A finite element model for bending behaviour of conducting polymer electromechanical actuators

Sensors and Actuators A 130–131 (2006) 1–11

A finite element model for bending behaviour of conducting polymer electromechanical actuators Philippe Metz a , G¨ursel Alici b,∗ , Geoffrey M. Spinks b a

Institut Francais De Mecanique Avancee, Campus De Clermont-Ferrand, BP 265 F-63172 AUBIERE, Cedex, France b School of Mechanical, Materials and Mechatronics Engineering, University of Wollongong, 2522 NSW, Australia Received 9 May 2005; received in revised form 2 September 2005; accepted 2 December 2005 Available online 19 January 2006

Abstract Emerging conducting polymer electromechanical actuators (CPEA) have many potential applications ranging from biomedical to micro/nano manipulation systems. In order to make use of their potential, it is needed to establish a valid mathematical model to provide enhanced degrees of understanding, predictability, control and efficiency in performance. Although it is known that the mechanism behind their operation is quite straightforward; establishing a mathematical model to predict their behaviours and quantify their performance is hampered by many mechanical, electrical and chemical parameters. With this in mind, the aim of this study is to establish and experimentally validate a lumped-parameter model of bending-type polypyrrole (PPy) actuators for use in improving their displacement and force outputs. With reference to their operation principle, we draw an analogy between the thermal strain and the real strain in the PPy actuators due to the volume change to set up the mathematical model, which is a coupled structural/thermal model. The finite element method (FEM) is used to solve the model. The effect of propagation of the ion migration into the PPy layers is mimicked with a temperature distribution model. Theoretical and experimental results demonstrate that the model is practical and effective enough in predicting the bending angle and bending moment outputs of the PPy actuators quite well for a range of input voltages, and the PPy layer thicknesses. © 2005 Elsevier B.V. All rights reserved. Keywords: Electroactive polymer actuators; Modelling; System identification; Finite element method; Coupled-field analysis

1. Introduction Polymers derived from pyrrole, aniline or thiophene can be used as conducting polymer (CP) actuators or artificial muscles [1,4]. The CP actuators based on pyrrole is known as polypyrrole (PPy) actuator. When the polymer is doped electrochemically, ions are sent inside the polymer causing volume expansion. Applying voltages as small as 1 V controls the volume change of the polymer in the form of expansion and contraction. The change in the volume generates a bending displacement. This follows that the electrochemical energy is converted into mechanical energy. There has been significant amount of research on CP actuators and their use in various applications in the last decade [1–8]. A comprehensive account of polymer actuators is given in [4,6]. Zhou et al. [2] have reported on three types of polymer actuators including an ionic conducting poly-

∗

Corresponding author. Tel.: +61 2 4221 4145; fax: +61 2 4221 3101. E-mail address: [email protected] (G. Alici).

0924-4247/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.sna.2005.12.010

mer film actuator, a polyaniline actuator, and a parylene thermal actuator. They have presented their fabrication and initial performance results. Smela et al. [5] have presented the development and performance outcomes of PPy and Au bilayer conducting polymer actuators operating in electrolyte solutions. As an extension of this study, Jager et al. [16] has fabricated a serially connected micromanipulator to pick, move, and place 100 ␮m glass beads. It has been demonstrated that the micromanipulator is very suitable for single-cell manipulation. Liu et al. [17] has presented a fabrication technique to make a microstructure consisting of a polymer substrate Kapton and PPy/Au bilayer. Santa et al. [18,19] have investigated into the modelling and characterization of a muscle-like conducting polymer axial/linear actuator operating in an electrolytic cell. It is a simple lumpedparameters model whose parameters are identified using the force and the change in the length data. Nemat-Nasser and Li [20,21] have established a micromechanical bending motion model to characterize ‘electrochemomechanical’ response of an ionic polymer–metal composite actuator consisting of Nafion (a trademark of DuPont Inc.) and platinum bilayer. The model

