Patent Publication Number: US-6664718-B2

Title: Monolithic electroactive polymers

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This application claims priority under 35 U.S.C. §119(e) from co-pending U.S. Provisional Patent Application No. 60/181,404, filed Feb. 9, 2000 which is incorporated by reference for all purposes. 
    
    
     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 electroactive polymers having multiple active areas. The present invention also relates to methods of actuating electroactive polymers having multiple active areas. 
     In many applications, it is desirable to convert between electrical energy and mechanical energy. Exemplary applications requiring conversion 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 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) or the weight or complexity must be minimized. Exemplary applications requiring conversion from mechanical to electrical energy include sensors and generators. These applications include one or more transducers that convert mechanical energy into electrical energy. Common electric generator technologies, such as electromagnetic generators, are 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 transducer 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 fluoride (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, 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 due to 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 OF THE INVENTION 
     In one aspect, the present invention relates to polymers that convert between electrical and mechanical energy. When a voltage is applied to electrodes contacting an electroactive polymer, the polymer deflects. This deflection may be used to do mechanical work. Similarly, when a previously charged electroactive polymer deflects, the electric field in the material is changed. The change in electric field may be used to produce electrical energy. An active area is a portion of a polymer having sufficient electrostatic force to enable deflection of the portion and/or sufficient deflection to enable a change in electrostatic force or electric field. The present invention relates to transducers and devices comprising multiple active areas. The invention also relates to methods for actuating one or more active areas. 
     In another aspect, the invention relates to a transducer for converting between electrical energy and mechanical energy. The transducer comprises an electroactive polymer having a plurality of active areas. The plurality of active areas comprise a first active area having at least two first active area electrodes and a first portion of the electroactive polymer arranged in a manner which causes the first portion to deflect in response to a change in electric field provided by the at least two first active area electrodes and/or arranged in a manner which causes a change in electric field in response to deflection of the first portion. The plurality of active areas also comprise a second active area having at least two second active area electrodes and a second portion of the electroactive polymer arranged in a manner which causes the second portion to deflect in response to a change in electric field provided by the at least two second active area electrodes and/or arranged in a manner which causes a change in electric field in response to deflection of the second portion. 
     In yet another aspect, the invention relates to a device for converting between electrical energy and mechanical energy. The device comprises an electroactive polymer having a plurality of active areas. The plurality of active areas comprise a first active area having at least two first active area electrodes and a first portion of the electroactive polymer arranged in a manner which causes the first portion to deflect in response to a change in electric field provided by the at least two first active area electrodes and/or arranged in a manner which causes a change in electric field in response to deflection of the first portion. The plurality of active areas also comprise a second active area having at least two second active area electrodes and a second portion of the electroactive polymer arranged in a manner which causes the second portion to deflect in response to a change in electric field provided by the at least two second active area electrodes and/or arranged in a manner which causes a change in electric field in response to deflection of the second portion. The device also comprises a substantially rigid member coupled to a third portion of the electroactive polymer. 
     In yet another aspect, the invention relates to a method for using an electroactive polymer having a plurality of active areas. The electroactive polymer comprises a first active area and a second active area, the first active area having at least two first active area electrodes and a first portion of the electroactive polymer, the second active area having at least two second active area electrodes and a second portion of the electroactive polymer. The method comprises providing a change in electric field to the at least two first active area electrodes. The method also comprises providing a change in electric field to the at least two second active area electrodes. 
     In still another aspect, the invention relates to a transducer for converting between electrical energy and mechanical energy. The transducer comprises an electroactive polymer having a plurality of active areas. The plurality of active areas comprise a first active area having a first electrode, a common electrode, and a first portion of the electroactive polymer arranged in a manner which causes the first portion to deflect in response to a change in electric field provided by the first electrode and the common electrode and/or arranged in a manner which causes a change in electric field in response to deflection of the first portion. The plurality of active areas also comprise a second active area having a second electrode, the common electrode, and a second portion of the electroactive polymer arranged in a manner which causes the second portion to deflect in response to a change in electric field provided by the second electrode and the common electrode and/or arranged in a manner which causes a change in electric field in response to deflection of the second portion. 
     In yet another aspect, the invention relates to a transducer for converting between electrical energy and mechanical energy. The transducer comprises an electroactive polymer having a plurality of active areas. The plurality of active areas comprise a first active area having at least two first active area electrodes and a first portion of the electroactive polymer arranged in a manner which causes the first portion to deflect in response to a change in electric field provided by the at least two first active area electrodes and/or arranged in a manner which causes a change in electric field in response to deflection of the first portion. The plurality of active areas also comprise a second active area having at least two second active area electrodes and a second portion of the electroactive polymer arranged in a manner which causes the second portion to deflect in response to a change in electric field provided by the at least two second active area electrodes and/or arranged in a manner which causes a change in electric field in response to deflection of the second portion. 
     In still another aspect, the invention relates to a device for converting between electrical energy and mechanical energy. The device comprises an electroactive polymer having a plurality of active areas. The plurality of active areas comprise a first active area having at least two first active area electrodes and a first portion of the electroactive polymer arranged in a manner which causes the first portion to deflect in response to a change in electric field provided by the at least two first active area electrodes and/or arranged in a manner which causes a change in electric field in response to deflection of the first portion. The plurality of active areas also comprise a second active area having at least two second active area electrodes and a second portion of the electroactive polymer arranged in a manner which causes the second portion to deflect in response to a change in electric field provided by the at least two second active area electrodes and/or arranged in a manner which causes a change in electric field in response to deflection of the second portion. The device further comprises a substantially rigid member having a first portion and a second portion. The first portion of the substantially rigid member coupled to a third portion of the electroactive polymer. The second portion of the substantially rigid member capable of motion assisted by deflection of the first portion of the polymer in response to a change in electric field provided by the at least two first active area electrodes and/or capable of motion that causes a change in electric field in the first portion of the polymer. The device additionally comprises a frame coupled to a fourth portion of 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 view of a transducer portion before and after application of a voltage, respectively, in accordance with one embodiment of the present invention. 
     FIG. 1C illustrates a monolithic transducer comprising a plurality of active areas in accordance with one embodiment of the present invention. 
     FIG. 1D illustrates a device comprising a plurality of symmetrically arranged electrodes in accordance with a specific embodiment of the present invention. 
     FIGS. 1E and 1F illustrate opposite sides of a monolithic transducer in accordance with a specific embodiment of the present invention. 
     FIG. 1G illustrates deflection of a portion of the monolithic transducer of FIGS. 1E and 1F in accordance with a specific embodiment of the present invention. 
     FIG. 1H illustrates a monolithic device providing three degrees of freedom in accordance with a specific embodiment of the present invention. 
