, cane sugarand Rochelle salt. They found out that when a mechanical stress was applied onthese crystals, electricity was produced and the voltage of these electrical chargeswas proportional to the stress. The converse effect however was discovered later byGabriel Lippmann in 1881 through the mathematical aspect of the theory. Thesebehaviors were labeled the piezoelectric effect and the inverse piezoelectric effect,respectively, from the Greek word piezein, meaning to press or squeeze. The firstapplications were made during World War I with piezoelectric ultrasonic transduc-ers. Nowadays, piezoelectricity is used in everyday life. For example, in the cars

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3 Piezoelectricity

airbag sensor where the material detects the change in acceleration of the car bysending an electrical signal which triggers the airbag.

3.3 How it Works?

The nature of piezoelectric materials is closely linked to the significant quantityof electric dipoles within these materials. These dipoles can either be induced byions on crystal lattice sites with asymmetric charge surroundings (as in BaTiO3and P Z T s) or by certain molecular groups with electrical properties. A dipole is

a vector, often named P, so it has a direction and a value in accordance with theelectrical charges around. These dipoles tend to have the same direction when nextto each other, and they altogether form regions called Weiss domains. The domainsare generally randomly oriented but they can be aligned using the process of poling,which is a process by which a strong electric field is applied across the material.However not every piezoelectric materials can be poled. The reason why piezoelec-tric material creates a voltage is because when a mechanical stress is applied, thecrystalline structure is disturbed and it changes the direction of the polarization Pof the electric dipoles. Depending on the nature of the dipole (if it is induced byion or molecular groups), this change in the polarization might either be caused bya reconfiguration of the ions within the crystalline structure or by a reorientation

of molecular groups [27]. As a consequence, the bigger the mechanical stress, thebigger the change in polarization and the electricity produced. A traditional piezo-electric ceramic is a mass of perovskite ceramic crystals, each consisting of a small,tetravalent metal ion, usually titanium or zirconium (see figure 3.1), in a latticeof larger, divalent metal ions, usually lead or barium, and ions. Under conditionsthat confer tetragonal or rhombohedral symmetry the crystals, each has a dipolemoment. The change inPappears as a variation of surface charge density upon thecrystal faces, i.e. as a variation of the electrical field extending between the faces.For example, a 1cm3 cube of quartz with 2kNof correctly applied force can producea voltage of 12500V [28, 29].

3.4 How are they made?

Piezoelectric materials can be natural or manmade. The most common naturalpiezoelectric material is quartz, but man-made piezoelectric materials are more ef-ficient and mostly ceramics. Due to their complex crystalline structure, the processwith which they are made is very precise and has to follow very specific steps. As ex-plained in Electroceramics:Materials,Properties and Applications [30], to preparea piezoelectric ceramic, fine PZT powders of the component metal oxides are mixed

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3 Piezoelectricity

Figure 3.1. Cristalline structure of a ceramic piezoelectric material: the 1st sketchwithout a dipole P(t > TC);the 2nd sketch with a dipole P(t < TC) [26]

in specific proportions, then heated to form a uniform powder. The piezo powder ismixed with an organic binder and is formed into structural elements having the de-sired shape (discs, rods, plates, etc.). The elements are fired according to a specifictime and temperature program, during which the piezo powder particles sinter andthe material attains a dense crystalline structure. The elements are cooled, thenshaped or trimmed to specifications, and electrodes are applied to the appropriatesurfaces. However, piezoelectric material exhibits an electric behavior and acts as adipole only below a certain temperature called Curie temperature. Above the Curiepoint, the crystalline structure will have a simple cubic symmetry so no dipole mo-ment (see first sketch of Figure3.1). On the contrary, below the Curie point, thecrystal will have a tetragonal or rhombihedral symmetry hence a dipole moment(see second sketch of Figure3.1). As explained earlier, adjoining dipoles form re-gions called Weiss domains and exhibit a larger dipole moment as every dipole inthe domain has roughly the same direction, thus a net polarization. The change ofdirection of polarization between two neighboring domains is random, making the

