Flexible autonomous scavengers: the combination of dielectric polymers and electrets.

C. Jean-Mistral*a, T. Vu Congb, A. Sylvestreb

aLAMCoS, 18-20 rue de la science, 69621 Villeurbanne, France; bG2Elab, 25 rue des martyrs, BP166, 38042 Grenoble, Cedex 9, France

ABSTRACT

Thanks to their high energy density and their flexibility, scavenging energy with dielectric polymer is a promising alternative to ensure the autonomy of various sensors such as in e-textiles or biomedical applications. Nevertheless, they are passive materials requiring a high bias voltage source to polarize them. Thus, we present here a new design of scavenger using polymer electrets for poling the dielectric polymer. Our scavenger is composed of commercial dielectric polymer (3M VHB 4910) with Teflon electrets developing a potential of -300V, and patterned grease electrodes. The transducer works in a pure shear mode with a maximal strain of 50% at 1Hz. The typical “3D-textured” structure of the scavenger allows the electrets to follow the movement of the dielectric. A complete electromechanical analytical model has been developed thank to the combination of electrets theory and dielectric modelling. Our new autonomous structure, on an optimal resistance, can produce about 0.637mJ.g-1. Keywords: Dielectric polymer, electret, energy scavenging

1. INTRODUCTION In the past decade, few generators using dielectric polymers have been developed. In 2001, Pelrine et al. have proposed a dielectric generator embedded in a shoe [1]. This structure is able to scavenge up to 0.8J per step, or about 1W while walking (energy density of 0.3J.g-1), but with a bias voltage of 2.5kV. Then, they focus their developments on high level of energy (production: W, kW) rather then low level of energy (scavenging: mW) and create a water mill generator and a wave power generator [2] [3]. Their first ocean-wave generator is composed of dielectric elastomer in a roll configuration (150g) and can produce up to 12J for one cycle (energy density of 0.08J.g-1), but with a bias voltage of 2000V. The second generation uses 220g of active material for an output energy of 25J (energy density of 0.1J.g-1). The energy harvesting circuit is quite simple and insures an efficiency of 78%. More recently, Iskandarani et al. scavenge 94.5mJ with the polymer PolyPowerTM from Danfoss, under 15% of strain and 1.8kV of poling voltage during a cycle at constant charge Q [4]. The generator proposed by Mac Kay et. al. also use a high bias voltage (2kV) and is able to scavenge an average output power up to 0.8mW. They associate their generator with a pump charge, converting 5V to 2kV, avoiding the use of a high voltage source but delaying the starting of the generator [5]. More recently, Eitzen et. al. develop specified bidirectional flyback converters for dielectric generator [6] [7]. These circuits insure the realization of the energetic cycle (charge and discharge of the dielectric) and the adaptation between low storage voltage (few volts) and the high bias voltage (2kV). Nevertheless, they use transformers and a lot of switches, which make these circuits heavy and complex. On an other hand, Jean-Mistral et. al. have chosen to develop dielectric generator working under moderate voltage. They have created a patch that harvests energy from a person’s knee while walking. This structure is designed to produce 100μW with a bias voltage of 170V, but can easily produce up to 1.74mW under a poling voltage of 1000V [8]. The challenge is therefore to realize a transducer perfectly autonomous, namely without any external voltage source (either high or low voltage source). This generator must also be close to the application and integrable, deformable, adaptable. It would be able to produce enough energy to supply a low consumption system. One solution to this issue is to combine dielectric polymer and electrets. We present, in this paper, a new design of scavenger combining these two active polymers and the corresponding analytical model. This model would describe a scavenging cycle for simple structure as plate. Finally, an optimization is proposed. *Claire.jean-mistral@insa-lyon.fr (+33)472438727;

Electroactive Polymer Actuators and Devices (EAPAD) 2012, edited by Yoseph Bar-Cohen, Proc. of SPIE Vol. 8340, 834029 · © 2012 SPIE · CCC code: 0277-786X/12/$18 · doi: 10.1117/12.915149

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2. PRINCIPLE 2.1 Classic scavenging cycle with dielectric polymer

Dielectric polymers work as a variable capacitors. When a voltage is applied to the structure, an electrostatic pressure, called Maxwell stress, appears (equation 1).

20= Eεεσ rm (1)

0ε is the permittivity of the vacuum, rε is the dielectric constant of the polymer and E is applied electric field. This pressure induces mechanical pressure on the top and bottom electrodes. Thus, the polymer becomes thinner and expands in the plane.

