Electrostrictive polymers for mechanical energy harvesting

Electrostrictive Polymers for Mechanical Energy Harvesting

Micka€el Lallart, Pierre-Jean Cottinet, Daniel Guyomar, Laurent Lebrun

INSA de Lyon, LGEF, Villeurbanne, France

Correspondence to: D. Guyomar (E-mail: [email protected])

Received 3 November 2011; accepted 22 December 2011; published online 6 February 2012

DOI: 10.1002/polb.23045

ABSTRACT: This article reviews the developments in electro-

strictive polymers for energy harvesting. Electrostrictive poly-

mers are a variety of electroactive polymers that deform due

to the electrostatic and polarization interaction between two

electrodes with opposite electric charge. Electrostrictive poly-

mers have been the subject of much interest and research

over the past decade. In earlier years, much of the focus

was placed on actuator configurations, and in more recent

years, the focus has turned to investigating material proper-

ties that may enhance electromechanical activities. Since the

last 5 years and with the development of low-power elec-

tronics, the possibility of using these materials for energy

harvesting has been investigated. This review outlines the

operating principle in energy scavenging mode and conver-

sion mechanisms behind this generator technology, high-

lights some of its advantages over existing actuator

technologies, identifies some of the challenges associated

with its development, and examines the main focus of

research within this field, including some of the potential

applications. VC 2012 Wiley Periodicals, Inc. J Polym Sci Part

B: Polym Phys 50: 523–535, 2012

KEYWORDS: actuators; dielectric properties; electrostrictive

polymers; energy harvesting; ferroelectricity; nanoparticles

INTRODUCTION The performance of energy harvesters isdirectly linked to the efficiency of the mechanical–electrical con-version within the active materials. For piezoelectric materials,the efficiency of the conversion can be estimated with the helpof the coupling coefficient. For a given vibration mode, this coef-ficient expresses the ratio of the converted energy to the inputone. Another key point for electroactive materials concerns theeasiness of their integration within the whole structure.1,2

For energy harvesters, bulk materials are widely used in theform of ceramics or single crystals. Beyond various types ofmaterials, lead zirconate titanate ceramics (PZT) and lead-based relaxor single crystals are of significant interest. PZTceramics are cost effective and available in various yet lim-ited shapes and with a wide range of properties dependingon their composition. They exhibit medium coupling factorsof 70% at least for the longitudinal 33 mode of vibration.3,4

Single crystals of lead magnesium niobate-lead titanate orlead zinc niobate-lead titanate have focused a lot of attentionas they exhibit coupling coefficients as high as 90%, close tothe theoretical values of 100%.5,6 Because of their high cou-pling coefficients, these two types of materials seem to bepromising for the energy conversion; however, drawbackssuch as brittleness and high density may prevent their usein some applications.

An alternative solution to the use of these bulk materials isthe use of electroactive polymers (EAPs). They present theadvantages of being easily processed in various and complex

shapes, easily deposited on large surfaces while being costeffective and very light.7

EAPs are divided into two main groups:7

• Electronic EAPs: Dielectric EAP, electrostrictive graft elasto-mers, electrostrictive papers, electroviscoelastic elastomers,ferroelectric polymers, liquid crystal elastomers, and so forth.

• Ionic EAPs: Carbon nanotubes, conductive polymers, elec-trorheological fluids, ionic polymer gels, ionic polymer me-tallic composites, and so forth.

Electrostriction is generally defined as a quadratic couplingbetween strain (Sij) and polarization (Pm):

8,9

Em ¼ e0Tmn:Pn þ 2:Qklmn:Tkl:Pn

Sij ¼ sPijkl:Tkl þ Qijmn:Pm:Pn

�(1)

where sPijkl is the elastic compliance, Qijkl is the polarization-related electrostriction coefficient, e

0Tjk is the inverse of the

linear dielectric permittivity, Tkl is the stress and Em the elec-tric field. Assuming a linear relationship between the polar-ization and the electric field, the strain Sij and electric fluxdensity Di are expressed as independent variables of theelectric field intensity Ek, El, and stress Tkl by the constitu-tive relations according to the equation set:8,9

Sij ¼ Mijkl:Ek:El þ sEijkl:Tkl

Di ¼ eTik:Ek þ 2:Mijkl:El:Tkl

((2)

VC 2012 Wiley Periodicals, Inc.

WWW.MATERIALSVIEWS.COM JOURNAL OF POLYMER SCIENCE PART B: POLYMER PHYSICS 2012, 50, 523–535 523

JOURNAL OFPOLYMER SCIENCE WWW.POLYMERPHYSICS.ORG REVIEW

where sEijkl is the elastic compliance under constant electricfield, Mijkl is the electric field-related electrostriction coeffi-cient, and eTik is the linear dielectric permittivity.

Because of their high deformation abilities and elasticity, EAPscover a wide range of application possibilities, as shown inFigure 1, which depicts the typical strain–stress abilities ofconversion materials when compared with typical applicationcases. In the same manner, the operating frequency of suchmaterials suits in a much better way with the mechanical fre-quency contents of typical systems (Fig. 2).