     FIGS. 2A and 2B illustrate a device comprising a monolithic transducer for converting between electrical energy and mechanical energy in accordance with another embodiment of the present invention. 
     FIG. 2C illustrates a stacked multilayer device suitable for use with the present invention. 
     FIG. 2D illustrates a stretched film device in accordance with one embodiment of the present invention. 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     The present invention is described in detail with reference to a few preferred embodiments 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. 
     1. Overview 
     Electroactive polymers convert between mechanical and electrical energy. In one aspect, the present invention relates to electroactive polymer transducers that comprise multiple active areas. The multiple active areas may be arranged on a single polymer. The ability to arrange multiple active areas on a single polymer allows for numerous transducer configurations. The multiple active areas may be used in a variety of ways. The ability to use these multiple active areas independently increases electroactive polymer flexibility in converting between electrical and mechanical energy and allows the polymers to be used in many new applications. For example, multiple active areas on a single electroactive polymer may be independently actuated to deflect a portion of the polymer along a two-dimensional path. The two-dimensional path may be a circular path used in driving a crank in a motor. Combining different ways to arrange active areas on a polymer, 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 designs for actuators, motors, sensors, generators, and other transducer devices. These devices find use in a wide range of applications. 
     For ease of understanding, the present invention is mainly 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, i.e., when a transducer is operating in an actuator. 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, and devices described herein are also a transducer for converting mechanical energy to electrical energy (a generator). Similarly, any of the exemplary electrodes described herein may be used with a generator of the present invention. Typically, a generator of the present invention comprises a polymer arranged in a manner that causes a change in electric field in response to deflection of a portion of the polymer. The change in electric field, along with changes in the polymer dimension in the direction of the field, produces a change in voltage, and hence a change in electrical energy. 
     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, or a portion of the transducer associated with a single active area, as being an actuator or a generator is in the change in net area orthogonal to the thickness associated with the polymer deflection. For these transducers or active areas, when the deflection causes the net area of the transducer/active area to decrease and there is charge on the electrodes, the transducer/active area is converting from mechanical to electrical energy and acting as a generator. Conversely, when the deflection causes the net area of the transducer/active area to increase and charge is on the electrodes, the transducer/active area is converting electrical to mechanical energy and acting as an actuator. The change in area in both cases corresponds to a reverse change in film thickness, i.e. the thickness contracts when the planar area expands, and the thickness expands when the planar area contracts. Both the change in area and change in thickness determine the amount of energy that is converted between electrical and mechanical. Since the effects due to a change in area and corresponding change in thickness are complementary, only the change in area will be discussed herein for sake of brevity. In addition, although deflection of an electroactive polymer will primarily be discussed as a net increase in area of the polymer when the polymer is being used in an actuator to produce mechanical energy, it is understood that in some cases (i.e. depending on the loading), the net area may decrease to produce mechanical work. Thus, devices of the present invention may include both actuator and generator modes, depending on how the polymer is arranged and applied. 
     2. General Structure of Electroactive Polymers 
     The transformation between electrical and mechanical energy in devices of the present invention is based on energy conversion of one or more active areas of an electroactive polymer. Electroactive polymers deflect when actuated by electrical energy. To help illustrate the performance of an electroactive polymer in converting electrical energy to mechanical energy, FIG. 1A illustrates a top perspective view of a transducer portion  100  in accordance with one embodiment of the present invention. The transducer portion  100  comprises an electroactive polymer  102  for converting between electrical energy and mechanical 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. 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 . Polymer  102  deflects with a change in electric field provided by the top and bottom electrodes  104  and  106 . Deflection of the transducer portion  100  in response to a change in electric field provided by the electrodes  104  and  106  is referred to as actuation. As polymer  102  changes in size, the deflection may be used to produce mechanical work. 
     FIG. 1B illustrates a top perspective view of the transducer portion  100  including deflection in response to a change in electric field. In general, 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 applied to or by the electrodes  104  and  106  produces mechanical pressure within polymer  102 . In this case, the unlike electrical charges produced by electrodes  104  and  106  attract each other and provide a compressive force between electrodes  104  and  106  and an expansion force on polymer  102  in planar directions  108  and  110 , causing polymer  102  to compress between electrodes  104  and  106  and stretch in the planar directions  108  and  110 . 
     In some cases, electrodes  104  and  106  cover a limited portion of polymer  102  relative to the total area of the polymer. This may be done to prevent electrical breakdown around the edge of polymer  102  or to achieve customized deflections for one or more portions of the polymer. As the term is used herein, an active area is defined as a portion of a transducer comprising polymer material  102  and at least two electrodes. When the active area is used to convert electrical energy to mechanical energy, the active area includes a portion of polymer  102  having sufficient electrostatic force to enable deflection of the portion. When the active area is used to convert mechanical energy to electrical energy, the active area includes a portion of polymer  102  having sufficient deflection to enable a change in electrostatic energy. As will be described below, a polymer of the present invention may have multiple active areas. In some cases, polymer  102  material outside an active area may act as an external spring force on the active area during deflection. More specifically, polymer 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. 
     Electrodes  104  and  106  are compliant and change shape with polymer  102 . The configuration of polymer  102  and electrodes  104  and  106  provides for increasing polymer  102  response with deflection. More specifically, as the transducer portion  100  deflects, compression of polymer  102  brings the opposite charges of electrodes  104  and  106  closer and the stretching of polymer  102  separates similar charges in each electrode. In one embodiment, one of the electrodes  104  and  106  is ground. 
     In general, the transducer portion  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 electrodes  104  and  106 , and any external resistance provided by a device and/or load coupled to the transducer portion  100 , etc. The deflection of the transducer portion  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 size of polymer  102 . 
     Electroactive polymers in accordance with the present invention are capable of deflection in any direction. After application of the voltage between electrodes  104  and  106 , polymer  102  expands (stretches) in both planar directions  108  and  110 . In some cases, polymer  102  is incompressible, e.g. has a substantially constant volume under stress. For an incompressible polymer  102 , 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 electrodes  104  and  106  on the transducer portion  100  shown in FIG. 1A will cause transducer portion  100  to change to a thinner, larger area shape as shown in FIG.  1 B. In this manner, the transducer portion  100  converts electrical energy to mechanical energy. The transducer portion  100  may also be used to convert mechanical energy to electrical energy. 
