Patent Publication Number: US-8981621-B2

Title: Electroactive polymer manufacturing

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation of Ser. No. 13/039,714, which is a divisional of Ser. No. 11/775,021 filed Jul. 9, 2007, now U.S. Pat. No. 7,923,064, issued Apr. 12, 2011, which is incorporated herein for all purposes and is a continuation of and claims priority under U.S.C. §120 from U.S. patent application Ser. No. 11/335,805, filed Jan. 18, 2006, now U.S. Pat. No. 7,259,503, issued Aug. 21, 2007, which is incorporated herein for all purposes; the Ser. No. 11/335,805 patent application is a continuation application and claimed priority under U.S.C. §120 from U.S. patent application Ser. No. 10/893,730, filed Jul. 16, 2004, now U.S. Pat. No. 7,049,732; issued May 23, 2006, which is incorporated herein for all purposes; the Ser. No. 10/893,730 patent application is a divisional application of and claimed priority under U.S.C. §120 from U.S. patent application Ser. No. 09/619,847, filed Jul. 20, 2000, now U.S. Pat. No. 6,812,624 B1, issued Nov. 2, 2004, which is incorporated herein for all purposes; the U.S. Pat. No. 6,812,624 B1 patent claimed priority under 35 U.S.C. §119(e) from i) U.S. Provisional Patent Application No. 60/144,556 filed Jul. 20, 1999, naming R. E. Pelrine et al. as inventors, and titled “High-speed Electrically Actuated Polymers and Method of Use”, which is incorporated by reference herein for all purposes, ii) U.S. Provisional Patent Application No. 60/153,329 filed Sep. 10, 1999, naming R. E. Pelrine et al. as inventors, and titled “Electrostrictive Polymers As Microactuators”, which is incorporated by reference herein for all purposes, iii) U.S. Provisional Patent Application No. 60/161,325 filed Oct. 25, 1999, naming R. E. Pelrine et al. as inventors, and titled “Artificial Muscle Microactuators”, which is incorporated by reference herein for all purposes, iv) U.S. Provisional Patent Application No. 60/181,404 filed Feb. 9, 2000, naming R. D. Kornbluh et al. as inventors, and titled “Field Actuated Elastomeric Polymers”, which is incorporated by reference herein for all purposes, v) U.S. Provisional Patent Application No. 60/187,809 filed Mar. 8, 2000, naming R. E. Pelrine et al. as inventors, and titled “Polymer Actuators and Materials”, which is incorporated by reference herein for all purposes; vi) U.S. Provisional Patent Application No. 60/192,237 filed Mar. 27, 2000, naming R. D. Kornbluh et al. as inventors, and titled “Polymer Actuators and Materials II”, which is incorporated by reference herein for all purposes, and vii) U.S, Provisional Patent Application No. 60/184,217 filed Feb. 23, 2000, naming R. E. Pelrine et al. as inventors, and titled “Electroelastomers and their use for Power Generation” , which is incorporated by reference herein for all purposes. 
    
    
     U.S. GOVERNMENT RIGHTS 
     This application was made in part with government support under contract number N00014-96-C-0026 awarded by the Office of Naval Research; this application was also made in part with government support under contract number DAAG55-98-K-001 awarded by the United States Army Research Office and Defense Advanced Research Project Agency. The government has certain rights in the invention. 
    
    
     BACKGROUND OF THE INVENTION 
     The present invention relates generally to electroactive polymers that convert between electrical energy and mechanical energy. More particularly, the present invention relates to polymers and their use as generators, sensors, in actuators and various applications. The present invention also relates to additives added to a polymer, laminates comprising a transducer and methods of fabricating a transducer. 
     In many applications, it is desirable to convert between electrical energy and mechanical energy. Exemplary applications requiring translation from electrical to mechanical energy include robotics, pumps, speakers, general automation, disk drives and prosthetic devices. These applications include one or more actuators that convert electrical energy into mechanical work—on a macroscopic or microscopic level. Common electric actuator technologies, such as electromagnetic motors and solenoids, are not suitable for many of these applications, e.g., when the required device size is small (e.g., micro or mesoscale machines). Exemplary applications requiring translation from mechanical to electrical energy include mechanical property sensors and heel strike generators. These applications include one or more transducers that convert mechanical energy into electrical energy. Common electric generator technologies, such as electromagnetic generators, are also not suitable for many of these applications, e.g., when the required device size is small (e.g., in a person&#39;s shoe). These technologies are also not ideal when a large number of devices must be integrated into a single structure or under various performance, conditions such as when high power density output is required at relatively low frequencies. 
     Several ‘smart materials’ have been used to convert between electrical and mechanical energy with limited success. These smart materials include piezoelectric ceramics, shape memory alloys and magnetostrictive materials. However, each smart material has a number of limitations that prevent its broad usage. Certain piezoelectric ceramics, such as lead zirconium titanate (PZT), have been used to convert electrical to mechanical energy. While having suitable efficiency for a few applications, these piezoelectric ceramics are typically limited to a strain below about 1.6 percent and are often not suitable for applications requiring greater strains than this. In addition, the high density of these materials often eliminates them from applications requiring low weight. Irradiated polyvinylidene difluoride (PVDF) is an electroactive polymer reported to have a strain of up to 4 percent when converting from electrical to mechanical energy. Similar to the piezoelectric ceramics, the PVDF is often not suitable for applications requiring strains greater than 4 percent. Shape memory alloys, such as nitinol, are capable of large strains and force outputs. These shape memory alloys have been limited from broad use by unacceptable energy efficiency, poor response time and prohibitive cost. 
     In addition to the performance limitations of piezoelectric ceramics and irradiated PVDF, their fabrication often presents a barrier to acceptability. Single crystal piezoelectric ceramics must be grown at high temperatures coupled with a very slow cooling down process. Irradiated PVDF must be exposed to an electron beam for processing. Both these processes are expensive and complex and may limit acceptability of these materials. 
     In view of the foregoing, alternative devices that convert between electrical and mechanical energy would be desirable. 
     SUMMARY 
     In one aspect, the present invention relates to polymers that convert between electrical and mechanical energy. When a voltage is applied to electrodes contacting a pre-strained polymer, the polymer deflects. This deflection may be used to do mechanical work. Similarly, when the polymer deflects, an electric field is produced in the polymer. This electric field may be used to produce electrical energy. Some polymers of the present invention include additives that improve conversion between electrical and mechanical energy. Other polymers of the present invention include laminate layers that improve conversion between electrical and mechanical energy. 
     Some polymers of the present invention are pre-strained. The pre-strain improves the mechanical response of an electroactive polymer relative to a non-strained polymer. The pre-strain may vary in different directions of a polymer to vary response of the polymer to the applied voltage. 
     In one aspect, the present invention relates to generators and actuators comprising an electroactive polymer and mechanical coupling to convert between mechanical and electrical energy. Several generators and actuators include structures that improve the performance of an electroactive polymer. 
     In another aspect, the present invention relates to compliant electrodes that conform to the changing shape of a polymer. Many of the electrodes are capable of maintaining electrical communication at the high deflections encountered with pre-strained polymers of the present invention. In some embodiments, electrode compliance may vary with direction. 
     In yet another aspect, the present invention provides methods for fabricating electromechanical devices comprising one or more electroactive polymers. Additives that improve conversion between electrical and mechanical energy may be added during fabrication. Polymers of the present invention may be made by casting, dipping, spin coating, spraying or other known processes for fabrication of thin polymer layers. 
     In yet another aspect, the invention relates to a transducer for converting between mechanical and electrical energy. The transducer comprising at least two electrodes and a polymer arranged in a manner which causes a portion of the polymer to deflect in response to a change in electric field and/or to change in electric field in response to deflection. The transducer also comprising a layer laminated to at least a portion of one of the polymer and the at least two electrodes, and mechanically coupled to the polymer and/or one of the at least two electrodes. 
     In another aspect, the invention relates to a method of fabricating a transducer comprising a polymer comprising an additive and one or more electrodes. The method comprising adding an additive to a polymer. The method also comprising fixing a portion of the polymer to a solid member. The method further comprising forming the one or more electrodes on the polymer. 
     These and other features and advantages of the present invention will be described in the following description of the invention and associated figures. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIGS. 1A and 1B  illustrate a top perspective view of a transducer before and after application of a voltage in accordance with one embodiment of the present invention. 
         FIG. 1C  illustrates a textured surface for an electroactive polymer having a wavelike profile. 
         FIG. 1D  illustrates an electroactive polymer including a textured surface having random texturing. 
         FIG. 1E  illustrates a cross-sectional side view of a diaphragm transducer including an electroactive polymer before application of a voltage in accordance with one embodiment of the present invention. 
         FIG. 1F  illustrates a cross-sectional view of the electroactive polymer diaphragm of  FIG. 1E  after application of a voltage in accordance with one embodiment of the present invention. 
         FIGS. 2A and 2B  illustrate a device for converting between electrical energy and mechanical energy before and after actuation in accordance with a specific embodiment of the present invention. 
         FIG. 2C  illustrates a device for converting between electrical enemy and mechanical energy including additional components to improve deflection in accordance with a specific embodiment of the present invention. 
         FIGS. 2D and 2E  illustrate a device for converting between electrical energy and mechanical energy before and after actuation in accordance with a specific embodiment of the present invention. 
         FIG. 2F  illustrates a cross-sectional side view of a transducer including multiple polymer layers in accordance with one embodiment of the present invention. 
         FIG. 2G  illustrates a stacked multilayer device as an example of artificial muscle in accordance with one embodiment of the present invention. 
         FIG. 2H  illustrates a device for converting between electrical energy and mechanical energy comprising an electroactive polymer diaphragm in accordance with another embodiment of the present invention. 
         FIG. 2I  illustrates an inchworm-type actuator including a rolled electroactive polymer in accordance with one embodiment of the present invention. 
         FIG. 2J  illustrates a device for converting between electrical energy and mechanical energy in one direction in accordance with another embodiment of the present invention. 
         FIG. 2K  illustrates a device for converting between electrical energy and mechanical energy in accordance with another embodiment of the present invention. 
         FIG. 2L  illustrates the device of  FIG. 2K  with a 90 degree bending angle. 
         FIG. 2M  illustrates a device for converting between electrical energy and mechanical energy including two polymer layers in accordance with another embodiment of the present invention. 
         FIGS. 2N and 2O  illustrate a device for converting between electrical energy and mechanical energy in accordance with another embodiment of the present invention. 
         FIG. 3  illustrates a structured electrode that provides one-directional compliance according to a specific embodiment of the present invention. 
         FIG. 4  illustrates a pre-strained polymer comprising a structured electrode that is not directionally compliant according to a specific embodiment of the present invention. 
         FIG. 5  illustrates textured electrodes in accordance with one embodiment of the present invention. 
         FIG. 6  illustrates a two-stage cascaded pumping system including two diaphragm device pumps in accordance with a specific embodiment of the present invention. 
         FIG. 7A  illustrates a process flow for fabricating an electromechanical device having at least one pre-strained polymer in accordance with one embodiment of the present invention. 
         FIGS. 7B-F  illustrate a process for fabricating an electromechanical device having multiple polymer layers in accordance with one embodiment of the present invention. 
     
    
    
     DETAILED DESCRIPTION OF EMBODIMENTS 
     The present invention will now be described in detail with reference to a few preferred embodiments thereof as illustrated in the accompanying drawings. In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention. It will be apparent, however, to one skilled in the art, that the present invention may be practiced without some or all of these specific details. In other instances, well known process steps and/or structures have not been described in detail in order to not unnecessarily obscure the present invention. 
     Overview 
     Electroactive polymers deflect when actuated by electrical energy. In one embodiment, an electroactive polymer refers to a polymer that acts as an insulating dielectric between two electrodes and may deflect upon application of a voltage difference between the two electrodes. In one aspect, the present invention relates to polymers that are pre-strained to improve conversion between electrical and mechanical energy. The pre-strain improves the mechanical response of an electroactive polymer relative to a non-strained electroactive polymer. The improved mechanical response enables greater mechanical work for an electroactive polymer, e.g., larger deflections and actuation pressures. For example, linear strains of at least about 200 percent and area strains of at least about 300 percent are possible with pre-strained polymers of the present invention. The pre-strain may vary in different directions of a polymer. Combining directional variability of the pre-strain, different ways to constrain a polymer, scalability of electroactive polymers to both micro and macro levels, and different polymer orientations (e.g., rolling or stacking individual polymer layers) permits a broad range of actuators that convert electrical energy into mechanical work. These actuators find use in a wide range of applications. 
     For ease of understanding, the present invention is described and shown by focusing on a single direction of energy conversion. More specifically, the present invention focuses on converting electrical energy into mechanical energy. However, in all the figures and discussions for the present invention, it is important to note that the polymers and devices may convert between electrical energy and mechanical energy bi-directionally. Thus, any of the polymer materials, polymer configurations, transducers, devices and actuators described herein are also a transducer for converting mechanical energy to electrical energy (a generator) in the reverse direction. Similarly, any of the exemplary electrodes described herein may be used with a generator of the present invention. Typically, a generator includes a polymer arranged in a manner which causes a change in electric field in response to deflection of a portion of the polymer. 
     Thus, polymers and transducers of the present invention may be used as an actuator to convert from electrical to mechanical energy or a generator to convert from mechanical to electrical energy. For a transducer having a substantially constant thickness, one mechanism for differentiating the performance of the transducer as being an actuator or a generator is in the change in net area orthogonal to the thickness during use. For these transducers, when the net area of the transducer decreases, the transducer is acting as a generator. Conversely, when the net area of the transducer increases, the transducer is acting as an actuator. 
