Performance and work capacity of a polypyrrole conducting polymer linear actuator

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ELSEVIER

Synthetic Metals 90 (1997) 93-100

Performance and work capacity of a polypyrrole conducting polymer linear actuator A. Della Santa, D. De Rossi *, A. Mazzoldi Centro 'E. Piaggio ', School of Engineering, Universit3' of Pisa, 56126 Pisa, Ira;

Received 16 April 1997; accepted 16 May 1997

Abstract

This paper reports a performance analysis of a conducting polymer film actuator made of polypyrrole (PPy). Electrochemomechanical characterizations of the active displacement and the developed force of a PPy free-standing film at different loading conditions are performed. Two driving signals are used: the former, a cyclic voltammetry at 1 mV/s between +__1 V, is used to carry out an accurate on-line analysis of the fihn displacement; the latter, a current square wave between 0.02 and 0.1 Hz, is helpful for evaluating the effectiveness of the actuator in terms both of actuation strain and of developed force. The experimental results indicate that 1% displacement, 3 MPa force and working density of 73 kJ/m s are achievable goals for a conducting polymer linear actuator, which are interesting results if compared with the limiting specifications of skeletal muscle. Additionally, two different approaches to the electrochemomechanical modeling of the conducting polymerfluid electrolyte system are illustrated, together with a discussion about foreseen improvements in the implementation of actuating structures. © 1997 Elsevier Science S.A. Keywords: Polypyrrole and derivatives; Actuators

1. Introduction

In many fields of application, as anthropomorphic robotics, minimally invasive microsurgery, microhydraulics and applications demanding a high level of miniaturization, the development of new microactuators represents a primary task [ 1 ]. The ideal actuator must feature properties, such as Iinearity, high power-to-weight ratio, a large degree of compliance and the possibility to be direct-driven. Basically, linear actuators of this "kind must be simple enough to allow a degree of miniaturization that is unlikely for the conventional rotatory actuators. For such an ambitious goal, the utilization of energy conversion properties of transducing materials, like shape memory alloys, piezoelectric polymers, polyelectrolyte gels and conducting polymers, appears to be a possible solution. In this paper the potentialities of w-electron conjugated conducting polymers (CPs) as constitutive materials of novel actuators are presented. The electrochemomechanical properties of CPs manifest themselves when ionic species are exchanged with the surrounding medium, i.e. solid or liquid electrolyte; this phenomenon, usually referred to as doping and de-doping, is well known and the related length changes * Corresponding author. 0379-6779/97/$17.00 © 1997 Elsevier Science S.A. All rights reserved PIIS0379-6779 (97) 039 19-2

are being investigated, especially for polyaniline and polypyrrole [2-7]. Usually, doping causes the elongation of the CP electrode, while de-doping causes its contraction. A CP linear actuator could be made of two CP electrodes separated by a solid electrolyte which stores the dopant anion of the first CP and the dopant cation of the second one. During the stimulation the system toggles between a state in which both the CP electrodes are doped (and hence elongated) to a state in which they are undoped or less doped (and hence contracted) [ 8]. The projected large dimensional changes upon doping of CPs (up to 1%), as compared with piezoelectric polymers, and the high stresses developed (up to 50 MPa) can provide a correspondingly high work capacity per cycle [ 2,9 ]. Moreover, the required stimulation voltages are two orders of magnitude lower than for common electrostatic or piezoelectric microactuators. On the other hand, CP actuators typically show a slower response. It is worth noting that CPs are rather 'young' materials and many improvements in their properties can be foreseen. Several degrees of freedom in the design of better CP actuators must be explored: the choice of the monomer and of different dopants, the polymerization technique, the possibility of scaling down their dimension, the processability in different

shapes.

94

A. Della Santa et aL / Synthetic Metals 90 (t997) 93-100

Servo-eontroller

PC ~lp

.it

Potenttostat

Electroehemtcsi cell Fig. l. Experimental set-up.