     FIGS. 1A and 1B may be used to show one manner in which the transducer portion  100  converts mechanical energy to electrical energy. For example, if the transducer portion  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 (less than that necessary to actuate the film to the configuration in FIG. 1B) is applied between electrodes  104  and  106 , the transducer portion  100  will contract in area between the electrodes to a shape such as in FIG. 1A when the external forces are removed. Stretching the transducer refers to deflecting the transducer from its original resting position—typically to result in 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 portion  100  having no external electrical or mechanical input and may comprise any pre-strain in the polymer. Once the transducer portion  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 portion  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 polymer  102  becomes thicker, it separates electrodes  104  and  106  and their corresponding unlike charges, thus raising the electrical energy and voltage of the charge. Further, when electrodes  104  and  106  contract to a smaller area, like charges within each electrode compress, also raising the electrical energy and voltage of the charge. Thus, with different charges on 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 portion  100  is acting as a generator. 
     In some cases, the transducer portion  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.  1 A. 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 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 portion  100  may be mechanically coupled to a mechanical input that deflects the polymer and provides mechanical energy. 
     The transducer portion  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 portion  100  is fully contracted in the plane defined by directions  108  and  110 . Alternatively, some or all of the charge and energy can be removed during contraction. If the electric field pressure in the polymer increases and reaches balance with the mechanical elastic restoring forces and external load 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. Thus, removing some of the charge may further convert mechanical energy to electrical energy. The exact electrical behavior of the transducer portion  100  when operating as a generator depends on any electrical and mechanical loading as well as the intrinsic properties of polymer  102  and electrodes  104  and  106 . 
     In one embodiment, 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 a direction after pre-straining relative to the dimension in that direction before pre-straining. The pre-strain may comprise elastic deformation of polymer  102  and be formed, for example, by stretching the polymer in tension and fixing one or more of the edges while stretched. For many polymers, pre-strain improves conversion between electrical and mechanical energy. The improved mechanical response enables greater mechanical work for an electroactive polymer, e.g., larger deflections and actuation pressures. In one embodiment, prestrain improves the dielectric strength of the polymer. In another 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 also be implemented locally for a portion of the polymer. 
     In one embodiment, pre-strain is applied uniformly over a portion of polymer  102  to produce an isotropic pre-strained polymer. By way of example, an acrylic elastomeric polymer may be stretched by 200 to 400 percent in both planar directions. In another embodiment, pre-strain is applied unequally in different directions for a portion of polymer  102  to produce an anisotropic pre-strained polymer. In this case, 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, more deflection occurs in the low pre-strain direction. In one embodiment, the deflection in direction  108  of transducer portion  100  can be enhanced by exploiting large prestrain in the perpendicular direction  110 . For example, an acrylic elastomeric polymer used as the transducer portion  100  may be stretched by 100 percent in direction  108  and by 500 percent in the perpendicular direction  110 . The quantity of pre-strain for a polymer may be based on the polymer material and the desired performance of the polymer in an application. Pre-strain suitable for use with the present invention is further described in commonly owned, copending U.S. patent application Ser. No. 09/619,848, which is incorporated by reference for all purposes. 
     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. 
     Generally, after the polymer is pre-strained, it may be fixed to one or more objects. Each object is preferably 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 type of 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. 
     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. Other exemplary materials suitable for use as a pre-strained polymer include silicone elastomers, acrylic elastomers such as VHB 4910 acrylic elastomer as produced by 3M Corporation of St. Paul, Minn., 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. Combinations of some of these materials may also be used as the electroactive polymer in transducers of this invention. 
     An electroactive polymer layer in transducers of the present invention may have a wide range of thicknesses. In one embodiment, polymer thickness may range between about 1 micrometer and 2 millimeters. Polymer thickness may be reduced by stretching the film in one or both planar directions. In many cases, electroactive polymers of the present invention may be fabricated and implemented as thin films. Thicknesses suitable for these thin films may be below 50 micrometers. 
     Suitable actuation voltages for electroactive polymers, or portions thereof, may vary based on the material properties of the electroactive polymer, such as the dielectric constant, as well as the dimensions of the polymer, such as the thickness of the polymer film For example, actuation electric fields used to actuate polymer  102  in FIG. 1A may range in magnitude from about 0 V/m to about 440 MV/m. Actuation electric fields in this range may produce a pressure in the range of about 0 Pa to about 10 MPa. In order for the transducer to produce greater forces, the thickness of the polymer layer may be increased. Actuation voltages for a particular polymer may be reduced by increasing the dielectric constant, decreasing the polymer thickness, and decreasing the modulus of elasticity, for example. 
     As electroactive polymers of the present invention may deflect at high strains, electrodes attached to the polymers should also deflect without compromising mechanical or electrical performance. Generally, electrodes suitable for use with the present invention may be of any shape and material provided that they are able to supply a suitable voltage to, or receive a suitable voltage from, an electroactive polymer. The voltage may be either constant or varying over time. 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. Correspondingly, the present invention may include compliant electrodes that conform to the shape of an electroactive polymer to which they are attached. The electrodes may be only applied to a portion of an electroactive polymer and define an active area according to their geometry. Several examples of electrodes that only cover a portion of an electroactive polymer will be described in further detail below. 
     Various types of electrodes suitable for use with the present invention are described in commonly owned, copending U.S. patent application Ser. No. 09/619,848, which was previously incorporated by reference above. Electrodes described therein and suitable for use with the present invention include structured electrodes comprising metal traces and charge distribution layers, textured electrodes comprising varying out of plane dimensions, conductive greases such as carbon greases or silver greases, colloidal suspensions, high aspect ratio conductive materials such as carbon fibrils and carbon nanotubes, and mixtures of ionically conductive materials. 
     Materials used for electrodes of the present invention may vary. 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, and 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 NyoGel 756G as provided by Nye Lubricant Inc. of Fairhaven, Mass. 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 one or more of the following: low modulus of elasticity, low mechanical damping, low surface resistivity, uniform resistivity, chemical and environmental stability, chemical compatibility with the electroactive polymer, good adherence to the electroactive polymer, and the ability to form smooth surfaces. In some cases, a transducer of the present invention may implement two different types of electrodes, e.g. a different electrode type for each active area or different electrode types on opposing sides of a polymer. 
     Electronic drivers are typically 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. For 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. 
     3. Multiple Active Areas 
     In accordance with the present invention, the term “monolithic” is used herein to refer to electroactive polymers, transducers, and devices comprising a plurality of active areas. FIG. 1C illustrates a monolithic transducer  150  comprising a plurality of active areas in accordance with one embodiment of the present invention. The monolithic transducer  150  converts between electrical energy and mechanical energy. The monolithic transducer  150  comprises an electroactive polymer  151  having two active areas  152   a  and  152   b.  Polymer  151  may be held in place using, for example, a rigid frame (not shown) attached at the edges of the polymer. 
