MEMS 1082 Department of Mechanical Engineering and Materials Science – Electromechanical and Fall 2018 Swanson School of Engineering, University of Pittsburgh

Large Strain Electroactive for use in Applications

Corey May, Wesley Keck, Ryan Black 12/9/2018

Abstract (EAPs) are synthetic materials that undergo strain when a or charge is applied, therefore causing deformation. Because of their potential for large strains, EAPs are perfect candidates for applications in both sensors and actuators. Electroactive polymers can undergo deformation when electrical currents are applied because the semi-crystalline structure is polarized causing the positive and negative poles to orient within the material. The deformation and strain within the EAP materials can be determined using the piezoelectric effect and electrostrictive effect equations. The Gibb’s Free Energy equations can be used to determine several transduction effects with EAP materials. The research into EAPs became popular in the early 1990’s, but their use to date has been limited due to inefficiencies, lack of production, inability for precision control, and quick degradation of the materials with use. Advances to improve these issues in the last decade have made great strides toward one day being able to use these in many applications. Electroactive polymers have the potential to repair degraded muscles, work as pumps, and give more lifelike movement with better dexterity.

MEMS 1082 Department of Mechanical Engineering and Materials Science – Electromechanical Sensors and Actuators Fall 2018 Swanson School of Engineering, University of Pittsburgh

Introduction: Humans have always been fascinated with making art inspired by the biological form. One key biological aspect to replicate is the intricacy of human movement. Movement based around the design of pumps, motors, hydraulics, pneumatics, and electrics fall short with micro-movement because of the need for bulky gears, a need for a compressor, and metal casings. None of these power generation methods could capture micro-scale movement seen in the human form effectively. Any device needing intricate movement could benefit from a replacement actuation method. Electroactive Polymers may be a solution. These are polymers that respond to electric fields by contracting or expanding according to an induced polarization. These polymers have extremely high positioning accuracy and self-sensing capability. They require a large actuation voltage, but have the ability to generate large and strains. Because of their pliable, light, moldable shape they could be used to create unique intricate strain configurations, like to repair muscle, actuate a robot, or to micro-adjust sensors onboard a drone. One student from Virginia Tech used EAPs to drive an arm-wrestling robot. Currently, these sensors are still in a design stage and are not widely available commercially. While great research has been made in the last 20 years, EAPs are still fragile and prone to fatigue. Definitions Electroactive polymers (EAPs) are synthetic materials that undergo strain when a voltage or charge is applied, therefore causing deformation. Because of their potential for large strains, EAPs are perfect candidates for applications in both sensors and actuators. Sensors are defined as components that have the ability to detect changes (e.g. temperature change, strain, force, pressure, etc.) and communicate that information electronically with a computer, typically through the use of a data acquisition system (DAQ). Conversely, actuators are defined as components which cause mechanical changes, such as an which opens and closes a valve or causes the movement of a diaphragm. Actuators require an electrical signal to operate.

History In a world constantly advancing and innovating, electroactive polymers have made massive strides over the years. Today, EAPs are being explored as possible substitutes for muscles tissue, as they are able to expand and contract with varying applied . The study of Electroactive polymers (EAP) gained traction in the early 1990s but the origins of experiments in EAPs date back to 1880 by a scientist named Roentgen. In his experiment, Roentgen applied a voltage to the ends of strips of 16 by 100cm natural

MEMS 1082 Department of Mechanical Engineering and Materials Science – Electromechanical Sensors and Actuators Fall 2018 Swanson School of Engineering, University of Pittsburgh

rubber and placed weights on the other end to see how the weights would move [1]. As the popularity of these materials started to pick up in the early 1990s, they were not able to produce much strain, they were energy inefficient and the materials broke down rapidly with use. By March of 1999 the first EAP conference was held to help expand the cooperation between organizations working with the materials and to showcase the materials capabilities. At this conference Yoseph Bar-Cohen posed a challenge to the engineering and scientific community to produce an electroactive powered arm that could beat a person at arm wrestling. In 2005, the first arm wrestling competition was held. Three teams faced off with a local high school girl. This challenge proved to be too ambitious for the time when the student easily beat two of the teams and the third broke. The idea has since become a long-term goal for the community. It is believed that once this goal is reached, the technology is at a point it can simulate human functions in robotics. Since no teams were able to provide a design up to the challenge in 1999, a device was created to test how well designs performed against each other.

