Electrochemical Impedance Spectroscopy and Electromechanical

J. Phys. Chem. C 2010, 114, 14627–14634

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Electrochemical Impedance Spectroscopy and Electromechanical Behavior of Bucky-Gel Actuators Containing Ionic Liquids Ichiroh Takeuchi,† Kinji Asaka,*,† Kenji Kiyohara,† Takushi Sugino,† Ken Mukai,† and Hyacinthe Randriamahazaka‡ National Institute of AdVanced Industrial Science and Technology (AIST), 1-8-31 Midorigaoka, Ikeda, Osaka 563-8577, Japan, and Interfaces, Traitements, Organisation et Dynamique des Syste`mes (ITODYS), CNRS-UMR 7086, UniVersite´ Paris DiderotsParis 7, Baˆtiment LaVoisier, 15 rue Jean-Antoine de Baı¨f, 75205 Paris Cedex 13, France ReceiVed: March 1, 2010; ReVised Manuscript ReceiVed: June 11, 2010

In this paper, bucky-gel electrodes containing various ionic liquid species were prepared by casting, using “bucky gel”, a gelatinous room-temperature ionic liquid (IL) containing single-walled carbon nanotubes (SWCNT). Their electrochemical impedance responses were measured and analyzed. Also, the electromechanical responses of the actuators composed of two bucky-gel electrodes sandwiching an ionic liquid gel layer were studied by measuring the displacement due to an applied sinusoidal voltage at various frequencies. All impedance data were successfully simulated by the equivalent circuit model of a porous electrode based on the transmission line circuit model. By using the same parameter values of the porous electrode model, the frequency dependence of the strain generated in the bucky-gel actuators can be simulated. On the basis of the experimental and simulation results, the electromechanical responses of the bucky-gel actuator were analyzed by taking into account the electrochemical properties of the bucky-gel electrode. Accordingly, an electromechanical model for a bucky-gel actuator was obtained. Introduction Recently, much attention has been focused on electromechanical polymer actuators, which can be driven by a low voltage. These systems can be used as artificial muscle-like actuators for various biomedical and human-friendly applications.1 In previous papers,2,3 we have reported a dry actuator that can be fabricated simply by layer-by-layer casting, using “bucky gel”,4 a gelatinous room-temperature ionic liquid (IL) containing single-walled carbon nanotubes (SWCNT). Our actuator (the bucky-gel actuator) has a bimorphic configuration with a polymer-supported internal ionic liquid electrolyte layer sandwiched by polymer-supported bucky-gel layers (bucky-gel electrode layers), which allows quick and long-lived operation in air at low applied voltage. In a previous paper,5 we studied both the voltage-current and voltage-displacement characteristics of a bucky-gel actuator by applying a triangle waveform voltage of various frequencies. In order to describe quantitatively the frequency dependence of the strain generated in the actuator, we proposed an electrochemical equivalent circuit model consisting of the lumped resistance and capacitance of the electrode layer and the lumped resistance of the electrolyte layer. The bucky-gel electrode consists of the dispersed SWCNT as conducting nanoparticles, ILs as electrolytes, and supported polymers as binders. In previous papers,2,3,5 we showed that our actuator bends due to the dimensional changes of the two electrode layers, which are driven by the double-layer charging/discharging of ions to the SWCNT. Hence, in order to explore the electromechanical response of the bucky-gel actuator, it is important to study the electrochemical kinetics * Corresponding author. E-mail: [email protected]. † AIST. ‡ ITODYS.

