Abstract—Dielectric elastomers have demonstrated most
potential as muscle-like actuators because they can undergo large deformation, have a high energy density and a relatively fast response. The basic structure of a dielectric elastomer (DE) is simple - an elastomer film sandwiched between two electrodes. The electrodes that sandwich the elastomer play a key role in the electromechanical performance. The electrodes must be highly compliant, have low mechanical stiffness and remain conductive for large area strains. Much research emphasis is being placed on the design of more sophisticated complaint electrodes that combine very good conductivity with improved robustness in the face of electrical breakdown. This contribution discusses compliant metal electrode technology and reviews some of the research being carried out in this area at the Mads Clausen Institute.
I. INTRODUCTION For decades both material scientists and engineers have
sought to find an artificial equivalent of muscle to help in the development of new transducer technology. This is because muscles, simply by changing their length in response to nerve stimulation, can exert controlled amounts of force. They are also scale invariant. In the search for an artificial equivalent of muscle electroactive polymers (EAP), have gained considerable attention. These polymers exhibit interesting properties, such as sizable strain and stress in response to an applied electric field. A specific class of EAP known as ‘dielectric elastomers’ have demonstrated most potential as muscle-like actuators because they can undergo large deformation (strain up to 380% in area), have a high energy density (3.4 J g-1) and a relatively fast response [1, 2].
Fig. 1. Basic principle of DE transduction. The basic structure of a dielectric elastomer (DE) is simple - an elastomer film sandwiched between two electrodes. In actuator mode the applied electrical energy is converted into mechanical energy - the force of attraction between the electrodes squeezing the incompressible soft polymer film
thereby causing a change in the area and thickness of the film, see Fig. 1.
The electrodes that sandwich the elastomer also play a key role in the electromechanical performance of the DE. The electrodes, ideally, must be highly compliant. The electrode surface must remain conductive for large area strains such that charge can continue to flow onto the electrodes and maintain deformation of the dielectric film. Also the mechanical stiffness of the electrodes should be low so that it does not impede the expansion of the soft elastomer film. Much research emphasis is being placed on the design of more sophisticated complaint electrodes that combine very good conductivity with improved robustness in the face of electrical breakdown [3]. This contribution discusses compliant metal electrode technology and reviews some of the related research being carried out at the Mads Clausen Institute (MCI).
II. EAP MATERIAL The fundamental performance characteristics of a variety of
popular EAP materials are compared with natural muscle in Table 1. This data refers to the performance of materials – practical EAP actuators often achieve only a small fraction of these maximum values.
TABLE I: PROPERTIES OF EAP MATERIAL
Electromechanical coupling is 60-80% for acrylic and up to 90% for silicone elastomer - the two most popular DE
materials. Large strains lead to a high energy density in the elastomer. A value of 3.4 Jg-1 has been obtained for acrylic VHB 4910, pre-strained by a factor between 3 and 5. This is 50 times the energy density of human muscle.
III. FUNDAMENTAL CHARACTERISTICS The fundamental equations for DE transduction provide the coupling between the applied electric field and the resulting mechanical behaviour. DE material is basically a capacitor with very compliant dielectric and electrodes. The Maxwell stress, P, created in the DE due to the electric field-based attraction of the two electrodes is [4]:
20P Erε ε= (1)
where ε0 is the permittivity of free space, εr the permittivity of the dielectric, A the area and t the thickness of the dielectric. E represents the electric field and P is the compressive stress exerted over A. This expression gives twice the corresponding normal stress than a parallel plate capacitor because the complaint electrodes in a DE increase in area as well as becoming closer together as the electric field is increased. Since E=V/t, the higher the permittivity then the lower the voltage needed to achieve a given compressive stress with a given film thickness. This observation has led to research into the development of dielectric materials with high permittivity’s in order to reduce the operating voltage and reduce susceptibility to electrical breakdown [5]. Adding fillers and additives to the polymer matrix, in many cases, has been found to reduce the mechanical strength as well as the electrical breakdown properties of the DE [6]. In conjunction with ‘novel’ application development this is one of the most active DE-related research areas. Theoretically it is also possible to reduce the operating voltage by using thinner sheets of elastomer. Unfortunately the performance and stability of a DE actuator also relies heavily on the quality and uniformity of the fabricated elastomer film. Inherent material defects, defects induced during fabrication and environmental factors, such as moisture, can cause accelerated dielectric breakdown and terminal failure of the entire device.