Figure 1: Device used to measure the output force from EAP activated arm wrestling designs. Figure reproduced from World Wide Electroactive website [2] The first commercial use of EAPs came in late 2002 when a Japanese company by the name of Eamex created robotic fish. The fish are powered by electro-magnetic induction coils in the upper and lower portion of the fish tank [3]

General background Types of materials EAPs are generally broken down into two sub categories, electrically stimulated polymers known as polymers, and ionically stimulated polymers.

MEMS 1082 Department of Mechanical Engineering and Materials Science – Electromechanical Sensors and Actuators Fall 2018 Swanson School of Engineering, University of Pittsburgh

Within the dielectric polymers there are subclasses including ferro electric polymers, electrostrictive polymers, and polymers. Ferroelectric polymers are materials that, when exposed to a significant , can spontaneously repolarize in the direction of the electric field [4]. Ionic polymer-metal composites (IPMCs) and stimuli responsive are two types of ionically stimulated polymers. IPMCs are polymers such as nafion and flemion which are plated in noble metals like gold or platinum. When a voltage is applied the cations and water molecules migrate to one side of the material causing deformation. Stimuli responsive gels Comparing the two types, dielectric polymers can hold their shape when a DC voltage is applied. Ionically activated materials show better strain abilities and require much less power, but they must stay wet in order to work.

How EAPs Function: Electroactive polymers contain arranged poles within their structural chains. Natural semicrystaline materials generally have randomlly arranged polar orientation. Through a variety of methods, material scientists have developed methods to arrange the poles in specific orientations. When exposed to an electric field the poles of EAPs rearrange causing a strain in the material. By producing polymer chains in different configurations, and getting better polar organization, newly developed materials are displaying more strain with less applied electric fields. The method to arrange the poles in a way that cause strain varies depending on the class and type of material, but it usually involves applying a large amount of power into the material at a specific stage of production. Polyvinylideneflouride (PVDF) is a common and promising electrically stimulated EAP. It’s a semicrytaline poled . To create the polarized structure in PVDT the materials are placed in a strong electric field. Often, this is done while the material is still in a liquid state, then it is cooled to a solid state before being removed from the electric field. Another method is to use coronal discharges into the material from a needle electrode [4].

MEMS 1082 Department of Mechanical Engineering and Materials Science – Electromechanical Sensors and Actuators Fall 2018 Swanson School of Engineering, University of Pittsburgh

Figure 2: Representation of the polymer structure of PVDF when an electric field is applied. Figure reproduced from as Electromechanical [5]

Theory: Solid State Materials Professor Robert Newnham produced work in solid state field. When a solid-state material responds to electric field it is said to electro-constrict. Any E field will induce polarization in a solid-state material. For instance, plastic is not a piezoelectric but applying a DC voltage we will induce polarization and turn plastic into a piezoelectric. Vibration response during electrostriction is around 1/10 nm, but is dependent on thickness and field. Charges and stresses are generated in specific directions, producing longitudinal and transverse strain effects. Use of Lasers can help analyze polarization effects in solid-state materials. Engineers are looking for materials with high polarization and high dielectric in order to apply an E-field and get solid state strain. Glass does not strain much under electric field, but some elastomers may. Tensor Equations are presented below. [6] Piezoelectric effect The piezoelectric effect is electromechanical and linear in nature. The following equation describes the piezoelectric effect: 푆 = 푑퐸 (1)

퐷 = 푑푇 (2)

MEMS 1082 Department of Mechanical Engineering and Materials Science – Electromechanical Sensors and Actuators Fall 2018 Swanson School of Engineering, University of Pittsburgh