of the charging/discharging of the ions to the conductive nanoparticles in the electrode layers. In order to study the electrochemical kinetics of electrode containing conductive nanoparticules, the electrochemical impedance spectroscopy (EIS) method is a powerful analysis tool.6-18 The impedance for such electrodes in electrolyte solutions is presented as that of porous electrodes. Levie6,7 first developed a transmission line circuit (TLC) model consisting of the solution resistance and the double-layer capacitance of the porous electrode. After that, many authors proposed modified TLC models for the impedance of porous electrodes on the basis of Levie’s model, considering the effects of pore shape,8 redox reactions at the pore wall,9,10 pore-size distribution,11 and that of the frequency dispersion of the conductivity.12 This model has been applied to electrochemical double-layer capacitors,13-15 dye-sensitized solar cells,16 and lithium ion batteries.17 Bisquert et al.16,18 presented and reviewed the impedance model for porous electrodes. These models have been successfully used to identify the key electric circuit elements determining the functioning of solar cells.18 In this paper, bucky-gel electrodes containing various ionic liquid species were prepared and their impedance responses were measured and analyzed by means of the porous electrode model. Actuators were prepared from the bucky-gel electrodes, and the displacements were measured by applying sinusoidal voltages of various frequencies. The frequency dependence of the displacement responses are discussed in relation with the impedance properties of the bucky-gel electrodes. The electrochemical equivalent circuit of the bucky-gel actuator is discussed on the basis of the impedance analysis. Accordingly, we are able to develop an electrochemical model allowing one to analyze the behavior of these actuators.

10.1021/jp1018185  2010 American Chemical Society Published on Web 08/09/2010

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Figure 1. Chemical structures of ionic liquids used.

Figure 2. Schematic drawing of a bucky-gel actuator.

TABLE 1: Amounts of SWCNT in Bucky-Gel Electrode Layers Prepared for Each Ionic Liquid ionic liquid EMIBF4 BMIBF4 HMIBF4 OMIBF4

wt % (mg) of SWCNT in bucky-gel electrode layers 12 (26.7) 10 (24.3) 9 (26.6) 9 (25.1)

20 (49.1) 20 (49.9) 16 (51.4) 15 (49.2)

27 (70.4) 26 (70.8) 21 (70.4) 20 (69.9)

Experimental Section Materials. ILs used were 1-ethyl-3-methylimidazolium tetrafluoroborate (EMIBF4) (MW ) 198.0 g/mol), 1-butyl-3-methylimidazolium tetrafluoroborate (BMIBF4) (MW ) 226.0 g/mol), 1-hexyl-3-methylimidazolium tetrafluoroborate (HMIBF4) (MW ) 254.1 g/mol), and 1-octyl-3-methylimidazolium tetrafluoroborate (OMIBF4) (MW ) 282.1 g/mol), of which the chemical structures are shown in Figure 1. The ionic liquids were purchased from Fluka and were used as received. SWCNTs (purified HiPco) from Unidym Inc. and polyvinylidene fluoride-cohexafluoropropylene [PVdF(HFP), Kynar Flex2801] from Arkema Chemicals Inc. were used as received without any further purification. Methylpentanone (MP) and propylene carbonate (PC) were purchased from Aldrich, and dimethylacetamide (DMAc) was from Kishida Chemicals Co. Preparation of the Actuator Film. The configuration of our bucky-gel actuator is illustrated in Figure 2. In this paper, bucky-gel electrodes containing four kinds of imidazoliumbased ionic liquids and three kinds of different loads of SWCNT were prepared as summarized in Table 1. In the previous paper,3 it was found that the ball-milling method is very useful for dispersing technique of the highly loaded SWCNTs (22 wt %) in the bucky gel. Mixing in an ultrasonic bath was also effective. The physical mixing methods should trigger the cation-π interaction of the imizadolium cation on the SWCNT surface and make the SWCNTs disperse. In this paper, by using a long-time ultrasonic dispersion technique, the highly loaded SWCNTs up to 27 wt % was homogeneously dispersed in the bucky-gel electrode. In another previous paper,5 seven kinds of ILs were studied for the bucky-gel actuators. The following relation on the generated strains can be read: RMIBF4 > EMITFSI >