The goal of this paper is to characterize the mechanical behavior of a simple free-standing CP film, acting as working electrode in an electrochemical cell. In our experiments, a polypyrrole (PPy) film doped with benzenesulfonate anions is used as the CP and a liquid electrolyte bath serves as an ionic reservoir. The actuating properties of the material are investigated and quantified in terms of isotonic displacement, isometric developed force and work capacity. The results of electromechanical characterization are useful for evaluating potentialities in actual applications. The paper also briefly reviews two different approaches to the electrochemomechanical modeling of the CP-fluid electrolyte system. The first approach leads to a continuum, physical model which can give useful indication for better design of the materials. The second one is a discrete, phenomenological model and it can be instrumental for the implementation of control and driving methods for a CP actuating device.

2. Materials and m e t h o d s

The polymer used is PPy doped with benzenesulfonate anions ( B S - ) , provided by BASF AG (Germany) in the form of thin sheets (32 txm thickness), under the trade name of Lutamer®. The experimental set-up used for the characterization is schematically depicted in Fig. 1. A CP thin strip, 90 mm long and 1 mm wide, is immersed in an electrolyte bath of 10 - 2 M sodium benzenesulfonate (Sigma Co., USA) in a mixture of acetonitrile (J.T. Baker BV, The Netherlands) (95% in volume) and de-ionized distilled water (5% in volume). The lower extremity of the strip is mechanically fixed by a clamp inside which a gold electrode provides electric stimulation during electromechanical experiments. The upper extremity of the polymer strip is fixed to a computer driven servo-controlled actuator (model 300H, Cambridge Technology Inc., USA) which is used to measure both force under isometric conditions and displacement under isotonic conditions. A potentiostat-galvanostat (model 273, EG&G, USA) provides voltage or current waveforms between the PPy working electrode and a Pt counter-electrode, while a SCE electrode works as reference electrode. Both the servo-con-

troller and the potentiostat are driven via a PC with dedicated software (Asyst Software Package, Macmillan Inc., USA).

3. E l e e t r o c h e m o m e e h a n i e a l characterization

The electromechanical characterization of the material refers to its wet and stabilized state. A stabilization period is needed since preliminary investigations showed that the material considerably changes its properties not only when it is immersed in the electrolyte solution, but also during the first electrochemical stimulation cycles. When the polymer sample is immersed in the solution, it undergoes a free-swelling phase, during which a counter-load of 1 g (0.33 MPa) is applied to the sample just to maintain it straight. The polymer strip saturates its porous structure with the solution, varying its linear dimension by 2%. Meanwhile, the Young modulus of the material system shows a 60% decrement from the dry state (3000 MPa) to the final wet state ( 1200 MPa). In Fig. 2 the percentage variations of these quantities are shown. After the equilibration phase, the material is stimulated by a series of slow voltammetric cycles until a new steady state is reached. Details about this phase, which is decisive for the stabilization of the material, can be found in the literature [ 1 ]. The cyclic voltammetry (CV) is carried out at a scan 2.5

- 0 -10

2

ao

~

-70 0

-80 0

20

40

60

80

TIME (min) Fig. 2. Free-swelling curve: length ( ) and relaxed elastic modulus ( A ) vs. time of a PPy sample after its immersion into the electrolyte bath.

95

A. Della Santa er al. / Synthetic Metals 90 (1997) 93-100

VOLTAGE vs S CE (sdt) -1 0

0.4

0,75

1

0.4

2.5

0,5 0,25

g

2

-20% -30%

"~ -O25 [..,

Z

1.5

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¢9

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=

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-0.75

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Z

0,25

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0.5

.a

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-80% ua

CURRENT(mA) Fig. 3. CV of the PPy sample at the scan rate of 1 mV/s. The initial potential is 0.42 V and the scan direction is towards PPy reduction (see the arrow).