Dielectric elastomers are passive materials which need the realization of energy cycle to scavenge mechanical energy, as depicted in the figure 1 [9].

Deformation modeDeformation mode

A: Pre-stretchedmembraneA: Pre-stretchedmembrane

λD: membrane on equilibrium

VStretch off

λD: membrane on equilibrium

VStretch off

λ act

B: Mechanicalstretched membrane

Stretch on

λ act

B: Mechanicalstretched membrane

λ act

B: Mechanicalstretched membrane

Stretch on

V

C: Polarizedmembrane

Polarization on

V

C: Polarizedmembrane

Polarization onPolarization offPolarization off

λ p

0: Referencemembrane

Pre-stretch

λ p

0: Referencemembrane

Pre-stretch

Sensor or generator modeSensor or generator mode

Fig 1. Scavenging energy cycle

λp λact λ are tensors related to the expansion coefficients.

An energy cycle is composed of four phases: stretch, charge, active phase and discharge. The polymer is stretched in order to increase its capacitance: stretch phase or phase A to B on figure 1. Then, at this point, the capacitor is charged by a voltage V: charge phase or phase B to C on figure 1. At this point, the polymer stores an input energy. To increase this stored energy, the capacitance of the structure has to be reduced. The material is therefore relaxed and moves to a point of equilibrium between elastic and electric stresses (phase C to D). This is the active phase: the variation of the expansion coefficient λ induces a decrease in capacitance, thus generating electric energy. The input electric energy is thus amplified thanks to the mechanical strain energy. Finally, all charges are removed from the structure and the material returns to its initial dimensions: discharge phase or phase D to A on figure 1. To overcome the use of a very high constant voltage (V), the material can be pre-strained with an expansion coefficient λp (phase O to A). Figure 2 shows the variations of Maxwell stress TM as a function of the expansion coefficient λ. For each expansion coefficient λ imposed on the polymer, the elastic and electrical stresses offset one another for a specific electric field. A law of equilibrium can be deduced, separating the operating area into one actuator area and one generator area. For instance, if Maxwell stress is greater than elastic stress, the dielectric polymer is in actuator mode. In the generator area, the three main energy cycles described in figure 2, are cycles at constant voltage V (cycle ABCD’’), at constant charge Q (cycle ABCD’) or at constant electric field E (cycle ABCD).

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Fig 2. Actuator and generator areas

For energy cycles at constant voltage V and cycles at constant charge Q, the expression of the electric energy produced ePRO during these cycles is reported in equation 2.

)(21 2

CC2DDPRO VCVCe = (2)

CD, VD are capacity and voltage at point D of the cycle in figure 1. CC, and VC are capacity and voltage at point C on the same figure. Information on state D is obtained by resolving the motion equation of the active phase of an energy cycle (equation 3).

wextMm FFFFamrrrrr +++= (3)

m is the structure’s mass and ar its acceleration. mF

ris the mechanical force in the dielectric structure and MF

r is the

electrostatic force imposed on the polymer. extFr

represents all the external forces applied to the structure by an operator

or an object such as a spring. wFr

is the weight of the structure and is usually neglected because of the very low mass density of dielectric polymers. For this study, thermal aspects and electrostrictive stresses are neglected. The final scavenged energy Escavenged is reported in equation 4.

Escavenged = E pro − Elosses (4)

Electric losses Elosses include losses by conduction, by diffusion on the dielectric polymer and dielectric losses function of the operating frequency. All these losses are included in the loss factor of the dielectric polymer. The losses induced by the surface resistance can be added to these bulk losses.

2.2 Energy scavenging with electret

An electret is a dielectric material able to keep a charge during years. It is acting like an electric dipole and can ensure a permanent polarisation of a capacitance (figure 3).

Expansion coefficient λ1

Actuator area

Generator area

Equilibrium

A

B

C D

D’

D’’ Max

wel

l stre

ss o

n z

axis

in P

a

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- - - - - - - - - - - - - - - - - - -

dσ

V

ε0εr

0

C

V

- - - - - - - - - - - - - - - - - - -

dσ

V

ε0εr

0

C

V

Fig 3. Modeling of an electret The electret is generally inserted in an electrostatic generator (figure 4). It has a fixed charge Qi and is deposited on an electrode. A counter-electrode separated with an air gap faces the electrode. If Q1 is the charge on the electrode and Q2 the charge on the counter-electrode, the charge equilibrium Qi = Q1+ Q2 must be respected at any time.