Because of their low losses that make them a premiumchoice for energy-harvesting purposes, this research will befocused on electronic EAPs and more specifically on electro-strictive elastomers. The ‘‘Energy-Harvesting Techniques’’section provides an overview of the different methods forharvesting energy using such materials. The ‘‘Increase of theDielectric Constant and of the Electrostrictive Coefficientwith the Help of Fillers’’ section lies in presenting methodsfor enhancing the electromechanical responses of electro-strictive polymers and thus their energy-harvesting abilities.

Micka€el Lallart graduated from the Institut National des Sciences Appliqu�ees de Lyon (INSA

Lyon), Lyon, France, in electrical engineering in 2006 and received his PhD in electronics,

electrotechnics, and automatics from the same university in 2008, where he worked for the

Laboratoire de G�enie Electrique et Ferro�electricit�e (LGEF). After working as a post-doctoral

fellow in the Center for Intelligent Material Systems and Structures (CIMSS) in Virginia Tech,

Blacksburg, VA, USA, in 2009, Dr. Lallart has been hired as an associate professor in the

LGEF. His current field of interest focuses on vibration damping, energy harvesting, and

structural health monitoring using piezoelectric, pyroelectric, or electrostrictive devices, as

well as autonomous, self-powered wireless systems.

Pierre-Jean Cottinet graduated from the Institut National des Sciences Appliqu�ees de Lyon

(INSA Lyon), Lyon, France, in 2008. He received a PhD degree in Acoustics in 2008 from the

Institut National des Sciences Appliqu�ees de Lyon (INSA), France, for his thesis on

electostrictive polymer for energy harvesting and actuation. During 2011, he was at the

Florida State University as a post-doctoral and working on buckypaper in High-Performance

Materials Institute (HPMI). Currently, he is an associate professor at INSA de Lyon, with

research interests concerning electroactive materials (polymers, CNT, etc.) and smart

structures.

Daniel Guyomar received a degree in physics from the Amiens University, Amiens, France,

an engineering and a doctor-engineer degree in acoustics from the Compiegne University,

France, as well as a PhD degree in physics from the Paris VII University, Paris, France. In

1982–1983, he worked as a research associate in fluid dynamics at the University of Southern

California, Los Angeles, CA. He was a National Research Council Awardee (1983–1984)

detached at the Monterey Naval Postgraduate School, California, to develop transient wave

propagation modeling. He was hired by Schlumberger in 1984 to lead several projects

dealing with borehole imaging, and then moved to Thomson Submarine activities in the

field of underwater acoustics. In 1992, Dr. Guyomar co-created the Techsonic Company,

which is involved in research, development, and production of piezoelectric and ultrasonic

devices. He is presently a full-time university professor at the Institut National des Sciences

Appliqu�ees de Lyon (INSA), Lyon, France, where he manages the Laboratoire de G�enie

Electrique et Ferro�electricit�e (LGEF). He also works as a consultant for several companies. His

present research interests include the field of piezo-material characterization, piezoactuators,

acoustics, power ultrasonics, vibration control, and energy harvesting.

Laurent Lebrun graduated from the Ecole Nationale Sup�erieure d’Ing�enieurs de Caen,

France, in 1991. He received a PhD degree in acoustics in 1995 from the Institut National des

Sciences Appliqu�ees (INSA), de Lyon, France, for his thesis on piezoelectric motors. During

2001, he was a visiting scientist at the Materials Research Institute of the Pennsylvania State

University, State College, PA, in the group of Prof. Tom Shrout. Currently, he is a professor at

INSA de Lyon, with research interests concerning electroactive materials (ceramics, single

crystals, and polymers) and smart structures.

REVIEW WWW.POLYMERPHYSICS.ORGJOURNAL OF

POLYMER SCIENCE

524 JOURNAL OF POLYMER SCIENCE PART B: POLYMER PHYSICS 2012, 50, 523–535

Then, the ‘‘Practical Consideration and Figure of Merit of theConversion’’ section discusses practical considerations suchas materials properties, circuit topologies, and so forth.Finally, the ‘‘Application of Electrostrictive Polymer Genera-tors’’ section concerns with the description of potentialapplication.

ENERGY-HARVESTING TECHNIQUES

The aim of this section is to propose a review of the possibletechniques for harvesting the energy converted by the mate-rials. Basically, three approaches can be considered forenergy scavenging from vibrations using electrostrictivepolymers:

• Electrostatic cycles, inspired from purely capacitive techni-ques.10–14

• Electrostrictive cycles, using charge and discharge opera-tions.9,15–17

• Pseudo-piezoelectric cycles, consisting in applying a biasvoltage on the material and working around this staticregime.18–20

Electrostatic-Derived CyclesAs electrostrictive polymers feature dielectric behaviors, it ispossible to consider harvesting schemes usually used inpurely capacitive approaches.10–14 Typically, there are twocycles that can be envisaged for such techniques:

• Ericsson (voltage constrained) cycle, which consists in:1. Stretching the polymer.2. Applying the electric field.3. Releasing the applied mechanical stress while maintain-

ing the electric field, leading to a decrease of the elec-tric flux density.

4. Removing the electric field.• Stirling (charge constrained) cycle, whose principles rely on:1. Stretching the polymer.2. Applying the electric field.3. Releasing the applied mechanical stress under constant

electric flux density (open-circuit conditions), resultingin an increase of the electric field.