rate of 1 mV/s, with a maximum and a minimum voltage of + 1 and - 1 V versus SCE (see Fig. 3). During the first cycle there is a remarkable reduction peak due to the irreversible loss of benzenesulfonate anions. A continued, irreversible de-doping of the B S - anions persists for the following 20 cycles together with a second doping process which is the cyclic quasi-reversible doping and de-doping of the Na + cations. The first process implies that the material, which is progressively depleted ofBS - bulk dopant ions, deteriorates both in terms of mechanical characteristics and electrical conductivity. It also implies a progressive exponential-like shortening of the sample, which is completed within 20 cycles. The second process, which consists of the cyclic intake and release of the Na ÷ cations, causes a cyclic reversible elongation and contraction of the sample. After around 20 cycles of CV stimulation the material reaches a new steady condition, in which the only mobile dopant is Na + and a residual B S - works as trapped bulk dopant. The displacement and the elastic modulus changes during the first cycle are shown in Fig. 4. The CV starts at the equilibrium potential of PPy (0.42 V versus SCE), it goes down to - 1 V at a scan rate of 1 mV/s and then it comes back up to + 1 V and again down to 0.42 V. During the reduction phase, there is a shortening caused by the irreversible dedoping of B S - and an elongation peak due to the intake of Na+; in the subsequent oxidation a contraction peak due to the release of Na + is followed by an elongation peak due to the intake and release of the B S - present in solution. This second elongation peak gradually disappears during the first 20 CVs. As far as elastic modulus is concerned, a pronounced negative peak appears during the reduction phase (due to the doping of Na + ) and a second smooth peak occursduring the oxidation phase (due to the over-doping of B S - ) . In the following cycles, on-line changes in the elastic modulus cannot be detected by our apparatus. However, with continued cycling, its value gradually decreases approaching a final constant value equal to 660 + 40 MPa, which is about 50% less than the initial value of 1200 MPa. During the first cycle, the correspondence between displacement and elastic rood-

.90%

0 0

10

20

30 40 TIME (rain)

50

60

70

Fig. 4. Length changes ( ) and relaxed elastic modulus (11) of the PPy sample during the first cycle of the CV at 1 mV/s.

ulus peaks is evident. As expected, a minimum in the value of Young modulus corresponds to a maximum length. After such pre-conditioning of the material, the electromechanical characterization is carried out. The PPy sample is stimulated by means of a current square wave (SW) driving signal; meanwhile measurements of sample length changes and developed force are made in order to evaluate the actuator performance of the material. Current SW driving assures a fixed amount of charge to be exchanged every, cycle by the sample with the external solution. The exchanged charge, which is directly correlated to the amount ofNa + entering or coming out the polymer, results in a corresponding elongation and contraction of the sample. Charge control can be exploited by varying amplitude or period of SWs; both methods permit a quasi-linear driving of isotonic sample length changes. In Fig. 5, the dependence of the peak-to-peak length change waveform upon the exchanged charge is illustrated: an average value of length change-charge ratio of about 1 m m / C can be computed by linear regression, for values of charge below about 0.25 to 0.3 C. An increment of the exchanged charge beyond 0.25 C enhances the achievable dimension change of the material, but it drastically decreases the sample cycle life. Note that in the figure all the quantities have been normalized with respect to the sampIe 'active length' and 'active volume'; the strain-charge density ratio is equal to 3% mm3/C. In order to determine the correct value for the normalized quantities, it must be considered that a non-homogeneous electrochemomechanical response of the immersed sample (caused by the electric potential gradients along its length) is unavoidable in our experimental configuration. Indeed, the material, which has an initial electrical conductivity of about 150 S/cm in its fully doped state, shows an irreversible decrement of its conductivity due to the loss of bulk B S - dopants during stimulation CVs. Experiments have shown that the active part of the sample is confined to a 30 mm long portion, next to the gold electrode; the related 'active volume' is 0.9 mm 3.

96

A. Della Santa et al. / Synthetic Metals 90 (1997) 93-100

EXCHANGED CHARGE(C) 0.1

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0 I I I I [ I [ I--[ I 0 0 62.5 125 188 250 313 375 438 500 563 625

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E X C H A N G E D CHARGE DENSITY ( C/mm3 ) Fig. 5. Isotoniclengthchangesvs. exchangedchargeduringdifferentcurrent SW stimulationsof the PPy sample. Both quantities are also shown as normalizedwithrespect to the active lengthand activevolumeof the sampte. In order to evaluate the actuation performance of the polymer, isometric stress measurements have also been carried out. These measurements are made during a SW stimulation with I = 5 mA, T = 62.5 s, so that 0.156 C of exchanged charge is involved. The equivalent charge density is 0.173 C / m m 3. Such a small amount of charge assures compatibility of the measured value of the force with the full range of the instrument. In Fig. 6, the isotonic strain wave ( 1 g load) and the isometric stress wave are plotted versus time. Note that the two measurements are not done simultaneously; they are shown on the same plot in accordance with the same stimulation current. Under isotonic conditions, the sample elongates during the reduction semi-cycle and it contracts during the oxidation one. The amplitude of the length wave form has a mean value of 0.16 ram, in agreement with the results shown in Fig. 5; the related strain is 0.53%. Underisometric conditions,