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is based on the micromechanics theory [21] that electrically unbalanced negative ions permanently fixed to the Nafion polymer generate the internal stresses. The parameters in the model are estimated using experimentally measured tip displacement. Experimental and prediction results are provided to demonstrate the validity of the model. To the best of our knowledge, this is the only model in the literature accounting for the electrical, chemical, and mechanical properties of an ionic polymer actuator. Based on the bending beam method, Pei and Inganas [22] developed a mathematical model of a bilayer strip made up of a polyethylene layer with a thin gold layer on one of its surfaces, and a polypyrrole layer to evaluate in situ volume changes in the polypyrrole layer during electrochemical undoping and doping. It was concluded that the model based was effective enough to predict mass transport and phase relaxation during the undoping and the doping. Please note that this model and the model reported by Berry and Pritchet [23] to predict humidity-induced bending of polymers are for a bilayer bending-type polymer strip, which is different than tri-layer bending actuator considered in this study. The objects of this paper are: (i) to establish a mathematical model by drawing an analogy between the real actuation of a trilayer bending-type PPy actuator and a corresponding structure subjected to a temperature difference, (ii) to validate the model through comparing the simulation results from the finite element analysis with experimental results. As a part of the model validation, we propose to use a gradient of the actuation efficiency in the PPy layer to improve the ability of the model to predict the bending angle and bending moment outputs as a function of the actuator thickness. This study is a part of an ongoing-project on the establishment of micro/nano manipulation systems [15] such as grippers and planar mechanisms articulated with the fourth generation PPy actuators, which are fabricated at the Intelligent Polymer Research Institute at the University of Wollongong [1]. Conducting polymers have many promising features including low actuation voltage, operation in aquatic mediums and in air, low cost, high force output to weight ratio, and suitability to openloop control. Their main drawback is their low speed of response and nonlinearity due to their actuation principle, which is based on mass transfer. There are a large number of variables and interrelated parameters that affect the actuation ability of PPy actuators. The complex nature of the actuation mechanisms and

lack of analogous classical theories have hindered the development and conclusive experimental verification of analytical mathematical models. As the working principle of a PPy actuator involves a number of mechanical, electrical and chemical parameters, we believe that it is a fruitless task to generate a fairly accurate mathematical model. This can be further backed with the non-existence of an analytical mathematical model in the published literature to predict the bending behaviour of tri-layer PPy actuators. With this in mind, we develop a lumpedparameter model to predict the displacement and force outputs of PPy conducting polymer actuators. As compared to the models presented in [22,23], the model can successfully describe the behaviour of the bending-type PPy actuators with little insight into the actuation mechanism, which is the main drawback of lumped-parameter models. The mathematical model has been validated in the voltage domain and in the thickness domain so that it can be used to optimise the geometry of PPy layers for a range of applied voltages [24]. The model has been solved using the FEM, which is an effective method for the modelling of actuation systems or structures. The FEM has been used in the design and evaluation of devices including piezoelectric actuators [25,26] and MEMS piezoelectric devices [27]. 2. Conducting polymer actuators The structure and composition of the actuator considered in this study are shown in Fig. 1a. This actuator is a composite structure consisting of five layers of three different materials; two layers of polypyrrole with a thickness of 30 ␮m each, two layers of platinum with a thickness ranging between 10 and ˚ and one layer of porous polyvinylidine fluoride (PVDF) 100 A with a thickness of 110 ␮m. Thin layers of platinum which are sputter-coated serve to increase the conductivity between the electrolyte (PVDF) and PPy layers. The PVDF is an inert, nonconductive, porous polymer that serves as the electrochemical cell separator. It also serves as a reservoir for the electrolytic ions tetrabutylammonium hexafluorophosphate (TBA·PF6 ) in an organic solvent propylene carbonate (PC) at a concentration of 0.25 M. It has been reported [7,14] that the Young’s modulus of polypyrrole varies between 20 and 180 MPa, depending of the value of the voltage applied. However, in this study, it is assumed that the operation voltage ranges between −1.0 and 1.0 V and the

Fig. 1. (a) Schematic structure of the conducting polymer bending actuator, and (b) schematic representation of the bending principle.