4. Removing the electric field.

The associated strain (S)–stress (T) and electric displace-ment (D)–electric field (E) cycles are shown in Figure 3.From this curves, it can be shown that the Stirling cycle per-mits converting more energy than the Ericsson approach.However, the latter allows a better control of the electricfield, ensuring that the maximal admissible value is neverreached. The energy balance for the considered techniques isgiven in Table 1, where e refers to the permittivity, M to theelectrostrictive coefficient, and T0 and E0 to the maximalstress and applied electric field, respectively.

Electrostrictive CyclesHowever, other cycles than those already used in otherenergy conversion systems may be considered, takingadvantage of the electrostrictive nature of the materials.Many cycles have been described in ref. 16, and particularly:

• Constant electric field stretching and open-circuit release:1. Stretching under a given electric field E0.2. Releasing in open circuit (constant charge).3. Decreasing the electric flux density to the original

position.FIGURE 2 Comparison of frequency contents of conversion

materials and typical applications.

FIGURE 1 Comparison of stress–strain abilities of conversion materials and typical applications.



• Constant electric field stretching and release:1. Stretching under constant electric field E0.2. Increasing electric field to E1.3. Releasing the applied stress.4. Decreasing electric field to E0.

• Open-circuit stretching and release:1. Stretching in open circuit (constant electric flux density)

with an initial electric field E0.2. Increasing electric field to E1.3. Releasing in open circuit (constant electric flux density).4. Decreasing electric field to E0.

The associated energy cycles and energy balances are givenin Figure 4 and Table 2, respectively. In contrast to the previ-ously discussed cycles (electrostatic based), the pure electro-strictive cycles require nonzero electrical initial conditions(leading to nonzero initial strain as well), therefore possiblywasting energy due to the losses in the material. It can alsobe noted that the constant field during stretching and releas-ing phases and constant electric flux during stretching andreleasing phases use the same principles than the Ericssonand Stirling cycles of electrostatic devices, respectively (seeprevious section), except that initial electrical conditions arezeros in the latter cases.

In addition, these cycles require driving the electrical condi-tions of the materials for a significant time period, hencemaking them quite complex to implement in an autonomous,self-powered fashion. A simpler way for harvesting energyfrom electrostrictive polymers using diodes is proposed inrefs. 16 and 21. This system therefore permits harvestingenergy in a purely passive fashion, hence making its imple-mentation quite easy. The principles of this device, depictedin Figure 5, consist of providing energy to the polymerwhen its voltage reaches VL (it is considered that the diodethreshold voltages are negligible) and harvesting when itattains VH.

At the beginning of a new cycle, the material voltage is VH,and the stress is increasing, resulting in a decreasing electricfield. Therefore, the two diodes are blocked, and the systemis in open-circuit condition. After a critical value of thestress, the voltage VL is reached and the left diode conductsso that the electric displacement increases with the stress,yielding a provided energy density:

Wprov ¼ EL 2MELT0 � e EH � ELð Þ½ � (3)

where EH and EL are the electric field values associated withthe voltages VH and VL. As the stress is released, the materialvoltage increases and the left diode is blocked. When thevoltage reaches VH, the right diode conducts and energy isextracted, until the stress is minimum. The harvested energydensity is given by:

Wextr ¼ EH 2MELT0 � e EH � ELð Þ½ � (4)

leading to the energy density balance:16

Wharv ¼ 2MELT0 � e EH � ELð Þ½ � EH � ELð Þ (5)

FIGURE 3 Electrostatic energy-harvesting cycles considering Ericsson and Stirling cycles.

TABLE 1 Energy Balance Considering Electrostatic-Based

Harvesting Techniques

Ericsson16 Stirling16

Provided electrical

energy density

12 eþ 2MT0ð ÞE2

012 eþ 2MT0ð ÞE2

0

Extracted electrical

energy density

12 eþ 4MT0ð ÞE2

012

eþ2MT0ð Þ2e E2

0

Harvested energy

density

MT0E20 1þ 2M

e T0

� �MT0E

20


POLYMER SCIENCE


which is maximal when

EL ¼ 1� MT0

eþ 2MT0

� �EH (6)

yielding:

Wmax ¼ MT0EHð Þ2eþ 2MT0

(7)

The associated energy cycles are given in Figure 6. Despiteits simplicity, such an approach requires that the voltage VHis reached by the electrostrictive material, hence necessitat-ing a minimal stress value to operate, whose value is givenas follows:

Tmin ¼ e2M

EH

EL� 1

� �(8)

TABLE 2 Energy Balance Considering Electrostrictive Harvesting Techniques

Constant Electric Field

Stretching and Open-Circuit Release16Constant Electric Field

Stretching and Release16Open-Circuit Stretching

and Release16

Provided electrical energy density 2MT0E20 MT0 E2

0 þ E21

� �þ 12e E2

1 � E20

� � 1

2eþ 2MT0ð ÞE2

1

� 1

2

e2

eþ 2MT0ð ÞE20

Extracted electrical energy density2MT0 1þ MT0

e

� �E2

0 2MT0E21

þ 12e E2

1 � E20

� � 12

eþ2MT0ð Þ2e E2

1 � eE20

h i

Harvested energy density2M2

e T 20E

20

MT0 E21 � E2

0

� �eþ 2MT0

e

� �MT0E

21

� eeþ 2MT0

� �MT0E

20

FIGURE 4 Energy cycles for the electrostrictive energy-harvesting techniques (adapted from ref. 16).