     As the electroactive polymers of the present invention may deflect at linear strains of at least about 200 percent, electrodes attached to the polymers should also deflect without compromising mechanical or electrical performance. Correspondingly, in another aspect, the present invention relates to compliant electrodes that conform to the shape of an electroactive polymer they are attached to. The electrodes are capable of maintaining electrical communication even at the high deflections encountered with pre-strained polymers of the present invention. By way of example, strains at least about 50 percent are common with electrodes of the present invention. In some embodiments, compliance provided by the electrodes may vary with direction. 
     As the pre-strained polymers are suitable for use in both the micro and macro scales, in a wide variety of actuators and in a broad range of applications, fabrication processes used with the present invention vary greatly. In another aspect, the present invention provides methods for fabricating electromechanical devices including one or more pre-strained polymers. Pre-strain may be achieved by a number of techniques such as mechanically stretching an electroactive polymer and fixing the polymer to one or more solid members while it is stretched. 
     General Structure of Devices 
       FIGS. 1A and 1B  illustrate a top perspective view of a transducer  100  in accordance with one embodiment of the present invention. The transducer  100  includes a polymer  102  for converting between electrical energy and mechanical energy. Top and bottom electrodes  104  and  106  are attached to the electroactive polymer  102  on its top and bottom surfaces respectively to provide a voltage difference across a portion of the polymer  102 . The polymer  102  deflects with a change in electric field provided by the top and bottom electrodes  104  and  106 . Deflection of the transducer  100  in response to a change in electric field provided by the electrodes  104  and  106  is referred to as actuation. As the polymer  102  changes in size, the deflection may be used to produce mechanical work. 
       FIG. 1B  illustrates a top perspective view of the transducer  100  including deflection in response to a change in electric field. Generally speaking, deflection refers to any displacement, expansion, contraction, torsion, linear or area strain, or any other deformation of a portion of the polymer  102 . The change in electric field corresponding to the voltage difference produced by the electrodes  104  and  106  produces mechanical pressure within the pre-strained polymer  102 . In this case, the unlike electrical charges produced by the electrodes  104  and  106  are attracted to each other and provide a compressive force between the electrodes  104  and  106  and an expansion force on the polymer  102  in planar directions  108  and  110 , causing the polymer  102  to compress between the electrodes  104  and  106  and stretch in the planar directions  108  and  110 . 
     In some cases, the electrodes  104  and  106  cover a limited portion of the polymer  102  relative to the total area of the polymer. This may done to prevent electrical breakdown around the edge of polymer  102  or to achieve customized deflections in certain portions of the polymer. As the term is used herein, an active region is defined as a portion of the polymer material  102  having sufficient electrostatic force to enable deflection of the portion. As will be described below, a polymer of the present invention may have multiple active regions. Polymer  102  material outside an active area may act as an external spring force on the active area during deflection. More specifically, material outside the active area may resist active area deflection by its contraction or expansion. Removal of the voltage difference and the induced charge causes the reverse effects. 
     The electrodes  104  and  106  are compliant and change shape with the polymer  102 . The configuration of the polymer  102  and the electrodes  104  and  106  provides for increasing polymer  102  response with deflection. More specifically, as the transducer  100  deflects, compression of the polymer  102  brings the opposite charges of the electrodes  104  and  106  closer and stretching of the polymer  102  separates similar charges in each electrode. In one embodiment, one of the electrodes  104  and  106  is ground. 
     Generally speaking, the transducer  100  continues to deflect until mechanical forces balance the electrostatic forces driving the deflection. The mechanical forces include elastic restoring forces of the polymer  102  material, the compliance of the electrodes  104  and  106 , and any external resistance provided by a device and/or load coupled to the transducer  100 . The resultant deflection of the transducer  100  as a result of the applied voltage may also depend on a number of other factors such as the polymer  102  dielectric constant and the polymer  102  size. 
     Electroactive polymers in accordance with the present invention are capable of deflection in any direction. After application of the voltage between the electrodes  104  and  106 , the electroactive polymer  102  increases in size in both planar directions  108  and  110 . In some cases, the electroactive polymer  102  is incompressible, e.g. has a substantially constant volume under stress. In this case, the polymer  102  decreases in thickness as a result of the expansion in the planar directions  108  and  110 . It should be noted that the present invention is not limited to incompressible polymers and deflection of the polymer  102  may not conform to such a simple relationship. 
     Application of a relatively large voltage difference between the electrodes  104  and  106  on the transducer  100  shown in  FIG. 1A  will cause transducer  100  to change to a thinner, larger area shape as shown in  FIG. 1B . In this manner, the transducer  100  converts electrical energy to mechanical energy. The transducer  100  also converts mechanical energy to electrical energy. 
       FIGS. 1A and 1B  may be used to show one manner in which the transducer  100  converts mechanical to electrical energy. For example, if the transducer  100  is mechanically stretched by external forces to a thinner, larger area shape such as that shown in  FIG. 1B , and a relatively small voltage difference is applied between electrodes  104  and  106 , when the external forces are removed the transducer  100  will contract in area between the electrodes to a shape such as in  FIG. 1A . Stretching the transducer generally refers to deflecting the transducer from its original resting position—typically to have a larger net area between the electrodes, e.g. in the plane defined by directions  108  and  110  between the electrodes. The resting position refers to the position of the transducer  100  having no external electrical or mechanical input and may include any pre-strain in the polymer. Once the transducer  100  is stretched, the relatively small voltage difference is provided such that the resulting electrostatic forces are insufficient to balance the elastic restoring forces of the stretch. The transducer  100  therefore contracts, and it becomes thicker and has a smaller planar area in the plane defined by directions  108  and  110  (orthogonal to the thickness between electrodes). When the polymer  102  becomes thicker, it separates electrodes  104  and  106  and their corresponding unlike charges, thus raising the electrical energy of the charge. Further, when the electrodes  104  and  106  contract to a smaller area, like charges within each electrode compress, also raising the electrical energy of the charge. Thus, with different charges on the electrodes  104  and  106 , contraction from a shape such as that shown in  FIG. 1B  to one such as that shown in  FIG. 1A  raises the electrical energy of the charge. That is, mechanical deflection is being turned into electrical energy and the transducer  100  is acting as a generator. 
     In some cases, the transducer  100  may be described electrically as a variable capacitor. The capacitance decreases for the shape change going from that shown in  FIG. 1B  to that shown in  FIG. 1A . Typically, the voltage difference between electrodes  104  and  106  will be raised by contraction. This is normally the case, for example, if additional charge is not added or subtracted from the electrodes  104  and  106  during the contraction process. The increase in electrical energy, U, may be illustrated by the formula U=0.5 Q 2 /C, where Q is the amount of positive charge on the positive electrode and C is the variable capacitance which relates to the intrinsic dielectric properties of polymer  102  and its geometry. If Q is fixed and C decreases, then the electrical energy U increases. The increase in electrical energy and voltage can be recovered or used in a suitable device or electronic circuit in electrical communication with electrodes  104  and  106 . In addition, the transducer  100  may be mechanically coupled to a mechanical input that deflects the polymer and provides mechanical energy. 
     The transducer  100  will convert mechanical energy to electrical energy when it contracts. Some or all of the charge and energy can be removed when the transducer  100  is fully contracted in the plane defined by directions  108  and  110 , or charge and energy can be removed during contraction. If the electric field pressure increases and reaches balance with the elastic restoring stresses during contraction, the contraction will stop before full contraction, and no further elastic mechanical energy will be converted to electrical energy. Removing some of the charge and stored electrical energy reduces the electrical field pressure, thereby allowing contraction to continue and further converting more mechanical energy to electrical energy. The exact electrical behavior of the transducer  100  when operating as a generator depends on any electrical and mechanical loading as well as the intrinsic properties of the polymer  102  and electrodes  104  and  106 . 
     The electroactive polymer  102  is pre-strained. Pre-strain of a polymer may be described in one or more directions as the change in dimension in that direction after pre-straining relative to the dimension in that direction before pre-straining. The pre-strain may comprise elastic deformation of the polymer  102  and be formed, for example, by stretching the polymer in tension and fixing one or more of the edges while stretched. The pre-strain improves conversion between electrical and mechanical energy. In one embodiment, prestrain improves the dielectric strength of the polymer. For the transducer  100 , the pre-strain allows the electroactive polymer  102  to deflect more and provide greater mechanical work when converting electrical to mechanical energy. For a generator, pre-strain allows more charge to be placed on the electrodes  104  and  106 , thereby resulting in more generated electrical energy, e.g. in a cycle of the transducer  100  deflection. In one embodiment, the pre-strain is elastic. After actuation, an elastically pre-strained polymer could, in principle, be unfixed and return to its original state. The pre-strain may be imposed at the boundaries using a rigid frame or may be implemented locally for a portion of the polymer. 
     In one embodiment, pre-strain is applied uniformly over a portion of the polymer  102  to produce an isotropic pre-strained polymer. By way of example, an acrylic elastomeric polymer may be stretched by 200-400 percent in both planar directions. In another embodiment, pre-strain is applied unequally in different directions for a portion of the polymer  102  to produce an anisotropic pre-strained polymer. In this case, the polymer  102  may deflect greater in one direction than another when actuated. While not wishing to be bound by theory, it is believed that pre-straining a polymer in one direction may increase the stiffness of the polymer in the pre-strain direction. Correspondingly, the polymer is relatively stiffer in the high pre-strain direction and more compliant in the low pre-strain direction and, upon actuation, the majority of deflection occurs in the low pre-strain direction. In one embodiment, the transducer  100  enhances deflection in the direction  108  by exploiting large pre-strain in the perpendicular direction  110 . By way of example, an acrylic elastomeric polymer used as the transducer  100  may be stretched by 100 percent in the direction  108  and by 500 percent in the perpendicular direction  110 . Construction of the transducer  100  and geometric edge constraints may also affect directional deflection as will be described below with respect to actuators. 
     Anisotropic prestrain may also improve the performance of a transducer to convert mechanical to electrical energy in a generator mode. In addition to increasing the dielectric breakdown strength of the polymer and allowing more charge to be placed on the polymer, high pre-strain may improve mechanical to electrical coupling in the low pre-strain direction. That is, more of the mechanical input into the low pre-strain direction can be converted to electrical output, thus raising the efficiency of the generator. 
     The quantity of pre-strain for a polymer may be based on the electroactive polymer and the desired performance of the polymer in an actuator or application. For some polymers of the present invention, pre-strain in one or more directions may range from −100 percent to 600 percent. By way of example, for a VHB acrylic elastomer having isotropic pre-strain, pre-strains of at least about 100 percent, and preferably between about 200-400 percent, may be used in each direction. In one embodiment, the polymer is pre-strained by a factor in the range of about 1.5 times to 50 times the original area. For an anisotropic acrylic pre-strained to enhance actuation in a compliant direction, pre-strains between about 400-500 percent may be used in the stiffened direction and pre-strains between about 20-200 percent may be used in the compliant direction. In some cases, pre-strain may be added in one direction such that a negative pre-strain occurs in another direction, e.g. 600 percent in one direction coupled with −100 percent in an orthogonal direction. In these cases, the net change in area due to the pre-strain is typically positive. 
     Pre-strain may affect other properties of the polymer  102 . Large pre-strains may change the elastic properties of the polymer and bring it into a stiffer regime with lower viscoelastic losses. For some polymers, pre-strain increases the electrical breakdown strength of the polymer  102 , which allows for higher electric fields to be used within the polymer—permitting higher actuation pressures and higher deflections. 
     Linear strain and area strain may be used to describe the deflection of a pre-strained polymer. As the term is used herein, linear strain of a pre-strained polymer refers to the deflection per unit length along a line of deflection relative to the unactuated state. Maximum linear strains (tensile or compressive) of at least about 50 percent are common for pre-strained polymers of the present invention. Of course, a polymer may deflect with a strain less than the maximum, and the strain may be adjusted by adjusting the applied voltage. For some pre-strained polymers, maximum linear strains of at least about 100 percent are common. For polymers such as VHB 4910 as produced by 3M Corporation of St. Paul, Minn., maximum linear strains in the range of 40 to 215 percent are common. Area strain of an electroactive polymer refers to the change in planar area, e.g. the change in the plane defined by directions  108  and  110  in  FIGS. 1A and 1B , per unit area of the polymer upon actuation relative to the unactuated state. Maximum area strains of at least about 100 percent are possible for pre-strained polymers of the present invention. For some pre-strained polymers, maximum area strains in the range of 70 to 330 percent are common. 
     Generally, after the polymer is pre-strained, it may be fixed to one or more objects. Each object may be suitably stiff to maintain the level of pre-strain desired in the polymer. The polymer may be fixed to the one or more objects according to any conventional method known in the art such as a chemical adhesive, an adhesive layer or material, mechanical attachment, etc. 
     Transducers and pre-strained polymers of the present invention are not limited to any particular geometry or linear deflection. For example, the polymer and electrodes may be formed into any geometry or shape including tubes and rolls, stretched polymers attached between multiple rigid structures, stretched polymers attached across a frame of any geometry—including curved or complex geometries, across a frame having one or more joints, etc. Deflection of a transducer according to the present invention includes linear expansion and compression in one or more directions, bending, axial deflection when the polymer is rolled, deflection out of a hole provided in a substrate, etc. Deflection of a transducer may be affected by how the polymer is constrained by a frame or rigid structures attached to the polymer. In one embodiment, a flexible material that is stiffer in elongation than the polymer is attached to one side of a transducer induces bending when the polymer is actuated. In another embodiment, a transducer that deflects out of the plane is referred to as a diaphragm. A diaphragm device for converting between electrical energy and mechanical energy will be described in more detail with respect to  FIGS. 1E and 1F . 