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Young’s modulus is constant. Platinum has a Young’s modulus of 171 GPa. The porous PVDF is a membrane filter DuraporeTM manufactured by Millipore Pty. Ltd. As the Young’s modulus of this material is not available in the literature, the modulus needs to be estimated. The approximation E ≈ EP (ρ/ρP )n where EP , ρP are the Young’s modulus and the density of the solid PVDF gives EPVDF = 612 MPa [9–11]. Please note that n = 1 for most of the porous polymers. When a current or a voltage is applied, a Red/Ox reaction occurs in the polypyrrole. So it has two states: oxidized (or doped), reduced (or de-doped) or neutral. In the oxidised state, when the polymer is positively charged, the polypyrrole attracts an anion (oxidation) to balance the removal of the electron from the polymer. Following the same principle, the reduction involves the addition of electron in the polymer and so the removal of the anion when it is negatively charged. These anions come from the porous PVDF, which contains an electrolyte. The doping level could be controlled by the voltage applied. The movement of ions in one hand, and the solvent molecule in the other hand, induce a volume expansion or contraction. The volume of the doped PPy layer increases and following the same physical behaviour, the volume of the other PPy layer decreases. Furthermore, the polymer backbone interacts electrostatically with the displaced ions. The resultant electrostatic forces cause the PPy layer to expand or contract. This creates the bending motion, as shown in Fig. 1b. 3. Model establishment With reference to the operation principle of the actuator, we draw an analogy between the thermal strain and the real strain in PPy actuator due to the volume change to establish the mathematical model, which is a coupled structural/thermal mathematical model. The software ANSYS is used to solve the coupled structural/thermal model in order to obtain the outputs: (i) the bending angle (θ), and (ii) the bending moment (M), of the actuator. 3.1. Actuation effect As argued before, the mechanical, electrical and chemical properties of the actuator cannot be taken into account directly in establishing a mathematical model. Indeed, ANSYS cannot model the migration of ions or the electrostatic interactions between the polymer backbone and the ion. It is important to understand the distinction between the classical beam models and the model to be developed here. The classical models are valid when a passive beam is under a load. Here the beam is the actuator, which bends under its own ‘electrochemomechanical’ action. The actuation effect is actually produced by the volume change of the PPy layers (expansion or contraction). Hence the mathematical model must be based on a load generated as a result of the volume change. ANSYS can take into account some coupled effects, like thermal-structural effects. Therefore, an augmentation of the volume via a thermal expansion coefficient in a thermal-structural simulation comes to mind.

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3.2. Finite element (mathematical) analysis The object of this section is to give details of the theory behind the coupled structural/thermal model. In a classical structural analysis, the equations of the theory of elasticity are based on the Hooke’s law expressed in 3D by Eq. (1), where the strain εS and the stress σ in the body are linked by the deformation matrix [D]: ⎧ ⎫ ⎫ ⎧ σx ⎪ ε ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ x ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ εy ⎪ σy ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨σ ⎪ ⎬ ⎬ ⎨ε ⎪ z z , {σ} = and {σ} = [D] · {εS } {εS } = ⎪ ⎪ γxy ⎪ τxy ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ γyz ⎪ τ ⎪ ⎪ ⎪ ⎪ ⎪ yz ⎪ ⎪ ⎪ ⎪ ⎩ ⎭ ⎭ ⎩ γzx τzx (1) The actuator engineered at the Intelligent Polymer Research Institute of the University of Wollongong can develop an isotonic strain up to 2.5% that depends on the applied voltage [13]. Previous studies show that the strain can be related linearly to the applied voltage V [7]: εV = β · V

(2)

The strain due to the expansion or contraction of the PPy under a voltage load can be considered as isotonic and without shearing. In order to take into account the interaction between the mechanical behaviour and the actuation principle, we can express the equation of the ‘electro-elasticity’ that occurs in the actuator as follows: {σ} = [D] · ({εS − εV }), where {εV } = β · V · [ 1

1

1

0

0

0]