If the strain is small, the value of Tmin can thus be approxi-mated by

Tmin ¼ e2M

VH

VL� 1

� �(9)

Pseudo-Piezoelectric CyclesThe final family for harvesting energy from electrostrictivematerials consists of applying a bias electric field to the sam-ple, as shown in Figure 7, allowing simpler operations thancharge and discharge cycles (with possibly reduced losses).In this device, the constant electric field, supposed to bemuch larger than the electric field generated by the vibra-tion, allows the device to operate dynamically in a similarfashion than piezoelectric materials. Starting from the linear-ized electrostrictive equations:

S ¼ sT þM EDC þ EACð Þ2D ¼ e EDC þ EACð Þ þ 2M EDC þ EACð ÞT (10)

with EDC and EAC the bias and generated electric fields and sthe elastic compliance of the material, the dynamic behaviormay be expressed as follows:

_S ¼ s _T þ 2M EDC þ EACð Þ _EAC

_D ¼ eþ 2MTð Þ _EAC þ 2M EDC þ EACð Þ _T (11)

Considering that the electric field EAC can be neglected facingthe bias electric field EDC and as long as the stress magni-tude remains small enough so that e >> 2MT , the expres-sions turn to:

_S � s _T þ 2MEDC _EAC

_D � e _EAC þ 2MEDC _T(12)

which are similar to those obtained when using piezoelectricelement, with an equivalent piezoelectric coefficientd ¼ 2MEDC, which depends on the bias electric field.

The energy cycles (obtained without the previous assump-tions) are depicted in the top of Figure 8 when consideringthat energy is harvested on a purely resistive load (R inFig. 7), yielding a harvested energy density (consideringEDC << EAC and e >> 2MT):20

Wharv � 4pq

1þ eqxð Þ2 !

MEDCð Þ2xT20 (13)

where q denotes the load resistivity. The maximum energydensity is therefore given by:20

Wmax � 2pM2

eE2DCT

20 (14)

However, to increase the conversion efficiency, it is possibleto use a nonlinear approach similar to the ‘‘synchronizedswitch harvesting on inductor’’ for piezoelectric elements,23–27

which consists of reversing the dynamic voltage each time thedisplacement reaches a maximum or a minimum value,22

leading to the cycles depicted in the bottom of Figure 8, andallowing a harvested energy density given by:

Wharv � 4pq

1þ eqxð Þ2� � eqxð Þ3

1þ eqxð Þ2� � 1þ cð Þ

ep

eqx � c� �2 e

2peqx � 1

� �p

þ 1

24

35

� MEDCð Þ2xT20 ð15Þ

with c given as the voltage inversion factor.23

Although the losses of pseudo-piezoelectric working mode maybe smaller than electrostatic-based and electrostrictive cyclesas the system is working around a bias point (hence no chargelosses appear), the dynamic voltage across the load remainsAC, preventing the use of such a system to power up electroniccomponents that usually require DC voltage. In ref. 28, an archi-tecture was proposed to allow a DC voltage output of electro-strictive materials used as energy harvesters in pseudo-

FIGURE 6 Energy cycles for the passive electrostrictive energy-harvesting device (adapted from ref. 16).

FIGURE 5 Passive energy-harvesting circuit.FIGURE 7 Pseudo-piezoelectric energy-harvesting device.


POLYMER SCIENCE


piezoelectric mode. This technique consists of filtering the biascomponent using a capacitor Cd and connecting a diode recti-fier associated with smoothing capacitors Cs, as depicted in Fig-ure 9. It has to be noted that in this case, the resistance RS is nolonger used for harvesting energy, but consists of preventing adynamic short circuit of the material. Assuming EDC >> EACand e >> 2MT , the harvested energy density and maximumenergy density using this approach are given by:28

Wharv � 8pq

p2 þ eqx� �2

!MEDCð Þ2xT2

0 (16)

Wmax � 4M2

eE2DCT

20 (17)

As previously noted, it is also possible to use the nonlinearapproach to increase the performance of the microgenera-tor,29 leading to harvested and maximal harvested energydensities (Fig. 10):

Wharv � 32pq

eq 1� cð Þxþ pð Þ2 !

MEDCð Þ2xT20 (18)

Wmax � 81� c

M2

eE2DCT

20 (19)

DiscussionThe comparison of the maximal harvested energy densitiesfor each of the exposed technique is depicted in Figure 11,using parameters of Table 3, which corresponds to typicalparameter values for a poly(vinylidene fluoride-trifluoroethy-lene-chlorofluoroethylene) [P(VDF-TrFE-CFE)] terpolymer.This figure shows that the electrostatic-based approachespermit the highest harvested energies. However, as statedabove, losses during charge and discharge may significantlyreduce the performance of these techniques. The pseudo-

piezoelectric methods, and especially those using the nonlin-ear switching approaches, allow an harvested energy densityabout 5–10 times less than the electrostatic-based techni-ques (Fig. 12), but permit reduced losses as the system isoperating around a bias value, hence preventing losses dur-ing charge and discharge from zero initial conditions. Inaddition, working around a bias point permits operating atmuch higher frequencies than charge/discharge-based sys-tems, as the application of high electric fields in a low-costfashion may take time.