Where S is the mechanical strain, T is the stress, E is the electric field, d is the piezoelectric coefficient, and D is the charge density. The piezoelectric effect is able to generate a strain from a charge, or a charge from a strain. In this manner, it can be used as both an actuator or a . To construct the constitutive equations in full tensor form for the piezoelectric effect, Hooke’s Law and the dielectric relationships must be applied to Equations (1) and (2), yielding:

퐸 푆푖푗 = 푑푘푖푗퐸푘 + 푆푖푗푘푙푇푘푙 (3)

푇 퐷푖 = 휀푖푘퐸푘 + 푑푖푘푙푇푘푙 (4)

퐸 푇 Where 푆푖푗푘푙 is the elastic compliance, 휀푖푘 is the dielectric permittivity, and i, j, k, & l have values ranging from 1 to 3. The superscripts (E & T) refer to the condition under which the variable was measured. For example, elastic compliance is measured under a constant electric field and dielectric permittivity is measured under constant stress. The tensors in Equations (3) and (4) can be written in matrix form, allowing the piezoelectric coefficient, dielectric permittivity, and elastic compliance matrices to be written as [4]:

0 0 0 0 푑15 0 ( 0 0 0 푑15 0 0) 푑31 푑31 푑33 0 0 0

푘11 0 0 ( 0 푘11 0 ) 0 0 푘33

푠11 푠12 푠13 0 0 0 푠12 푠11 푠13 0 0 0

푠13 푠13 푠33 0 0 0 ,푤ℎ푒푟푒 푠66 = 2(푠11 − 푠12) 0 0 0 푠44 0 0 0 0 0 0 푠44 0 ( 0 0 0 0 0 푠66)

Within all polymers exists what is called the electrostrictive effect. The electrostrictive effect is a quadratic dependence of stress (or strain) on the polarization of the polymer. The equation for the electrostrictive effect is given by:

푆푖푗 = 푄푖푗푘푙푃푘푃푙 (5)

MEMS 1082 Department of Mechanical Engineering and Materials Science – Electromechanical Sensors and Actuators Fall 2018 Swanson School of Engineering, University of Pittsburgh

Where 푄푖푗푘푙 is the charge-related electrostrictive coefficient and P is the polarization. For an isotropic polymer, however, the equations become:

2 푆3 = 푄33푃 (6)

2 푆1 = 푄13푃 (7)

Where 푆1 and 푆3 are the transverse and longitudinal strains, respectively. They are the strains perpendicular and in line with the polarization. These equations show that increasing polarization will cause contraction along the polarization direction. Polarization for a linear dielectric polymer can be determined from the following equation:

푃 = (휀 − 휀0)퐸 (8)

−12 Where 휀0 is the dielectric permittivity in a vacuum (휀0 = 8.85 푥 10 퐹/푚). Substituting Equation (8) into Equation (5), the resulting equation is:

2 2 2 푆 = 푄(휀 − 휀0) 퐸 = 푀퐸 (9)

Where M is the electric-field-related electrostriction coefficient. From this equation, it is determined that the polymer will contract along the thickness direction and expand along the film direction if the electric field is applied across its thickness. It can be said that, for a poled ferroelectric polymer, the piezoelectric state is thought of as the remnant polarization-biased response. Thusly, the following equations can be constructed:

푑33 = 2푄33푃퐷(휀 − 휀0) (10)

푑31 = 2푄13푃퐷(휀 − 휀0) (11)

MEMS 1082 Department of Mechanical Engineering and Materials Science – Electromechanical Sensors and Actuators Fall 2018 Swanson School of Engineering, University of Pittsburgh

Where 푃퐷 is the DC-bias-field-induced polarization, 푑31 is the piezoelectric coefficient perpendicular to the induced polarization direction, and 푑33 is the piezoelectric coefficient parallel to the induced polarization direction. For electroactive polymers, there exists a coupling factor, k, that describes how effective the material is at converting between electrical energy and mechanical energy. Generally, the square of k is either equal to the converted mechanical energy over the input electrical energy, or the converted electrical energy over the input mechanical energy. With this in mind, Equation (12) can be written, representing an electric field in the 3-direction and the coupling factor and actuation in the same direction.