T

(3)

where ‘T’ is the transpose of the vector. We use the FE software ANSYS to solve the mathematical model described by the Eq. (3). ANSYS does not offer a module for this particular equation. Nevertheless, the software includes a coupled-field analysis based on the theory of thermo-elasticity. This analysis takes into account the interaction between the mechanical and thermal fields and uses the following equation: {σ} = [D] · ({εS − εT }) with {εT } = α · T · [ 1

1

1

0

0

0]

T

(4)

where T(x, y, z) is the non-uniform temperature field in the body and α is the coefficient of thermal expansion. In our study, we can use the thermo-elasticity equation if we mimic the voltage by the temperature T, and the coefficient of thermal expansion by the slope β of the strain–voltage linear approximation (Eq. (2)). That is: V → T,

β→α

The performance of the bending-type PPy actuator is quantified in terms of bending angle and bending moment. The finite

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element software: (i) combines and solves the model equations, (ii) combines each element’s strain equations in order to find the form of the structure made up of these elements, and in the same way, (iii) it combines all the forces produced by each element to determine the total force generated by the structure. 3.3. Electro-structural coupled-field analysis This study uses by necessity a thermal-structural analysis in ANSYS that mimics an electro-structural analysis. This coupled-field analysis takes into account the influence of an external factor on a classical structural analysis. In this case, the variation of the volume of the PPy induces internal forces in the model. The FE software needs to use a special type of element in the calculation that includes these coupling effects. The following matrix equation describes the coupling effect:   [K11 ({X1 }, {X2 })] 0 X1 0 [K22 ({X1 }, {X2 })] X2

 {F1 ({X1 }, {X2 })} = (5) {F2 ({X1 }, {X2 })} The coupling effect can be seen in [K11 ] and [K22 ]. However, this relation is only valid for small displacements because [K11 ] is not constant for large displacements. ANSYS solves the model

by a method based on iteration and using convergence analysis. This method is well described by Bathe [28]. 3.4. Steps involved in establishing mathematical model The flowchart in Fig. 2 shows the steps involved in establishing and validating the mathematical model based on the FEM. The principle parameters used here are EX1 and EX2 that correspond to the Young’s moduli of the PPy and the PVDF layers, respectively. As the ultimate goal of this study is to optimize the geometry of the bending actuator [24], it is convenient to use a nondimensional parameter so that we can draw conclusions valid for any scale of actuators. The shape of the bending actuator can be approximated by a circle [12], as shown in Fig. 3. We choose the angle θ as the output parameter, which is a nondimensional parameter. If the dimensions of the PPy strip are doubled, θ will not change. We can use the following formula: θ = arctan(dz /L1 ) to calculate the angle. The data needed to calculate the angle are obtained using the setup shown in Fig. 4. To measure the bending moment in the FE software, a force is applied at the free end of the actuator to prevent its displacement. The force is then multiplied by the length to find the bending moment, as shown in Fig. 5. Experimentally, a lever-type force sensor constrains the free end displacement of the actuator. The steady-state value of the force generated was recorded as the force output of the actuator.

Fig. 2. Flowchart for mathematical model establishment and validation.

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Fig. 3. Definition of the output parameters: (a) bending angle θ to measure the displacement output, and (b) bending moment M to measure the force output.

Fig. 4. Experimental (left figure) and theoretical (right figure) readings of the horizontal and vertical displacements of the actuator in order to calculate the bending angle.

is due to the input/output based black-box nature of the mathematical model. Fig. 5. Determination of the force output in the simulation results obtained using ANSYS.