     The active area  152   a  has top and bottom electrodes  154   a  and  154   b  that are attached to polymer  151  on its top and bottom surfaces  151   c  and  151   d,  respectively. The electrodes  154   a  and  154   b  provide a voltage difference across a portion  151   a  of the polymer  151 . The portion  151   a  deflects with a change in electric field provided by the electrodes  154   a  and  154   b.  The portion  151   a  comprises the polymer  151  between the electrodes  154   a  and  154   b  and any other portions of the polymer  151  having sufficient electrostatic force to enable deflection upon application of voltages using the electrodes  154   a  and  154   b.  When the device  150  is used as a generator to convert from electrical energy to mechanical energy, deflection of the portion  151   a  causes a change in electric field in the portion  151   a  that is received as a change in voltage difference by the electrodes  154   a  and  154   b.    
     The active area  152   b  has top and bottom electrodes  156   a  and  156   b  that are attached to the polymer  151  on its top and bottom surfaces  151   c  and  151   d,  respectively. The electrodes  156   a  and  156   b  provide a voltage difference across a portion  151   b  of the polymer  151 . The portion  151   b  deflects with a change in electric field provided by the electrodes  156   a  and  156   b.  The portion  151   b  comprises the polymer  151  between the electrodes  156   a  and  156   b  and any other portions of the polymer  151  having sufficient stress induced by the electrostatic force to enable deflection upon application of voltages using the electrodes  156   a  and  156   b.  When the device  150  is used as a generator to convert from electrical energy to mechanical energy, deflection of the portion  151   b  causes a change in electric field in the portion  151   b  that is received as a change in voltage difference by the electrodes  156   a  and  156   b.    
     The active areas for monolithic polymers and transducers of the present invention may be flexibly arranged. In one embodiment, active areas in a polymer are arranged such that the elasticity of the active areas is balanced. In another embodiment, a transducer of the present invention comprises a plurality of symmetrically arranged active areas. While one embodiment of present invention will now be described as a device, those skilled in the art will recognize that the present invention encompasses methods having as steps the actions performed by various parts of the device described below. 
     FIG. 1D illustrates a monolithic device  160  comprising a plurality of symmetrically arranged active areas in accordance with a specific embodiment of the present invention. The device  160  comprises a monolithic transducer comprising four active areas  162   a-d.  Each of the active areas  162   a-d  comprises top and bottom electrodes  164   a-d  attached to a polymer  161  on its top and bottom surfaces, respectively (only electrodes  164   a-d  on the facing surface of the polymer  161  are illustrated). The electrodes  164   a-d  each provide a voltage difference across a portion of the polymer  161 . The electrodes  164   a-d  and their corresponding active areas  162   a-d  are symmetrically and radially arranged around a center point of the circular polymer  161 . Correspondingly, the elasticity of the polymer material included in the active areas  162   a-d  is balanced. 
     A first active area  162   a  is formed with the two first active area electrodes  164   a  and a first portion of the electroactive polymer  161   a.  The portion  161   a  is arranged in a manner which causes the first portion  161   a  to deflect in response to a change in electric field provided by the first active area electrodes  164   a.  The portion  161   a  includes the polymer  161  between the electrodes  162   a  and any other portions of the polymer  161  having sufficient stresses induced by the electrostatic force to enable deflection upon application of voltages using the electrodes  162   a.  Similarly, a second active area  162   c  is formed with the two second active area electrodes  164   c  and a second portion of the electroactive polymer  161   c.  The portion  161   c  is arranged in a manner which causes the second portion  161   c  to deflect in response to a change in electric field provided by the at least two second active area electrodes  164   c.  A similar arrangement applies to the active areas  162   b  and  162   d.    
     A substantially rigid frame  167  is fixed to the perimeter of the circular polymer  161  by using an adhesive. A substantially rigid member  168  is attached to a central portion  163  of polymer  161  and allows mechanical output for device  160 . Rigid member  168  provides mechanical output for device  160  based on deflection of the central portion  163  relative to the rigid frame  167 . The central portion  163  is located at least partially between active area  162   a  and active area  162   c  and at least partially between active area  162   b  and active area  162   d.  Although central portion  163  is illustrated as a centrally located circle, it should be understood that central portion  163  may be any portion of polymer  161  between the active areas  162   a-d.  Thus, rigid member  168  may be attached to polymer  161  in any part of polymer  161  between the active areas  162   a-d  and transfer deflection of that portion as mechanical output of device  160 . 
     The present invention also includes methods for deflecting one or more electroactive polymers having a plurality of active areas. These methods comprise deflection as a result of electrical energy input (actuation) to the polymer and electrical energy output from the polymer (generation). Methods for using a monolithic transducer as an actuator generally comprise providing a change in electric field with two first active area electrodes to deflect a first portion of the monolithic transducer; and providing a change in electric field with two second active area electrodes to deflect a second portion of the monolithic transducer. Other active areas may be used in the monolithic transducer. In one embodiment, active areas on one or more electroactive polymers are sequentially actuated, either individually or cumulatively, to produce a desired deflection of a portion of the polymer. In a specific embodiment, the active areas on a monolithic polymer may be actuated sequentially to move a portion of the polymer along a path. 
     For example, the active areas  162   a-d  may be actuated sequentially to move the central portion  163  along a circular path  169 . Actuation of the active area  162   a  moves the central portion  163  down. Actuation of the active area  162   b  moves the central portion  163  to the left. Actuation of the active area  162   c  moves the central portion  163  up. Actuation of the active area  162   d  moves the central portion  163  to the right. When electrical energy is removed from the electrodes  164   a,  the central portion  163  elastically returns up to its position before actuation of the active area  162   a.  A similar elastic return occurs for the other active areas  164   b-d.  To achieve the circular path  169 , the active areas  162   a-d  are actuated sequentially in clockwise order and in a timely manner. More specifically, electrical energy is supplied to the electrodes  164   b  while the active area  162   a  contracts. Electrical energy is supplied to the electrodes  164   c  while the active area  162   b  contracts. 
     A similar timing is applied in actuating the other active areas to produce the circular path  169 . This sequential clockwise actuation may be repeatedly performed to continuously move the central portion  163  in the circular path  169 . Continuous circular output of the central portion  163  may be used to drive a motor. In a specific embodiment, rigid member  168  may be used as a crank in a rotary crank motor. In another specific embodiment, rigid member  168  may be a plate with bearings to allow the plate to move in both planar directions of the plate. The monolithic device  160  then functions as an x-y (two degree-of-freedom) translation table. 
     The monolithic transducers  150  and  160  illustrated and described herein comprise active areas with similar geometries and symmetrical configurations. It is understood that monolithic polymers of the present invention may comprise one or more active areas each having a non-symmetrical and custom geometry. It is also understood that active areas on a monolithic polymer may be combined in any configuration. These custom geometry active areas and configurations may be used to produce any custom two-dimensional path or output for a portion of a polymer. In another embodiment, the two-dimensional path illustrated above may be achieved with only two active areas without the use of expanding and relaxing pairs as described above. In this case, actuation of one active area and its corresponding elastic return may be used to provide controlled deflection along one linear dimension. Actuation of the other active area and its corresponding elastic return may be used to provide controlled deflection in an orthogonal linear dimension. 