T B I E (see) Fig. 6. Isotonic length changes (L(t)) and isometric developed forces (F(t)) of the PPy sample during the same SW stimulation (•=5 mA, T= 62.5 s, Q = 0.156 C). Duringthe reductionse~rfi-cycle,the sampleelongates under isotonicconditions,whereas it develops a negativeforce with respect of the offset pre-stretchingforce (dotted line) underisometricconditions. The lengthchangesrefer to a samplewhose wet, electrochemically active portion is 30 mm long. the sample develops a negative force (with respect of the offset force) during reduction and a positive force during the oxidation. The peak-to-peak amplitude of the force waveform has a mean value of 10 g, which corresponds to an equivalent stress of 3.25 MPa. The same results have been obtained for different values of current amplitude and period, while their product (equal to the exchanged charge) is kept constant. The polymer sample maintains its activity as long as the period of the SW driving signal is longer than about 5 s. Note that both the force and length waveforms show a drifting offset. This is because, at the beginning of the isometric force measurement, the imposed pre-stretching causes a stressrelaxation transient (resulting in a negative slope drift). Analogously, in the case of isotonic length measurement, the prestressing implies a creep transient (resulting in a positive slope drift).

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100

200

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300 400 500 600 TIME (rain) Fig. 7. Isotonic length changes (for a sample whose wet and active portion is 30 mm long) during CV at 1 mV/s. Betweeneach ~oup of CVs the load is changed by a step of 15 g and, consequently,the sample length creeps according to a viscoelastic behavior. During the CV stimulationthe sample length changes are around 1%.

A. Della Santa et al. / S y n t h e t i c Metals 90 (1997) 93-100

The results of a series of consecutive isotonic experiment are shown in Fig. 7; the test shows both the passive and active behavior of the material sample. The sample is stimulated with a slow cyclic voltammetry under different isotonic conditions (1, 15, 30, 45 g). Between each group of isotonic cycles the sample length creeps according to a standard viscoelastic behavior. During CV stimulation, the sample elongates during the reduction phase and contracts during the oxidation phase; such a behavior is maintained from quasifree conditions (with a load of 1 g, equal to 0.325 MPa) up to the load of 45 g (14.625 MPa). The mean value of the peak-to-peak displacement is 0.3 mm ( 1% strain), which is higher than that achieved during SW stimulation. This is due to the slow CV stimulation ( 1 mV/s from - 1 to + 1 V, with a stimulation period T = 4000 s) which assures an exchanged charge of about 0.3 C (correspondent to a 0.33 C / m m 3 amount of charge density). These results are consistent with the plot of Fig. 4.

reference

state /

li=Io[1 +

aL(q) Aq]

Ei=Eo[ 1 + OCE(q) Aq]

(1) (2)

where Aq is the change in the doping level with respect to the reference level measured in C / m 3, eel is the electrochemical expansioncoefficientand C~Eis the elasticvariationcoefficient, both expressed as percentage variation per C / m 3. The equation of length variation refers to the case of the quasizero loading condition for the sample. Note that the two coefficients are generally a function of the doping level q. They are also opposite in sign, an increment in length implies a decrement in elastic modulus.

7

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4. Discussion and evaluation of actuator performances

The performance of a CP actuator may be evaluated by a comparison with that of biological muscle. A complete analysis of all the salient features of skeletal human muscle, as they pertain to a pseudo-muscular actuator for advanced robotics, can be found in the literature [10]. Briefly, we should consider the following values as design objectives: • skeletal muscles can generate a stress ranging from 0.1 to 0.5 MPa; • the response time of muscle strongly depends upon the resisting load; however, a value of 0.2-0.3 s is typical; • the volumetric work capacity per cycle of human muscles is of the order of 10 kJ/m3; • the power-weight ratio is of the order of 0.1 kW/kg, although it depends on training; in terms of power density a value of 100 k W / m 3 can be achieved [8]. Let us discuss our experimental results with respect to such target specifications. The experiments previously described can be represented in the plots of Fig. 8. We refer to an arbitrary reference doping state with the subscript 0 and to every other state with the subscript i. The polymer changes its length l and its elastic modulus E according to the equations:

97

j

7/ "-aJ I i

I LENGTH

i

~

~

t

Fig. 8. State curves in the stress-strainplane of a generic CP actuator. A different doping level is associatedwith every stress-straincurve. The stress-strain experiments during the stimulation are represented by a series of straight lines: each one of them has a different slope (proportional to the elastic modulus) corresponding to a different doping state i. In our case, during the SW stimulation, the elastic modulus appears to remain = = constant; hence all the stress-strain curves have the same slope and the coefficient o~E of Eq. (2) is assumed to be zero. The isotonic length measurement is represented by an horizontal line laying on the length axis. The material behavior can be described as a cyclic pivoting from two states of maximum and minimum doping level (each of them characterized by its stress-strain straight line), where the load is approximately null. As it has been shown, the coefficient C~L is constant for a broad range of dopant levels. This means that, in our case, Eq. (1) becomes linear. The strain can be up to 1%, with a minimum response time of 5 s. The isometric force measurement experiment is represented by a vertical line. From the plot, the generated stress should be equal to Eo times the electrochemical strain. Experimental results confirm this assertion. The peak-to-peak amplitude of the measured force waveform corresponds to an

98

A. Della Santa et aL / Synthetic Metals 90 (1997) 93-100

equivalent stress of 3.25 MPa, which is approximately ten times the developed stress of human muscle. The response time is again higher that 5 s. The multiple cycle isotonic experiment can be represented in the stress-strain plane by a series of horizontal lines; each of them represent an incremental loading. Any increment in the load results in a ramp along a stress-strain curve. The work capacity W is represented by the area below the load horizontal line: 1

W=~o-e

(3)

where o- is, in our case, the load and • is the actuating strain. It is evident that the quantity W increases as the applied load increases. The value of Wranges from 1.6 k J / m 3 for the first group of quasi-free isotonic cyctes up to 73 kJ/m ~ for the group of isotonic cycles with a 45 g load. This latter value is higher than in human muscle and also higher than in other CP bending devices [9]. However, a less attractive performance figure results from the calculation of the average power, defined as the ratio of the work per cycle and the half period of the cycle: W P= T/2

to the solid polymer phase and to the fluid electrolyte phases, respectively) ; the coefficients N, A, Q, R are the poroelastic coefficients [ 9 ] and the term %~h represents the electrochemical stress, acting as a fluid pressure on the solid phase. (ii) The equilibrium equation of the total stress field (in which we neglect the body force ,or) is

at o"b) = at o-~ + o-~) = 0

O.~j

~xj

(iii) The Onsager-like laws for the coupled fluxes of charges (ions) J and mass (fluid) V f are J = kl l V g~+ kt2VP; (8)

V f = k 2 1 V ~ + k22VP

where k 0 are phenomenological coefficients relating the two fluxes with the two driving forces: the electrical potential gradient Vq~ and the pressure gradient VP [ 14]. The problem has been solved in the limit of a globally incompressible biphasic aggregate, which corresponds to the condition: e_f_

1-/3 d

(ga)

/3

(4)

In the above case this period is so tong (2000 s) that the achieved power is only 0.036 k W / m 3, for the best case of 45 g load. If we compute the same quantities for the case of faster isotonic experiments (in which a 0.53% strain is achieved in 5 s for a load of 1 g), we obtain a lower value of W (0.81 kJ/m3), but a higher value for P (0.16 k W / m 3 ) . In any case, it is evident that the response time is still the limiting factor of CP actuators.

where/3 represents the porosity of the polymer matrix (that is, the ratio between the fluid volume and the total volume of the biphasic system) and in the absence of electrochemical stimulation. Therefore, the second Eq. (8) becomes V2p = - f ~ t ( • f - d)

(9b)

wherefis the solid-fluid friction coefficient. By means of this relation we obtain: vE

E

5. Modeling

G'ij = ~ " ~ p Eb "} (1 + v ) ( 1 - 2 v ) "~w'*

The CP-electrolyte system can be modeled according to two substantially different approaches: a continuum, physical model and a discrete, phenomenological model. The former can be built up starting from the Biot poroelastic theory [ 11 ] and its application to polyelectrolyte gels [ 12] ; it has been applied also to our system [ 13]. The C P electrolyte system is modeled as a biphasic system. The first phase is the polymeric matrix, which is elastic and porous (at least 10% of porosity). The second phase is the electrolyte fluid, completely filling the pores. The set of equations includes: (i) The constitutive equation of the system, in the case of polymer matrix isotropy, is

ae-S 1

o-~ = 2N¢} + A C 8,j + Qd6,j + oM.