Takeuchi et al. ammonium-based ILs. Hence, in this paper, four kinds of RMIBF4 (E, B, H, O) are selected as ILs for electrolytes of the bucky-gel actuators. Typically, the bucky-gel electrode layer consisting of 20 wt % of SWCNT, 48 wt % of EMIBF4, and 32 wt % of PVdF(HFP) was prepared as follows. A mixture of 50 mg of SWCNT, 120 mg (0.6 mmol) of EMIBF4, and 80 mg of PVdF(HFP) in 9 mL of DMAc was dispersed by ultrasonication for more than 24 h. A gelatinous mixture of SWCNT, EMIBF4, and PVdF(HFP) in DMAc was obtained. The casting solution was obtained by mixing 0.6 mmol of an IL (136 mg of BMIBF4, 152 mg of HMIBF4, or 169 mg of OMIBF4) and 80 mg of PVdF(HFP) with different amounts of SWCNT in 9 mL of DMAc, as summarized in Table 1. The electrode layer was fabricated by casting 1.6 mL of the electrolyte solution into a Teflon mold (area 2.5 × 2.5 cm2) and evaporating the solvent. The electrode film obtained was 70-80 µm thick. Gel electrolyte layers were fabricated by casting 0.3 mL of solutions of each IL and PVdF(HFP) (0.5 mmol/100 mg) in a mixture of 1 mL of MP and 300 mg of PC into an aluminum mold (area 2.5 × 2.5 cm2) and evaporating the solvent. The gel electrolyte film obtained was 20-30 µm thick. An actuator film was fabricated by hot-pressing electrode and electrolyte layers that have the same internal IL at 73 °C. The actuator film was 130-145 µm thick, which is less than the sum of those of two electrode and one electrolyte layers, since the thickness of each layer is decreased by hot-pressing. Displacement Measurement. As shown in Figure 2, the actuator experiments were conducted by applying sinusoidal wave voltages to a 10 × 1 mm2 sized actuator strip clipped between two gold disk electrodes; the displacement at a point 5 mm away (free length) from the fixed point was continuously monitored from one side of the actuator strip by using a laser displacement meter (Keyence model LC2100/2220). We used sinusoidal wave voltages of 4 V peak-to-peak amplitude at various frequencies in order to study the frequency dependence of the displacement. A Hokuto Denko potentio/galvanostat model HA-501G with a Yokagawa Electric model FC 200 waveform generator was used to activate the bucky-gel actuator. Electrical parameters were measured simultaneously. The peakto-peak displacement value δ was read from the displacement curve. This was transformed into the strain difference between the two bucky electrode layers (ε) by using the following equation, on the assumption that the cross sections are planar at any position along the actuator; there is no distortion of the cross sections:

ε)2

dδ (L2 + δ2)

(1)

where L is the free length and d is the thickness of the actuator strip. Impedance Measurements. Impedance measurements were made for ionic gel electrolyte layers sandwiched between two 7 mm diameter bucky-gel electrode layers, by using a twoelectrode electrochemical cell (Hosen Co. Ltd.). The impedance spectra were obtained by using Solatron 1260 frequency response analyzer, operating at an applied voltage of 10 mV rms amplitude from 10 mHz to 100 kHz. Equivalent circuit analysis was carried out using electrochemical impedance software (Scribner Associates, Inc.). Measurements were made at a room temperature.

Behavior of Bucky-Gel Actuators

J. Phys. Chem. C, Vol. 114, No. 34, 2010 14629

Figure 3. Complex plane plots of impedance spectra of bucky-gel electrodes consisting of SWCNT, PVdF(HFP), and ILs: (a) EMIBF4, (b) BMIBF4, (c) HMIBF4, and (d) OMIBF4.

Results and Discussion Impedance Spectra. Figure 3 shows the complex plane plots of the impedance of bucky-gel electrodes prepared from various ionic liquids containing different SWCNT contents in the electrode layer. The plots show the measured values and the curves simulated by using the equivalent circuit shown later. From the complex plane plots, the impedance data are found to correspond to a resistance in the high-frequency region, diffusion (Warburg impedance) in the medium-frequency region, and capacitance in the low-frequency region. Following Bisquert’s review,16,18 the results are analyzed in terms of the impedance model for porous electrodes. In our case, the total impedance of the system can be described as the sum of three impedances in series, as shown in Figure 4a, in which Zs represents the solution resistance and Zc describes the contact impedance between the SWCNT layers and the metallic electrode contact. Ze is the impedance of the porous film electrode

that consists of an electron-conductive film, for instance the SWCNT layers, and an ion-conductive pore, as shown in Figure 4b. The bucky-gel actuator has three-layered structure composed of two bucky-gel electrode layers sandwiching one gel electrolyte layer. Hence, two electrode impedances, two contact impedances, and one electrolyte impedance in series should be assumed for the total impedance of the system. However, the complex plane plots shown in Figure 3 shows that the equivalent circuit is composed of three components in series, as shown in Figure 4a. The reason is considered as follows. Two electrode impedances of the buckygel electrode layers are considered to be almost equal to each other and the same is considered for two contact impedances. Therefore, we should not consider additional impedance components but only observe two times of impedance: Ze and Zc. This is not an important issue in this paper. Therefore, we adopt the equivalent circuit as shown in Figure 4a. Ze can be represented by a general distributed equivalent circuit, given in Figure 4c. In the case where the