4. Adjusting model parameters The object of this section is to adjust a set of parameters resulting in a close correspondence between the experimental and theoretical bending angles and bending moments. These parameters are: (i) the Young’s moduli of the PPy and the PVDF, (ii) the coefficient of thermal expansion, and (iii) the temperature difference as the input parameter. It is important to notice that the mathematical model is a black-box model; the numerical values of the parameters do not necessarily represent their physical values and meanings. For instance, a load of 1 V gives, a strain of 0.3% which corresponds to a bending angle of θ = 14.3◦ and a bending moment of M = 0.18 mN cm. These parameters will be referred to θ exp. and Mexp. . A thermal load of T = 1 ◦ F with EPVDF = 612 MPa, EPPy = 80 MPa (experimental values), α = 0.03 do not produce the real θ exp. and Mexp. values. This

4.1. Bending angle As given before, the output displacement of a strip-type PPy actuator is evaluated in terms of the bending angle for the sake of making it independent of the actuator length. It has been assumed that the bending angle of a PPy strip is directly proportional to the strain. Further, the bending angle θ depends on the strain of each layer of the structure, and this strain can be obtained from Eq. (4). Obviously, changing the coefficient of the thermal expansion α will change the strain of each element and consequently, the bending angle of the strip. 4.2. Bending moment As described by Eq. (4), the stress and the strain are linked by the equation {σ}=[D]·({εS − εV }) where σ is the stress, ε the strain and D is the proportional to the Young’s modulus E. Based on Eq. (4), it is possible to calculate the value of the bending moment of the polypyrrole actuator by setting the Young modulus. Please note that we keep the value of the ratio EX1/EX2,

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Fig. 7. Bending moment experimental results (−1, 1 V at 0.33 Hz).

5. Model validation by experimentation The input for the ANSYS model is a temperature difference that is analogous to the voltage applied to a real PPy actuator. It should be noted that the experiments are run using voltage control as input because it is simpler to control. Indeed, current control could lead to high and damaging voltage for the PPy [1]. The experimental results given in Figs. 7 and 8 are for a PPy strip 10 mm in length, 1 mm in width and 12 h PPy grow with a current density of 1 mA/cm2 (approximately 30 ␮m of PPy in each side of the 110 ␮m PVDF layer). The experimental results are recorded after a number of cycles, due to the fact that the isotonic strain in the strip falls significantly during the 20 first cycles [1]. In the experiments reported in this study, the force and displacement values are measured after the actuator response reaches its steady-state value, as illustrated in Fig. 9. Fig. 6. Procedure to determine the model parameters.

but not the values of EX1 and EX2. Although each one will not have the same their true values, the mathematical model will take into account the stiffness of the PPy layer relative to the PVDF layer. The procedure to determine the parameters in the model is outlined in Fig. 6. After determining the model parameters, the analogous model is ready to estimate the bending angle and bending moment outputs of the PPy bending actuator under time-invariant voltages. 4.3. Simulation parameters ANSYS is able to account for the effect of a large deformation. This option is used in the simulation. The meshing of the model is done with the SOLID98 element type, with the degree of freedom UX, UY, TEMP. The simulation runs properly with nearly 3000 elements, and the calculation takes nearly 1 min to converge.

Fig. 8. The configuration of the actuator while experimentally measuring its tip’s vertical and horizontal displacements to calculate the bending angle (−1, 1 V at 0.33 Hz).

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Fig. 9. Reduction in the force output of the actuator after few cycles.

The experiments were run for 0.25, 0.5, 0.75 and 1 V. Many actuators were tested for each voltage to eliminate large inaccuracies in the experiments. The average values of the bending angle and the bending moment for each set of tests are shown in Figs. 10 and 11, respectively. Please note that the experimental results for 1 V are used to adjust the model parameters. The procedure described in Fig. 6 has produced EX1 = 30.345 MPa, EX2 = 232.143 MPa and α = 0.01288. With reference to Figs. 10 and 11, the experimental and theoretical results are in a good agreement. This proves that the analogous temperature model is valid to predict the bending angle and bending moment of the PPy actuator for any voltage applied in the range −1 to 1 V.

Fig. 10. Experimental and simulated bending angle results.

Fig. 11. Experimental and simulated bending moment results.