The electrodes that sandwich the elastomer also play a major role in the DE electromechanical performance. Thus far, carbon grease, carbon powder and graphite have been the most popular choices, especially with acrylic elastomers, because they do not change the mechanical stiffness of the elastomer, thereby not impeding expansion.
IV. COMPLIANT METAL ELECTRODES Alternative compliant electrode technology includes
conducting polymers, carbon nanotubes and compliant metal electrodes. Compliant metal electrodes satisfy conductivity requirements and provide increased robustness when electrical breakdown occurs because of a self-healing property. Metal coatings are commonly used in the plastics industry as gas and moisture barriers but also for electrostatic discharge and electric circuitry applications, so the processing methods are
well established and used for high volume production. This is a distinct advantage as these established processing methods will provide the basis for the commercial development of compliant metal electrode-based DE’s [7].
Pelrine et al. [4] were the first to seriously address the role of compliant electrodes in detail. A number of approaches were suggested with it being pointed out that metals would be highly preferable, but that they would have to be designed to be compliant on the elastomer surface, to allow expansion of the DE, since simple flat metal films cannot undergo large strains. Bowden et al., [8] found that gold films evaporated on polydimethylsiloxane (PDMS) buckled as a result of the thermal contraction of the PDMS producing ordered buckling structures. Research into compliant metal electrodes is not confined to DE research with there also being growing interest in electronics for flexible applications [9, 10]. The initial attempts at producing compliant electrodes for DE’s involved using photolithography to create gold electrodes in the form of zig-zag stripes [4] and the design of a full connected pattern that only provided unidirectional motion [11]. The current state of development of the technology is illustrated in Fig. 2 where the corrugated electrode design allows unidirectional motion of the DE on the application of a potential to the electrodes.
Fig. 2. Unidirectional motion using corrugated metal electrodes. The disadvantage of compliant metal electrodes is that they will increase the mechanical stiffness of the elastomer. The moduli of elasticity of metals are orders of magnitude times higher than elastomers therefore there is interest in applying the thinnest layer of metal electrode on to the elastomer surface to minimise any increase in mechanical stiffness in the DE material. To show an appreciable conductivity though the metal film must be sufficiently thick to be continuous. The maximum strain that a compliant metal electrode is able to achieve is dependent upon the corrugation profile. For a rectangular electrode profile, of thickness, h, 50 nm, with amplitude, a, 2 μm and period, p, of 10 μm the maximum DE strain is 80% (in the direction of the corrugation). The compliance factor, that is the increase in compliance of a corrugated electrode relative to a flat metal electrode of the same thickness, was determined by Benslimane and Gravesen [11] for a rectangular profile to be 216( / )( / )cf a p a h= and the effective Young’s modulus for a corrugated electrode to be
/corr metal cY Y f= . The force constants of the compliant
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electrode and the elastomer, thickness, d, are added together in parallel to provide a total modulus for the DE material of
( / )total corr elastY Y h d Y≈ + . At the MCI mechanical testing is used to determine the elastic modulus of DE material. Table 2, adapted from [12], reviews the maximum strain, Smax obtainable for a range of corrugation profiles. Note that x= 4a/p. The Smax values given in the right hand column are for a = 2 μm and p = 10 μm.
TABLE II: MAXIMUM STRAIN AND CORRUGATION PROFILES
V. POLYPOWER MATERIAL Danfoss PolyPower, a company based in Southern
Denmark have utilised compliant metal electrode technology to develop their own DE material called PolyPowerTM [13]. The DE film sheet is processed such that a wave form pattern is replicated on one side of the sheet, while the opposite side remains flat. About 80 nm of silver is deposited on the corrugated surface, using a physical vapour deposition (PVD) process. Fig. 3 shows a schematic of the profile of the compliant silver electrode DE material currently produced by Danfoss PolyPower. The approximate sinusoidal profile has a period 10 μm, peak to peak amplitude 5 μm and elastomer thickness 40 μm. Attaching sheets back to back produces a DE laminate of thickness 80 μm.
Fig. 3. Elastomer with silver electrodes - electrode thickness, h, is 80 nm. Thickness, H of the metal film is 40 μm.