whole material neutral with no overall polarization (see first sketch of Figure3.2).In order to be polarized, is exposed to a strong and direct current electric field

whose goal is to align all dipoles in the material. Of course this transformationhas to be made below the Curie point so that dipoles are present. Thanks to thispolarization, the material gets its dipoles almost aligned with the electric field andnow has a permanent polarization. This permanent polarization is the remanent po-larization after the electric field is removed, due to a hysteretic behavior (Figure3.3)and it also gets lengthen in the direction of the field (see second sketch of Figure3.1),for the same hysteretic reason. [31]

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3 Piezoelectricity

Figure 3.2. Method to pole a piezoelectric material [26]

Figure 3.3. Histeric curve of polarization [26]

3.5 Examples of Piezoelectric Materials

The piezoelectric effect occurs only in non conductive materials. Piezoelectric ma-terials can be divided in 3 main groups: crystals, ceramics and polymers. The mostwell-known piezoelectric material is quartz (SiO2).

3.5.1 Crystals

-Quartz (SiO2) : Quartz shows a strong piezoelectricity due to its crystalline struc-ture, wich is meaning that when a pressure is applied on a quartz crystal an electricalpolarization can be observed along the pressure direction.-Berlinite (AlPO4)-Gallium orthophosphate (GaPO4) : Gallium orthophosphate has almost the samecrystalline structure as quartz, that is why it has the same characteristics. Howeverits piezoelectric effect is almost twice as important as the one for the quartz, making

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3 Piezoelectricity

it a valuable asset for mechanical application. It is not a natural element, it has tobe synthesised.-Tourmaline : crystal commonly black but can range from violet to green and pink.

Figure 3.4. Example of Piezoelectric Crystal

3.5.2 Ceramics

-Barium Titanate (BaTiO3) : This element is an electrical ceramics, it is usuallyreplaced by lead zirconate titanate (PZT) for piezoelectricity. It is used for micro-phones and transducers-Lead Zirconate Titanate (PZT) : It is considered today one of the most economicalpiezoelectric element, hence it is used in a lot of applications.

-Zinc oxide (ZnO): Zinc oxide has a cubic chemical structure and its crystallinestructure shows piezoelectric properties.-Aluminum Nitride (AiN): Aluminum nitride, crystallizes in an hexagonal spacegroup P63mc. AlN is piezoelectric but not much. Molar mass 40.988g/mol Cur-rent research focuses on developing light-emitting diodes.

3.5.3 Polymers

There are different polymer categories that can be considered piezoelectric. Figure3.5shows a graphical representation of the different types. The first category of piezo-electric polymers is the bulk polymer. These are solid polymer films that have thepiezoelectric mechanism through their molecular structure and its arrangement. Thesecond category is the piezoelectric composite polymer. These are polymer struc-tures with integrated piezoelectric ceramics from which the piezoelectric effect is

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3 Piezoelectricity

generated. These composites make use of the mechanical flexibility of polymers andthe high electromechanical coupling of the piezoelectric ceramics. The third type isthe voided charged polymer, a radically different type of piezoelectric polymer thanthe first two categories. This is a polymer film in which gas voids are introducedand surfaces are charged in a way to form internal dipoles. The polarization of thesedipoles changes with the applied stress on the polymer film (i.e. has a piezoelectricresponse).

Figure 3.5. Schematic diagram of piezoelectric polymer types:bulkpiezopolymers,piezocomposites, voided charged polymers [32]

Bulk piezoelectric polymers

Bulk piezoelectric polymers have a piezoelectric effect due to the molecular structure

of the polymer and its orientation. There are two types of bulk polymers that havedifferent operating principles: the semicrystalline polymers and amorphous poly-mers. A detailed review of both types and their theory and piezoelectric propertiesis presented by Harrison in [33]. In these two types, there are structural requirementsthat should exist for a bulk polymer material to be piezoelectric. First, the molec-ular structure of the polymer should inherently contain molecular dipoles. Second,these dipoles can be reoriented within the bulk material and kept in their preferredorientation state. This reorientation is done through a process called poling (seeFigure 3.3).