(5)

o -ri j_- Qe~6o + Rer6o

(6)

where o-0 and eij are the stress and the strain tensors, e is the trace of the strain tensor (the superscript letters s and f refer

(7)

(10)

(1-v)E

a T = f ( 1 -+- p)( 1 --2P) "rafts

(11)

where the poroelastic coefficients have been expressed in terms of the well-known Young modulus coefficient E and Poisson ratio p. A simple and meaningful validation of the previous equations can be carried out for the case of a stressrelaxation test in which a sudden strain is applied along the length of a polymer thin strip. The tensile force F(t) can be evaluated as a function of time during the stress-relaxation test [ 13 ] : F(t)=abEeo

( 1 - 2 p ) ": 8 1 lq [t~-u'] ._~772(2n+1) 2

where a and b are the thickness and the width of the strip, eo is the applied strain and r is a characteristic time equal to

99

A. DeIla Santa et al. / Synthetic Metals 90 (1997) 9 3 - 1 0 0

aaf (1 + u ) ( 1 - 2 v ) E( 1 - u)

........ (13)

'r= ,rr2

From the expression (12), it appears that the force decays in a monotone, multi-exponential fashion, from its initial value, a b E ( 2 - u ) / ( l + v ) e o to the final value, EGo. The behavior is similar to that of a standard viscoelastic solid, but the physics of the phenomenon is quite different: the apparent viscoelasticity is due to the bipbasic nature of the system. By computing the interstitial fluid pressure [ 13 ], it can be shown that, during the stress-relaxation, the pressure jumps from the reference external bath null value to a negative value, that indicates suction of fluid from the external bath; then it asymptotically returns to the initial null value, as far as the biphasic system recovers a new equilibrium. Hence, the transient behavior of the fluid, that viscously enters the polymeric matrix, is responsible for the viscoelastic-like behavior of the whole system. This is correct unless the polymer matrix is not viscoelastic by itself; such a case is not considered by the model which assumes that the polymer is purely elastic, an hypothesis which is not always verified. Actually, the goodness of fit between experimental data (collected during several stress-relaxation tests on the PPyelectrolyte system) and theoretical data confirms the validity of the model, but a discrepancy appears for the first 3-4 s of the total 30 s long transient. Such a discrepancy can be attributed to the effect of the intrinsic viscoelasticity of the PPy matrix; this effect exists in our case, although it is secondary both in amplitude and in frequency (the viscoelastic characteristic time of the dry polymer is around 1 s, while the one of the polymer-electrolyte system is around 5 s). If the data collected from stress-relaxation tests on the dry PPy are subtracted from the previous data, the fitting becomes accurate for the entire transient. Finally, Eq. (13) shows that the mechanical characteristic time of the material system is proportional to the friction between the two phases, while it is inversely proportional to the stiffness of the polymer. What is more, the response time depends on the square of polymer strip thickness. This last issue indicates that the scaling down of the material dimensions can provide great improvements to the device response time.