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Takeuchi et al. F sn-1. In the case of β ) 1, χ3 is a perfect capacitor. From the TLC analysis, the impedance of the porous electrode Ze is given as follows

( )

Ze ) R1

iω ωL

( )

-β/2

coth

iω ωL

β/2

(5)

where R1 ) r1Lp and the characteristic frequency ωL is defined as

ωL )

1 1 ) 2 1/β (r1q3Lp ) (R1Q3)1/β

(6a)

Where Lp is the effective length of the pore and Q3 ) q3Lp. The characteristic time τL is defined as

1 ωL

τL )

(6b)

The impedance behavior described by eq 5 has well-resolved regimes separated by the characteristic frequency ωL. In the high-frequency branch (ω > ωL), eq 5 is

Ze )

( ) R1 Q3

1/2

(iω)-β/2

(7)

The impedance represented by eq 7 is of the Warburg diffusion type and corresponds to a 45° straight line in the complex plane plot. In the low-frequency branch (ω < ωL), eq 5 simplifies to the series combination of two elements: a resistance and the constant phase element at the pore surface Figure 4. Porous electrode model: (a) the total impedance of the system where Zs is the impedance of the gel, Ze that of the porous electrode, and Zc that for the contact between the SWCNT layers and the metal electrode. (b) Schematic drawing of the porous electrode. (c) Equivalent circuit model of the porous electrode consisting of the distributed impedance of the electrolyte in the pore, χ1; that of the electrode, χ2; and that across the pore wall, χ3. (d) Equivalent circuit model of the porous electrode consisting of the distributed resistance of the electrolyte in the pore and the distributed constant phase element. The resistance of the electrode is negligibly small compared to that of the electrolyte in the pore. (e) Equivalent circuit model of the bucky-gel electrode and the gel electrolyte consisting of the resistance of the gel electrolyte layer Rs, the impedance of the porous electrode Ze, the constant phase element Qc, and the resistance Rc for the contact.

impedance of the electron-conductive film is negligible compared to that of the ion-conductive pore, the equivalent circuit can be simplified (Figure 4d). As shown in Figure 4d, the equivalent circuit consists of a distributed resistance of the ion-conductive pore, r1, and a constant phase element, q3. Accordingly, one has

χ1 ) r1

(2)

χ2 ) 0

(3)

χ3 )

1 (iω)-β q3

(4)

where ω ) 2πf is the angular frequency. In eq 4, the exponent β is a number (with 0 < β < 1), and q3 is a constant with dimension

1 1 Ze ) R1 + (iω)-β 3 Q3

(8)

The impedance (eq 8) gives a vertical straight line in the complex plane plot. It can be noted that eq 5 has the same form as the classical space diffusion element.19-21 The space diffusion model is based on the assumption that the structure of the film is homogeneous. However, the impedance formulation obtained is the same as the porous electrode model. On the basis of the classical space diffusion impedance model, a model considering the nonuniformity of the electroactive polymer film was developed and applied to the intercalation electrode and p-doped poly(3,4-ethylenedioxythiophene).22-24 If the impedance of a porous electrode can be described by an equivalent circuit shown in Figure 4d, the total impedance (Figure 4a) contains two characteristic time constants: τc ) (RcQc)1/βc for the contact (Rc and Qc are the resistance and constant phase element for the contact, respectively), and τL ) (R1Q3)1/β for the ionic diffusion within the pore. Moreover, if the values of τc and τL are very different, then the total impedance can be simplified. Thus, the impedance of the buckygel electrode shown by the complex plane plots in Figure 3 can be represented by the equivalent circuit shown in Figure 4e, where Rs is the ionic resistance of the gel electrolyte layer, Rc the contact resistance, and Qc the constant phase element between the bucky-gel electrode layer and the stainless electrode contact whose impedance is given by 1/Qc(iω)-βc. The semicircles in the complex plane plot in Figure 3 can