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3 Piezoelectricity

Figure 3.6. Example of Polymer Film[32]

Voided Charged polymers

In simple terms, voided charged polymers (sometimes called cellular polymers) arepolymer materials that contain internal gas voids. When the polymer surfaces sur-rounding the voids are charged, the voided charged polymer behaves like a piezo-

electric material, coupling electrical and mechanical energy. Such structures canhave a high piezoelectric coefficientd33 comparably with the ones of piezoceramics.This structure was first invented by Gerhard Sessler in the early 1960s[35] when hedeveloped a charged polymer device to be used as a microphone. It was only viewedand named as space charged electrets. It was not until the late 1980sthat researchersaccepted the concept of treating the space charged electrets as a black box and inves-tigated the piezo and pyroelectricity of such films [36]. Starting with a polymer filmwith embedded air voids, internal charging of voids can be done through electricalpoling. When a large electric field is applied across the film, gas molecules in thevoids get ionized and opposite charges are accelerated and implanted on each sideof the voids, depending on the applied electric field direction [36]. Such artificially

embedded dipoles respond externally to an applied electrical field or mechanicalforce similar to piezoelectric material. Instead of ion displacement in a crystallinestructure of a regular piezoelectric material, deformation of the charged voids is thecause of the piezoelectric effect.

Piezocomposites

A piezoelectric polymer composite (or a piezocomposite) is a polymer material withembedded inorganic piezoelectric material. The advantage of mixing piezoelectric

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3 Piezoelectricity

ceramics with polymers is to combine the advantages of both materials, which in-clude the higher coupling factor and dielectric constant of ceramics and the me-chanical flexibility of polymers. Piezocomposites are also the material of choice foracoustic devices because of the polymers low acoustic impedance and fewer spuriousmodes [34]. Arrangement of ceramic/polymer composites can have many differentcombinations [34]. Arranged or randomly scattered rods in polymer bulk films arecommercially available from companies like Smart Material, which are classified ascomposites. Another approach is to impinge microscale or nanoscale particles insidea polymer matrix. Different analytical and numerical models have been developedto estimate the material properties of such composites. These models are useful

in designing and predicting the diff

erent electrical, mechanical and electromechan-ical properties of piezocomposites but are difficult to estimate. That is why it israre to find a developed composite material with measured values of dielectric con-stant, Youngs modulus and piezoelectric coefficients all reported. This introducesdifficulties in comparing such properties of the different materials.

Figure 3.7. Example of Piezocomposite

3.6 Introduction to Mathematical Model of Piezo-

electric Materials

Several review articles have appeared in four years (20042008) with an emphasis onpiezoelectric transduction to generate electricity from vibrations. The main advan-tages of piezoelectric materials in energy harvesting (compared to using the othertwo basic transduction mechanisms) are their large power densities and ease of ap-plication. The power density versus voltage comparison given in Figure3.8 (due toCook-Chennault et al. [24]) shows that piezoelectric energy harvesting covers thelargest area in the graph with power density values comparable to those of thin-filmand thick-film lithium-ion batteries and thermoelectric generators. As can be seenin Figure 3.8, voltage outputs in electromagnetic energy harvesting are typically

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3 Piezoelectricity

Figure 3.8. Power density versus voltage comparison of trasduction mechanisms[40]

very low and often multistage post-processing is required in order to reach a voltagelevel that can charge a storage component. In piezoelectric energy harvesting, how-ever, usable voltage outputs can be obtained directly from the piezoelectric materialitself. Futhermore, the voltage output in piezoelectric energy harvesting emergesfrom the constitutive behavior of the material, which eliminates the requirement ofan external voltage input. As another advantage, unlike electromagnetic devices,piezoelectric devices can be fabricated both in macro-scale and micro-scale due to

the well-established thick-film and thin-film fabrication techniques . Poor propertiesof planar magnets and the limited number of turns that can be achieved using planarcoils are some of the main practical limitations in enabling micro-scale electromag-netic energy harvesters. Research in the area of piezoelectric energy harvesting isstrongly connected to various disciplines of engineering. Consequently, the promis-ing way of powering small electronic components and remote sensors has attractedresearchers from different disciplines of engineering, including mechanical, aerospace,electrical, and civil, as well as researchers from the field of materials science, andvarious modeling approaches have appeared. A comprehensive mathematical model