The current corrugation profile is sinusoidal with a maximum strain of 35% [14] in the compliant direction. An automatic fabrication process, has been developed that is able to produce Kilometres of PolyPower a week [7]. As well as the basic material two actuator types - a fold sheet ‘pull’ actuator and a rolled core-free tubular ‘push’ actuator, are also
produced. These products are aimed towards low strain (<3%), medium/high force applications. The mainstay of the business is the fabrication process but Danfoss PolyPower are also extremely keen on developing collaborative research and development projects that utilise their DE material. See [13] for details.
A. Unidirectional Elongation On application of an electric field unidirectional motion
is produced in the direction of the corrugation. This is an extremely useful property especially for actuation purposes. For DE’s with carbon-based electrodes the DE usually has to be encased in a mechanism that translates the 3D expansion of the material into linear motion [14].
(a) (b) Fig. 4. Compliant metal electrodes. (a) Photograph of a PolyPower DE laminated sheet (b) Folding the sheet creates a ‘pull’ actuator.
B. Self-healing Property Electrical breakdown is the main failure mode for DE
materials especially for acrylic elastomers with carbon-type electrodes. The phenomenon occurs when the electric field in a material becomes greater than its dielectric strength and the insulating barriers properties are exceeded [8]. Low temperature melting electrodes, such as silver or aluminium, do have the property of ‘self-healing’. That is, in the event of an electrical breakdown the adjoining conductive electrodes evaporate isolating the defect as illustrated in Fig. 5(a).
(a) (b) Fig. 5. Self-healing Mechanism (a) Schematic of process (b) blackened electrical breakdown spots on a PolyPower laminate. Though there is a slight loss in performance, due to the decrease in ‘active’ area, the breakdown is not terminal for the
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material. Fig. 5(b) shows the self-healed electrical breakdown on a PolyPower laminate.
VI. MECHANICAL PROPERTIES Tensile testing has been carried out on a PolyPower DE laminate to determine the elastic modulus of the material in both the compliant and stiff directions [14]. The laminate was framed with stiff beams as indicated in Fig. 6 with the initial dimensions of the test sheet being length, l0 =160 mm, width, w0 =160 mm and thickness, t0 = 60 μm.
Fig. 6. Frame used for tensile testing of the DE laminate.
The elastic modulus was determined, for small strains of < 5% in the material, to be Y = 1.925 MPa in the compliant direction (for a silver electrode coated laminate 60 μm thick with a sinusoidal like profile). A straight line fit was applied to the stress/strain data to find the modulus. The elastic modulus in the stiff direction is ≈ 50 times this value with only a very small strain (< 0.5%) required to break the electrode. Fig. 7 shows the DE laminate undergoing 3 cycles of tensile testing up to a maximum value of 25% strain. The viscoelastic properties of the DE material can be seen to produce a dynamic hysteresis characteristic.
Fig. 7. 3 cycles of tensile testing on DE laminate for strain up to 25%.
VII. ELECTRIC FIELD PROPERTIES Investigating the electric field distribution in the DE
material provides a greater understanding of how the profile of the compliant metal electrode might possibly influence the electrical breakdown properties. This will ultimately lead to improved design of the profile of the corrugated electrode trading off robustness of the material (with regard to electrical breakdown) with strain performance. The compliant electrodes on the two sides of the DE laminate are distributed with opposite charges. The accumulation of charge on the electrodes attracts each other and induces an electrostatic pressure perpendicular to the area of the compliant metal electrodes. The mathematical model of the electric field behaviour of a single PolyPower sheet is developed using classical electrodynamics theory. The mathematical model is then implemented in a finite element simulation package. The electric field characteristics of multiple layers of the DE material, as well the effect of possible fabrication defects (penetration of the metal electrode into the elastomer body and the presence of air bubbles in the elastomer) are examined in [17]. The electric field E is equal to the negative gradient of the electric potential, E V= −∇ . The governing equation used to investigate the electrical potential and electric fields of the DE material [17], is:
0 0(( / ) ) /c r T V Tσ ε ε ρ−∇ + ∇ = (2) where σc represents the conductivity, V is the electrical charge distribution, ρ0 is the initial spatial charge density and T corresponds to the dielectric relaxation of the DE material.