TABLE 2: Parameter Values from Curve-Fitting of the Impedance Results Shown in Figure 3 by Using the Equivalent Circuit Described in Figure 4e IL EMIBF4 BMIBF4 HMIBF4 OMIBF4

SWCNT wt %

Rs/Ω

R1/Ω

ωL/rad s-1

β

Q3/mF

Rc/Ω

Qc/µF sn-1

βc

10 20 27 10 20 26 9 16 21 9 15 20

23.4 22.7 19.8 42.3 60.3 70.9 131.7 204.1 128.4 161.6 123.9 86.6

14.1 28.1 30.1 23.8 55.9 82.9 78.6 160.1 136.9 155.9 209.2 226.2

23.76 7.05 3.99 15.81 2.04 1.27 4.01 0.98 0.76 2.10 0.88 0.50

0.92 0.94 0.94 0.96 0.98 0.96 0.94 0.94 0.96 0.96 0.94 0.94

2.99 5.04 8.34 2.65 8.79 9.50 3.17 6.37 9.67 3.06 5.41 8.89

5.9 11.7 3.5 14.0 4.1 9.6 26.7 35.0 13.1 46.7 76.2 71.6

36.3 22.1 28.8 45.5 120.9 45.8 51.7 70.9 157.7 33.9 31.8 22.0

0.86 0.84 0.91 0.81 0.82 0.81 0.82 0.74 0.77 0.83 0.82 0.82

be represented by circuit elements consisting of Rc and Qc. In Figure 3, the complex plane plots show the depressed semicircles, since the contact impedance is represented by the constant phase element. By fitting the experimental data shown in Figure 3, using the equivalent circuit shown in Figure 4e, we obtained the results for the parameters of the equivalent circuit, summarized in Table 2. The simulated curves are shown in Figure 3. In all cases, simulated curves and experimental points are in good agreement with each other. The salient points reported in Table 2 are as follows: 1. All values of the parameter β are almost 1. This result means that the distributed parameter of the constant phase element q3 of the pore surface is almost a perfect capacitance. 2. The value of ωL decreases with increasing SWCNT content in the electrode layer and decreasing conductivity of the ionic

liquid used. From eq 6a, ωL is inversely proportional to the resistance in the pore and the square of the pore length. As the SWCNT content in the electrode layer increases, the length of the pore increases. The electrical resistance in the pore increases as the conductivity of the ionic liquid therein decreases. Furthermore, some specific interactions involving ILs and SWCNT may occur. Both effects result in a decrease in the value of ωL from eq 6a. 3. The value of R1 increases with decreasing conductivity of the ionic liquid used. R1 is proportional to the electrode resistance in the pore and its length. 4. The values of βc of the constant phase element at the boundary between the bucky-gel electrode layer and the stainless electrode contact are 0.8-0.9. Displacement Responses. Figure 5 shows the frequency dependence of the strain ε of the bucky-gel actuators when

Figure 5. Frequency dependence of strain in bucky-gel actuators containing EMIBF4 (a), BMIBF4 (b), HMIBF4 (c), and OMIBF4 (d). Simulated curves are calculated using eqs 9-13 with the parameter values summarized in Table 2 except the values of ε0. The values of ε0 used are 0.33% (SWCNT: 12%), 0.56% (20%), 0.56% (27%) for EMIBF4; 0.35% (10%), 0.50% (20%), 0.56% (26%) for BMIBF4; 0.56% (9%), 0.57% (16%), 0.57% (21%) for HMIBF4; and 0.44% (9%), 0.55% (15%), 0.57% (20%) for OMIBF4.

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Takeuchi et al.

Θ(f ) ) Θ0 Figure 6. Equivalent circuit in the low-frequency range with R being the resistance and C being the capacitance.

sinusoidal voltages are applied. In all cases, the strain decreases as the frequency increases. Here, we propose that the electrochemical kinetics, as shown by the impedance analysis of the bucky-gel electrode, determine the frequency dependence of the displacement. The equivalent circuit (Figure 4d) is used to simulate this frequency dependence of the displacement (Figure 5). Here, the strain is assumed to be proportional to the induced charge in the bucky-gel electrode