     Monolithic transducers and devices are not limited to planar deflections. In a specific embodiment, monolithic transducers may be used to deflect and control out-of-plane motion. For example, actuating all four active areas  162   a-d  at the same time typically will not change the planar position of the centrally attached rigid member  168 , but it will reduce the forces from polymer  161  which tend to hold rigid member  168  in the plane of the film. Thus, if rigid member  168  is suitably loaded by an out-of-plane force, such as a spring or gravity, actuating all four active areas  162   a-d  at once will cause rigid member  168  to move further out of the plane in the direction of the out-of-plane force. By controlling the amount of energizing (e.g. controlling the voltage) on each of the active areas  162   a-d,  one can thus control the position of a suitably loaded rigid member  168  in three translational degrees-of-freedom. 
     In another embodiment, monolithic transducers may be used to actuate degrees-of-freedom other than translational degrees-of-freedom. FIG. 1H illustrates a monolithic device  190  having three degrees of freedom in accordance with a specific embodiment of the present invention. The device  190  comprises two frames  191   a  and  191   b  positioned adjacent to each other on a single polymer film  192 . The two frames  191   a  and  191   b  may be separate frames or they may be made as two integral subframes on a single larger frame of the desired shape. Within each of the frames  191   a  and  191   b  are a set of four active areas  194   a-d  and  196   a-d,  respectively, arranged similar to the monolithic device  160 . The result is a figure “8” rigid frame with each circular area of the “8” patterned to form a device having four active areas similar to the monolithic device  160 . Rigid members  195   a  and  195   b  of the two circular areas of the “8” are connected, for example, by a rigid bar  196 . As a result of the coupling between the two circular areas of the “8”, the total device  190  controls both the planar translational directions of the rigid bar  196 , as well as the rotational direction in the plane for the rigid bar  196 . For example, the bottom active areas  194   c  and  196   c  may both be actuated to move the rigid bar  196  up. Alternatively, the bottom active area  194   c  and the top active area  196   a  may both be actuated to rotate the rigid bar  196  clockwise. 
     The ability to control the x-y planar positions of two separated points on a rigid body in a plane allows control for the x-y position and angular orientation of the rigid body in the plane (3 degrees-of-freedom). Other embodiments of the present invention can even do without the “8” shaped frame and use electrode patterns on a single polymer to control the position of two points of an object connected to the polymer at two separate points, allowing control of two translational and one rotational degree-of-freedom for the object. 
     By controlling three spatial positions of 3 separate points on a rigid body, one can control all six degrees-of-freedom of the rigid body in space (three translational and three rotational degrees-of-freedom). Thus, by suitable combinations of electrode patterns one can control all 6 degrees-of-freedom of a rigid body, or even all six degrees-of-freedom of multiple rigid bodies, using a single polymer film. The advantage of this design is that only a single piece of film and frame is needed to control multiple degrees-of-freedom rather than multiple films and frames, thereby simplifying the device, reducing manufacturing cost, reducing assembly steps, and reducing total size. 
     Methods for using a monolithic transducer as a generator generally comprise mechanically deflecting the electroactive polymer (or a portion thereof), providing a change in electric field with two first active area electrodes, providing a change in electric field with two second active area electrodes, and mechanically deflecting the electroactive polymer (or a portion thereof) a second time. The order of these events may vary for different generator designs. Typically, the first mechanical deflection occurs before changing the electric field using the two first active area electrodes. This change in electric field provided to the two first active area electrodes is less than the electric field needed to further deflect the first portion associated with the two first active area electrodes. The method also comprises a second mechanical deflection of the first portion after the change in electric field has been provided. Typically, the second mechanical deflection increases the electrical field between the at least two first active area electrodes. 
     Electroactive polymer material provides a spring force during deflection. Typically, polymer material resists deflection during actuation by its contraction (polymer material outside of an active area) or its expansion (polymer material included in an active area). Removal of the actuation voltage and the induced charge causes the reverse effects. The effects of electroactive polymer elasticity are also witnessed when the polymer is used to convert mechanical energy to electrical energy. In general, when actuation voltages and any external loads are removed, electroactive polymers, or portions thereof, elastically return to their resting position. In one embodiment of the present invention, elastic properties of one or more portions of an electroactive polymer are considered when arranging active areas on a monolithic polymer. In a specific embodiment, a monolithic polymer of the present invention is arranged such that deflection of a portion of the polymer in response to a change in electric field is at least partially assisted by elastic energy of another portion. More specifically, elastic return of one portion may be used to assist actuation of another. 
     Deflection of the active areas  162   a-d  included in the device  160  may be assisted by elastic energy contributions provided by contractions and expansions of the other active areas  162  and portions of the polymer  161  outside the active areas  162 . The active areas  162  are arranged relative to each other such that elastic energy of one active area may assist deflection of another. For example, the active area  162   a  is arranged relative to the active area  162   c  such that elastic energy of the active area  162   a  may assist deflection of the active area  162   c.  When actuated in a timely manner, contraction of the active area  162   a  may at least partially assist expansion of the active area  162   c,  and vice versa. More specifically, deflection of the active area  162   a  comprises a direction of contraction that is at least partially linearly aligned with a direction of expansion for the active area  162   c  towards the active area  162   a.  Advantageously, transferring elastic energy among different portions of a monolithic electroactive polymer may eliminate the need for electroactive forces generated by electrodes for one portion of the polymer to overcome some of the elastic resistance of that portion. 
     The amount of elastic energy transfer vary. In one embodiment, the total elastic energy contributions provided by different portions of polymer  161  is substantially equal to the elastic energy required to deflect the first active area  162   a  for a part of the deflection. In another embodiment, the elastic energy contributions provided by different portions of polymer  161  is substantially equal to the elastic energy required to deflect the first active area  162   a  for an entire deflection corresponding to an actuation of one of the active areas  162 . 
     An active area may include multiple directions of contraction and expansion. Correspondingly, elastic energy generated during actuation of one active area may used to facilitate deflection of more than one other active area. For device  160 , the active areas  162  are arranged relative to one another such that elastic return of one active area  162   a-d  may facilitate deflection of more than one of the other active areas  162   a-d  in a direction of actuation. More specifically, active areas  162   a  and  162   c  are arranged such that contraction of the active area  162   a  may facilitate expansion of the active area  162   c  in a direction towards active area  162   a.  In addition, active areas  162   a  and  162   b  are arranged such that contraction of the active area  162   a  may facilitate expansion of the active area  162   b  in a direction towards active area  162   a.    