K1

q1 [-[F

Kr

<

©

ech

Table 1 Lumped parameters model

T~2

K2 qVV~

7o-

The second approach, the discrete and phenomenological one, leads to a simpler lumped parameter description of the CP wet strip based on standard viscoelastic solid elements plus an appropriate strain generator to take into account the active behavior of the system during electric stimulation, in analogy with muscle models [ 15]. This approach permits a drastic reduction of the model complexity and it can be instrumental for the implementation of driving and control strategies of a future CP actuator. The model refers to a linear PPy actuator whose length is much greater than its transverse dimensions. All the parameters of the model are normalized, so that these are independent of actuator dimensions. The used lumped parameters model is the parallel arrangement of two Maxwell elements and one elastic body; the electrochemical strain generator is inserted in series with the elastic body Kr (Fig. 9). In a stress-relaxation passive test, such a model predicts an exponential decrease of the force from an initial state (in which the solid is elastic with an instantaneous Young modulus equal to the sum Kr+K1 +K2) to a final state (in which the solid is again elastic with a lower, relaxed Young elastic modulus equal to Kr); the dynamics between the initial and final state is exponential-like, with two characteristic times r1 =rh/K1 and % = TIa/K2. The strain generator is modeled as proportional to the exchanged charge through the phenomenological coefficient oe~h, previously referred as the electrochemical expansion coefficient (percentage displacement for C/ram3). A comparison between experimental data and theoretical resolution of the lumped parameters model for the case of a stress relaxation test allows us to obtain the values of the three elastic and two viscous parameters of the model. Then, the model is analytically solved (both under isotonic and isometric conditions) assuming a current SW stimulation, that is a charge triangular wave. The solutions are compared with the experimental curves of length and force (see Fig. 5), so that the strain generator is determined in two different and independent ways [ 16]. The values of the five passive model parameters (Kr, Kl, /<2, "r/l, "q2) and the electrochemical expansion coefficient ae~h are shown in Table 1. The model furnishes useful indica{10ns about the relationship between the actuation strain and the developed stress; the latter is approximately equal to Kr times the isotonic strain, if the stimulation frequency is lower than the cut-off frequencies of the system, f~ = 1/rx and f2 = 1/r2. The period of stimulation must be higher than the characteristic times rl (5 s) and r2 (0.7 s); it implies that the actuator works most

>

8 Fig. 9. Lumped parameters model. The general Nth order linear system has

been set as an order II linear systemfor our experimentalconfiguration.

Kr (MPa)

K1 (MPa)

K2 (MPa)

/.q (MPa s)

/.t2 (MPa s)

a~h

95

58

473

40

3

(% mm3/C)

7

650

100

A. Della Santa et al, / Synthetic Metals 90 (1997) 93-t00

effectively at frequencies below 0.2 Hz, where the pseudoviscoelastic properties of the CP-electrolyte fluid system do not quench the actuating displacement. From a physical point of view, the electrochemical stimulation causes the expansion (or contraction) of the porous polymeric solid matrix and, consequently, the suction (or expulsion) of fluid from the external bath inside the solid; the dynamics of this process is rate-limited by friction effects between the fluid and the pores of polymer backbone, as shown by the previously mentioned continuum model. Finally, the actuator speed may be also limited by the electrodiffusion rate of counter-ions from the external bath towards the polymeric backbone. The evident coupling between fluid motion and ionic electrodiffusion does not altow, at this stage, any assertion about which phenomenon is actually the rate-limiting one.

6. Conclusions The experimental results have shown the possibility of using PPy as an actuation material. The measurements of developed stress and the evaluation of the work capacity and the power density indicate that the actuator has promising performance, once the response time is decreased by scaling down the film thickness. It is worth underlining that the polymer needs the presence of a ionic reservoir. At the moment this is an electrolyte bath, which again limits the applicability of the actuating system, for instance, to microhydraulJc systems [ 17]. Hence, we can conclude that the two key issues for the realization of a viable actuator are: (i) the development of a suitable solid polymer electrolyte with good electrochemical and mechanical coupling properties with the CP element; (ii) the implementation of microsized CP actuators which can be used in parallel (in order to increase the force) and/ or in series (in order to increase the displacement) to constitute the final actuator; such an 'elementary' microactuator may be better shaped in the form of 10 to 30 txm thick fibers; such fibers are already available [ 18-20]. The whole CP-solid electrolyte structure could be constituted by CP microfibers embedded in the solid electrolyte elastomeric matrix. The utilization of a low-stiffness matrix would be suitable for linear actuators, since it must merely work as an ionic resorvoir. A stiffer matrix can be useful for bending actuators, in which the matrix would possess also a structural function. Computer simulations of this kind of composite structure have atready given favorable indications of their effectiveness [ 21 ].

Acknowledgements The software for the driving of servo-controller and potentiostat and for the acquisition of collected data has been implemented by Massimo Solari (Biotech, Italy). We thank Dr R.H, Baughman from Allied Signal Inc., USA, Professor A. Frediani and DrM. Chiarelli, from the Aerospace Department of the University of Pisa, for the stimulating discussions and useful suggestions. This work has been partially supported by the Italian Space Agency, under Grant ASI 1992 RS 121.

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