RL

i

- - - - - - - - - - - - - -

+ + + + + + + + + + +

+ + + + + + + + + + + Electret

Counter electrode

Electrode

RL

i

C1

C2

Q2

Qi

Q1

RL

i

- - - - - - - - - - - - - -

+ + + + + + + + + + +

+ + + + + + + + + + + Electret

Counter electrode

Electrode

RL

i

C1

C2

Q2

Qi

Q1 Fig 4. Basic structure of an electret generator

Generally, the electrode is fixed and the counter electrode can move on the plane (parallel to the electrode) or on the thickness (get closer to the electrode). These changes in the geometry of the capacitor are induced by vibrations from the environment. Thus, the value of the capacitance (C2) varies, and the charges on the electrode and on the counter electrode reorganize themselves through the load RL. A current circulation through the load is generated: mechanical energy is scavenged.

Electret generators are classically resonant structures that harvest energy from vibrations. A resonant structure is a “mass-damping-spring” structure (m, bm, k) submitted to external vibrations y(t). A part of the mechanical energy is lost due to mechanical damping (bm) modelled as a viscous friction force, while the other part is converted into electricity (electrostatic force felec). Equation 5 describes the electromechanical coupled equation of an electret generator.

2 21m elec

L eq L

mx b x kx f myQ QVt R C R

+ + + = −∂

= −∂

&& & &&

(5)

V is the surface potential of the electret and Ceq is the equivalent capacitor composed of the electret capacitor C1 in series with the variable capacitor C2. Electret energy harvesters are used for MEM’s applications and produce low level of power. For example, Sanyo et. al. produce 40µW with their structure (9cm²) at 2Hz [10]. And Omron et. al. scavenge 10µW at 20Hz with a structure sizing of 4cm² [11]. 2.3 The autonomous scavengers

The idea is to combine an electret and a dielectric polymer. We replace the air gap of the electret generator structure by a dielectric polymer (figure 5). C1 is the capacitor describing the electret, C2 is a variable capacitor describing the dielectric polymer and RL is a load.

The structure depicted on figure 5 has the same operating principle than a classic electret generator. The relative movement between the electrode and the counter electrode generate a re-arrangement of electrical charge between these two electrodes through the load resistance RL, and generates an alternative current i. As dielectric polymer work on

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quasi-static range (<10Hz), the relative movement between the electrode is induced by an external mechanical force and allow a movement in the three direction (plane and thickness). The governing equations are reported in equation 6.

RL

i

- - - - - - - - - - - - - -

+ + + + + + + + + + +

+ + + + + + + + + + + Electret

Counter electrode

Dielectric

Electrode

RL

i

C1

C2

Q2

Qi

Q1

RL

i

- - - - - - - - - - - - - -

+ + + + + + + + + + +

+ + + + + + + + + + + Electret

Counter electrode

Dielectric

Electrode

RL

i

C1

C2

Q2

Qi

Q1 Fig 5. Electret/Dielectric generator

2 21ext meca elec

L eq L

ma f f fQ QVt R C R

= + +∂

= −∂

r r rr

(6)

To increase the output electrical power, the charge flow must be important and so the variation of capacity must be huge. One way to attend this goal is to use a dielectric polymer with a high dielectric constant. Another way is to allow large deformation of the dielectric polymer. Nevertheless, electret and dielectric polymer suffer different level of deformations. Thus, the generator must be textured to well function and increase the output power.

3. ANALYTICAL MODEL

3.1 Dielectric polymer

We have chosen a polymer with large deformations (300% on average) and high relative permittivity (4.7). Mechanical behavior of this polymer has been largely investigated in the last decade [8] [12]. Our analytical model is based on the quasi-linear viscoelastic model. In hyper-elasticity, true stresses Ti are defined by equation 7.

i ii

WT pλλ

∂= −

∂ (7)

λi is the extension coefficient on principal axes (x=1, y=2, z=3), W is the strain energy and p the hydrostatic pressure. This pressure is unknown and depends on the boundary conditions of the mechanical structure. Strain energy W is taken as Money-Rivlin form (equation 8).

)3()3( 220110 −+−= ICICW (8)

I1, I2 are the first and second invariants of the left Cauchy Green deformation tensor:

23

22

211 λλλ ++=I

23

22

21

2111λλλ

++=I (9)

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The polymer 3M VHB 4910 (or 4905) works at constant volume ( 13213 == λλλI ). The ijC parameters describe the hyper-elastic response and can be calculated by fitting the model to a uniaxial tensile test (C10= 0.01875MPa and C20= 0.03368MPa). Another crucial parameter for the model is the dielectric constant of the polymer. This physical parameter and its variation with frequency, temperature, pre-strain and nature of the electrode has been investigated with a dielectric spectrometry apparatus from Novocontrol company [13].