     For device  160 , there is a complementary nature of the active areas  162   a-d  on opposite sides of the rigid member  168 . It should be noted that active areas for a monolithic device need not be grouped in complementary pairs as described for the device  160 . For example, an odd number of active areas arranged around rigid member  168  may still employ the elastic energy balance features described above. More specifically, three active areas arranged around rigid member  168  at 120 degree intervals may still employ the elastic energy features described above. In this case, the expansion of one active area is paired with the contraction of more than one other active area. 
     The timing of deflection between active areas may affect elastic energy transfer therebetween. To increase elastic energy transfer for transducer  160 , the active areas  161   a-d  may be actuated at a high enough rate such that elastic return of one active area assists the deflection of more than one active area subsequently actuated. This may be useful for active areas having more than one direction of actuation. For example, to increase elastic energy transfer to the active areas  162   b  and  161   c,  actuation of active areas  162   b  and  161   c  may begin actuation during elastic return of active area  161   a.  In this manner, elastic energy generated during actuation of active area  162   a  is transferred to two active areas  162   b  and  162   c  actuated thereafter. A similar timing may be continuously applied as the active areas  162   a-d  are actuated in turn to produce the circular path  169 . 
     In one embodiment, actuation of a second active area begins when a first active area is at peak deflection. In one embodiment, an active area in an electroactive polymer is actuated in resonant mode. Operating an electroactive polymer at resonance using materials, such as silicone, with low losses (e.g., low viscoelastic losses) allows energy available from the elastic return to stay in the polymer in the form of resonant mode vibration for use in a subsequent actuation. 
     Each of the electrode pairs  164   a-d  are arranged such that they provide independent electrical communication with each of the active areas  164   a-d.  Independence of the electrodes  164   a-d  allows electrical energy to be separately supplied to (or removed from) the electrodes  164   a-d;  thus allowing independent control and separate actuation for each of the active areas  164   a-d.  In another embodiment, two or more electrodes for a monolithic transducer are electrically coupled. In a specific embodiment, electrically coupled electrodes are included in a common electrode. A common electrode is an electrode that is capable of electrically communicating with more than one active area of an electroactive polymer. In many cases, a common electrode allows monolithic transducers to be implemented with less complexity. Alternatively, a common electrode may be used to sequentially actuate multiple active areas according to a propagation of the electrical charge through the common electrode. 
     FIGS. 1E and 1F illustrate opposite sides  171   a  and  171   b,  respectively, of a monolithic transducer  170  in accordance with one embodiment of the present invention. The monolithic transducer  170  comprises a common electrode  172  on the first side  171   a  of an electroactive polymer  174  (FIG.  1 E). Separate electrodes  173   a-h  are deposited on the opposite surface  171   b  (FIG.  1 F). The common electrode  172  allows electrical communication with multiple active areas for polymer  174 . The common electrode  172  and the separate electrodes  173   a-h  are provided to produce a voltage difference across multiple portions of polymer  174 . Each of the eight active areas  175   a-h  is individually formed by each of the eight separate electrodes  173   a-h,  a portion of the common electrode  172  substantially close to the separate electrode, and a portion of the polymer  174  therebetween. More specifically, a first active area  175   a  is formed by the separate electrode  173   a,  a portion of the common electrode  172  substantially close to the separate electrode  173   a,  and a portion of the polymer  174  therebetween. A second active area  175   b  is formed by separate electrode  173   b,  a portion of the common electrode  172  substantially close to the separate electrode  173   b,  and a portion of the polymer  174  therebetween. Electrical communication with each of the active areas  175   a-h  may be independently achieved using the common electrode  172  and one of the separate electrodes  173   a-h.  For example, active area  175   b  may be independently actuated using electrode  173   b  and the common electrode  172 . 
     Each portion of the polymer corresponding to the active areas  175   a-h  deflects in the plane of the polymer  174  with a change in electric field provided by the common electrode  172  and/or one of the separate electrodes  173   a-h.  For example, the actuation of active area  175   e  (FIG.  1 F), using electrode  173   e  and the common electrode  172  causes polymer  171  between the these electrodes to locally expand in the plane, as illustrated in FIG.  1 G. The common electrode  172  and separate electrode  173   e  are both compliant and also deflect with polymer  171 . When electric energy is removed from the active area  175   e,  there is insufficient electrical energy in the active area  175   e  to maintain deflection and elastic return of polymer  171  returns the active area  175   e  to its resting state (FIG.  1 E). 
     In one embodiment, the electrical energy for actuating each of the active areas  175   a-h  is provided using the common electrode  172 . In this case, electrical energy is supplied by a lead  176  at the initiating end  177  of the common electrode  172  and flows to the distal end  178 . As electrical energy flows through the common electrode  172 , each portion of the polymer corresponding to the active areas  175   a-h  deflects when it has sufficient electrical energy. As charge provided by the lead  176  flows counterclockwise through the common electrode  172 , portions of polymer  174  having sufficient electrostatic energy will deflect in turn according to a counterclockwise propagation of the charge. Thus, when charge in the common electrode  172  reaches the bottom portion of the common electrode  172 , polymer  174  deflects as illustrated in FIG.  1 G. The common electrode  172  is compliant and deflects with the polymer  174 . 
     In another embodiment, a common electrode  172  is deposited on both sides of polymer  174 . In this case, a second lead is attached to the second common electrode on the opposite side of the polymer  174 . The two leads may then be used to apply a voltage difference between the electrodes. The second common electrode can be considered as a limiting case of an infinite number of active areas connected together on one side of the film. 
     Portions of polymer  174  deflecting as a result of actuation elastically return to their resting position after the electrical charge has been removed. Removal of electric charge from polymer  174  may be obtained by removing the charge from the common electrode  172 . When two common electrodes are used on either side of polymer  174 , removal of electric charge from the polymer  174  may achieved by removing the voltage applied between the lead  176  and the second lead on the opposite side. 
     Electrical energy may be repetitively applied and removed using the common electrode  172 . By applying and removing voltage across lead  176  and a lead for the common electrode on the opposing side of the polymer, a wave-like effect is then produced by sequential deflection of portions of the polymer  174  as charge flows counterclockwise through the common electrode  172 . This wave-like effect may be repeatedly produced by repeatedly applying and removing voltage across lead  176  and a lead for the opposite common electrode. 