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3 Piezoelectricity

should be as simple as possible yet sophisticated enough to capture the importantphenomena needed to represent and predict the dynamics of the physical systemas required by the application of interest. Many models are proposed in literatureand the most complete that represent all the physycal system is described in thefollowing section.

3.6.1 Mathematical Model

The aim of the theory is to describe mathematically the material behavior. However,the equations governing piezoelectricity involve entities that cannot be measured ex-

perimentally, thus they need to be converted so that they make sense for experimentsand common use. A piezoelectric material develops an internal electric field whenstrained. On the contrary, a piezoelectric material experiences strain when an elec-trical field is applied to it. These reactions, electrical field and mechanical behavior,can be in either directions. Meaning that depending on the material, an electricalfield in one direction can lead to a mechanical reaction in any direction. Piezoelectricgenerators typically work in 33 mode: a force is applied in the same direction as thepoling direction, such as the compression of a piezoelectric block that has electrodeson its top and bottom surfaces.

Figure 3.9. 33 mode.[18]

The constitutive equations for a piezoelectric material are given by

=

Y + dE (3.1)

D= E+ d (3.2)

where is the mechanical strain, is mechanical stress, Y is Youngs modulusof the material, d is the piezoelectric strain coefficient, E is the electric field, Dis the electrical displacement (charge density) and is the dielectric constant of

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3 Piezoelectricity

the piezoelectric material. These expressions shows the relationship between themechanical and the electrical behaviors of those materials. The first equation showsthat part of an electrical field applied to the material is converted into mechanicalstress. Likewise, the second equation shows that part of a mechanical strain appliedto the material is converted into electrical field. One can note that in the absenceof electric field E, the second equation is Hookes Law. Likewise, in the absence ofmechanical stress in the first equation, it describes only the electrical behavior ofthe material. Figure3.10 shows a circuit representation of a piezoelectric generatorwith a resistive load,RL. Cis the capacitance between two electrodes andRs is theresistance of the piezoelectric material.

Figure 3.10. Circuit representation of a piezoelectric generator.[18]

The voltage source, VOC, is the open circuit voltage resulting from the secondequation when the electrical displacement is zero. It is given by

VOC= dt

(3.3)

where t is the thickness of the piezoelectric material. An expression for the piezo-electric damping coefficient is

be= 2m2

rk2

22r +

1RLCL

(3.4)

where k is the piezoelectric material electromechanical coupling factor and CLis the load capacitance. Again RL can be used to optimize and the optimum valuecan be found from next equation and as stated previously, maximum power occurswhene equals m:

Ropt= 1

rC

2m42m+ k

4(3.5)

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3 Piezoelectricity

The maximum power is

Pmax= 1

2r

RLC22Y dtb

2(42m+ k

4)2 + 4mk2(RLCr) + 22ma2 (3.6)

whereb is a constant related to dimensions of the piezoelectric generator andais the vibration acceleration.