2 2 푑33 (12) 푘33 = 푇 퐸 (휀33푠33) Additionally, if the actuation is perpendicular to the electric field (in this case, the 1- direction), the resulting equation is then

2 2 푑31 (13) 푘31 = 푇 퐸 (휀33푠11)

Relating the coupling factor to the material coefficient, the following equation can be formed:

퐷 2 퐸 푠33 = (1 − 푘33)푠33 (14)

Polymers having high coupling factors will have a large range of elastic compliance when exposed to varying external electric conditions. Because of this, the elastic modulus of the polymer may be altered by varying external electrical conditions. Gibbs Free Energy Derivation Various transduction effects can be derived from Gibbs Free energy. G is defined as:

(15)

The converse piezoelectric effect, which generates strain for actuation is:

MEMS 1082 Department of Mechanical Engineering and Materials Science – Electromechanical Sensors and Actuators Fall 2018 Swanson School of Engineering, University of Pittsburgh

(16)

The direct piezoelectric effect, which generates charge for sensing is:

(17)

The pyroelectric effect describes a change in voltage when a temperature is applied. Using Gibbs Free Energy:

(18)

The thermal expansion coefficient which describes how the size of a material will change with respect to a temperature change:

(19)

The electro-caloric effect occurs when a material shows a reversible temperature change under an applied electric field. This can be used for solid state refrigeration. With Gibbs Free Energy:

(20)

MEMS 1082 Department of Mechanical Engineering and Materials Science – Electromechanical Sensors and Actuators Fall 2018 Swanson School of Engineering, University of Pittsburgh

Hysteresis For a material beginning with a baseline polarization of zero, when an electric field (DC) is applied to a material then removed, if the material now as a non-zero baseline polarization it is said to exhibit remnant polarization hysteresis. This is a poling process. For instance, if BaTi03 is used as an underwater sonar , we want to use this technique to maximize its D value.

Figure 3: Remnant Polarization Hysteresis Conversely, for a material beginning with a baseline polarization of zero, when strain is applied to a material then removed, if the material now as a non-zero baseline polarization it is said to exhibit hysteresis effects. and metals cannot return to 0 after being strained, but elastomers can, so ceramics and metals exhibit this effect but elastomers don’t. Vibration Modes Piezoelectric materials can be driven in different modes for a simple cantilever system, depending on the orientation of the stresses or electric fields relative to the material. For a material with base, width, and height, b,w,l we can produce vibration mode, planar mode, thickness mode, shear mode, and bending mode. A unimorph has one active layer and one inactive layer. A bimorph has two active layers. The piezoelectric can be designed as a unimorph or a bimorph, and modeled in series or in parallel. Below are pictures representing various modes and designs:

MEMS 1082 Department of Mechanical Engineering and Materials Science – Electromechanical Sensors and Actuators Fall 2018 Swanson School of Engineering, University of Pittsburgh

Figure 4,5,6,7, Modes, Piezoelectric bending setup, Series setup, Parallel setup To construct a shear mode, 1. Align electrode in 1-direction 2. Remove electrode 3. Re-electrode on major surface 4. Polish electrode 5. Deposit on both surfaces 6. Drive 7. Get shear mode The frequency response of these piezoelectric systems can be described by admittance and impedance spectrums. Impedance describes the bulk resistance that an oscillatory system will exhibit vs frequency. Admittance is its inverse. Mechanical Admittance is defined as: Y = V / F (21)

Mechanical Impedance is defined as: Z = F / V (22)

MEMS 1082 Department of Mechanical Engineering and Materials Science – Electromechanical Sensors and Actuators Fall 2018 Swanson School of Engineering, University of Pittsburgh

Electrical Admittance is defined as: Y = I / V (23)

Electrical Impedance is defined as: Z = V / I (24)

Below are plots of the admittance and impedance spectrums of typical piezoelectric response (fr signifies resonant frequency and fa signifies anti-resonant frequency):