     For wave-like actuation of two common electrodes on either side of polymer  174  in this manner, or sequential actuation using a common electrode  172  and separate electrodes  173   a-h,  timing of actuation for each of the active areas  175   a-h  is modulated by a propagation of charge through the common electrode  172 . The propagation delay may be varied either by electrically controlling the voltage on the separate electrodes  173   a-h,  by connecting the separate active area  173   a-h  in series with a suitable resistance between each active area to effect a resistance-capacitance time delay, or by designing the resistance of the common electrode  172  to achieve a desired propagation delay. In one embodiment, a highly resistive material is used to increase the time it takes for charge to propagate through the common electrode  172 . In another embodiment, the separate electrodes  173   a-h  are in electrical communication, e.g., using a wire connecting therebetween, and used to modulate a propagation of charge through electrodes  173   a-h.    
     In a specific embodiment, the common electrode has a surface resistivity in the range of about 0.01 MQ to 50 MQ per square. These ranges are given as exemplary numbers, but the actual value chosen depends on the device and the desired propagation delay. An initial estimate of the desired surface resistivity can be obtained by setting the RC time constant (where R is the resistance and C is the polymer capacitance counting all active areas as parallel capacitances) to be equal to the desired time delay for the actuation to propagate around the device. The value of surface resistivity may then be adjusted by experimentation. Decreasing the resistance shortens the time delay, and increasing the resistance increases the time delay. The resistance of the common electrode is controlled during fabrication by using higher resistance electrode materials, or by adjusting the electrode thickness to change its resistance. 
     The common electrode  172  reduces the complexity of the monolithic transducer  170 . This may be advantageous for simplifying and reducing costs of devices with numerous electrodes that may be replaced by a common electrode. Applying the common electrode  172  to both sides of the monolithic transducer  170  may further simplify a design. Although the common electrode  172  is illustrated as electrically communicating with all the active areas on one side of the transducer  170 , it is understood that a common electrode in accordance with the present invention may electrically communicate with a subset of the active areas of an electroactive polymer. 
     4. Actuator and Generator Devices 
     The deflection of an electroactive polymer can be used in a variety of ways to produce or receive mechanical energy. Generally, monolithic electroactive polymers of the present invention may be implemented in a variety of actuators and generators—including conventional actuators and generators retrofitted with a monolithic polymer and custom actuators and generators specially designed for one or more monolithic polymers. Conventional actuators and generators include extenders, bending beams, stacks, diaphragms, etc. Several exemplary actuators and generators suitable for use with the present invention will now be discussed. Additional actuators suitable for use with various embodiments of the present invention are described in copending U.S. patent application Ser. No. 09/619,848, which was incorporated by reference above. 
     FIG. 2A illustrates a cross-sectional side view of a monolithic diaphragm device  130  comprising a monolithic polymer  131  before deflection in accordance with one embodiment of the present invention. The polymer  131  is attached to a frame  132 . The frame  132  includes apertures  133   a  and  133   b  that allow deflection of polymer portions  131   a  and  131   b  perpendicular to the area of the apertures  133   a  and  133   b,  respectively. The diaphragm device  130  comprises electrodes  134   a  and  134   b  attached on either side of the portion  131   a  to provide a voltage difference across the portion  131   a.  Electrodes  136   a  and  136   b  are deposited on either side of the portion  131   b  to provide a voltage difference across the portion  131   b.  The electrodes  134  and  136  are compliant and change shape with polymer  131  as it deflects. In the voltage-off configuration of FIG. 2A, polymer  131  is stretched and secured to frame  132  with tension to achieve pre-strain. 
     Using electrodes  134  and  136 , portions  131   a  and  131   b  are capable of independent deflection. For example, upon application of a suitable voltage between electrodes  134   a  and  134   b,  portion  131  a expands away from the plane of the frame  132 , as illustrated in FIG.  2 B. Each of the portions  131   a  and  131   b  is capable of expansion in both perpendicular directions away from the plane. In one embodiment, one side of polymer  131  comprises a bias pressure that influences the expansion of the polymer film  131  to continually actuate upward in the direction of arrows  143  (FIG.  2 B). In another embodiment, a swelling agent such as a small amount of silicone oil is applied to the bottom side to influence the expansion of polymer  131  in the direction of arrows  143 . The swelling agent allows the diaphragm to continually actuate in a desired direction without using a bias pressure. The swelling agent causes slight permanent deflection in one direction as determined during fabrication, e.g. by supplying a slight pressure to the bottom side when the swelling agent is applied. 
     The diaphragm device  130  may be used as a generator. In this case, a pressure, such as a fluid pressure, acts as mechanical input to the diaphragm device  130  on one side to stretch polymer  131  in the vicinity of apertures  133   a  and  133   b.  After the stretch, a voltage difference is applied between electrodes  134  while portions  131   a  is stretched. The resulting change in electric field provided to electrodes  134  is less than the electric field needed to further deflect polymer  131   a.  Similarly, a voltage difference is applied between electrodes  136  while portion  131   b  is stretched. Releasing the pressure allows portions  131   a  and  131   b  to contract and increase the stored electrical energy on electrodes  134  and  136 . 
     Although the monolithic diaphragm device  130  is illustrated and described with only two apertures that allow deflection of polymer portions perpendicular to the area of the apertures, it is understood the monolithic diaphragm device  130  may include a large number of apertures in any two dimensional array. Generally, an array for a monolithic polymer refers to a plurality of active areas on a single polymer arranged in any manner, number of configuration. For example, the diaphragm device  130  may include an array of 36 active areas arranged in a 6×6 grid. Alternatively, the array on a monolithic polymer may include a combination of custom geometry active areas. These separate active areas may or may not interact mechanically or electrically with each other. In one embodiment, at least two active areas in the array are capable of independent electrical communication and control. 
     In addition, multiple electroactive polymer layers may be used in place of a single polymer to increase the force or pressure output of an actuator. FIG. 2C illustrates a stacked multilayer device  245  suitable for use with the present invention. The stacked multilayer device  245  comprises three polymer layers  246   a-c  layered upon each other and attached by adhesive layers  247   a-c.  A rigid plate  250  is attached to the outermost polymer layer  246   c  and patterned to include a first hole  251   a  and a second hole  251   b  that guide deflection for left and right portions  252  and  253  of the polymer layers  246   a-c,  respectively. Within the adhesive layers  247  are electrodes  248   a-c  and  249   a-c  that provide actuation to left and right portions  252  and  253  of the polymer layers  246   a-c,  respectively. Upon actuation of the polymer layers  246   a-c,  the holes  251  guide deflection of the polymer layers in a direction substantially perpendicular to holes  251 . For example, hole  251  a guides deflection of the left portion  252  of polymer layers  246   a-c  in a direction substantially perpendicular to hole  251   a.  The left and right portions  252  and  253  of polymer layers  246   a-c  are capable of independent deflection. By combining the polymer layers  246   a-c,  the stacked multilayer device  245  provides cumulative force output of the individual polymer layers  246 . 