INCREASE OF THE DIELECTRIC CONSTANT AND OF THE

ELECTROSTRICTIVE COEFFICIENT WITH THE HELP OF FILLERS

The previous analyses show that, whatever the techniqueuse for EAP-based energy-harvesting purposes, the perform-ance of the microgenerators are obviously dependent on thematerial properties themselves (e.g., permittivity, electrostric-tive coefficient, and elasticity).

In particular, it can be shown that better performance inenergy harvesting can be obtained by increasing the dielec-tric constant of the electrostrictive material.18–20 To do so,one solution consists of processing polymer-based

FIGURE 8 Energy cycles for the pseudo-piezoelectric energy-harvesting device (adapted from ref. 22).

FIGURE 9 Pseudo-piezoelectric energy-harvesting device fea-

turing DC output (adapted from ref. 28).



composites by filling the polymer with high K fillers or con-ductive fillers. Currently, a variety of methods are availableto increase the dielectric permittivity of polymer materials.These may be classified into two main groups: those involv-ing composites and those based on new synthetic polymers.The first approach concerns the dispersion of a filler into thepolymer matrix. The second strategy, on the other hand,deals with the synthesis of new materials with tailoredcharacteristics.

In the first case, the content of fillers must be high (tenth ofpercents) to obtain a significant increase of the compositedielectric constant. The main drawback is the large increaseof the Young’s modulus and consequently the loose offlexibility.

On the contrary, the use of conductive fillers leads to anincrease of the dielectric constant at very low contents(some percents) especially if the size of the fillers is verysmall (some nm), as the required electric field is decreasedto obtain the same polarization than unfilled samples. As anadditional consequence, the variation of the Young’s modulusis kept low. This filling must be done without reaching thepercolation threshold for with the composite becomes con-ductive and without decreasing too much the breakdownvoltage. These two parameters not only depend on the fillersmorphology and size and on the polymer matrix but also onthe dispersion and the self-organization of the fillers withinthe matrix.

Table 4 summarizes some results obtained by filling polyur-ethane (PU) and P(VDF-TrFE-CFE) with conductive nanofil-lers. In the same manner, the filling can be achieved usingconductive polymers dispersed within the dielectric matrixleading to the development of all-polymer percolative sys-tems. As an example, coated polyanilines have been dis-persed in a terpolymer matrix in refs. 35 and 36.

Finally, to overcome the problem of agglomeration that canexist when fillers are dispersed within the matrix and to bet-ter control their spatial distribution, Huang and Zhang37

developed chemical bonding of the filler to the backbone ofthe polymer matrix.

The different methods available for enhancing the dielectricpermittivity of polymers are listed in Table 5, which alsogives advantages and drawbacks of each technique. Randomcomposites represent readily applicable approaches suitablefor increasing the dielectric permittivity of elastomers. In thelong run, the challenge consists in synthesizing a new highlypolarizable polymer. All this research is necessary to achievenew generations of electrostrictive polymers, operating atlower electric fields.

PRACTICAL CONSIDERATION AND FIGURE OF MERIT OF THE

CONVERSION

Many of the specific material properties affect all the bulkenergy-harvester properties. In this section, the materialproperties are enumerated and the mechanisms throughwhich they influence the microgenerator performance aredescribed to summarize the previous two sections. The rela-tionships between all introduced system parameters arecharted in Figure 13.

Maximum Electric FieldIn the different configurations, the harvested energy is pro-portional to the square of the applied electric field. Theoret-ically, it is appealing to work with high electric fields toconvert more energy. However, there exist maximum elec-tric fields (Emax), which can be defined as the maximumelectric field strength that the sample can withstandintrinsically without breaking down, that is, without experi-encing failure of its insulating properties. The electric fieldat which breakdown occurs depends on the respective

FIGURE 10 Energy cycles for the pseudo-piezoelectric DC energy-harvesting device (adapted from ref. 28).


POLYMER SCIENCE


geometries of the polymers and the electrodes on which theelectric field is applied, as well as the rate of increase ofthe electric field. Because materials usually contain minutedefects, the practical dielectric strength will be a fraction ofthe intrinsic dielectric strength of an ideal, defect-free,material.

In real cases, the electric field breakdown of EAP variesfrom 70 to 200 MV/m. It originates from various typesof phenomenon such as thermal effect, effect of internaland surface discharges, and effect of path. Moreover, inthe case of real microgenerators, it is important to workunder moderate electric fields to avoid problems inher-ent with high-voltage insulation and to limit the electricloss.

FIGURE 11 Comparison of the maximum harvested energy density for each technique (electrostrictive cycles based on constant

electric field or constant electric displacement during stretching/release are not depicted as they are similar to Ericsson and Stir-

ling cycles).

FIGURE 12 Comparison of the normalized harvested energy

densities.