Fig. 8. The electric field characteristics of a parallel plane capacitor. In an electrostatic field, the charges in the dielectric seem to be bound elastically to their equilibrium positions, and only move slightly in response to the electrical forces. The dipoles in the dielectric need a certain amount of time to align with the applied field [12] - this is known as the relaxation time, T.
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For the metal electrode T is extremely small meaning that relatively the metal does not contain any net charge in its interior - all the charges go to the surface quickly to provide the surface charge. In order to determine the influence of the profile of the corrugated electrode on the electric field behaviour a comparison has been carried out with the electric field behaviour of a flat electrode profile with the same elastomer and electrode material as the DE laminate.
Fig. 9. The electric field characteristics of a corrugated silver electrode.
Fig. 8 shows, the side view, of the electric field behaviour of the parallel plate electrode. The upper field is outside the DE material. It can be seen that the electric fields are uniform both inside and outside the elastomer with the electric field immediately outside of the conductive plane being normal to the surface of the conductor.
Fig. 10. A comparison of the electric field inside the parallel plate DE material (horizontal line) and the corrugated electrode DE material. With the corrugated electrode, Fig. 9, it can be seen that there is a concentration of the electric field in the valley of the
corrugation. Fig. 10 compares the electric field in the cross-section of the DE material, indicated by the lines below the electrode in Figs. 8 and 9. Comparing these two quantitative results, we can see that the maximum electric field, occurring in the valley of the corrugation, is more than one point five times greater than the constant field inside the parallel plate material. This comparison represents an idealised situation. As the applied voltage is increased to the DE material the corrugated electrodes will begin to flatten out thereby reducing the electric field concentration in the corrugation valleys and perhaps the comparative susceptibility to electrical breakdown.
VIII. THE TUBULAR ACTUATOR A variety of configurations have been developed to exploit DE’s for actuation purposes. These configurations range from diaphragms, stacked structures (like PZT stacks) to rolled tubular actuators. Rolling into tubes produces larger forces by making multiple thin layers of dielectric elastomer apply their actuation forces in parallel. These rolled tubular actuators closely mimic muscle functionality providing axial elongation on application of a voltage. The greatest potential for such a device lies as a positioning-push type device with a vast range of potential applications. The advantage of high-voltage operation is that the currents are very low, but this advantage is lost as multiple thin layers are used. As currents increase, it becomes increasingly important to have a high conductivity in the compliant electrode layer. This provides further justification for the use of complaint metal electrode technology. PolyPower-based tubular devices provide small strains (<3%), but are very durable, undergoing millions of cycles in lifetime testing due to a combination of the electric field being limited to a maximum value of 35 V/μm and the self-healing property of the electrodes.
Fig. 11 The rolled tubular actuator.
IX. DISCUSSION AND CONCLUSIONS Complaint metal electrode technology undoubtedly has many advantages when used in DE’s, especially with regards to conductivity and the ‘self-healing’ property. Currently a
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drawback would seem to be the limited strain in the tubular device, especially when one considers that most of the motivation for using DE’s in the first place for actuation purposes was their promise of high strain performance. The applied electric field is currently limited to 35 V/um [18]. This is much less than the electric fields tested on acrylic-based devices. At MCI the time related performance, as well as the durability, of the tubular actuator is currently being assessed for applied electric fields of 45 V/um and 55 V/um. This will provide additional insight into the relationship between electrical breakdown in the device and compliant metal electrodes. With more complex structures such as the rolled actuator the importance of conductivity increases. Even though metal electrodes are being used there is still a desire to improve this even more. Currently the standard approach for applying the potential to the DE material is to attach a single electrical connection to both the top and bottom electrode. Work is on-going to examine (a) the influence of multiple electrical connections, and (b) developing a method to provide electrical connections across the whole of one end of the tubular device. In this case the connection will supply a maximum length of DE material of 200 mm (currently the standard height of the active part of a tubular device). Contrast this with the single connector approach where the electrode connection supplies a laminate of 5 m, 7 m or 10 m in length, depending on the size of the tubular device.
ACKNOWLEDGMENT The authors would like to acknowledge Danfoss PolyPower
A/S for supplying PolyPower material and the lending of some experimental equipment. The contribution of Southern Denmark University, who sponsored the research assistantship position for Peng Wang, is much appreciated as is Danish Government support of the Industrial PhD scholarship for Rahimullah Sarban.
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