     FIG. 2D illustrates a stretched film device  270  in accordance with another embodiment of the present invention. The stretched film device  270  comprises a rigid frame  271  having a hole  272 . The perimeter of a monolithic electroactive polymer  273  is attached in tension to the frame  271  and spans the hole  272 . A substantially rigid member  274  includes two segments  274   a  and  274   b.  The first segment  274   a  is attached to the center of the polymer  273 . The second segment  274   b  provides mechanical output corresponding to deflection of the polymer  273 . 
     Compliant electrode pairs  275  and  276  are patterned on both opposing surfaces of the polymer  273  and on the left and right sides of the first segment  274   a,  respectively. The second segment  274   b  is capable of motion assisted by deflection of the polymer in response to a change in electric field provided by electrode pairs  275 . When the electrode pair  275  is actuated, a portion of the polymer  273  between, and in the vicinity of, the electrode pair  275  expands relative to the rest of the polymer  273  to move the second segment  274   b  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 pushes the second segment  274   b  to move to the left. Alternating actuation of the electrodes  275  and  276  provides a total stroke  279  for the second segment  274   b.    
     One variation of the stretched film device  270  includes adding an anisotropic prestrain to the polymer such that the polymer has high pre-strain (and stiffness) in the direction perpendicular to the rigid bar displacement. This increases the stroke  279 . The first segment  274   a  can be different lengths depending on the size of the polymer  273  and its prestrain. In one embodiment, the first segment  274   a  is about 75% of the length of the hole  272  along the direction of the central attachment (perpendicular to stroke  279 ). When acting as a generator, the second segment  274   b  is capable of motion that causes a change in electric field in the polymer associated with electrode pairs  275 . 
     Monolithic devices can use a wide variety of electrode patterns with rigid member outputs. In a preferred embodiment, a rigid member, such as rigid member  168  in FIG. 1D or rigid member  274  in FIG. 2D, is designed for high force coupling to the polymer. If the rigid member attachment is too small compared to the cross section of the active area perpendicular to the direction of motion, then the compliance of the polymer will prevent the active element from transmitting most of its actuation force. For example, if rigid member  168  in FIG. 1D were only attached at a small point on polymer  161 , then when one of the active areas  162   a-d  is actuated, the force generated could only be transmitted at that small point. With just a point attachment, a significant portion of the polymer deflection would just go around the point when the rigid member  168  is loaded with force. 
     Thus, in one embodiment for good force coupling to active areas of the polymer, the length of the attachment between the rigid member and the polymer in a direction perpendicular to a degree of freedom of the rigid member is greater than or comparable to the length of the active area or corresponding electrodes perpendicular to the desired motion of each active area. For example, if rigid member  168  was attached rigidly over most of the electrically inactive central portion of polymer in FIG. 1D, then the attachment length perpendicular to the desired motion of each active area  162   a-d  would be substantially comparable to the length of each active area perpendicular to a desired direction of motion for each active area  162   a-d.  For irregularly shaped active areas (i.e., not rectangles or squares), the length of the active area perpendicular to a desired motion of each active area may be taken as the maximum length of the active area perpendicular to the desired motion of each active area. 
     In some cases, however, the rigid element cannot be attached over the full perpendicular length of the active area. For example, in FIG. 2D if rigid member  274  were attached over the full length then it would extend all the way to, or very close, to the rigid frame  271 . In this case, the rigid frame might inhibit output motion of the device  270 . Thus, in another embodiment for good force coupling to maintain good deflection, the length of the attachment between the rigid member and the polymer in a direction perpendicular to the desired motion of each active area is less than 100% of the length of the active area (or corresponding electrodes) perpendicular to the desired motion of each active area. In another embodiment for good force coupling to maintain good deflection, the length of the attachment between the rigid member and the polymer in a direction perpendicular to the desired motion of each active area is greater than 50% of the length of the active area perpendicular to the desired motion of each active area. In a specific embodiment, the device in FIG. 2D uses a rigid bar  274  whose length and attachment is about 75% of the length of the hole  272 . More generally, the attachment of rigid elements to the polymer are greater than 25% of the length of the active areas perpendicular to the desired motion of each active area. 
     5. Applications 
     The devices and methods of the present invention finds use in a broad range of applications where conversion between electrical and mechanical energy is required. These applications include a wide variety of actuators, motors, generators, sensors, robotics, toys, micro-actuator applications and pumps. Transducers of the present invention may be implemented in both the micro and macro scales—thus increasing the range of application. Provided below are several exemplary applications for some of the transducers and devices described above. The exemplary applications described herein are not intended to limit the scope of the present invention. As one skilled in the art will appreciate, the transducers of the present invention may find use in any application requiring conversion between electrical and mechanical energy. 
     By repeatedly actuating active areas on a monolithic electroactive polymer, continuous deflection of the polymer may produce reciprocating linear motion or continuous rotary motion. Reciprocating linear motion may be converted to continuous rotary motion using clutches, gears, and the like. Continuous rotary motion generated by an electroactive polymer may be used to drive a motor. Combining different ways to configure one or more monolithic electroactive polymers within a motor, different motor designs, 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 motor designs having one or more monolithic electroactive polymers. These motors convert electrical energy into mechanical work and find use in a wide range of applications. As one of skill in the art will appreciate, there are countless applications for motors. Due to the weight savings gained by using electroactive polymers in producing mechanical energy for a motor, a motor comprising an electroactive polymer is well suited for motor applications that require lightweight. For example, the present invention is well suited for applications that require a lightweight motor that can operate at low speeds and yet obtain high performance from the electroactive polymer materials. There are countless applications for a lightweight, low rpm, efficient motor. 
     The present invention is also suitable for use as artificial muscle. In one example of artificial muscle, two or more layers of electroactive polymer are 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. Each of the polymer layers may include one or more active areas. An advantage of the layered construction is that multiple electroactive polymer layers may be stacked in parallel to produce a desired force that would otherwise not obtainable using a single polymer layer. In addition, the stroke of a linear device may be increased by adding similar linear motion devices in series. 
     In another embodiment, monolithic electroactive polymers suitable for use with the present invention may be rolled or folded into linear transducers and devices that deflect axially while converting between electrical energy and mechanical energy. Since the fabrication of monolithic electroactive polymers is often simpler with fewer numbers of layers, rolled actuators provide an efficient manner of fitting a large number of polymer layers into a compact shape. Rolled or folded transducers and devices 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, etc. 
     Monolithic polymers 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 comprising multiple active areas may also operate at high speeds for a variety of applications including sound generators and acoustic speakers, inkjet printers, fast MEMS switches etc. 
     6. 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. For example, although the present invention has been described in terms of several specific electrode materials, 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, the present invention is not limited to these materials and geometries. It is therefore intended that the scope of the invention should be determined with reference to the appended claims.