Maximum Stress and StrainThe strain and stress capacities also come into account inthe development of a vibration-based microgenerator. Theseparameters not only determine the maximum displacementsbut also the maximum forces necessary to produce suchelongations. For example, applications that involve humanmovement harvesting (Fig. 14) features low stress but highdeformations. Therefore, the material must be flexible (lowYoung’s modulus) to avoid interference with the user [thusminimizing the magnitude of forces and being transparentwith a low cost of harvesting (COH)]. Moreover, it must beable to feature deformation of more than 50% while mini-mizing mechanical and dielectric losses to ensure high con-version efficiency. However, for applications where only lowstrain is available (few percents) but with high stress, it isinteresting to have materials with high Young’s modulus toconvert more energy, because the latter is proportional tothe squared stress (assuming a linear strain–stress relation-ship), as depicted in Figure 14.

Frequency BandwidthElectrical and mechanical losses are varying with the fre-quency. These characteristics must be considered during thedevelopment of microgenerators to ensure an optimal extrac-tion of the energy over a wide frequency bandwidth. Figure15 shows the Young’s modulus and mechanical losses as afunction of the frequency considering a constant strain inthe case of pure PU material. For frequencies below 100 Hz,the losses in the material are limited; however, the lossesbecome higher for frequencies around 1 kHz, limiting theoperation of the system for frequencies below this threshold,which correspond to the typical vibration frequency contents(Fig. 2).

Concerning the electrical losses, it is well known that themechanisms of polarization strongly depend on the fre-quency and tend to disappear when the latter is increased,as shown in Figure 16, which depicts the variation of thedielectric permittivity and losses versus frequency in thecase of P(VDF-TrFE-CFE) sample. For example, Maxwell–Wag-ner type polarization is known to be active at the lowest fre-quencies, which explains why a decrease in the dielectricconstant was observed when the measurement frequencywas increased. The effective loss tangent shows the highestvalue for low frequencies due to the electric conduction.38,39

Losses then decrease with the frequency except for the fre-quencies where polarization mechanisms disappear.33

Maximum Energy HarvestingFor every energy-harvesting technique presented in the‘‘Energy-Harvesting Techniques’’ section, it can be seen thatthe electrostrictive coefficient M appears to be an importantparameter to increase the scavenging abilities of the system.Although the ‘‘Increase of the Dielectric Constant and of theElectrostrictive Coefficient with the Help of Fillers’’ sectionprovides a description of the various methods available toincrease this coefficient, the goal of this part is to present afigure of merits able to realize a comparison of the differenttechnique available for harvesting energy.

Ren et al.9 demonstrated that it is possible to harvest 22.4mJ/cm3 using the so-called constant electric field stretchingand open-circuit release methods; however, in case ofpseudo-piezoelectric mode, the harvested energy is equal to34 nJ/cm3.28 Hence, the energy-harvesting abilities using thepseudo-piezoelectric behavior seems to be lower than theelectrostrictive cycle-based energy-harvesting approaches.Although this could be considered a disappointing result,one should keep in mind that these values were not obtainedfor the same excitation and polarization field. For a fair com-parison between each technique, Lallart et al.20 proposed afigure of merit of the scavenging abilities that is able to com-pare the different methods used for energy harvesting. Thisfigure of merit consists of dividing the harvested energy den-sity by the squared mechanical and squared electrical stim-uli, therefore allowing a normalization of the energy withrespect to the external condition. The results obtained in

TABLE 4 Effect of Nanofillers on Material Properties

Polymer Fillers

Content

(vol %)

Dielectric

Constant

Frequency Measurement

of Permittivity (Hz) M33 (m2/V2) 10�15

Frequency

Measurement

of M33 (Hz) Reference

PU No 6.8 0.1 �1 0.1 33

PU SiC 0.5 10.9 0.1 �2.5 0.1 34

PU CB 1 15.4 0.1 �4 0.1 33

P(VDF-TrFE-CFE) No 65 0.1 �1.1 0.1 20

P(VDF-TrFE-CFE) CB 1 95 0.1 �2.4 0.1 20

P(VDF-TrFE-CFE) PANI 23 2,000 100 �0.15 1 35

P(VDF-TrFE-CFE) PANI 12.7 600 100 �0.02 1 35

SiC, silicon carbide; CB, carbon black; PANI, polyaniline.

TABLE 3 Simulation parameters

Parameter Value

Elastic compliance s 2.5 � 10�9 Pa�1

Relative permittivity e/e0 50

Electrostrictive coefficient M 2 � 10�18 V2/m2

Inversion coefficient c 0.8


POLYMER SCIENCE


ref. 20 demonstrate the validity of this new figure of meritand the potential as tools in helping the development of effi-cient microgenerators.

Passive MaterialPortable applications are powered with lower voltages com-patible with battery output. Hence, to generate the high elec-tric field (typically 5 V/lm) required for working in thepseudo-piezoelectric behavior or to realize energy cycles, astep-up voltage converter has to be a part of the generator

circuit as shown in Figure 17. Current challenges in the fieldof energy harvesting using electrostrictive polymers concernthe development of systems able to ensure the generation ofhigh electric fields at a small energy cost. This can be

TABLE 5 Comparison Between the Different Methods for Enhancing the Dielectric Permittivity

Type of fillers Advantages Drawbacks

Random composite Dielectric High dielectric permittivity Large percentage of filler

Increase in elastic modulus

Conductive High dielectric permittivity for

low percentage of filler

Increase in conductivity

Decrease of maximum voltage possible to apply

Polymer blend No fillers Very high dielectric permittivity Process of realization complex

No problem of conductivity

No mechanical reinforcement

FIGURE 13 Relation between electrostrictive microgenerators

and properties of materials.