     Transducers (including methods of using them and methods of fabricating them) in accordance with the present invention are described in reports available from the New Energy and Industrial Technology Development Organization (NEDO) offices under the reference title “Annual Research Progress Report for R&amp;D of Micromachine Technology (R&amp;D of High Functional Maintenance System for Power Plant Facilities)” for 1999, the “Annual Research Progress Report for R&amp;D of Micromachine Technology (R&amp;D of High Functional Maintenance System for Power Plant Facilities)” for 1998, the “Annual Research Progress Report for R&amp;D of Micromachine Technology (R&amp;D of High Functional Maintenance System for Power Plant Facilities)” for 1997, or the “Annual Research Progress Report for R&amp;D of Micromachine Technology (R&amp;D of High Functional Maintenance System for Power Plant Facilities)” for 1996, all of which are incorporated herein for all purposes. NEDO has several offices in Japan in addition to other offices in the United Sates, Australia, France, Thailand and China. 
     Electroactive polymers in accordance with one embodiment of the present invention may include a textured surface.  FIG. 1C  illustrates a textured surface  150  for an electroactive polymer  152  having a wavelike profile. The textured surface  150  allows the polymer  152  to deflect using bending of surface waves  154 . Bending of the surface waves  154  provides directional compliance in a direction  155  with less resistance than bulk stretching for a stiff electrode attached to the polymer  152  in the direction  155 . The textured surface  150  may be characterized by troughs and crests, for example, about 0.1 micrometer to 40 micrometers wide and about 0.1 micrometers to 20 micrometers deep. In this case, the wave width and depth is substantially less than the thickness of the polymer. In a specific embodiment, the troughs and crests are approximately 10 micrometers wide and six micrometers deep on a polymer layer with a thickness of 200 micrometers. 
     In one embodiment, a thin layer of stiff material  156 , such as an electrode, is attached to the polymer  152  to provide the wavelike profile. During fabrication, the electroactive polymer is stretched more than it can stretch when actuated, and the thin layer of stiff material  156  is attached to the stretched polymer  152  surface. Subsequently, the polymer  152  is relaxed and the structure buckles to provide the textured surface. 
     In general, a textured surface may comprise any non-uniform or non-smooth surface topography that allows a polymer to deflect using deformation in the polymer surface. By way of example,  FIG. 1D  illustrates an electroactive polymer  160  including a roughened surface  161  having random texturing. The roughened surface  160  allows for planar deflection that is not directionally compliant. Advantageously, deformation in surface topography may allow deflection of a stiff electrode with less resistance than bulk stretching or compression. It should be noted that deflection of a pre-strained polymer having a textured surface may comprise a combination of surface deformation and bulk stretching of the polymer. 
     Textured or non-uniform surfaces for the polymer may also allow the use of a barrier layer and/or electrodes that rely on deformation of the textured surfaces. The electrodes may include metals that bend according to the geometry of the polymer surface. The barrier layer may be used to block charge in the event of local electrical breakdown in the pre-strained polymer material. 
     Materials suitable for use as a pre-strained polymer with the present invention may include any substantially insulating polymer or rubber (or combination thereof) that deforms in response to an electrostatic force or whose deformation results in a change in electric field. One suitable material is NuSil CF19-2186 as provided by NuSil Technology of Carpenteria, Calif. More generally, exemplary materials suitable for use as a pre-strained polymer include silicone elastomers, acrylic elastomers, polyurethanes, thermoplastic elastomers, copolymers comprising PVDF, pressure-sensitive adhesives, fluoroelastomers, polymers comprising silicone and acrylic moieties, and the like. Polymers comprising silicone and acrylic moieties may include copolymers comprising silicone and acrylic moieties, polymer blends comprising a silicone elastomer and an acrylic elastomer, for example. Obviously, combinations of some of these materials may be used as the polymer in transducers of this invention. 
     One example of a suitable silicone elastomer is Dow Corning HS3 as provided by Dow Corning of Wilmington, Del. One example of a suitable fluorosilicone is Dow Corning 730 as provided by Dow Corning of Wilmington, Del. One suitable example of a thermoplastic elastomer is styrene butadiene styrene (SBS) block copolymer. 
     Some acrylics such as any acrylic in the 4900 VHB acrylic series as provided by 3M Corp. of St. Paul, Minn. have properties suitable for use as the transducer polymer for this invention. Thus, in some embodiments, polymers suitable for use with the present invention may be made from any monoethylenically unsaturated monomer (or combination of monomers) homopolymerizable to form a polymer having a glass transition temperature at most about 0 degrees Celsius. Preferred monoethylenically unsaturated monomers include isooctyl acrylate, 2-ethylhexyl acrylate, decyl acrylate, dodecyl acrylate, hexyl acrylate, isononyl acrylate, isooctyl methacrylate, and 2-ethylhexyl methacrylate. Any of the monomers may also include one or more halogens such as fluorine. 
     One example of a suitable copolymer includes both silicone and acrylic elastomer moieties. In some case, materials suitable for use with the present invention may contain combinations of one or more of the above listed materials. For example, one suitable polymer is a blend including a silicone elastomer and an acrylic elastomer. 
     In many cases, materials used in accordance with the present invention are commercially available polymers. The commercially available polymers may include, for example, any commercially available silicone elastomer, polyurethane, PVDF copolymer and adhesive elastomer. Using commercially available materials provides cost-effective alternatives for transducers and associated devices of the present invention. The use of commercially available materials may also simplify fabrication. In a specific embodiment, the commercially available polymer is a commercially available acrylic elastomer comprising mixtures of aliphatic acrylate that are photocured during fabrication. The elasticity of the acrylic elastomer results from a combination of the branched aliphatic groups and cross-linking between the acrylic polymer chains. 
     Materials used as a pre-strained polymer may be selected based on one or more material properties such as a high electrical breakdown strength, a low modulus of elasticity—(for large or small deformations), a high dielectric constant, etc. In one embodiment, the polymer is selected such that is has an elastic modulus at most about 100 MPa. In another embodiment, the polymer is selected such that is has a maximum actuation pressure between about 0.05 MPa and about 10 MPa, and preferably between about 0.3 MPa and about 3 MPa. In another embodiment, the polymer is selected such that is has a dielectric constant between about 2 and about 20, and preferably between about 2.5 and about 12. For some applications, an electroactive polymer is selected based on one or more application demands such as a wide temperature and/or humidity range, repeatability, accuracy, low creep, reliability and endurance. Often, halogenated polymers, such as fluorinated or chlorinated polymers, exhibit a higher dielectric constant than the base polymer. In one example, a high dielectric polyurethane may be made from partially fluorinated urethane monomers. 
     Electroactive polymers of the present invention may also include one or more additives to improve various properties. Examples of suitable classes of materials include plasticizers, antioxidants, and high dielectric constant particulates. Examples of suitable plasticizers include high molecular-weight hydrocarbon oils, high molecular-weight hydrocarbon greases, Pentalyne H, Piccovar® AP Hydrocarbon Resins, Admex 760, Plastolein 9720, silicone oils, silicone areases, Floral 105, silicone elastomers, nonionic surfactants, and the like. Of course, combinations of these materials may be used. In one embodiment, the antioxidant is a nonvolatile solid antioxidant. 
     In one preferred embodiment, the additives improve the ability of the polymer to convert between mechanical energy and electrical energy. Generally, the additive may improve any polymer property or parameter related to the ability of the parameter to convert between mechanical energy and electrical energy. Polymer material properties and parameters related to the ability of the polymer to convert between mechanical energy and electrical energy include, for example, the dielectric breakdown strength, maximum strain, dielectric constant, elastic modulus, properties associated with the visco-elastic performance, properties associated with creep, response time and actuation voltage. The addition of a plasticizer may, for example, improve the functioning of a transducer of this invention by reducing the elastic modulus of the polymer and/or increasing the dielectric breakdown strength of the polymer. 
     In one embodiment, an additive is included in a polymer to improve the dielectric breakdown strength of the polymer. Improving the dielectric breakdown strength allows the use of larger electrically actuated strains for the polymer. By way of example, a plasticizing additive may be added to a polymer to increase the dielectric breakdown strength of the polymer. Alternatively, a synthetic resin may be added to a styrene-butadiene-styrene block copolymer to improve the dialectic breakdown strength of the copolymer. For example, pentalyn-H as produced by Hercules, Inc. of Wilmington, Del. was added to Kraton D2104 as produced by Shell Chemical of Houston, Tex. to improve the dialectic breakdown strength of the Kraton D2104. Further detail on the fabrication of polymers including addition of one or more additives is provided below. In this case, the ratio of pentalyn-H added may range from about 0 to 2:1 by weight. In another embodiment, an additive is included to increase the dielectric constant of a polymer. For example, high dielectric constant particulates such as fine ceramic powders may be added to increase the dielectric constant of a commercially available polymer. Alternatively, polymers such as polyurethane may be partially fluorinated to increase the dielectric constant. 
     Alternatively, an additive may be included in a polymer to reduce the elastic modulus of the polymer. Reducing the elastic modulus enables larger strains for the polymer. In a specific embodiment, mineral oil was added to a solution of Kraton D to reduce the elastic modulus of the polymer. In this case, the ratio of mineral oil added may range from about 0 to 2:1 by weight. Specific materials included to reduce the elastic modulus of an acrylic polymer of the present invention include any acrylic acids, acrylic adhesives, acrylics including flexible side groups such as isooctyl groups and 2-ethylhexyl groups, or any copolymer of acrylic acid and isooctyl acrylate. 
     Multiple additives may be included in a polymer to improve performance of one or more material properties. In one embodiment, mineral oil and pentalyn-H were both added to a solution of Kraton D2104 to increase the dielectric breakdown strength and to reduce the elastic modulus of the polymer. Alternatively, for a commercially available silicone rubber whose stiffness has been increased by fine carbon particles used to increase the dielectric constant, the stiffness may be reduced by the addition of a carbon or silver filled silicone grease. 
     An additive may also be included in a polymer to provide an additional property for the transducer. The additional property is not necessarily associated with polymer performance in converting between mechanical and electrical energy. By way of example, pentalyn-H may be added to Kraton D2104 to provide an adhesive property to the polymer. In this case, the additive also aids in conversion between mechanical and electrical energy. In a specific embodiment, polymers comprising Kraton D2104, pentalyn-H, mineral oil and fabricated using butyl acetate provided an adhesive polymer and a maximum linear strain in the range of about 70 to 200 percent. 
     Suitable actuation voltages for pre-strained polymers of the present invention may vary based on the electroactive polymer material and its properties (e.g. the dielectric constant) as well as the dimensions of the polymer (e.g. the thickness between electrodes). By way of example, actuation electric fields for the polymer  102  in  FIG. 1A  may range in magnitude from about 0 V/m to about 440 MegaVolts/meter. Actuation voltages in this range may produce a pressure in the range of about 0 Pa to about 10 MPa. To achieve a transducer capable of higher forces, the thickness of the polymer may be increased. Alternatively, multiple polymer layers may be implemented. Actuation voltages for a particular polymer may be reduced by increasing the dielectric constant, decreasing polymer thickness and decreasing the modulus of elasticity, for example. 
     Pre-strained polymers of the present invention may cover a wide range of thicknesses. In one embodiment, polymer thickness may range between about 1 micrometer and 2 millimeters. Typical thicknesses before pre-strain include 50-225 micrometers for HS3, 25-75 micrometers for NuSil CF 19-2186, 50-1000 micrometers for SBS, and 100-1000 microns for any of the 3M VHB 4900 series acrylic polymers. Polymer thickness may be reduced by stretching the film in one or both planar directions. In many cases, pre-strained polymers of the present invention may be fabricated and implemented as thin films. Thicknesses suitable for these thin films may be below 50 micrometers. 
     Transducers for converting between mechanical and electrical energy of the present invention also encompass multilayer laminates. In one embodiment, a multilayer laminate refers to a structure including one or more layers in addition to a single electroactive polymer and its corresponding electrodes. In one embodiment, a multilayer laminate refers to a structure having a transducer including an electroactive polymer and its corresponding electrodes, a layer laminated to at least one of the electrode and the polymer, and the layer mechanically coupled to a portion of the transducer. Multilayer laminates may be referred to as either external or internal. For external multilayer laminates, the one or more additional layers are not between the electrodes. For internal multilayer laminates, the one or more additional layers are between the electrodes. For either external or internal layers, the layers may be adhered using an adhesive or glue layer, for example. 