Figure 8: Admittance and Impedance Spectrums The mode with the highest resonant frequency is the thickness mode. It, along with the shear mode, can operate up to a few GHz making them ideal candidates for radio and telecommunication applications. The mode with the lowest resonant frequency is bending mode, from 40 Hz – 30 kHz, making it ideal for audio frequency applications. Simple equivalent circuits can model piezoelectric response to simple designs:

Figure 9: Equivalent Circuit

MEMS 1082 Department of Mechanical Engineering and Materials Science – Electromechanical Sensors and Actuators Fall 2018 Swanson School of Engineering, University of Pittsburgh

Motion Equation The motion equation is related to piezoelectric materials, because we can use it to determine resonant frequency displacement. This would be useful, for example, in an inkjet printer resonator where we are sensing a change in frequency. We have the motion equation as:

(25)

And the differential equation as:

(26)

Acoustic propagation velocity is:

(27)

The wave number, related to acoustic propagation velocity, is:

(28)

For clamped ends, if we solve boundary conditions of V @ x=0 and x=L, we get B1 and B2 as:

(29)

MEMS 1082 Department of Mechanical Engineering and Materials Science – Electromechanical Sensors and Actuators Fall 2018 Swanson School of Engineering, University of Pittsburgh

(30)

The forces at the two ends become:

(31)

(32)

Acoustic impedance is defined as:

(33)

These equations form the basis of piezoelectric materials. [7]

Current status: Natural-Like Artificial Muscle Fabrication: EAPs can attempt to model muscle tissue both physiologically and electrically. We know muscle is 75% water, 18% protein, and 7% lipids [8]. High liquid content allows and molecules to transport easily while the muscle maintains strength and toughness by the bundles of protein fibers. These fibers provide the structural and active unit for contractions and elongations. They are a few cm long but with a diameter of only 10 to 100 micrometers. The material PAAM is an electroactive hydrogel that models the above characteristics of muscle and is able to sense and respond to biological environment. It has promising properties like being non-toxic, biocompatible, and non-biodegradable. Unfortunately, it fails to respond in microseconds like biological muscle can. It is still the closest replica to the human muscle currently available. [8]

MEMS 1082 Department of Mechanical Engineering and Materials Science – Electromechanical Sensors and Actuators Fall 2018 Swanson School of Engineering, University of Pittsburgh

Future trends: The potential for future use in the medical field is to use them in prosthetics or to repair deteriorated muscles. Other promising uses are for pumps for such things as insulin or as valves inside the body. Some researchers are looking at repairing sight with them by using them to squeeze the eye to focus it. A wrap could be made from EAP material that would surround the heart to keep it pumping. The major challenges these materials face are they require too much power, they are still too hard to control in precision applications and they don’t produce enough force for prosthetic applications. Additionally, more research is needed to make sure they don’t have adverse interactions with the body. Other developing areas of use outside of artificial muscles are in fabric and protective coatings. Some EAPs have been found to hydrophobic properties which make them an excellent protective coating. Some researchers are trying to incorporate them into fabric which would be used to sense movement. Currently, the company stretch sense ltd. has created a glove with EAP sensors lining the back of the hand which is used to sense the kinematic motion of the hand [9]. This can be used as a controller, in virtual reality or to record how a user's hand moved while performing a task. Incorporating EAP into material would allow this idea to be expanded to the entire body. George Studor, head of in-space inspection for NASA’s Engineering and Safety Center, has several ideas for how EAPs can be utilized in the future. He hopes an endoscope of sorts can be created that can be fully-operational in zero-gravity scenarios, specifically for use on the international space station (ISS). The endoscope must be able to traverse tight environments without making accidental contact with its surroundings. It must also be able to map the space it inhabits as it explores, rather than follow a predefined, mapped-out path. Additionally, it must be able to follow the same path when it is retracted [9]. EAPs are perfectly suited to make this idea a reality, as they could provide the minute, precise movements that are required for such an application, as well as other applications. By precisely controlling the voltage applied to the EAP actuators, the exact movements for the application can be achieved. Other future applications currently being investigated include electrostatic actuators that are able to heal themselves and act extremely similarly to muscles. These hydraulically amplified self-healing electrostatic (HASEL) actuators can recover from electric failure (exceeding breakdown voltage) while also having the benefits of both pneumatic and dielectric elastomer actuators. The benefits these actuators could have include large output power, large actuation force, large actuation strain, and self-sensing deformation, which could be used for precision actuation [9].