ε(f ) Θ(f ) ) ε0 Θ0

(9)

where ε0 is the strain generated at low-frequency limit, Θ(f ) an induced charge at a frequency, f, and Θ0 an induced charge at the low-frequency limit. Indeed, the equivalent circuit elements Qc and Rc in Figure 4e do not contribute to the frequency dependence of the strain in the actuator shown in Figure 5, since the characteristic frequency associated with Qc and Rc is very high (more than 10 kHz) compared to the frequency range discussed in Figure 5. Hence, the contributed circuit elements that determine the frequency dependence of the strain are Ze and Rs. Then, the induced charge Θ(f ) can be calculated with a simple equivalent circuit consisting of the series capacitance, C, and a resistance, R (Figure 6). The following relation holds between two equivalent circuit parameters shown in Figure 4e and Figure 6:

Rs + Ze + iZe′′ ) R -

1 iωC

(10)

where Ze′ and Ze′′ are the real and imaginary components of Ze. When a sinusoidal voltage is applied to the equivalent C-R circuit (Figure 6), the induced charge Θ(f) is given by the following relation

Θ(f ) )

E ω√Z′2 + Z′′2

(11)

where E is the amplitude of the applied sinusoidal voltage and

Z ) R ) Rs + Ze′ Z )

1 ) Ze′′ ωC

(12)

(13)

When ω f 0, Z′ ) Rs + 1/3R1 and Z′′ ) 1/ωQ3; hence,

Θ0 ) Q3E From eqs 11 and 14, we obtain the following relation:

(14)

1 Q3ω√Z′2 + Z′′2

(15)

By using eqs 9-15 with the parameter values summarized in Table 2, we can simulate the frequency dependence of the strain. The simulated curves are shown together with the experimental points. We found good agreement for all data. In the previous paper,5 we reported that the frequency dependence of the strain in the bucky-gel actuator could be simulated by the ionic resistance, the lumped capacitance, and the lumped resistance. In this paper, we find that it can be simulated by the ionic resistance of the gel electrolyte layer and the Warburg impedance, i.e., essentially the transmission line equivalent circuit model consisting of the distributed double layer capacitance between an electrode pore wall and the electrolyte in the pore and the ionic resistance in the pore, as shown in Figure 4b-d. The TLC model for the bucky-gel actuator proposed in this paper reflects the structure of the bucky-gel electrode more exactly than the model proposed in the previous paper.5 Hence, the empirical model for the kinetics of the bucky-gel actuator proposed in the previous paper is replaced by the physics-based model proposed in this paper. At this stage, it is interesting to discuss the capacitance for an equivalent circuit consisting of a capacitance C and resistance R in series in terms of a more general aspect. The current i for an equivalent circuit consisting of a capacitance C and resistance R in series is given by

{

(

i ) CV 1 - exp -

t RC

)}

(16)

where V is the scan rate (V ) dE/dt, where E is the potential or voltage and t is the time; in general, the capacitance C and the resistance R are frequency dependent). By introducing a time characteristic parameter τ, with τ ) RC, one has

{

( τt )}

{

( )}

i ) CV 1 - exp -

(17a)

or

i t ) C 1 - exp V τ

(17b)

On the basis of the definition of the current (i ) dΘ/dt) and the scan rate (V ) dE/dt), eq 17b can be rewritten as

{

dΘ t ) C 1 - exp dE τ

( )}

(18)

Equation 18 shows clearly that the electrical response depends upon the time scale (or frequency). Accordingly, we have two limiting cases. At a long time scale or the low-frequency range (τ , t), one has

dΘ ) C0 dE

(19)

On the other hand, the following equation is obtained at a short time scale or high frequency (τ . t)



dΘ )0 dE

(20)

Accordingly, eq 18 can be viewed as the frequency-dependent capacitance C(f), called the effective capacitance. Thus, we can rewrite eq 18 as

C(f ) ) C0 f

( ){

t t 1 - exp τ1 τ

( )}

(21)

Also, eq 21 describes clearly the influence of the time characteristic parameters τ and τ1 on the effective capacitance C(f ). τ is a characteristic time due to an ionic migration and diffusion, and τ1 is due to an ionic diffusion. In order to improve the effective capacitance C(f ), we must decrease τ by minimizing R. According to eq 9, the strain ε is proportional to the induced charge. From a thermodynamic point of view, the capacitance represents the ability of the system to store energy, and the resistance dissipates energy. Then, eq 9 can be rewritten as