     Internal multilayer laminates may be used for a wide variety of purposes. A layer may also be included in an internal multilayer laminate to improve any mechanical or electrical property of the transducer, e.g., stiffness, electrical resistance, tear resistance, etc. Internal multilayer laminates may include a layer having a greater dielectric breakdown strength. Internal multilayer laminates may include multiple layers of compatible materials separated by conducting or semiconducting layers (e.g. metallic or polymer layers) to increase breakdown strength of the laminate transducer. Compatible materials refer to materials that comprise the same or substantially similar material or have the same or substantially similar properties (e.g. mechanical and/or electrical). Internal laminates of compatible materials relative to the polymer may be used to compensate for manufacturing defects in the polymer and provide greater transducer uniformity. By way of example, a 100 micrometer thick, single layer polymer may have a defect that may affect the entire 100 micrometer thickness. In this case, a laminate of ten layers each having a thickness of 10 micrometers may be used such that any manufacturing defects are localized to a 10 micrometer polymer—thus providing a comparable 100 micrometer thick laminate structure, but with greater uniformity and fault tolerance compared to the single layer polymer. Internal laminates of compatible materials relative to the polymer may also be used to prevent any runaway pull-in effect. Runaway pull-in effect refers to when the electrostatic forces between electrodes getting closer increases faster than the elastic resistive forces of the polymer. In such cases, the transducer may become electromechanically unstable, leading to rapid local thinning and electrical breakdown. An internal layer may also be used to afford a layer of protection (electrical or mechanical) to another layer in the composite. In one embodiment, an electrical barrier layer is mechanically coupled between an electrode and the polymer to minimize the effect of any localized breakdown in the polymer. Breakdown may be defined as the point at which the polymer cannot sustain the applied voltage. The barrier layer is typically thinner than the polymer and has a higher dielectric constant than the polymer such that the voltage drop mainly occurs across the polymer. It is often preferable that the barrier layer have a high dielectric breakdown strength. 
     External multilayer laminates may be used for a wide variety of purposes. In one embodiment, an external multilayer composite includes a layer to control stiffness, creep, to distribute load more uniformly during deflection, to increase tear resistance, or to prevent runaway pull effect. External laminates of compatible polymers including electrodes may be used to distribute load across each of the polymer layers or increase polymer uniformity during deflection. A layer may also be included in an external laminate having a higher stiffness than the polymer, e.g., a material having a higher stiffness or a different amount of pre-strain for a compatible material, to bias a diaphragm, pump or bending beam. In a generator mode, a stretched transducer may contract and generate electrical energy as long as the electrical field stresses are lower than the elastic restoring stresses. In this case, adding a stiffening layer may allow the transducer to contract against greater field stresses, thereby increasing its energy output per stroke. An external layer may also be used to afford a layer of protection (electrical or mechanical) to another layer in the composite. In another specific embodiment, an external composite includes a foam layer to bias a small pump or diaphragm. The foam layer may comprise an open pore foam that allows fluids to move in and out of the foam. An external layer having a low stiffness may also be used for electric shielding without introducing excessive mechanical energy loss. 
     In one embodiment, a composite is formed by rolling or folding a polymer to produce a transducer with high-density packaging. In order to avoid detrimental electric fields in the vicinity of folds for laminates including folded layers, electrodes may be patterned on the polymer such that any polymer in the vicinity of the folds does not have overlapping opposite electrodes. In addition, the polymer and electrodes may be rolled or folded such that the outer exposed electrode or electrodes have the same polarity. Fabrication may be performed such that electrodes of opposite polarity are separate by polymer. For example, a rolled actuator can be made by rolling up two layers of polymer with electrodes, or a single layer can be first folded, then rolled. Additionally, the outer exposed electrode may be grounded to increase safety of the transducer. An external laminate outer skin layer may also be added to further increase safety. 
     Actuator and Generator Devices 
     The deflection of a pre-strained polymer can be used in a variety of ways to produce or receive mechanical energy. Generally speaking, electroactive polymers of the present invention may be implemented with a variety of actuators and generators—including conventional actuators and generators retrofitted with a pre-strained polymer and custom actuators and generators specially designed for one or more pre-strained polymers. Conventional actuators and generators include extenders, bending beams, stacks, diaphragms, etc. Several different exemplary custom actuators and generators in accordance with the present invention will now be discussed. 
       FIG. 1E  illustrates a cross-sectional side view of a diaphragm device  130  including a pre-strained polymer  131  before electrical actuation in accordance with one embodiment of the present invention. The pre-strained polymer  131  is attached to a frame  132 . The frame  132  includes a non-circular aperture  133  that allows deflection of the polymer  131  perpendicular to the area of the non-circular aperture  133 . The non-circular aperture  133  may be a rectangular slot, custom geometry aperture, etc. In some cases, a non-circular, elongated slot may be advantageous for a diaphragm device compared to a circular hole. For example, thickness strain is more uniform for an elongated slot compared to a hole. Non-uniform strains limit overall performance since the electrical breakdown of a polymer is typically determined by the thinnest point. The diaphragm device  130  includes electrodes  134  and  136  on either side of the polymer  131  to provide a voltage difference across a portion of the polymer  131 . 
     In the voltage-off configuration of  FIG. 1E , the polymer  131  is stretched and secured to the frame  132  with tension to achieve pre-strain. Upon application of a suitable voltage to the electrodes  134  and  136 , the polymer film  131  expands away from the plane of the frame  132  as illustrated in  FIG. 1F . The electrodes  134  and  136  are compliant and change shape with the pre-strained polymer  131  as it deflects. 
     The diaphragm device  130  is capable of expansion in both directions away from the plane. In one embodiment, the bottom side  141  of the polymer  131  includes a bias pressure that influences the expansion of the polymer film  131  to continually actuate upward in the direction of arrows  143  ( FIG. 1F ). In another embodiment, a swelling agent such as a small amount of silicone oil is applied to the bottom side  141  to influence the expansion of the polymer  131  in the direction of arrows  143 . The swelling agent causes slight permanent deflection in one direction as determined during fabrication, e.g. by supplying a slight pressure on the bottom side  141  when the swelling agent is applied. The swelling agent allows the diaphragm to continually actuate in a desired direction without using a bias pressure. 
     The amount of expansion for the diaphragm device  130  will vary based on a number of factors including the polymer  131  material, the applied voltage, the amount of pre-strain, any bias pressure, compliance of the electrodes  134  and  136 , etc. In one embodiment, the polymer  131  is capable of deflections to a height  137  at least about 50 percent of the hole diameter  139  and may take a hemispheric shape at large deflections, in this case, an angle  147  formed between the polymer  131  and the frame  132  may be less than 90 degrees. 
     The diaphragm device  130  may also be used as a generator. In this case, a pressure, such as a fluid pressure, acts as mechanical input to the diaphragm on the bottom  141  to stretch the transducer (polymer  134  and electrodes  134  and  136 ) in the vicinity of the aperture  133  as shown in  FIG. 1F . A voltage difference is applied between electrodes  134  and  136  while the transducer is stretched, and releasing the pressure allows the diaphragm to contract and increase the stored electrical energy on the transducer. 
     Expansion in one direction of an electroactive polymer may induce contractile stresses in a second direction such as due to Poisson effects. This may reduce the mechanical output for a transducer that provides mechanical output in the second direction. Correspondingly, actuators of the present invention may be designed to constrain a polymer in the non-output direction. In some cases, actuators may be designed to improve mechanical output using deflection in the non-output direction. 
     One device which uses deflection in one planar direction to improve energy conversion in the other planar direction is a bow device.  FIGS. 2A and 2B  illustrate a bow device  200  for converting between electrical energy and mechanical energy before and after electrical actuation in accordance with a specific embodiment of the present invention. The bow device  200  is a planar mechanism comprising a flexible frame  202  which provides mechanical assistance to improve conversion between electrical energy and mechanical energy for a polymer  206  attached to the frame  202 . The frame  202  includes six rigid members  204  connected at joints  205 . The members  204  and joints  205  provide mechanical assistance by coupling polymer deflection in a planar direction  208  into mechanical output in a perpendicular planar direction  210 . More specifically, the frame  202  is arranged such that a small deflection of the polymer  206  in the direction  208  improves displacement in the perpendicular planar direction  210 . Attached to opposite (top and bottom) surfaces of the polymer  206  are electrodes  207  (bottom electrode on bottom side of polymer  206  not shown) to provide a voltage difference across a portion of the polymer  206 . 
     The polymer  206  is configured with different levels of pre-strain in its orthogonal directions. More specifically, the electroactive polymer  206  includes a high pre-strain in the planar direction  208 , and little or no pre-strain in the perpendicular planar direction  210 . This anisotropic pre-strain is arranged relative to the geometry of the frame  202 . More specifically, upon actuation across electrodes  207 , the polymer contracts in the high pre-strained direction  208 . With the restricted motion of the frame  202  and the lever arm provided by the members  204 , this contraction helps drive deflection in the perpendicular planar direction  210 . Thus, even for a short deflection of the polymer  206  in the high pre-strain direction  208 , the frame  202  bows outward in the direction  210 . In this manner, a small contraction in the high pre-strain direction  210  becomes a larger expansion in the relatively low pre-strain direction  208 . 
     Using the anisotropic pre-strain and constraint provided by the frame  202 , the bow device  200  allows contraction in one direction to enhance mechanical deflection and electrical to mechanical conversion in another. In other words, a load  211  ( FIG. 2B ) attached to the bow device  200  is coupled to deflection of the polymer  206  in two directions—direction  208  and  210 . Thus, as a result of the differential pre-strain of the polymer  206  and the geometry of the frame  202 , the bow device  200  is able to provide a larger mechanical displacement and mechanical energy output than an electroactive polymer alone for common electrical input. 
     The bow device  200  may be configured based on the polymer  206 . By way of example, the geometry of the frame  202  and dimensions of the polymer  206  may be adapted based on the polymer  206  material. In a specific embodiment using HS3 silicone as the polymer  206 , the polymer  206  preferably has a ratio in directions  208  and  210  of 9:2 with pre-strains about 270 percent and −25 percent in the directions  208  and  210  respectively. Using this arrangement, linear strains of at least about 100 percent in direction  210  are possible. 
     The pre-strain in the polymer  206  and constraint provided by the frame  202  may also allow the bow device  200  to utilize lower actuation voltages for the pre-strained polymer  206  for a given deflection. As the bow device  200  has a lower effective modulus of elasticity in the low pre-strained direction  210 , the mechanical constraint provided by the frame  202  allows the bow device  200  to be actuated in the direction  210  to a larger deflection with a lower voltage. In addition, the high pre-strain in the direction  208  increases the breakdown strength of the polymer  206 , permitting higher voltages and higher deflections for the bow device  200 . 
     As mentioned earlier with respect  FIG. 1A , when a polymer expands as a result of electrostatic forces, it continues to expand until mechanical forces balance the electrostatic pressure driving the expansion. When the load  211  is attached to the bow device  200 , mechanical effects provided by the load  211  will influence the force balance and deflection of the polymer  206 . For example, if the load  211  resists expansion of the bow device  200 , then the polymer  206  may not expand as much as if were there no load. 
     In one embodiment, the bow device  200  may include additional components to provide mechanical assistance and enhance mechanical output. By way of example, springs  220  as shown in  FIG. 2C  may be attached to the bow device  200  to enhance deflection in the direction  210 . The springs load the bow device  200  such that the spring force exerted by the springs opposes resistance provided by an external load. In some cases, the springs  220  provide increasing assistance for bow device  200  deflection. In one embodiment, spring elements may be built into the joints  205  instead of the external springs  220  to enhance deflection of the bow device  200 . In addition, pre-strain may be increased to enhance deflection. The load may also be coupled to the rigid members  204  on top and bottom of the frame  202  rather than on the rigid members of the side of the frame  202  (as shown in  FIG. 2B ). Since the top and bottom rigid members  204  contract towards each other when voltage is applied as shown in  FIG. 2B , the bow actuator  200  provides an exemplary device contracts in the plane upon application of a voltage rather than expands. 
     When used as a generator, the bow device  200  improves conversion of mechanical to electrical energy. Recall that a generator (as in  FIGS. 1A and 1B ) of the present invention will convert mechanical energy to electrical energy when it contracts. Also recall that if the electric field pressure increases and reaches balance with the elastic restoring stresses during contraction, the contraction will stop and may diminish efficiency. The elastic energy per unit volume in a polymer is typically proportional to the elastic restoring stress or pressure, e.g. the stress applied at a boundary. One way to maximize the elastic energy for a given restoring stress or pressure is to use a lower modulus polymer. Lower modulus polymers may, however, generally have lower breakdown strengths, and may negate the advantages of a low modulus. The bow device  200  is one way to maximize the elastic energy for a given net restoring stress or pressure without using a lower modulus material. This is done using the frame  202  in conjunction with anisotropic pre-strains in directions  208  and  210  so that the net restoring pressure or force for a given strain is less than it would be for free boundary conditions on the polymer  206 . A high prestrain in direction  208  supplies elastic energy via the frame  202  to assist in the expansion in the direction  210 . With regards to expansion in direction  210 , the polymer acts as though it has a low modulus, and a large amount of elastic energy can be stored for a given input force or input stress at the boundary. Since the contraction in direction  208  is small and the area change from the small contraction is correspondingly small, the electrical behavior due to changes in direction  208  are minimal compared to the large electrical behavior (e.g. change in capacitance) due to the large strain changes in direction  210 . The polymer  206  therefore behaves as if it were a very low modulus material that stretches substantially in one direction (direction  210 ), allowing the bow device  200  to convert a relatively large amount of energy per unit volume of polymer per stroke at high efficiencies compared to other devices using the same polymer  206 . 
     The shape and constraint of the polymer may affect deflection. An aspect ratio for an electroactive polymer is defined as the ratio of its length to width. If the aspect ratio is high (e.g., an aspect ratio of at least about 4:1) and the polymer is constrained along its length by rigid members, than the combination may result in a substantially one dimensional deflection in the width direction. 