6. Model improvement The experimental bending moment output of the PPy actuator has been evaluated for different PPy thicknesses, and is provided in Fig. 12, where there is a non-negligible drop in the bending moment when each of the PPy layers is thicker than 60 ␮m. The model established and validated in the previous section assumes that the actuation ability of the PPy layers is constant along the thickness. This means that the outer surfaces of the PPy layers are as effective as the inner surfaces in contact with PVDF layer. In reality, the ‘electrochemomechanical’ reaction is more effective around the vicinity of the voltage application—the fixed end of the actuator. This behaviour is mainly due to the migration of the moving ions into the PPy layers. The moving ions are

Fig. 12. Experimental results showing the variation in the bending moment with the thickness.

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Fig. 13. Schematic description of the actuation effect changing along the thickness of the PPy layers.

relatively large and it is difficult for the PPy layer to be uniformly doped. The migration of ions starts close to the voltage application zone and diffuse to the depth of the PPy layer. This behaviour is complex to include in a fully analytical model. In this section, we improve the lumped-parameter model such that it takes into account the decrease in actuation performance in order to quantify the real behaviour of the actuator for different thicknesses. The improved model must take into account the decrease in actuation performance with the distance along the thickness direction. We propose to use a gradient of the actuation efficiency in the PPy layer along the thickness. The PPy layers close to the Pt-coated PVDF layer is more dominant than the other layers further from the PVDF layer, as schematically described in Fig. 13. Furthermore, we assume that the platinum coating on the PVDF helps to provide the same voltage, i.e. the same actuation ability, all over the length of the PPy strips. In Section 3, it has been shown that the voltage input to the real PPy actuator is analogous to the temperature difference in the coupled structural/thermal mathematical model. This follows that it is needed to create a gradient of the temperature difference in the PPy layers using finite element software, as shown in Fig. 14. With reference to the operation principle of bending-type actuators investigated in this study, the forms of the temperature gradients are heuristically chosen to fit the

Fig. 14. Temperature gradient in the PPy layers using the software ANSYS.

simulated bending moment results to those obtained through experimentation. Three examples of such gradients are provided in Fig. 15. After forming the structure of the temperature (actuation) gradient, the next step is to determine which temperature gradient describes the bending moment and bending angle outputs of the PPy actuators closely. A set of experiments was conducted to evaluate the influence of the thickness of the PPy layer in terms of bending moment. The experimental bending moment results are provided in Fig. 12. The results in Fig. 12 show that the actuation ability seems to occur with success in the first 60 ␮m of the PPy layer. More precisely, the actuation process is able to overcome the inertia of the strip. When the PPy layer is thicker than 60 ␮m, the bending moment begins to decrease. In this case, the PPy actuator is unable to overcome its increased flexural rigidity. For instance, an augmentation of the PPy thickness from 30 to 50 ␮m gives 25% increase to the total thickness of the strip, which is 66% increase in the volume of the PPy, but the flexural rigidity increases by 95%. Three sets of simulations have been run to determine the behaviour of the mathematical model such that it describes the variation of the bending moment and bending angle with the PPy thickness. The experimental and simulation results with three different actuation gradients are depicted in Fig. 16. The trends of each simulated bending moment curve are quite close to the experimental one. The third set of bending moment results is the closest to the experimental ones.

Fig. 15. Three different gradients of actuation ability in the PPy layer along the thickness.

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Fig. 16. Comparison of experimental and theoretical bending moment results for three temperature gradients in the PPy layers.

With reference to the flowchart given in Fig. 6, the initial Young’s moduli values of EX1 and EX2 can be set freely. For the results provided in Fig. 17, these values are found to be closer to the physical values, EPVDF = 612 and EPPy = 80 MPa. Please note that the EX2/EX1 ratio is 7.65, which is same as ratio for the results shown in Figs. 10 and 11. It must be noted that the behaviour of the model is quite close to the experimental data.

After 60 ␮m, the model is less efficient, the bending displacement is already falling to half of the maximum and the moment begins to decrease. Please note that the temperature gradient used to generate the results in Fig. 17 is the one described in the third plot of Fig. 16 from the left. Comparison of the simulation results with experimental ones proves that including the actuation gradient in the model improves the ability of the model to

Fig. 17. Comparison of experimental and theoretical bending moment results, and the theoretical bending angle results with the most suitable temperature gradient.