FIGURE 14 Illustration of the properties of young modulus for

different applications.

FIGURE 15 Mechanical properties of pure PU versus

frequency.

FIGURE 16 Dielectric properties of pure P(VDF-TrFE-CFE) ver-

sus frequency.



realized by the hybridization of electrostrictive polymer withother electroactive materials such as piezoelectric generatorsable to deliver high voltage.

In summary, this section highlighted important materialproperties and their relationships to microgenerators per-formance. The presentation of a figure of merit able toassess the performance of electrostrictive polymers in termsof energy scavenging has also been introduced. This criterionis related to the energy density per cycle per squared strainmagnitude and per squared bias or applied electric field,allowing to evaluate the energy-harvesting abilities inde-pendently from extrinsic parameters such as dimensions, ex-citation, or bias electric field.

APPLICATION OF ELECTROSTRICTIVE POLYMER

GENERATORS

Virtually, any application where there is a need of electricalenergy is a potential application for electrostrictive polymergenerators. However, electrostrictive polymer power genera-tion is much more competitive for some applications whencompared with others. For example, electrostrictive polymersare well suitable for harvesting energy for human motion.Natural muscle, the driving force for human motion, is typi-cally of low frequencies and intrinsically linear, both charac-teristics where electrostrictive polymers offer advantages.Many other interesting generator applications exist for elec-trostrictive polymers. Remote and/or wireless devices aregrowing in use, and these devices can ideally harvest theirown energy to eliminate the need of battery replacement.Electrostrictive polymers are well suited for these applica-tions if mechanical energy is available from oscillatory or vi-bratory motions such as that might occur in portable devicescarried by people, animals, plane, and so forth.

CONCLUSIONS

The further development of electrostrictive polymers as a via-ble micro-generators technology requires much work, and tothis end, numerous exciting challenges lie ahead. First, the de-velopment of improved electrostrictive polymer is essential.

Continued research into the effect of the incorporation ofdielectric and dielectric fillers could lead to the simultaneousenhancement of electromechanical activities and the reductionof operating voltage. Such improvements would serve tobroaden application spectrum of these types of microgenera-tors. For example, significant reduction of operating voltagecould enable applications of realistic autonomous system.

EAPs and in particular electrostrictive polymers werereviewed in this article as exciting candidate materials forthe development of a new age of microgenerator material.The different principles of operation of these materials werepresented. The advantages of electrostrictive polymers overconventional microgenerator technologies in a number ofmetrics, in addition to some of the unique characteristics,which they can offer, were discussed. Electrostrictive poly-mers were examined at both the material and the microgen-erators configuration level. Important material parameters,both mechanical and electrical, are highlighted and variousapproaches to optimize these properties for the developmentof superior energy harvester devices were addressed. Suchapproaches included the incorporation of dielectric fillersand conductive fillers. In conclusion, electrostrictive polymergenerators have been studied extensively under laboratoryconditions where they have shown promising performance.However, in practical applications, they have not yet achievedtheir full potential.

REFERENCES AND NOTES

1 Taylor, G. W.; Burns, J. R.; Kammann, S. A.; Powers, W. B.;

Welsh, T. R. IEEE J. Oceanic Eng. 2001, 26, 539–547.

2 Ottman, G. K.; Hofmann, H. F.; Bhatt, A. C.; Lesieutre, G. A.

IEEE Trans. Power Electron. 2002, 17, 669–676.

3 Choi, W. J.; Jeon, Y.; Jeong, J.-H.; Sood, R.; Kim, S. G. J.

Electroceram. 2006, 17, 543–548.

4 Sodano, H. A.; Park, G.; Inman, D. J. Strain 2004, 40, 49–58.

5 Ren, K.; Liu, Y.; Geng, X.; Hofmann, H. F.; Zhang, Q. M. IEEE

Trans. Ultrasonics Ferroelectrics Frequency Control 2006, 53,

631–638.

6 Sebald, G.; Seveyrat, L.; Guyomar, D.; Lebrun, L.; Guiffard,

B.; Pruvost, S. J. Appl. Phys. 2006, 100, 124112.

FIGURE 17 Schematic representation of autonomous electrostrictive l-generator.


POLYMER SCIENCE


7 Bar-Cohen, Y. Ind. Robot Int. J. 2003, 30, 331–337.

8 Damjanovic, D. Rep. Prog. Phys. 1998, 61, 1267–1324.

9 Ren, K.; Liu, Y.; Hofmann, H.; Zhang, Q. M.; Blottman, J.

Appl. Phys. Lett. 2007, 91, 132910.

10 Meninger, S.; Meninger, S. A low power controller for a

MEMS based energy converter, Masters Dissertation, Massa-

chusetts Institute of Technology, Massachusetts, 1999.

11 Koh, S. J. A.; Zhao, X.; Suo, Z. Appl. Phys. Lett. 2009, 94,262902.

12 Mahmoud, M. A. E.; Abdel-Rahman, E. M.; El-Saadany, E.

F.; Mansour, R. R. Smart Mater. Struct. 2010, 19, 025007.