       FIGS. 2D and 2E  illustrate a linear motion device  230  for converting between electrical energy and mechanical energy before and after actuation in accordance with a specific embodiment of the present invention. The linear motion device  230  is a planar mechanism having mechanical translation in one direction. The linear motion device  230  comprises a polymer  231  having a length  233  substantially greater than its width  234  (e.g., an aspect ratio at least about 4:1). The polymer  231  is attached on opposite sides to stiff members  232  of a frame along its length  233 . The stiff members  232  have a greater stiffness than the polymer  231 . The geometric edge constraint provided by the stiff members  232  substantially prevents displacement in a direction  236  along the polymer length  233  and facilitates deflection almost exclusively in a direction  235 . When the linear motion device  230  is implemented with a polymer  231  having anisotropic pre-strain, such as a higher pre-strain in the direction  236  than in the direction  235 , then the polymer  231  is stiffer in the direction  236  than in the direction  235  and large deflections in the direction  235  may result. By way of example, such an arrangement may produce linear strains of at least about 200 percent for acrylics having an anisotropic pre-strain. 
     A collection of electroactive polymers or actuators may be mechanically linked to form a larger actuator with a common output, e.g. force and/or displacement. By using a small electroactive polymer as a base unit in a collection, conversion of electric energy to mechanical energy may be scaled according to an application. By way of example, multiple linear motion devices  230  may be combined in series in the direction  235  to form an actuator having a cumulative deflection of all the linear motion devices in the series. When transducing electric energy into mechanical energy, electroactive polymers—either individually or mechanically linked in a collection—may be referred to as ‘artificial muscle’. For purposes herein, artificial muscle is defined as one or more transducers and/or actuators having a single output force and/or displacement. Artificial muscle may be implemented on a micro or macro level and may comprise any one or more of the actuators described herein. 
       FIG. 2F  illustrates cross-sectional side view of a multilayer device  240  for converting between electrical energy and mechanical energy as an example of artificial muscle in accordance with a specific embodiment of the present invention. The multilayer device  240  includes four pre-strained polymers  241  arranged in parallel and each attached to a rigid frame  242  such that they have the same deflection. Electrodes  243  and  244  are deposited on opposite surfaces of each polymer  241  and provide simultaneous electrostatic actuation to the four pre-strained polymers  241 . The multilayer device  240  provides cumulative force output of the individual polymer layers  241 . 
     Combining individual polymer layers in parallel or in series has a similar effect on transducers operated in a generator mode. In general, coupling layers in parallel increases the stiffness and maximum input force of the device without changing its maximum stroke, while combining layers in series increases the maximum stroke without increasing the maximum input force. Thus, by combining layers in series and parallel, a generator can be designed to match a specific input mechanical load. 
     In another embodiment, multiple electroactive polymer layers may be used in place of one polymer to increase the force or pressure output of an actuator. For example, ten electroactive polymers may be layered to increase the pressure output of the diaphragm device of  FIG. 1E .  FIG. 2G  illustrates such a stacked multilayer diaphragm device  245  for converting between electrical energy and mechanical energy as another example of artificial muscle in accordance with one embodiment of the present invention. The stacked multilayer device  245  includes three polymer layers  246  layered upon each other and may be attached by adhesive layers  247 . Within the adhesive layers  247  are electrodes  248  and  249  that provide actuation to polymer layers  246 . A relatively rigid plate  250  is attached to the outermost polymer layer and patterned to include holes  251  that allow deflection for the stacked multilayer diaphragm device  245 . By combining the polymer layers  246 , the stacked multilayer device  245  provides cumulative force output of the individual polymer layers  246 . 
     In addition to the linear motion device  230  of  FIGS. 2D and 2E , electroactive polymers of the present invention may be included in a variety of devices that convert between electrical energy and mechanical energy.  FIG. 2H  illustrates a linear actuator  255  comprising an electroactive polymer diaphragm  256  for converting between electrical energy and mechanical energy in accordance with another embodiment of the present invention. In this case, an output shaft  257  is attached to a central portion of the diaphragm  256  that deflects in a non-circular aperture  258  of a frame  261 . Upon actuation and removal of electrostatic energy, the output shaft  257  translates as indicated by arrow  259 . The linear actuator  255  may also include a compliant spring element  260  that helps position the output shaft  257 . 
     In one embodiment, the non-circular aperture  258  is an elongated slot. As noted previously, an elongated slot typically has more uniform strain than a circular hole. In addition, the polymer diaphragm  256  has a higher pre-strain in the long axis of the slot relative to the pre-strain in the perpendicular planar direction. By using relatively high pre-strain in the long slot direction, and relatively low pre-strain in the perpendicular planar direction, the displacement of the output shaft  257  can be increased relative to uniform pre-strain configurations. 
     In another embodiment, pre-strained polymers of the present invention may be rolled or folded into linear transducers and actuators that deflect axially while converting between electrical energy and mechanical energy. As fabrication of electroactive polymers is often simplest with fewer numbers of layers, rolled actuators provide an efficient manner of squeezing large layers of polymer into a compact shape. Rolled or folded transducers and actuators typically include two or more layers of polymer. Rolled or folded actuators are applicable wherever linear actuators are used, such as robotic legs and fingers, high force grippers, and general-purpose linear actuators. 
       FIG. 2I  illustrates an inchworm-type actuator  262  in accordance with a specific embodiment of the present invention. The inchworm-type actuator  262  includes two or more rolled pre-strained polymer layers with electrodes  263  that deflect axially along its cylindrical axis. The inchworm-type actuator  262  also includes electrostatic clamps  264  and  265  for attaching and detaching to a metal surface  268 . The electrostatic clamps  264  and  265  allow the total stroke for the inchworm-type actuator  262  to be increased compared to an actuator without clamping. As the clamping force per unit weight for the electrostatic clamps  264  and  265  is high, the force per unit weight advantages of pre-strained polymers of the present invention are preserved with the inchworm-type actuator  262 . The electrostatic clamps  264  and  265  are attached to the inchworm-type actuator at connection regions  267 . A body  266  of the inchworm-type actuator includes the connection regions  267  and the polymer  263  and has a degree of freedom along the axial direction of the rolled polymer  263  between the connection regions  267 . In one embodiment, the electrostatic clamps  264  and  265  include an insulating adhesive  269  that prevents electrical shorting from the conductive electrostatic clamps  264  and  265  to the metal surface  268 . 
     The inchworm-type actuator  262  moves upward in a six step process. In step one, the inchworm-type actuator  262  is immobilized at its respective ends when both electrostatic clamps  264  and  265  are actuated and the polymer  263  is relaxed. An electrostatic clamp is actuated by applying a voltage difference between the clamp and the metal surface  268 . In step two, clamp  265  is released. Releasing one of the clamps  264  and  265  allows its respective end of the inchworm-type actuator  262  to move freely. In step three, the electroactive polymer  263  is actuated and extends the inchworm-type actuator  262  upward. In step four, clamp  265  is actuated and the inchworm-type actuator  262  is immobilized. In step five, clamp  264  is released. In step six, the polymer  263  is relaxed and the inchworm-type actuator  262  contracts. By cyclically repeating steps one through six, the inchworm-type actuator  262  moves in the upward direction. By switching clamps  264  and  265  in the above six step process, the inchworm-type actuator  262  moves in a reverse direction. 
     Although the inchworm-type actuator  262  has been described in terms of actuation using a single electroactive polymer and two clamps, multiple segment inchworm-type actuators using multiple electroactive polymers may be implemented. Multiple segment inchworm-type actuators allow an inchworm-type actuator to increase in length without becoming thicker. A two-segment inchworm-type actuator would use two rolled polymers rather than one and three clamps rather than two. In general, an n-segment inchworm-type actuator comprises n actuators between n+1 clamps. 
       FIG. 2J  illustrates a stretched film device  270  for converting between electrical energy and mechanical energy in accordance with another embodiment of the present invention. The stretched film device  270  includes a rigid frame  271  having a hole  272 . A pre-strained polymer  273  is attached in tension to the frame  271  and spans the hole  272 . A rigid bar  274  is attached to the center of the polymer  273  and provides external displacement corresponding to deflection of the polymer  273 . Compliant electrode pairs  275  and  276  are patterned on both top and bottom surfaces of the polymer  273  on the left and right sides respectively of the rigid bar  274 . When the electrode pair  275  is actuated, a portion of the polymer  273  between and in the vicinity of the top and bottom electrode pair  275  expands relative to the rest of the polymer  273  and the existing tension in the remainder of the polymer  273  pulls the rigid bar  274  to move to the right. Conversely, when the electrode pair  276  is actuated, a second portion of the polymer  273  affected by the electrode pair  276  expands relative to the rest of the polymer  273  and allows the rigid bar  274  to move to the left. Alternating actuation of the electrodes  275  and  276  provides an effectively larger total stroke  279  for the rigid bar  274 . One variation of this actuator includes adding anisotropic pre-strain to the polymer such that the polymer has high pre-strain (and stiffness) in the direction perpendicular to the rigid bar displacement. Another variation is to eliminate one of the electrode pairs. For the benefit of simplifying the design, this variation reduces the stroke  279  for the stretched film device  270 . In this case, the portion of the polymer no longer used by the removed electrode now responds passively like a restoring spring. 
       FIG. 2K  illustrates a bending beam device  280  for converting between mechanical and electrical energy in accordance with another embodiment of the present invention. The bending beam device  280  includes a polymer  281  fixed at one end by a rigid support  282  and attached to a flexible thin material  283  such as polyimide or mylar using an adhesive layer, for example. The flexible thin material  283  has a modulus of elasticity greater than the polymer  281 . The difference in modulus of elasticity for the top and bottom sides  286  and  287  of the bending beam device  280  causes the bending beam device  280  to bend upon actuation. Electrodes  284  and  285  are attached to the opposite sides of the polymer  281  to provide electrical energy. The bending beam device  280  includes a free end  288  having a single bending degree of freedom. Deflection of the free end  288  may be measured by the difference in angle between the free end  288  and the end fixed by the rigid support  282 .  FIG. 2L , illustrates the bending beam device  280  with a 90 degree bending angle. 
     The maximum bending angle for the bending beam device  280  will vary with a number of factors including the polymer material, the actuator length, the bending stiffness of the electrodes  284  and  285  and flexible thin material  283 , etc. For a bending beam device  280  comprising Dow Corning HS3 silicone, gold electrodes and an active area of 3.5 mm in length, bending angles over 225 degrees are attainable. For the bending beam device  280 , as the length of the active area increases, increased bending angles are attainable. Correspondingly, by extending the active length of the above mentioned bending beam device to 5 mm allows for a bending angle approaching 360 degrees. 
     In one embodiment, one of the electrodes may act as the flexible thin material  283 . Any thin metal, such as gold, having a low bending stiffness and a high tensile stiffness may be suitable for an electrode acting as the flexible thin material  283 . In another embodiment, a barrier layer is attached between one of the electrodes  284  and  285  and the polymer  281  to minimize the effect of any localized breakdown in the polymer. 
       FIG. 2M  illustrates a bending beam device  290  for converting between mechanical and electrical energy in accordance with another embodiment of the present invention. The bending beam device  290  includes top and bottom pre-strained polymers  291  and  292  fixed at one end by a rigid support  296 . Each of the polymers  291  and  292  may be independently actuated. Independent actuation is achieved by separate electrical control of top and bottom electrodes  293  and  294  attached to the top and bottom electroactive polymers  291  and  292 , respectively. A common electrode  295  is situated between the top and bottom electroactive polymers  291  and  292  and attached to both. The common electrode  295  may be of sufficient stiffness to maintain the pre-strain on the polymer layers  291  and  292  while still permitting extension and bending. 
     Actuating the top electroactive polymer  291  using the top pair of electrodes  293  and  295  causes the bending beam device  290  to bend downward. Actuating the bottom polymer  292  using the bottom pair of electrodes  294  and  295  causes the bending beam device  290  to bend upward. Thus, independent use of the top and bottom electroactive polymers  291  and  292  allows the bending beam device  290  to be controlled along a radial direction  297 . When both top and bottom polymers  291  and  292  are actuated simultaneously—and are of substantially similar size and material—the bending beam device  290  extends in length along the linear direction  298 . Combining the ability to control motion in the radial direction  297  and the linear direction  298 , the bending beam device  290  becomes a two-degree-of-freedom actuator. Correspondingly, independent actuation and control of the top and bottom polymers  291  and  292  allows a free end  299  of the bending beam device  290  to execute complex motions such as circular or elliptical paths. 
       FIGS. 2N and 2O  illustrate a device  300  for converting between electrical energy and mechanical energy in accordance with another embodiment of the present invention. The device  300  includes a polymer  302  arranged in a manner which causes a portion of the polymer to deflect in response to a change in electric field and/or arranged in a manner which causes a change in electric field in response to deflection of the polymer. Electrodes  304  are attached to opposite surfaces (only the foremost electrode is shown) of the polymer  302  and cover a substantial portion of the polymer  302 . Two stiff members  308  and  310  extend along opposite edges  312  and  314  of the polymer  302 . Flexures  316  and  318  are situated along the remaining edges of the polymer  302 . The flexures  316  and  318  improve conversion between electrical energy and mechanical energy for the device  300 . 
     The flexures  316  and  318  couple polymer  302  deflection in one direction into deflection in another direction. In one embodiment, each of the flexures  316  and  318  rest at an angle about 45 degrees in the plane of the polymer  302 . Upon actuation of the polymer  302 , expansion of the polymer  302  in the direction  320  causes the stiff members  308  and  310  to move apart, as shown in  FIG. 2O . In addition, expansion of the polymer  302  in the direction  322  causes the flexures  316  and  318  to straighten, and further separates the stiff members  308  and  310 . In this manner, the device  300  couples expansion of the polymer  302  in both planar directions  320  and  322  into mechanical output in the direction  320 . 