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Chapter 4

Synthesis and Characterization ofZinc Oxide and

Polydimethyl-Siloxane Composite

Material

4.1 Introduction

In this chapter are illustrated the main steps for the production of the compositeZinc Oxide and Polydimethyl-Siloxane. The use of polymers for vibrational energyharvesting is advantageous since polymers are ductile, resilient to shock deformableand lightweight while zinc oxide (ZnO) nanowires, showed piezoelectric and semi-conducting properties. These particular properties have the potential of harvestingenergy from the environment for self-powered nanotechnology.ZnO has three key advantages. First, it exhibits both semiconducting and piezoelec-

tric (PZ) properties that can form the basis for electromechanically coupled sensorsand transducers. Second, ZnO is relatively biosafe and biocompatible and it canbe used for biomedical applications with little toxicity. Finally, ZnO exhibits themost diverse and abundant configurations of nanostructures known so far, such asnanowires NWs, nanobelts (NBs), nanosprings , nanorings , nanobows , and nanohe-lices. On the other hand Polydimethyl-siloxane (PDMS) was used as a polymericmatrix because of its advantages in terms of flexibility, low cost, chemical stabilityand transparency obtaining the composite Zinc Oxide and Polydimethyl-SiloxaneZnO + PDMS.

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4 Synthesis and Characterization of Zinc Oxide and Polydimethyl-Siloxane Composite Material

4.2 Introduction to Zinc Oxide

Zinc oxide is an inorganic compound with the formulaZnO. ZnO is a white powderthat is insoluble in water, and it is widely used as an additive in numerous materialsand products including rubbers, plastics, ceramics, glass, cement, lubricants, paints,adhesives, sealants, pigments, foods (source of Zn nutrient), batteries, ferrites, fireretardants, and first-aid tapes. It occurs naturally as the mineral zincite, but mostzinc oxide is produced synthetically. In materials science,ZnO is a wide-bandgapsemiconductor of theI I V Isemiconductor group (since oxygen was classed as anelement ofV IA group, the 6th main group, now referred to as 16th) of the peri-

odic table and zinc, a transition metal, as a member of the IIB (2nd B, now 12th,group). The native doping of the semiconductor (due to oxygen vacancies or zinc in-terstitials) is n-type. This semiconductor has several favorable properties, includinggood transparency, high electron mobility, wide bandgap, strong room-temperatureluminescence, semiconducting and piezo-electric (PZ) properties, which expeditesits potential wide applications in biosensors, ultraviolet nanolasers, photodetectors,solar cells, gas sensors,surface acoustic wave devices, ceramics, and nanogenerators.

Figure 4.1. ZnO white powder.

4.2.1 Variation ofZnO Morphologies

In recent years, ZnO nanostructures have been paid considerable attention dueto their rich morphologies, and piezoelectric properties. Among this research, the

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control over size and morphology of nanometer and micrometer ZnO semiconduc-tors represents a great challenge to design novel functional devices [37]. This isbecause optical and electronic properties ofZnO semiconductors, which finally de-termine practical applications, can be modulated by varying their size and morphol-ogy. For this reason, the preparation ofZ nOwith different morphologies, includingnano-belts, nanorods, firecracker-shaped, nanowires, nanobridges, nanonails, andnanowhiskers, is investigated in this thesis (Figure 4.2).

Figure 4.2. High-magnification SEM images of different flower-like morphologiesZnO [37]

The synthesis of ZnO is related to many academic subjects, such as physics,chemistry, and materials chemistry etc. On the basis of conventional preparation

methods, many methods have been developed, mainly involving hydrolysis in polyolmedia, chemical precipitation, microwave heating, templating, thermal oxidationprocesses and hydrothermal syntheses. Among these methods, the hydrothermaltechnique has been widely utilized to synthesize inorganic nanomaterials at temper-atures generally below 220C. The hydrothermal process has several advantages overother growth processes, such as the use of simple equipment, catalyst-free growth,low cost, large surface area, environmentally benign and less hazardous. However,various organic additives, such as template or surfactant, are commonly involvedduring hydrothermal process. Therefore, self-assembly of nanoparticles into the

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three-dimension structured morphologies and hierarchical architectures in the ab-sence of any surfactants, template supports and structure-directing reagents still re-mains a tremendous challenge. Recently, flower-like Z nO nanostructures have beensuccessfully synthesized by various methods. However, in these methods, surfactantor organic solvents were used, which are harmful to health and the environment.On the other hand, Li and Wang have fabricated ZnO hierarchical microstruc-tures with uniform flower-like morphology on a large scale through a template andsurfactant-free low-temperature (80C) aqueous solution route[38]. They observedthat changing the proportion of the reagents, flower-like Z nO microstructures weresynthesized and in particular the results indicated that rod-likeZnOwould be trans-

formed into flower-like ZnO microstructures with decreasing the concentration ofsodium hydroxide. Futhermore, they observed that the amounts and diameters ofthe petals of flower-like ZnO changed with increasing reaction time. P. Chen et al[39] conductedZnO multipods (MPs) synthesis through the direct reaction of theaqueous solutions of zinc salts and potassium hydroxide KOH.