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predict the influence of the PPy layers’ thickness on the bending angle and moment outputs of the actuator. The mathematical model developed and validated in the previous sections has been employed to optimise the actuator geometry for maximum possible bending angle and bending moment outputs [24]. 7. Conclusions We have established a lumped-parameter model of a bendingtype PPy actuator based on finite element analysis. The model describes the input/output behaviour rather than the physical/chemical phenomenon such as cation concentration and ionic diffusion behind the actuation. The model contains the volume change, the elastic deformation, the input voltage and the actuation ability gradient along the PPy thickness. The effect of propagation of the ion migration into the PPy layers is mimicked with a temperature distribution model. This model is effective enough to predict the bending angle and bending moment outputs of the PPy actuators quite well for a range of input voltages. The mathematical model has been validated in the voltage domain and in the thickness domain such that it can be used to optimise the geometry of PPy layers for different applied voltages. Future work involves: (i) improving the modelling methodology such that it includes the actuation gradient along the length of the PPy layers in addition to the actuation gradient along the thickness of the PPy layers, (ii) evaluating the minimum displacement the PPy actuators can generate in order to make mechanisms to be dedicated to micro/nano manipulation systems, and (iii) developing an analytical model to predict the influence of ion migration and diffusion, cation concentration on the behaviour of tri-layer the PPy actuators, which operate in a non-liquid medium, i.e. in the air.

Acknowledgements This project has been partly funded by a URC Small Grant. The authors wish to express their gratitude to the members of the Intelligent Polymer Research Institute at the University of Wollongong. In particular, the assistance of Mr. Richard Wu in fabricating the actuator samples is gratefully acknowledged. Useful discussions with the visiting student, Mr. Brian Mui, from the University of British Colombia are also greatly appreciated.