     In one embodiment, the polymer  302  is configured with different levels of pre-strain in orthogonal directions  320  and  322 . More specifically, the polymer  302  includes a higher pre-strain in the direction  320 , and little or no pre-strain in the perpendicular planar direction  322 . This anisotropic pre-strain is arranged relative to the geometry of the flexures  316  and  318 . 
     One advantage of the device  300  is that the entire structure is planar. In addition to simplifying fabrication, the planar structure of the device  300  allows for easy mechanical coupling to produce multilayer designs. By way of example, the stiff members  308  and  310  may be mechanically coupled (e.g. glued or similarly fixed) to their respective counterparts of a second device  300  to provide two devices  300  in parallel in order to increase the force output over single device  300 . Similarly, the stiff member  308  from one device may be attached to the stiff member  310  from a second device in order to provide multiple devices in series that increase the deflection output over a single device  300 . 
     In addition to good performance of the device  300  as in actuator which converts electrical energy into mechanical energy, the device  300  is also well-suited as a generator. For example, when a charge is placed on the polymer  302  while it is stretched, contraction of the device  300  converts mechanical energy to electrical energy. The electrical energy may then be harvested by a circuit in electrical communication with the electrodes  304 . 
     Performance 
     A transducer in accordance with the present invention converts between electrical energy and mechanical energy. Transducer performance may be characterized in terms of the transducer by itself, the performance of the transducer in an actuator, or the performance of the transducer in a specific application (e.g., a number of transducers implemented in a motor). Pre-straining electroactive polymers in accordance with the present invention provides substantial improvements in transducer performance. 
     Characterizing the performance of a transducer by itself usually relates to the material properties of the polymer and electrodes. Performance of an electroactive polymer may be described independent of polymer size by parameters such as strain, energy density, actuation pressure, actuation pressure density and efficiency. It should be noted that the performance characterization of pre-strained polymers and their respective transducers described below may vary for different electroactive polymers and electrodes. 
     Pre-strained polymers of the present invention may have an effective modulus in the range of about 0.1 to about 100 MPa. Actuation pressure is defined as the change in force within a pre-strained polymer per unit cross-sectional area between actuated and unactuated states. In some cases, pre-strained polymers of the present invention may have an actuation pressure in the range of about 0 to about 100 MPa, and more preferably in the range of about 0.1 to 10 MPa. Specific elastic energy density—defined as the energy of deformation of a unit mass of the material in the transition between actuated and unactuated states—may also be used to describe an electroactive polymer where weight is important. Pre-strained polymers of the present invention may have a specific elastic energy density above 3 J/g. 
     The performance of a pre-strained polymer may also be described, independent of polymer size, by efficiency. Electromechanical efficiency is defined as the ratio of mechanical output energy to electrical input energy for an actuator mode of operation or, alternatively, of the ratio of electrical output energy to mechanical input energy for a generator mode of operation. Electromechanical efficiency greater than 80 percent is achievable with some pre-strained polymers of the present invention. The time for a pre-strained polymer to rise (or fall) to its maximum (or minimum) actuation pressure is referred to as its response time. Pre-strained polymer polymers in accordance with the present invention may accommodate a wide range of response times. Depending on the size and configuration of the polymer, response times may range from about 0.01 milliseconds to 1 second, for example. A pre-strained polymer excited at a high rate may also be characterized by an operational frequency. In one embodiment, maximum operational frequencies suitable for use with the present invention may be in the range of about 100 Hz to 100 kHz. Operational frequencies in this range allow pre-strained polymers of the present invention to be used in various acoustic applications (e.g., speakers). In some embodiments, pre-strained polymers of the present invention may be operated at a resonant frequency to improve mechanical output. 
     Performance of an actuator may be described by a performance parameter specific to the actuator. By way of example, performance of an actuator of a certain size and weight may be quantified by parameters such as stroke or displacement, force, actuator response time. Characterizing the performance of a transducer in an application relates to how well the transducer is embodied in a particular application (e.g. in robotics). Performance of a transducer in an application may be described by a performance parameter specific to the application (e.g., force/unit weight in robotic applications). Application specific parameters include stroke or displacement, force, actuator response time, frequency response, efficiency, etc. These parameters may depend on the size, mass and/or the design of the transducer and the particular application. 
     It should be noted that desirable material properties for an electroactive polymer may vary with an actuator or application. To produce a large actuation pressures and large strain for an application, a pre-strained polymer may be implemented with one of a high dielectric strength, a high dielectric constant, and a low modulus of elasticity. Additionally, a polymer may include one of a high-volume resistivity and low mechanical damping for maximizing energy efficiency for an application. 
     Performance parameters for a transducer in a generator mode of operation are generally analogous to those of the actuator mode. Specific energy density of a generator transducer is defined as the electrical energy generated per stroke per unit mass of transducer (or polymer). Specific energy densities for embodiments of the present invention are commonly at least about 0.15 Joules per gram for the polymer and can be greater than 0.35 Joules per gram for some polymers. 
     Electrodes 
     As mentioned above, transducers of the present invention preferably include one or more electrodes for actuating an electroactive polymer. Generally speaking, electrodes suitable for use with the present invention may be of any shape and material provided they are able to supply or receive a suitable voltage, either constant or varying over time, to or from an electroactive polymer. In one embodiment, the electrodes adhere to a surface of the polymer. Electrodes adhering to the polymer are preferably compliant and conform to the changing shape of the polymer. The electrodes may be only applied to a portion of an electroactive polymer and define an active area according to their geometry. 
     The compliant electrodes are capable of deflection in one or more directions. Linear strain may be used to describe the deflection of a compliant electrode in one of these directions. As the term is used herein, linear strain of a compliant electrode refers to the deflection per unit length along a line of deflection. Maximum linear strains (tensile or compressive) of at least about 50 percent are possible for compliant electrodes of the present invention. For some compliant electrodes, maximum linear strains at least about 100 percent are common. Of course, an electrode may deflect with a strain less than the maximum. In one embodiment, the compliant electrode is a ‘structured electrode’ that comprises one or more regions of high conductivity and one or more regions of low conductivity. 
       FIG. 3  illustrates a top surface view of a structured electrode  501  that provides one-directional compliance in accordance with one embodiment of the present invention. The structured electrode  501  includes metal traces  502  patterned in parallel lines over a charge distribution layer  503 —both of which cover an active area of a polymer (not shown). The metal traces  502  and charge distribution layer  503  are applied to opposite surfaces of the polymer. Thus, the cross section, from top to bottom, of a transducer including structured electrodes  501  on opposite surfaces is: top metal traces, top charge distribution layer, polymer, bottom charge distribution layer, bottom metal traces. Metal traces  502  on either surface of the polymer act as electrodes for electroactive polymer material between them. In another embodiment, the bottom electrode may be a compliant, uniform electrode. The charge distribution layer  503  facilitates distribution of charge between metal traces  502 . Together, the high conductivity metal traces  502  quickly conduct charge across the active area to the low conductivity charge distribution layer  503  which distributes the charge uniformly across the surface of the polymer between the traces  502 . The charge distribution layer  503  is compliant. As a result, the structured electrode  501  allows deflection in a compliant direction  506  perpendicular to the parallel metal traces  502 . 
     Actuation for the entire polymer may be achieved by extending the length of the parallel metal traces  502  across the length of the polymer and by implementing a suitable number of traces  502  across the polymer width. In one embodiment, the metal traces  502  are spaced at intervals in the order of 400 micrometers and have a thickness of about 20 to 100 nanometers. The width of the traces is typically much less than the spacing. To increase the overall speed of response for the structured electrode  501 , the distance between metal traces  502  may be reduced. The metal traces  502  may comprise gold, silver, aluminum and many other metals and relatively rigid conductive materials. In one embodiment, metal traces on opposite surfaces of an electroactive polymer are offset from one another to improve charge distribution through the polymer layer and prevent direct metal-to-metal electrical breakdowns. 
     Deflection of the parallel metal traces  502  along their axis greater than the elastic allowance of the metal trace material may lead to damage of the metal traces  502 . To prevent damage in this manner, the polymer may be constrained by a rigid structure that prevents deflection of the polymer and the metal traces  502  along their axis. The rigid members  232  of the linear motion device of  FIGS. 2D and 2E  are suitable in this regard. In another embodiment, the metal traces  502  may be undulated slightly on the surface of the polymer  500 . These undulations add compliance to the traces  502  along their axis and allow deflection in this direction. 
     In general, the charge distribution layer  503  has a conductance greater than the electroactive polymer but less than the metal traces. The non-stringent conductivity requirements of the charge distribution layer  503  allow a wide variety of materials to be used. By way of example, the charge distribution layer may comprise carbon black, fluoroelastomer with colloidal silver, a water-based latex rubber emulsion with a small percentage in mass loading of sodium iodide, and polyurethane with tetrathiafulavalene/tetracyanoquinodimethane (TTF/TCNQ) charge transfer complex. These materials are able to form thin uniform layers with even coverage and have a surface conductivity sufficient to conduct the charge between metal traces  502  before substantial charge leaks into the surroundings. In one embodiment, material for the charge distribution layer  503  is selected based on the RC time constant of the polymer. By way of example, surface resistivity for the charge distribution layer  503  suitable for the present invention may be in the range of about 10 6 -10 11  ohms. It should also be noted that in some embodiments, a charge distribution layer is not used and the metal traces  502  are patterned directly on the polymer. In this case, air or another chemical species on the polymer surface may be sufficient to carry charge between the traces. This effect may be enhanced by increasing the surface conductivity through surface treatments such as plasma etching or ion implantation.  FIG. 4  illustrates a pre-strained polymer  510  underlying a structured electrode that is not directionally compliant according to a specific embodiment of the present invention. The structured electrode includes metal traces  512  patterned directly on one surface of the electroactive polymer  510  in evenly spaced parallel lines forming a ‘zig-zag’ pattern. Two metal traces  512  on opposite surfaces of the polymer act as electrodes for the electroactive polymer  510  material between them. The ‘zig-zag’ pattern of the metal traces  512  allows for expansion and contraction of the polymer and the structure electrode in multiple directions  514  and  516 . 
     Using an array of metal traces as described with respect to  FIGS. 3 and 4  permits the use of charge distribution layers having a lower conductance. More specifically, as the spacing between metal traces decreases, the required conductance of the material between the traces may diminish. In this manner, it is possible to use materials that are not normally considered conductive to be used as a charge distribution layer. By way of example, polymers having a surface resistivity of 10 10  ohms may be used as an charge distribution layer in this manner. In a specific embodiment, rubber was used as a charge distribution layer as part of a structured electrode on a polymer layer having a thickness of 25 micrometers and spacing between parallel metal traces of about 500 micrometers. In addition to reducing the required conductance for a charge distribution layer, closely spaced metal traces also increase the speed of actuation since the charge need only travel through the charge distribution layer for a short distance between closely spaced metal traces. 
     Although structured electrodes of the present invention have been described in terms of two specific metal trace configurations; structured electrodes in accordance with the present invention may be patterned in any suitable manner. As one skilled in the art will appreciate, various uniformly distributed metallic trace patterns may provide charge on the surface of a polymer while providing compliance in one or more directions. In some cases, a structured electrode may be attached to the surface of polymer in a non-uniform manner. As actuation of the polymer may be limited to an active region within suitable proximity of a pair of patterned metal traces, specialized active and non-active regions for an electroactive polymer may be defined by custom patterning of the metal traces. These active and non-active regions may be formed to custom geometries and high resolutions according to conventional metal trace deposition techniques. Extending this practice across the entire surface of an electroactive polymer, custom patterns for structured electrodes comprising numerous custom geometry active regions may result in specialized and non-uniform actuation of the electroactive polymer according to the pattern of the structured electrodes. 
     Although the present invention has been discussed primarily in terms of flat electrodes, ‘textured electrodes’ comprising varying out of plane dimensions may be used to provide a compliant electrode.  FIG. 5  illustrates exemplary textured electrodes  520  and  521  in accordance with one embodiment of the present invention. The textured electrodes  520  and  521  are attached to opposite surfaces of an electroactive polymer  522  such that deflection of the polymer  522  results in planar and non-planar deformation of the textured electrodes  520  and  521 . The planar and non-planar compliance of the electrodes  520  and  521  is provided by an undulating pattern which, upon planar and/or thickness deflection of the polymer  522 , provides directional compliance in a direction  526 . To provide substantially uniform compliance for the textured electrodes  520  and  521 , the undulating pattern is implemented across the entire surface of the electroactive polymer in the direction  526 . In one embodiment, the textured electrodes  520  and  521  are comprised of metal having a thickness which allows bending without cracking of the metal to provide compliance. Typically, the textured electrode  52 Q is configured such that non-planar deflection of the electrodes  520  and  521  is much less than the thickness of the polymer  522  in order to provide a substantially constant electric field to the polymer  522 . Textured electrodes may provide compliance in more than one direction. In a specific embodiment, a rough textured electrode provides compliance in orthogonal planar directions. The rough textured electrode may have a topography similar to the rough surface of  FIG. 1D . 
     In one embodiment, compliant electrodes of the present invention comprise a conductive grease such as carbon grease or silver grease. The conductive grease provides compliance in multiple directions. Particles may be added to increase the conductivity of the polymer. By way of example, carbon particles may be combined with a polymer binder such as silicone to produce a carbon grease that has low elasticity and high conductivity. Other materials may be blended into the conductive grease to alter one or more material properties. Conductive greases in accordance with the present invention are suitable for the deflection of at least about 100 percent strain. 