Table 1. Electric parameters of 3M VHB 4910-10 polymer at 1Hz and ambient temperature (20°C)

Gold electrode

no pre-strain no pre-strain area pres-train of 16

Dielectric constant 4,7 5,4 4,6

Loss factor 0,015 0,04 0,05

Grease electrode

Changing the nature of the electrode changes the value of the dielectric constant [13]. Moreover, the pre-strain applied to the polymer tends to decrease the value of the dielectric constant.

3.2 Electret

We chose an organic electret in order to build a fully flexible generator. Moreover, only electret with a low dielectric permittivity (low-k) can develop a high surface potential, for thin layers.

Table 2. Parameters of the most used organic electret [14] [15] [16]

Organic material Potential surface (V) Comments

CYTOP CTL-M -550 stable (>165 days)

Parylene C -80 stable after 40days

Parylene HT -650 stable (few days)

Teflon AF -85 decrease of 0,06V/day

Teflon FEP -250 decrease of 0,25V/day

Teflon PFA -400 stable

Teflon PTFE -290 decrease of 0,1V/day An electret in Teflon is chosen because of his high surface potential (up to -400V) and good stability (no surface potential decrease with time). This polymer is a commercial sheet charged by Corona discharge. From an electrical point of view, the dielectric constant is 2.2 and the surface potential is chosen to be -300V. From a mechanical point of view, the Young modulus is about 1GPa and the deformation is quite small (<1%).

3.3 Device

As the electret material and the dielectric polymer suffer different deformations, the generator structure is textured. Moreover, we do not have any reliable information on the behavior of the electret under stress: maybe the charges are dissipated and the surface potential decrease when stress increase. Thus, we decide not to strain the electret but only the dielectric polymer. The figure 6 described the final structure. It is composed of a frame (rigid plastic), a rigid electrode (gold or copper scotch) a non deformable electret (Teflon), a dielectric polymer (3M VHB 4910) and a conductive compliant electrode (carbon grease). Only the dielectric polymer and its compliant electrode can be deformed. The others constituents of the structure can only move between two pre-defined extreme positions (those showed on figure 6).

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Strain

RL

i

Electret

Compliantelectrode

Electrode

Dielectric

Frame

+ +

+ +

RL

i

x

z

+ +

- -

+ +- -

+ +

- -

+ +- -

+ + + + + +

+ + + + + + - - - - - - -+ + + + + +

+ + + + + + - - - - - - -

Strain

RL

i

Electret

Compliantelectrode

Electrode

Dielectric

Frame

+ +

+ +

RL

i

x

z

+ +

- -

+ +- -

+ +

- -

+ +- -

+ +

- -

+ +- -

+ +

- -

+ +- -

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + + - - - - - - -+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + + - - - - - - -

Fig 6. Electret/Dielectric generator – Side view

Due to the configuration of the generator, the dielectric polymer supports a pure shear deformation along the x direction. The width (along y) is keeping constant. The length of the scavenger is 20cm and the width is 2cm (figure 7). We choose a maximal deformation of 50%, and a period of 1s.

……

Top view Side view

Electret

Compliantelectrode

Electrode

Dielectric

Frame

x

y

x10

x20

x1d0

xf

x1d0

x30

xair

xf

z

x

xf

xb

xe

……

……

Top view Side view

Electret

Compliantelectrode

Electrode

Dielectric

Frame

x

y

x10

x20

x1d0

xf

x1d0

x30

xair

xfxf

z

x

xfxf

xb

xe

Fig 7. Detail of the electret/Dielectric generator – Top and Side view

Thanks to equation 6 and the mechanical law of the polymer (equation 7 to 9), the intrinsic equation of the scavenger can be detailed (equation 10).

( )

22220 2

1 0 10 202 230

2 2

122

1

d exteq

L eq L

x Qmx C C ft x C

Q QVt R C R

λλ λλ λ

⎡ ⎤⎛ ⎞⎡ ⎤∂ ∂⎛ ⎞= − + − + +⎢ ⎥⎜ ⎟⎢ ⎥⎜ ⎟ ⎜ ⎟∂ ∂⎝ ⎠ ⎢ ⎥⎣ ⎦ ⎝ ⎠⎣ ⎦∂

= −∂

(10)

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V is the surface potential of the electret. Ceq is the equivalent capacitance composed of the electret capacitor C1 in series with the variable capacitor C2. This variable capacitor is the capacitor formed by the dielectric and the air with an equivalent dielectric constant obtained thanks to mixing rule.

rair rdreq

rair d rd airV Vε εε

ε ε=

+ (11)

Vd and Vair are volume fraction of dielectric and air respectively. εrair and εrd are the dielectric constant of air (1) and dielectric polymer (4.6) respectively. Thanks to geometric considerations, capacitors are approximated and analytically calculated with plane capacitance equation. Finally, the average output power Pout, in steady state, is given by equation 12.