13 McKay, T.; O’Brien, B.; Calius, E.; Anderson, I. Appl. Phys.

Lett. 2010, 97, 062911.

14 Lee, C.; Ye, M.; Bin, Y.; Rama, K.; Chun-Huat, H. Sens.

Actuators A 2009, 156, 208–216.

15 Liu, Y. Proc. SPIE 2004, 5385, 17–28.

16 Liu, Y.; Ren, K. L.; Hofmann, H. F.; Zhang, Q. IEEE Trans.

Ultrasonics Ferroelectrics Frequency Control 2005, 52,

2411–2417.

17 Jean-Mistral, C.; Basrour, S.; Chaillout, J.-J. Smart Mater.

Struct. 2010, 19, 085012.

18 Lebrun, L.; Guyomar, D.; Guiffard, B.; Cottinet, P.-J.; Putson,

C. Sens. Actuators A 2009, 153, 251–257.

19 Cottinet, P.-J.; Guyomar, D.; Guiffard, B.; Putson, C.; Lebrun,

L. IEEE Trans. Ultrasonics Ferroelectrics Frequency Control

2010, 57, 774–784.

20 Lallart, M.; Cottinet, P.-J.; Lebrun, L.; Guiffard, B.; Guyomar,

D. J. Appl. Phys. 2010, 108, 034901.

21 Madden, J. D. W.; Vandesteeg, N. A.; Anquetil, P. A.; Mad-

den, P. G. A.; Takshi, A.; Pytel, R. Z.; Lafontaine, S. R.; Wier-

inga, P. A.; Hunter, I. W. IEEE J. Oceanic Eng. 2004, 29,

706–728.

22 Guyomar, D.; Lallart, M.; Cottinet, P.-J. Phys. Lett. A 2011,375, 260–264.

23 Guyomar, D.; Badel, A.; Lefeuvre, E.; Richard, C. IEEE

Trans. Ultrasonics Ferroelectrics Frequency Control 2005, 52,

584–595.

24 Qiu, J.; Jiang, H.; Hongli, J.; Kongjun, Z. Frontiers Mech.

Eng. China 2009, 4, 153–159.

25 Shu, Y. C.; Lien, I. C.; Wu, W. J. Smart Mater. Struct. 2007,16, 2253–2264.

26 Qiu, J.; Jiang, H.; Ji, H.; Zhu, K. Frontiers Mech. Eng. China

2009, 4, 153–159.

27 Guyomar, D.; Sebald, G.; Pruvost, S.; Lallart, M.; Khodayari,

A.; Richard, C. J Intell. Mater. Syst. Struct. 2009, 20, 609–624.

28 Cottinet, P.-J.; Lallart, M.; Guyomar, D; Guiffard, B.; Lebrun,

L.; Sebald, G.; Putson, C. IEEE Trans. Ultrasonics Ferroelectrics

Frequency Control 2011, 58, 30–42.

29 In the case of pseudo-piezoelectric DC energy harvesting,

the nonlinear interface can be either added in parallel or in se-

ries with the active material.24 However, only the parallel case

will be presented here for the sake of simplicity. All the other

developed interface for piezoelectric energy-harvesting systems

may also be used,30–32 but will not be presented here, as their

application is straightforward.

30 Makihara, K.; Onoda, J.; Miyakawa, T. Smart Mater. Struct.

2006, 15, 1493–1498.

31 Lallart, M.; Garbuio, L.; Petit, L.; Richard, C.; Guyomar, D.

IEEE Trans. Ultrasonics Ferroelectrics Frequency Control 2008,55, 2119–2130.

32 Lallart, M.; Guyomar, D. Appl. Phys. Lett. 2010, 97, 014104.

33 Wongtimnoi, K.; Guiffard, B.; Bogner-Van de Moortele, A.;

Seveyrat, L.; Gauthier, C.; Cavaill�e, J.-Y. Compos. Sci. Technol.

2011, 71, 885–892.

34 Guiffard, B.; Seveyrat, L.; Sebald, G.; Guyomar, D. J. Phys.

D: Appl. Phys. 2006, 39, 3053–3057.

35 Huang, C.; Zhang, Q.M.; Su, J.Appl. Phys. Lett. 2003, 82, 3502.

36 Bobnar, V.; Levstik, A.; Huang, C.; Zhang, Q. M. J. Non--

Cryst. Solids 2007, 353, 205–209.

37 Huang, C.; Zhang, Q.-M. Adv. Mater. 2005, 17, 1153–1158.

38 Putson, C.; Lebrun, L.; Guyomar, D.; Muensit, N.; Cottinet,

P.-J.; Seveyrat, L.; Guiffard, B. J. Appl. Phys. 2011, 109, 024104.

39 Chu, B.; Zhou, X.; Ren, K.; Neese, B.; Lin, M.; Wang, Q.;

Bauer, F.; Zhang, Q. M. Science 2006, 313, 334–336.



Date post:	14-Nov-2023
Category:	Documents
Upload:	independent
View:	0 times
Download:	0 times

Electrostrictive polymers for mechanical energy harvesting

Documents