     Compliant electrodes of the present invention may also include colloidal suspensions. Colloidal suspensions contain submicrometer sized particles, such as graphite, silver and gold, in a liquid vehicle. Generally speaking, any colloidal suspension having sufficient loading of conductive particles may be used as an electrode in accordance with the present invention. In a specific embodiment, a conductive grease including colloidal sized conductive particles is mixed with a conductive silicone including colloidal sized conductive particles in a silicone binder to produce a colloidal suspension that cures to form a conductive semi-solid. An advantage of colloidal suspensions is that they may be patterned on the surface of a polymer by spraying, dip coating and other techniques that allow for a thin uniform coating of a liquid. To facilitate adhesion between the polymer and an electrode, a binder may be added to the electrode. By way of example, a water-based latex rubber or silicone may be added as a binder to a colloidal suspension including graphite. 
     In another embodiment, compliant electrodes are achieved using a high aspect ratio conductive material such as carbon fibrils and carbon nanotubes. These high aspect ratio carbon materials may form high surface conductivities in thin layers. High aspect ratio carbon materials may impart high conductivity to the surface of the polymer at relatively low electrode thicknesses due to the high interconnectivity of the high aspect ratio carbon materials. By way of example, thicknesses for electrodes made with common forms of carbon that are not high-aspect ratio may be in the range of 5-50 micrometers while thicknesses for electrodes made with carbon fibril or carbon nanotube electrodes may be less than 2-4 micrometers. Area expansions well over 100 percent in multiple directions are suitable with carbon fibril and carbon nanotube electrodes on acrylic and other polymers. High aspect ratio carbon materials may include the use of a polymer binder to increase adhesion with the electroactive polymer layer. Advantageously, the use of polymer binder allows a specific binder to be selected based on adhesion with a particular electroactive polymer layer and based on elastic and mechanical properties of the polymer. 
     In one embodiment, high-aspect-ratio carbon electrodes may be fabricated thin enough such that the opacity of the electrodes may be varied according to polymer deflection. By way of example, the electrodes may be made thin enough such that the electrode changes from opaque to semitransparent upon expansion. This ability to manipulate the opacity of the electrode may allow transducers of the present invention to be applied to a number of various optical applications as will be described below. 
     In another embodiment, mixtures of ionically conductive materials may be used for the compliant electrodes. This may include, for example, water based polymer materials such as glycerol or salt in gelatin, iodine-doped natural rubbers and water-based emulsions to which organic salts such as potassium iodide are added. For hydrophobic electroactive polymers that may not adhere well to a water based electrode, the surface of the polymer may be pretreated by plasma etching or with a fine powder such as graphite or carbon black to increase adherence. 
     Materials used for the electrodes of the present invention may vary greatly. Suitable materials used in an electrode may include graphite, carbon black, colloidal suspensions, thin metals including silver and gold, silver filled and carbon filled gels and polymers, ionically or electronically conductive polymers. In a specific embodiment, an electrode suitable for use with the present invention comprises 80 percent carbon grease and 20 percent carbon black in a silicone rubber binder such as Stockwell RTV60-CON as produced by Stockwell Rubber Co. Inc. of Philadelphia, Pa. The carbon grease is of the type such as Circuit Works 7200 as provided by ChemTronics Inc. of Kennesaw, Ga. The conductive grease may also be mixed with an elastomer, such as silicon elastomer RTV 118 as produced by General Electric of Waterford, N.Y., to provide a gel-like conductive grease. 
     It is understood that certain electrode materials may work well with particular polymers and may not work as well for others. By way of example, carbon fibrils work well with acrylic elastomer polymers while not as well with silicone polymers. For most transducers, desirable properties for the compliant electrode may include any one of a low modulus of elasticity, low mechanical damping, a low surface resistivity, uniform resistivity, chemical and environmental stability, chemical compatibility with the electroactive polymer, good adherence to the electroactive polymer, and an ability to form smooth surfaces. In some cases, it may be desirable for the electrode material to be suitable for precise patterning during fabrication. By way of example, the compliant electrode may be spray coated onto the polymer. In this case, material properties which benefit spray coating would be desirable. In some cases, a transducer of the present invention may implement two different types of electrodes. By way of example, a diaphragm device of the present invention may have a structured electrode attached to its top surface and a high aspect ratio carbon material deposited on the bottom side. 
     Electronic drivers are connected to the electrodes. The voltage provided to electroactive polymer will depend upon specifics of an application. In one embodiment, a transducer of the present invention is driven electrically by modulating an applied voltage about a DC bias voltage. Modulation about a bias voltage allows for improved sensitivity and linearity of the transducer to the applied voltage. By way of example, a transducer used in an audio application may be driven by a signal of up to 200 to 1000 volts peak to peak on top of a bias voltage ranging from about 750 to 2000 volts DC. 
     Applications 
     As the present invention includes transducers that may be implemented in both the micro and macro scales, and with a wide variety of actuator designs, the present invention finds use in a broad range of applications where conversion between electrical and mechanical energy is required. Provided below are several exemplary applications for some of the actuators described above. Broadly speaking, the transducers and actuators of the present invention may find use in any application requiring conversion between electrical and mechanical energy. These applications include robotics, sensors, motors, toys, micro-actuator applications, pumps, generators, etc. 
     As mentioned before, electroactive polymers, either individually or mechanically linked in a collection, may be referred to as artificial muscle. The term artificial muscle in itself implies that these actuators are well-suited for application to biologically inspired robots or biomedical applications where the duplication of muscle, mammalian or other, is desired. By way of example, applications such as prosthetic limbs, exoskeletons, and artificial hearts may benefit from pre-strained polymers of the present invention. The size scalability of electroactive polymers and the ability to use any number of transducers or polymer actuators in a collection allow artificial muscle in accordance with the present invention to be used in a range in applications greater than their biological counterparts. As transducers and actuators of the present invention have a performance range far outside their biological counterparts, the present invention is not limited to artificial muscle having a performance corresponding to real muscle, and may indeed include applications requiring performance outside that of real muscle. 
     In one example of artificial muscle, a collection of linear motion devices comprises two or more layers of pre-strained polymer sandwiched together and attached to two rigid plates at opposite edges of each polymer. Electrodes are sealed into the center between each of the polymer layers. All of the linear motion devices in the collection may take advantage of geometric constraints provided by the rigid plates and anisotropic pre-strain to restrict deformation of the polymer in the actuated direction. An advantage of the layered construction is that as many electroactive polymer layers as required may be stacked in parallel in order to produce the desired force. Further, the stroke of this linear motion device configuration may be increased by adding similar linear motion devices in series. 
     In the micro domain, the pre-strained polymers may range in thickness from several micrometers to several millimeters and preferably from several micrometers to hundreds of micrometers. Micro pre-strained polymers are well-suited for applications such as inkjets, actuated valves, micropumps, inchworm-type actuators, pointing mirrors, sound generators, microclamps, and micro robotic applications. Micro robotic applications may include micro robot legs, grippers, pointer actuators for CCD cameras, wire feeders for micro welding and repair, clamping actuators to hold rigid positions, and ultrasonic actuators to transmit data over measured distances. In another application, a diaphragm device may be implemented in an array of similar electroactive polymer diaphragms in a planar configuration on a single surface. By way of example, an array may include sixty-two diaphragms with the diameter of 150 micrometers each arranged in a planar configuration. In one embodiment, the array of diaphragm devices may be formed on a silicon wafer. Diaphragm device arrays produced in this manner may include, for example, from 5 to 10,000 or more diaphragms each having a diameter in the range of about 60 to 150 micrometers. The array may be placed upon grid plates having suitably spaced holes for each diaphragm. 
     In the macro domain, each of the actuators described above may be well suited to its own set of applications. For example, the inchworm-type actuator of  FIG. 2I  is suitable for use with small robots capable of navigating through pipes less than 2 cm in diameter. Other actuators are well-suited, for example, with applications such as robotics, solenoids, sound generators, linear actuators, aerospace actuators, and general automation. 
     In another embodiment, a transducer of the present invention is used as an optical modulation device or an optical switch. The transducer includes an electrode whose opacity varies with deflection. A transparent or substantially translucent pre-strained polymer is attached to the opacity varying electrode and deflection of the polymer is used to modulate opacity of device. In the case of an optical switch, the opacity varying transducer interrupts a light source communicating with a light sensor. Thus, deflection of the transparent polymer causes the opacity varying electrode to deflect and affect the light sensor. In a specific embodiment, the opacity varying electrode includes carbon fibrils or carbon nanotubes that become less opaque as electrode area increases and the area fibril density decreases. In another specific embodiment, an optical modulation device comprised of an electroactive polymer and an opacity varying electrode may be designed to precisely modulate the amount of light transmitted through the device. 
     Diaphragm devices may be used as pumps, valves, etc. In one embodiment, a diaphragm device having a pre-strained polymer is suitable for use as a pump. Pumping action is created by repeatedly actuating the polymer. Electroactive polymer pumps in accordance with the present invention may be implemented both in micro and macro scales. By way of example, the diaphragm may be used as a pump having a diameter in the range of about 150 micrometers to about 2 centimeters. These pumps may include polymer strains over 100 percent and may produce pressures of 20 kPa or more. 
       FIG. 6  illustrates a two-stage cascaded pumping system including diaphragm pumps  540  and  542  in accordance with a specific embodiment of the present invention. The diaphragm pumps  540  and  542  include pre-strained polymers  544  and  546  attached to frames  545  and  547 . The polymers  544  and  546  deflect within holes  548  and  550  in the frames  545  and  547  respectively in a direction perpendicular to the plane of the holes  548  and  550 . The frames  545  and  547  along with the polymers  544  and  546  define cavities  551  and  552 . The pump  540  includes a plunger  553  having a flexure spring  560  for providing a bias to the diaphragm  544  towards the cavity  551 . 
     A one-way valve  555  permits inlet of a fluid or gas into the cavity  551 . A one-way valve  556  permits outlet of the fluid or gas out of the cavity  551  into the cavity  552 . In addition, a one-way valve  558  permits exit of the fluid or gas from the cavity  552 . Upon actuation of the polymers  544  and  546 , the polymers deflect in turn to change the pressure within the cavities  551  and  552  respectively, thereby moving fluid or gas from the one-way valve  555  to the cavity  551 , out the valve  556 , into the cavity  552 , and out the valve  558 . 
     In the cascaded two-stage pumping system of  FIG. 6 , the diaphragm pump  542  does not include a bias since the pressurized output from the diaphragm pump  540  biases the pump  542 . In one embodiment, only the first pump in a cascaded series of diaphragm pumps uses a bias pressure—or any other mechanism for self priming. In some embodiments, diaphragm pumps provided in an array may include voltages provided by electronic timing to increase pumping efficiency. In the embodiment shown in  FIG. 6 , polymers  544  and  546  are actuated simultaneously for best performance. For other embodiments which may involve more diaphragm pumps in the cascade, the electronic timing for the different actuators is ideally set so that one pump contracts in cavity volume while the next pump in the series (as determined by the one-way valves) expands. In a specific embodiment, the diaphragm pump  540  supplies gas at a rate of 40 ml/min and a pressure about 1 kPa while the diaphragm pump  542  supplies gas at substantially the same flow rate but increases the pressure to 2.5 kPa. 
     Bending beam devices, such as those described with respect to  FIGS. 2K-2M , may be used in a variety of commercial and aerospace devices and applications such as fans, electrical switches and relays, and light scanners—on the micro and macro level. For bending beam actuators used as light scanners, a reflective surface such as aluminized mylar may be bonded to the free end of a bending beam actuator. More specifically, light is reflected when the bending beam is actuated and light passes when the bending beam is at rest. The reflector may then be used to reflect incoming light and form a scanned beam to form an arc or line according to the deflection of the actuator. Arrays of bending beam actuators may also be used for flat-panel displays, to control airflow over a surface, for low profile speakers and vibration suppressors, as “smart furs” for controlling heat transfer and/or light absorption on a surface, and may act as cilia in a coordinated manner to manipulate objects. 
     Polymers and polymer films that are rolled into a tubular or multilayer cylinder actuator may be implemented as a piston that expands axially upon actuation. Such an actuator is analogous to a hydraulic or pneumatic piston, and may be implemented in any device or application that uses these traditional forms of linear deflection. 
     An electroactive polymer actuator may also operate at high speeds for a variety of applications including sound generators and acoustic speakers, inkjet printers, fast MEMS switches etc. In a specific embodiment, an electroactive polymer diaphragm is used as a light scanner. More specifically, a mirror may be placed on a flexure that pushes down on a 5 mm diameter electroactive polymer diaphragm to provide a mirrored flexure. Good scanning of images at a scanning angle from about 10 to 30 degrees may be accomplished with voltages in the range of about 190 to 300 volts and frequencies in the range of about 30 to 300 Hz. Much larger scanning angles, up to 90 degrees for example, may also be accommodated using voltages in the range of 400 to 500 V. In addition, higher frequencies may be used with a stiffer mirrored flexure. 