4.3 Experimental

4.3.1 ZnO microparticle synthesis

In this section will be discussed the main steps followed for the preparation ofZnO micro-particles. Starting from the previous discussion on the varation of mor-phology, the synthesis of ZnO microparticles was carried out under conventionalhydrothermal tecnique, combining zinc nitrate hexahydrate (ZnNO36H2O, 0.5M,Sigma) with different molar amount of potassium hydroxide (KOH, Merck). Inthis way, different Z nOmorphologies were obtained by varying theK OH:ZnNO3

molar ratio from 2 to 8, and 12 (see Figure 4.3 for the obtained morphologies withrespect to the molar ratio). In details, 7.4g ofZnNO36H2O and the correspondingamount of KOH were dissolved separately in 50mL bidistilled water each (fromDirect-Q System, Millipore). The zinc nitrate solution was then dropwise added totheKOHsolution under vigorous stirring, thus the total volume was 100mL. Theobtained gels were transferred in closed Teflon bottles at 70C for 4h. At the endof this time, ZnO microparticles having different shapes were separated from thesolution by filtration, washed repetitively with deionized water until the pH wasneutralized, and dried in air at 60C overnight.

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Figure 4.3. Powder form, prior to in corporation in the PDMS matrix

4.3.2 Material Characterization

After the synthesis ofZ nOin powder forms, they were characterized and in particu-lar: X-ray diffraction (XRD) analysis was performed on the different Z nOparticlessythetized.The morphologies of all the ZnO particles and the prepared ZnO-PDMS com-

posites were observed by a Field Emission Scanning Electron Microscope (FESEM,Dual Beam Auriga from Carl Zeiss, operating at 5keV).Nitrogen sorption isotherms, measured at 77Kon a Quadrasorb instrument (Quan-tachrome), were used to calculate the Brunauer-Emmett-Teller (BET) specific sur-face area, using a multipoint method within the relative pressure range of 0 .10.3p/p0.

4.3.3 Material: Results and Discussion

To obtain different morphologies, during the hydrothermal synthesis at mild temper-ature (70C) it was applied a K OH :ZnNO3 molar ratio variation (Figure 4.3). In

particular the resulted shapes were: desert roses (DRs), branched multipods (MPs)and single microwires (MWs), obtained with this shape-controlled synthesis by ad-justing theKOH :ZnNO3 molar ratio to 2, 8 and 12, respectively. The respectivemorphologies, together with the image of the commercially purchased particles (C)are reported in Figure 4.4 after FESEM characterization. All the synthesized struc-tures have approximately uniform morphologies and dimensions. DRs structures(insets of Figure 4.4 a) consist in several flower-like aggregates of about 2 m indiameter and each one of them is composed by nanosized petals with a thickness ofabout 50nm. The MPs particles (inset of Figure 4.4b) are about 7m in diameter

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and composed of many wires with flat tips and hexagonal cross sections. Thesewires are assembled spokewise and projected from a common central zone to formthe multipod architecture. The ZnO MWs in the inset of Figure 4.4c are singlewire with flat tips and hexagonal cross section, with a length varying from 10 to15mand a wire diameter of about 300500nm. It is worth noting that each petalin the DRs or wire in both MPs and MWs structure have approximately the samethickness or dimension, indicating that their growth is strictly oriented and limitedto the 2D plane during the whole growing process.