MEMS 1082 Department of Mechanical Engineering and Materials Science – Electromechanical Sensors and Actuators Fall 2018 Swanson School of Engineering, University of Pittsburgh

Conclusion Piezoelectric materials are useful and reliable for sensor and actuator applications. They are able to collect analogue (mechanical) information from an environment and convert it to an electrical signal for a digital computer to read. A strong example of this in effect is microphones which read pressure waves as electrical voltages. Conversely, piezoelectric materials can convert a digital signal into a strain allowing for actuation. A strong example of actuation is a loudspeaker which converts electrical voltages to pressure changes. Specific research was focused on Electroactive Polymers and their history. Polymers can handle high-strain applications, making them tough and malleable. This report highlighted the use of hydrogel artificial muscle fibers that convert an input electrical signal into muscle movement. Also highlighted was a Virginia Tech project for an artificial muscle arm-wrestler machine. This type of device would require both sensing and actuation abilities. Then, intuition behind EAP chemistry and mechanics was preceded by elaboration on piezoelectric tensor equations. Hysteresis principle and Poling Process was introduced. Example figures were provided on common piezoelectric modes, and admittance/impedance spectrums were introduced with a simple equivalent circuit of a piezoelectric actuation. The wave equation was touched on for piezoelectric resonation, and future trends were laid out. Piezoelectric materials still are fragile and under- researched, especially for the use of large strain EAPs. Advances in technology could allow EAPs to approach similar intricacy and physical strength as real human muscles.

MEMS 1082 Department of Mechanical Engineering and Materials Science – Electromechanical Sensors and Actuators Fall 2018 Swanson School of Engineering, University of Pittsburgh

References: [1] Bar-Cohen, Yoseph. Electroactive Polymers (EAP). Electrochemistry Encyclopedia, Dec. 2004 [2] World Wide Electroactive Polymer website, https://ndeaa.jpl.nasa.gov/nasa- nde/lommas/eap/EAP-armwrestling.htm [3] Bar-Cohen, Yoseph. Worldwide Electroactive Polymer Newsletter. Vol 5 [4] Bar-Cohen, Yoseph. (2004). Electroactive Polymer (EAP) Actuators as Artificial Muscles - Reality, Potential, and Challenges (2nd Edition) - 4. Electric EAP. SPIE. Accessed on knovel. https://app.knovel.com/hotlink/pdf/id:kt00851WR7/electroactive-polymer/electric-eap [5] John D.W. Madden, in Dielectric Elastomers as Electromechanical Transducers, 2008 [6] Cheng Z., Zhang Q., Su J., Tahchi M.E. (2008) Electropolymers for Mechatronics and Artificial Muscles. In: Safari A., Akdoğan E.K. (eds) Piezoelectric and Acoustic Materials for Transducer Applications. Springer, Boston, MA. Accessed on Pitt Cat [7] Wang, Qing-Ming. “Piezoelectric Materials and Wave Propagation” Lecture, University of Pittsburgh, Pittsburgh, PA, Oct/Nov 2018. [8] Davenas J., Tahchi M., Bassil M. (2008). A Closer Look at the Polyacrylamide Fibers for Natural-Like Artificial Muscle Fabrication. “Advances in Science and Technology Vol. 61” p. 85-90. Doi: 10.4028/www.scientific.net/AST.61.85 [9] Bar-Cohen, Yoseph. WW-EAP Newsletter, Vol. 20, No. 1, June 2018 https://ndeaa.jpl.nasa.gov/nasa-nde/newsltr/WW-EAP_Newsletter20-1.pdf