2

1

2

2

2 1

1_

t

outt

dQP R dtt t dt

⎛ ⎞= ⎜ ⎟⎝ ⎠∫ (12)

4. NUMERICAL SIMULATIONS

4.1 Optimization

The output power will be maximal for an appropriate geometry and an optimal load. We link all the geometric parameters (figure 7) and underline two specific parameters for the optimization: the compliant electrode length x1d0 and the width of the pattern xb. Figure 8 plots the average output power obtained with a load resistance of 1MΩ. This power is for the total structure (20cm per 2cm), namely for 20 patterns when the pattern width is 1cm, 13 patterns when the pattern is 1,5cm and 10 patterns when the pattern width is 2cm.

0

10

20

30

40

50

60

70

80

0 0,5 1 1,5 2

Compliant electrode width (cm)

Ave

rage

out

put p

ower

(µW

)

xb=1,5xb=1xb=2

Fig 8. Average output power in function of two geometric parameters

On an other hand, figure 9 shows the variation of the average output power in function of the load RL for two particular cases: pattern width of 1,5cm and the compliant electrode width of 1cm; and pattern width of 2cm and the compliant electrode width of 1.5cm.

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0

10

20

30

40

50

60

70

0 1 2 3 4 5 6 7 8 9 10

Optimal load (Mohm)

Ave

rage

out

put p

ower

(µW

)

xb=1.5cm and x1d0=1cm

xb=2cm and x1d0=1.5cm

Fig 9. Average output power in function of the optimal load

Thanks to these simulations, we chose a structure with a width pattern of 2cm and a compliant electrode width of 1,5cm. The optimal resistance is about 1MΩ.

4.2 Output characteristic

With the geometry chosen, figure 10 shows the evolution of the expansion coefficient along the length and the output voltage on the load RL.

2 3 4 5 6 7 8 9 101

1.05

1.1

1.15

1.2

1.25

1.3

1.35

1.4

1.45

1.5

Time (s)

Expa

nsio

n co

effic

ient

alo

ng th

e le

ngth

1.45 1.46 1.47 1.48 1.49 1.5 1.51 1.52 1.53 1.54 1.55

-200

-150

-100

-50

0

50

100

150

Time (s)

Out

put v

olta

ge (V

)

Fig 10. Expansion along the length and output voltage

Due to the sinusoidal imposed external load (fext) and the pure hyper-elastic properties of the dielectric polymer, the expansion coefficient among the length is quite sinusoidal. This induces a symmetric variation for the charge Q2 and for the output voltage on the load, between stretching and compressive phase.

The proposed generator developed a high output voltage (120V) under a low current (0,12mA). For cycle at 1Hz, the average output power is about 61µW and the density of produced energy is 0,637mJ.g-1. This value is ten times those obtained with a piezoelectric polymer (60µJ.g-1) and twice those obtained with electrostrictive polymer (0.3mJ.g-1). This structure is able to scavenge 245µW on 1MΩ at 1Hz with an electret developing a surface polarization of -600V, and up to 680µW on 1MΩ at 1Hz with a bias voltage of -1000V. In this last case, the output voltage is about 400V, letting us using simple component for the electronic circuit. Finally, the associated power circuit is quite simply and consists in a simple diode rectifier.

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5. CONCLUSION In this paper, we have presented a new concept of scavenger combining dielectric polymer and electret. This generator is completely flexible, light and deformable, allowing an adequate integration and a lot of applications such as e-textile. Moreover, thanks to the use of electret polymers, any external voltage source or electric circuit (pump charge) is needed to create the bias voltage. One can underline the simple associated power electronic (diode rectifier). In this paper, we have developed a complete analytical modeling of the structure combining the theories of dielectric polymer and electret generator. The optimized structure is expected to scavenge up to 61µJ at 1Hz, with a potential surface of -300V for the electret. The improvement of generator will requires the use of performing polymer electret, i.e. with a high surface potential and a very good stability. Finally, the realization and tests of these news scavengers are under development.

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