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[5] E. Smela, M. Kallenbach, Jens Holdenried, Electrochemically driven polypyrrole bilayers for moving and positioning bulk micromachined silicon plates, IEEE J. Microelectromech. Syst. 8 (4) (1999) 373– 383. [6] R.H. Baughman, Conducting polymer artificial muscles, Synth. Met. 78 (1996) 339–353. [7] G.M. Spinks, L. Liu, G.G. Wallace, D. Zhou, Strain response from polypyrrole actuators under load, Adv. Funct. Mater. 12 (6–7) (2002) 437–440. [8] J.D. Madden, R.A. Cush, T.S. Kanigan, I.W. Hunter, Fast contracting polypyrrole actuators, Synth. Met. 113 (2000) 185–192. [9] H. Lobo, J.V. Bonilla, Handbook of Plastics Analysis, Marcel Dekker Inc., New York, 2003. [10] H.-G. Elias, An Introduction to Plastics, Wiley-VCH, Germany, 2003. [11] I.M. Ward, D.W. Hadley, An Introduction to the Mechanical Properties of Solid Polymers, John Wiley and Sons Ltd., Chichester, New York, 1993. [12] Y. Bar-Cohen, S. Leary, Electroactive polymers (EAP) characterization methods, in: Proceedings of the SPIE Smart Structures and Materials: Electroactive Polymer Actuators and Devices, vol. 3987, Newport, CA, March, 2000, pp. 1–5. [13] G.M. Spinks, G.G. Wallace, L. Liu, D. Zhou, Conducting polymer electromechanical actuators and strain sensors, Macromol. Symp. 192 (2003) 161–169. [14] A.S. Hutchinson, T.W. Lewis, S.E. Moulton, G.M. Spinks, G.G. Wallace, Development of polypyrrole-based electromechanical actuators, Synth. Met. 113 (2000) 121–127. [15] G. Alici, B. Shirinzadeh, Kinematics and stiffness analysis of a flexurejointed planar micromanipulation system for a decoupled compliant motion, in: Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, Las Vegas, USA, October, 2003, pp. 3282–3287. [16] E.W.H. Jager, O. Inganas, I. Lunstrom, Microrobots for micrometer-size objects in aqueous media: potential tools for single cell manipulation, Science 288 (2000) 2335–2338. [17] Y. Liu, L. Oh, S. Fanning, B. Shapiro, E. Smela, Fabrication of folding microstructures actuated by polypyrole/gold bilayer, in: Proceedings of the IEEE 12th International Conference on Solid State Sensors, Actuators and Microsystems, Boston, June, 2003, pp. 786–789. [18] A. Della Santa, D. De Rossi, A. Mazzoldi, Performance and work capacity of a polypyrrole conducting polymer linear actuator, Synth. Met. 90 (1997) 93–100. [19] A. Della Santa, D. De Rossi, A. Mazzoldi, Characterisation and modelling of a conducting polymer muscle-like linear actuator, Smart Mater. Struct. 6 (1997) 23–34. [20] S. Nemat-Nasser, J.Y. Li, Electromechnanical response of ionic polymer–metal composites, J. Appl. Phys. 87 (7) (2000) 3321–3331. [21] S. Nemat-Nasser, Micro-mechanics of actuation of ionic polymer-metal composites, J. Appl. Phys. 92 (5) (2002) 2899–2915. [22] Q. Pei, O. Inganas, Electrochemical applications of the bending beam method. 1. Mass transport and volume changes in polypyrrole during redox, J. Phys. Chem. 96 (25) (1992) 10507–10514. [23] B.S. Berry, W.C. Pritchet, Bending-cantilever method for the study of moisture swelling in polymers, IBM J. Res. Dev. 28 (6) (1984) 662–667. [24] G. Alici, P. Metz, G.M. Spinks, A methodology towards geometry optimisation of high performance polypyrrole (PPy) actuators, J. Smart Mater. Struct. 15 (2006). [25] D.H. Wu, W.T. Chien, C.J. Yang, Y.T. Yen, Coupled-field analysis of piezoelectric beam actuators using FEM, Sens. Actuators 118 (2005) 171–176. [26] Y. Jing, J. Luo, X. Yi, X. Gu, Design and evaluation of PZT thin-film micro-actuator for hard disk drives, Sens. Actuators 116 (2004) 329–335. [27] S. Greek, N. Chitica, Deflection of surface-micromachined devices due to internal homogeneous or gradient stresses, Sens. Actuators 78 (1999) 1–7. [28] K.-J. Bathe, Numerical Methods in Finite Element Analysis, PrenticeHall, 1976.

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Biographies Philippe Metz received the MSc – Res. degree in mechanical engineering from Blaise Pascal University, Clermont-Ferrand, France, in 2005 and MSc degree in Mechanical and Industrial Engineering from the French Institute for Advanced Mechanics Engineering Diploma (IFMA) in 2005. He is currently a development engineer at Michelin, Clermont-Ferrand, France, where he works on new simulation and predictive manufacturing tools. ¨ Gursel Alici received the BSc degree with high honours from Middle East Technical University, Gaziantep, Turkey, in 1988 and the MSc degree from Gaziantep University in 1990 (both degrees in mechanical engineering) and the PhD degree in Robotics from Oxford University, UK, in 1993. He is currently a senior lecturer at the School of Mechanical, Materials and Mechatronics Engineering in the University of Wollongong, Australia, where he

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leads mechatronics engineering. His research interests are in the areas of mechanics, optimum design, control and calibration of mechanisms/robot manipulators/parallel manipulators, motion design, micro/nano manipulation systems, and modelling, analysis, characterization and microfabrication of conducting polymer based actuators and sensors for use in functional robotic devices. Geoffrey Spinks obtained his PhD from the University of Melbourne with a study of the fracture behavior of thermosetting polyesters. He has continued research into the mechanical properties of polymers since joining the University of Wollongong in 1989. A particular research interest is the application of polymers and carbon nanotubes as artificial muscles and mechanical sensors. This research has generated more than 100 refereed journal and conference papers. Current research is dedicated to understanding the mechanisms of electro-mechanical energy transduction in polymer systems from the nanoscale to the macro-scale.