Figure 4.4. FESEM images of ZnO microparticles sythetized having different mor-phologies: (a) Desert Roses (DRs); (b) Multipods (MPs); (c) Microwires (MWs);

(d) Commercial powder (C)

X-ray diffraction patterns (Figure 4.5a) of all the ZnO particles either synthe-sized and commercially purchased shows reflection which can be all assigned to singlephase wurtzite ZnO crystals (JCPDS 80 0074, hexagonal, space group P63mc).All the diffraction peaks are sharp, indicating that the product has a high degree ofcrystallinity and high purity.

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Figure 4.5. (a) X-ray diffraction pattern and (b) Nitrogen sorption isotherms ofall the ZnO microparticles in powder form.

The growth mechanism leading to different particle morphologies can be specu-lated. In general during the hydrothermal reaction, the hydroxyl groups ofKOHreact with the zinc cations Zn2+ through coordination or electrostatic interactions,formingZn(OH)24 growth units (Equations 4.1 and 4.2). ThenZnOnucleates fromthe solution ofZn(OH)24 forming multinuclei aggregates (Equation 4.3).

Zn2+ + 2OH

Zn(OH)2 (4.1)

Zn(OH)2+ 2OH Zn(OH)24 (4.2)

Zn(OH)24 ZnO+ H2O+ 2OH (4.3)At the low temperature used here (70C) both the nucleation and growth mecha-

nism ofZ nOstructure proceeded slowly, leading to thermodynamically stable prod-ucts. This is because the crystallizing structures tend to aggregate and to follow the

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lowest-energy path. Being the (001) face the highest-energy surface of the wurtziteZnO crystal, the c-axis resulted the fastest grow direction, thus leading to 2Dwiresin the case of MPs and MWs structures or 2D petals in the DRs morphology.

Figure 4.6. Growth sketch of ZnO crystal.

However, from both Equations 4.1 and 4.2, it is clear that the concentrationof hydroxyl groups [OH] plays a fundamental role in the reaction with ZnO pre-cursors, thus leading to different morphologies. In particular we experimentallyobserved that by increasing the molar ratio ofKOH :ZnNO3, thus increasing theconcentration of hydroxyl ions in the solution, a morphology shift from flower-liketo wires is obtained. Indeed at high [OH], thus in the case of MWs synthesis, bothnucleation and crystal growth proceed faster with respect to the synthesis of MPsand DRs. Therefore, large amounts ofZnO nuclei and Zn(OH)4 growth units areformed rapidly at the same time. As mentioned above, the growth along the [001]direction, thus along the c-axis, is preferred, therefore the Zn(OH)4 growth unitsadd preferentially to the highest energy surface (001) of every nucleus. This causesthe generation of numerous and singleZnOwires, as in the case of the sample MWs.The lower [OH] lead in contrast to slower nucleation and crystal growth. Thusthe crystallizing units tend to aggregate, following the lowest-energy path, leadingto wires or petals aggregates, as in the case of MPs and DRs, respectively.Nitrogen sorption measurements were used to calculate the specific surface area

(SBET) of all the four ZnO particles obtained. The Figure 4.5b shows adsorption-desorption isotherms of type IIIfor all the ZnO samples, thus imputable to non-porous material. The presence of nanostructured petals in the DRs sample leadssome level of porosities.

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4.3.4 Composite Preparation

To prepare the composite ZnO + PDMS, ZnO particles were used as filler in aDow Corning bi-component polydimethylsiloxane (PDMS, Sylgard 184) rubber.The dried particles were firstly dispersed in the PDMS base to obtain composites:PDMS to ZnO 50 : 50 and PDMS to ZnO 60 : 40 . The blend was gently mixedin order to avoid the destruction of the tips on the particles surface. Afterwards,the PDMScuring agent was added at the weight ratio of 1 : 10 with respect to

thePDMSbase and the resulting paste was outgassed for 1 hour under vacuum atroom temperature to eliminate all the trapped air bubbles. Composite curing wascarried out in polymethylmethacrylate (P M M A) moulds at 70Cfor 24h, leading to10x10mmcomposite with a constant thickness (1mm).