     Transducers of the present invention also find wide use as generators for converting mechanical energy into electrical energy. In particular, generators of the present invention are well-suited for use as heel strike generators. More specifically, one or more transducers of the present invention may be used in a shoe to harness mechanical energy produced from walking into electrical energy. Typically, a generator includes a polymer arranged in a manner which causes a change in electric field and stored electrical energy in response to deflection of a portion of the polymer. A mechanical input, such as a heel-strike, expands the transducer in one or both planar directions parallel to the surface of the electrodes, thus increasing the stored elastic mechanical energy of the transducer. If electrical charge is then placed on the electrodes in the stretched state (or more charge is added in the stretched state) and the transducer is allowed to contract, the transducer converts some or all of its elastic mechanical energy to a greater amount of stored electrical energy. The greater stored electrical energy may then be recovered or harvested by circuitry in electrical communication with the electrodes. Some portion of the harvested energy can then be recycled back to provide the initial input electrical charge on the next cycle of expansion-contraction. Generators applications also include transducers coupled to conventional combustion engines to make fuel-driven electrical generators, hand-driven crank generators, wave-powered generators, wind-powered generators, and other types of generators where a mechanical input is available for stretching the transducer. 
     It should be noted that transducers of the present invention may be implemented to have more than one functionality. In other words, a transducer may act as an actuator, a generator and a sensor in the same design. 
     Fabrication 
     As the pre-strained polymers may be implemented both in the micro and macro scales, in a wide variety of actuator designs, with a wide range of materials, and in a broad range of applications, fabrication processes used with the present invention may vary greatly. In one aspect, the present invention provides methods for fabricating electromechanical devices including one or more pre-strained polymers. 
       FIG. 7A  illustrates a process flow  600  for fabricating an electromechanical device having at least one electroactive polymer layer in accordance with one embodiment of the present invention. Processes in accordance with the present invention may include up to several additional steps not described or illustrated here in order not to obscure the present invention. In some cases, fabrication processes of the present invention may include conventional materials and techniques such as commercially available polymers and techniques used in fabrication of microelectronics and electronics technologies. For example, micro diaphragm devices may be produced in situ on silicon using conventional techniques to form the holes and apply the polymer and electrodes. 
     The process flow  600  begins by receiving or fabricating a polymer ( 602 ). The polymer may be received or fabricated according to several methods. In one embodiment, the polymer is a commercially available product such as a commercially available acrylic elastomer film. In another embodiment, the polymer is a film produced by one of casting, dipping, spin coating or spraying. In one embodiment, the polymer is produced while minimizing variations in thickness or any other defects that may compromise the maximize electric field that can be applied across the polymer and thus compromise performance. 
     Spin coating typically involves applying a polymer mixture on a rigid substrate and spinning to a desired thickness. The polymer mixture may include the polymer, a curing agent and a volatile dispersant or solvent. The amount of dispersant, the volatility of the dispersant, and the spin speed may be altered to produce a desired polymer. By way of example, polyurethane films may be spin coated in a solution of polyurethane and tetrahydrofuran (THF) or cyclohexanone. In the case of silicon substrates, the polymer may be spin coated on an aluminized plastic or a silicon carbide. The aluminum and silicon carbide form a sacrificial layer that is subsequently removed by a suitable etchant. Films in the range of one micrometer thick may been produced by spin coating in this manner. Spin coating of polymer films, such as silicone, may be done on a smooth non-sticking plastic substrate, such as polymethyl methacrylate or teflon. The polymer film may then be released by mechanically peeling or with the assistance of alcohol or other suitable release agent. Spin coating is also suitable for producing thicker polymers in the range of 10-750 micrometers. In some cases, the polymer mixture may be centrifuged prior to spin coating to remove unwanted materials such as fillers, particulates, impurities and pigments used in commercial polymers. To increase centrifuge efficacy or to improve thickness consistency, a polymer may be diluted in a solvent to lower its viscosity; e.g. silicone may be disbursed in naptha. 
     The polymer may then be pre-strained in one or more directions ( 604 ). In one embodiment, pre-strain is achieved by mechanically stretching a polymer in or more directions and fixing it to one or more solid members (e.g., rigid plates) while strained. Another technique for maintaining pre-strain includes the use of one or more stiffeners. The stiffeners are long rigid structures placed on a polymer while it is in a pre-strained state, e.g. while it is stretched. The stiffeners maintain the pre-strain along their axis. The stiffeners may be arranged in parallel or other configurations to achieve directional compliance of the transducer. It should be noted that the increased stiffness along the stiffener axis comprises the increased stiffness provided by the stiffener material as well as the increased stiffness of the polymer in the pre-strain direction. 
     Surfaces on the pre-strained polymer may be textured. In one embodiment to provide texturing, a polymer is stretched more than it can stretch when actuated, and a thin layer of stiff material is deposited on the stretched polymer surface. For example, the stiff material may be a polymer that is cured while the electroactive polymer is stretched. After curing, the electroactive polymer is relaxed and the structure buckles to provide the textured surface. The thickness of the stiff material may be altered to provide texturing on any scale, including submicrometer levels. In another embodiment, textured surfaces are produced by reactive ion etching (RIE). By way of example, RIE may be performed on a pre-strained polymer comprising silicon with an RICE gas comprising 90 percent carbon tetrafluoride and 10 percent oxygen to form a surface with wave troughs and crests 4 to 5 micrometers in depth. 
     One or more electrodes are then formed on the polymer ( 606 ). For the silicone polymer altered by RIE mentioned above, a thin layer of gold may be sputter deposited on the RIE textured surface to provide a textured electrode. In another embodiment, one or more graphite electrodes may be patterned and deposited using a stencil. Electrodes comprising conductive greases mixed with a conductive silicone may be fabricated by dissolving the conductive grease and the uncured conductive silicone in a solvent. The solution may then be sprayed on the electroactive polymer material and may include a mask or stencil to achieve a particular pattern. 
     The metal traces of the structured electrodes of  FIGS. 3 and 4  may be patterned photolithographically on top of the polymer or charge distribution layer. By way of example, a layer of gold is sputter deposited before depositing a photoresist over the gold. The photoresist and gold may be patterned according to conventional photolithographic techniques, e.g. using a mask followed by one or more rinses to remove the photoresist. A charge distribution layer added between the polymer and the metal traces may be deposited by spin coating, for example. 
     In a specific embodiment, a structured electrode is formed on a polymer by sputter depositing gold for about 2 to 3 minutes (according to a desired thickness) at about 150 angstroms per minute, HPR 506 photoresist as provided by Arch Chemicals, of Norwalk, Conn. is then spin coated on the gold at about 500 to 1500 rpm for about 20 to 30 seconds and then baked at about 90 degrees Celsius. A mask is then applied before exposing the photoresist to UV light and development to remove unmasked portions of the photoresist. The gold is then etched away and the film is rinsed. The remaining photoresist is removed by exposure to UV light, development and rinsing. The gold traces may then be stretched to enhance strain tolerance. 
     Textured electrodes of the present invention may also be patterned photolithographically. In this case, a photoresist is deposited on a pre-strained polymer and patterned using a mask. Plasma etching may remove portions of the electroactive polymer not protected by the mask in a desired pattern. The mask may be subsequently removed by a suitable wet etch. The active surfaces of the polymer may then be covered with the thin layer of gold deposited by sputtering, for example. 
     The transducer, comprising the one or more polymer layers and electrodes, is then packaged according to an application ( 608 ). Packaging may also include assembly of multiple transducers mechanically linked or stacked as multiple layers. In addition, mechanical and electrical connections to the transducers may be formed according to an application. 
     Fabrication of polymers may also include the addition of one or more additives. In the additives example described above, mineral oil was added to a solution of Kraton D2104 as produced by Shell Chemical of Houston, Tex. in a solvent such as butyl acetate to increase the dielectric breakdown strength. In a specific example, the solution contained 14.3 percent weight mineral oil and 32.1 percent weight Kraton D2104. The solution was then cast onto glass and heated in an oven at 95 degrees Celsius to remove any residual solvent and produce the electroactive polymer. The polymer was then stretched on a frame by 150 percent by 150 percent. Carbon grease electrodes were then smeared on opposite surfaces of the polymer. This process produced a transducer having a maximum linear strain in the range of about 70 to 100 percent. 
     The present invention also provides alternative methods for fabricating electromechanical devices including multiple layers of pre-strained polymer. In one embodiment, a process for fabricating electromechanical devices begins by obtaining or fabricating a polymer layer. The polymer is then stretched to the desired pre-strain and attached to a first rigid frame. Next electrodes are deposited onto both sides of the polymer so as to define active areas and establish electrical connections. The electrodes may be patterned by a variety of well-known techniques such as spray coating through a mask. If desired, a second polymer layer is then stretched on a second frame. Electrodes are then patterned on this second polymer layer. The second polymer layer is then coupled to the first layer by stacking their respective frames. Layers of suitable compliant adhesives may be used to bond the two layers and electrodes, if needed. The size of the frames is chosen so as not to interfere with the polymer layers making intimate contact. If interference is present, then it may be desirable to remove the second frame, e.g., by cutting away the polymer layer around the periphery of the first frame. If desired, a third layer of polymer with electrodes may be added in a manner similar to how the second layer was added to the first. This procedure may be continued until a desired number of layers is reached. 
     Rigid frames, rigid members or other electrical and mechanical connectors are then attached to the polymer layers, e.g., by gluing. If desired, the polymer may then be removed from the first frame. In some cases, the first frame may serve as a structural part of the final actuator or actuators. For example, the first frame may be an array of holes to produce an array of diaphragm devices. 
       FIGS. 7B-F  illustrate a second process for fabricating an electromechanical device  640  having multiple layers of electroactive polymer in accordance with another embodiment of the present invention. Processes in accordance with the present invention may include up to several additional steps not described or illustrated here in order not to obscure the present invention. The process begins by producing a pre-strained polymer  622  on a suitable rigid substrate  624 , e.g. by spin coating a polymer on a polymethyl methacrylate (PMMA) disk, stretching the polymer ( FIG. 7B ) and then attaching it to rigid substrate  624 . After the polymer  622  is cured, electrodes  625  are patterned on the exposed side  626  of the polymer  622 . A solid member  627  such as a flexible film including one of polyimide, mylar or acetate film is then deposited onto the electroactive polymer  622  ( FIG. 7C ) with a suitable adhesive  628 . 
     The rigid substrate  624  is then released from the electroactive polymer  622  ( FIG. 7D ). A releasing agent such as isopropyl alcohol may be used to facilitate the release. Electrodes  629  are then patterned on the previously unexposed side of the polymer  622 . The assembly is then bonded to another electroactive polymer layer  630  attached to a rigid substrate  631  ( FIG. 7E ). Polymer layers  622  and  630  may be bonded by an adhesive layer  632  comprising GE RTV 118 silicone, for example. The rigid substrate  631  is then released from the polymer  630  and electrodes  633  are patterned on the available side  634  of the polymer  630 . If additional polymer layers are desired, the steps of adding a polymer layer, removing the rigid substrate, and adding electrodes may be repeated to produce as many polymer layers as desired. Polymer layer  635  has been added in this manner. To facilitate electrical communication to electrodes in the inner layers of the device  640 , a metal pin may be pushed through the structure to make contact with electrodes in each layer. 
     The solid member  627  may then be patterned or removed as needed to provide the frame or mechanical connections required by the specific actuator type. In one embodiment, diaphragm devices may be formed by patterning solid member  627  to form holes  636  which provide active regions for the electromechanical device  640  using a suitable mask or etch technique ( FIG. 7F ). In another embodiment, if the active area is not large and electrodes may be added to the active regions of the polymers without damage, the solid member  627  may be patterned with the holes  636  prior to attachment to the polymer  622 . 
     For the process of  FIGS. 7B-F , the rigid substrate  624  is typically released from the electroactive polymer  622  by peeling the flexible electroactive polymer. Peeling is well-suited for fabricating devices comprising electroactive polymers with a substantially flat profile. In another embodiment, sacrificial layers may be used between the polymer or electrodes and the rigid substrate to facilitate release. The sacrificial layers allow the polymer, electrodes and attached assembly to be released from a rigid substrate by etching away the sacrificial layer. Metals comprising aluminum and silver are suitable for use as the sacrificial layers, for example. The use of metals allows the sacrificial layers to be etched away by liquids that do not affect the polymer layers. Metal sacrificial layers may also be easily patterned with various masking techniques to provide frames, connectors for other structural components for the electromechanical device  640 . The sacrificial layers may also be used to fabricate devices comprising transducers with non flat profiles, e.g. using rigid substrates shaped as tubes. For geometrically complex transducers, sacrificial layers may be used in combination with dip coating to provide the complex geometry. 
     Although fabrication of pre-strained polymers has been briefly described with respect to a few specific examples, fabrication processes and techniques of the present invention may vary accordingly for any the actuators or applications described above. For example, the process for fabricating a diaphragm device in accordance with a specific embodiment may include spin coating a polymer on a substrate before a structured electrode is fabricated on the polymer. The polymer is then stretched and rigid frames including one or more holes sized for the active area of each diaphragm device are bonded to the pre-strained polymer, including any overlap portions of the structured electrode. In another embodiment, holes are etched into the substrate instead of using a separate rigid frame, e.g. when the substrate is comprised of silicon. The substrate is then released from the polymer and an electrode is attached to the bottom side of the polymer. 
     Conclusion 
     While this invention has been described in terms of several preferred embodiments, there are alterations, permutations, and equivalents that fall within the scope of this invention which have been omitted for brevity&#39;s sake. By way of example, although the present invention has been described in terms of several numerous applied material electrodes, the present invention is not limited to these materials and in some cases may include air as an electrode. In addition, although the present invention has been described in terms of several preferred polymer materials and geometries having particular performance ranges, the present invention is not limited to these materials and geometries and may have performances outside the ranges listed. It is therefore intended that the scope of the invention should be determined with reference to the appended claims.