4.3.5 Composite Characterization

After the preparation of the composite many samples were obtained and character-ized. In particular, samples were sandwiched between two sheets of copper-metalizedKapton and connected with two copper wires so to have easily access to output sig-nals to perform an electrical characterization. Square flat samples with area of100mm2and thickness of 1mm are mounted on the top of a load cell (208 C02 by

PCB Piezotronics), screwed in the plate of a Tira S51110 shaker, powered witha Tira BAA120 amplifier and controlled by VibrationResearch V R9500 controller.Once the shaker is activated, the beam height is regulated until the force measuredby the load cell reaches the value of 10N: this condition ensures that the con-tact is effectively achieved, and it is used as an initial condition for measurements.Measurements are performed with National Instruments DAQ model 6259, directlyconnecting the composite material with the input of the board. Time-domain, openload voltage data are collected, in order to evaluate influence of particles structureand percentage on the output amplitude.

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4.3.6 Composite: Results and Discussion

Figure 4.7. Peak Voltages produced by the different morphologies obtained atdifferent molar ratio.

As can be seen from the above figure (Figure 4.7 ) a general enhancement of theperformance, in terms of peak-to-peak voltage, is achieved increasing the amountof filler (note that the percentage is intended with respect to the overall weight).Results related with 50% composite are not reliable, since the amount of powder

dispersed into the PDMS copolimer is too high to allow a correct mixing and de-gasification of the composite. This leads to non-homogeneous samples, that are notsuitable for charge generation. According to the measurements, the best compositeis PDMS to Z nO 60 : 40.

Figure 4.8. Voltages produced by the sample ZnO to P DMS60 : 40, measuredwith different load conditions.

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Figure 4.9. Currents produced by the sample ZnO to P D M S 60 : 40, measuredwith different load conditions.

In fig4.8 and 4.9 voltage and currents measured from the sample ZnOto PDMS60 : 40 with different load conditions are presented. Discrete values of resistanceare chosen, so to cover a wide range of realistic load conditions. Due to the ex-tremely high internal impedance of the composite at realistic working conditions(50 100Hz) output voltage can be correctly measured only with high values of

load, i.e. R >100k. On the other hand, current values can be collected for lowervalues of resistances, i.e. R < 200k. Aggregated results are presented in figure4.10.

Figure 4.10. V/I characteristic measured with different load conditions.

Peak output power is then calculated as Pp = VpIp and its values are shown in

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figure 4.11.

Figure 4.11. Powers calculeted with different load conditions.

It is evident a peak power of 30W produced by the sample ZnO to PDMS60 : 40.

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Chapter 5

Energy Harvesting Circuits

5.1 Introduction

In order to extract the electrical energy produced by the piezoelectric material, it isnecessary to connect it to a circuit.Charging a storage component such as a battery or a capacitor requires a stable DCsignal to be obtained. For this purpose, it is necessary to use an AC-DC converterthat consists of a rectifier bridge and a smoothing capacitor. The rectified voltagelevel usually depends on the vibration amplitude. Therefore, one cannot achieve

the optimal rectified voltage for all vibration levels if a simple AC-DC converter isused. Often a DC-DC converter is connected after the AC-DC converter to regulateits DC output for the maximum power transfer to the battery through impedancematching. [40] This chapter briefly describes some of the major papers from the liter-ature of piezoelectric energy harvesting circuits. First, lumped-parameter modelingof a piezoelectric energy harvester with a standard (one-stage) energy harvestinginterface (AC-DC converter) is summarized to express the rectified voltage and theaverage power in terms of the vibration input. Then, the two-stage approach ofcombining a DC-DC converter with the AC-DC converter is discussed

5.2 Devices based on AC-DC RectificationThis section discusses an analysis of the standard interface used for converting theAC output of the harvester to a stable DC output. Figure5.1 shows a cantileveredpiezoelectric energy h

electronic system of energy harvesting for a new piezoelectric material

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