ε(f ) C(f ) ) ε0 C0

(22)

and we obtain

ε(f ) ) ε0

( ){

C(f ) t t ) ε0 f 1 - exp C0 τ1 τ

( )}

(23)

Equation 23 shows clearly the influence of the time constant τ on the stain ε(f). One observes that the dynamic response is mainly controlled by the time constant τ, whereas the static response is governed by ε0 (or C0). In other words, eq 23 describes not only the dynamic responses (statics versus dynamics) but also the thermodynamic properties (energy storage versus energy dissipation). As shown in Figure 5, the strain in the bucky-gel actuator increases as the frequency decreases and reaches constant values at the low-frequency limit. We found that the characteristic frequency, where the frequency dependence of the strain changes, corresponds to the same value as that of the impedance response ωL. At frequencies higher than ωL, we found that the impedance response of the bucky-gel electrode indicates Warburg diffusion. In this range charging does not take place on the entire SWCNT surface. The area of the charged surface decreases as the frequency increases. As a result, the strain also decreases, since it is proportional to the induced charge in the electrode. When the frequency is lower than ωL, the impedance is perfectly capacitive. This trend means that charging takes place on all these SWCNT surfaces. Hence, the strain is constant irrespective of the frequency. As mentioned previously, the parameter ωL is inversely proportional to a square of the thickness Lp2 and the resistance of the pore R1. Lp increases with the SWCNT content. The resistance of the pore depends on the ion conductivity of the IL. Hence, the frequency response of the bucky-gel actuator shown in Figure 5 depends on the SWCNT content in the electrode layer and the IL conductivity. As mentioned before, the constant phase element Q3 is an almost perfect capacitor. Hence, we calculated Q3 as the perfect capacitance from the characteristic frequency ωL and the pore resistance R1 by assuming that β ) 1. The results are shown in

Table 2. The capacitance increases with the SWCNT content of the electrode layer. The strain is proportional to the capacitance. The proposed model suggests that not only the ionic conductivity in the gel electrolyte layer but also in the pores of the electrode layer affects the response of the bucky-gel actuator. Also, the pore structure of the electrode layer affects its response. The pore structure and the ionic resistance in the pores of the electrode layer depend on various factors, such as its preparation, the species of ionic liquids used, nanocarbons used, etc. From a practical point of view, the model indicates that the performance of the actuator may be improved by increasing the low-frequency capacitance C0 and by lowering the time constant τ. Since τ depends on the thickness, decreasing film thickness may improve performance. We are now conducting research into the improvement of the response of the bucky-gel actuator by using the electromechanical model reported in this paper. We will report these results in a future paper. Conclusions In this paper, bucky-gel electrodes containing various ionic liquid species were prepared. Their electrochemical impedance responses were measured and analyzed in terms of the impedance model for porous electrodes. All the impedance data were successfully simulated by the equivalent circuit model based on the transmission line circuit model. The displacements of the actuators in response to sinusoidal voltages applied at various frequencies were analyzed. By analyzing both the electrochemical and electromechanical responses of the bucky-gel actuator we have developed an electromechanical model that takes into account both the static and dynamic properties. By using the same parameter values of the porous electrode, the results of the frequency dependence of the strain of the bucky-gel actuators can be simulated. The proposed model suggests that not only the ionic conductivity in the gel electrolyte layer but also in the pore of the electrode layer affects the response of the buckygel actuator. Also, the pore structure of the electrode layer affects its response. Acknowledgment. K.A. acknowledges Iketani Science and Technology Foundation for the financial support for the part of this work. The authors are particularly grateful to Dr. J. S. Lomas (ITODYS, University Paris 7) who kindly revised our text. References and Notes (1) Carpi, F.; Smela, E. (Eds.) Biomedical Applications of ElectroactiVe Polymer Actuators; Wiley and Sons, Ltd.: Chichester, UK, 2009. (2) Fukushima, T.; Asaka, K.; Kosaka, A.; Aida, T. Angew. Chem., Int. Ed. 2005, 44, 2410–2413. (3) Mukai, K.; Asaka, K.; Kiyohara, K.; Sugino, T.; Takeuchi, I.; Fukushima, T.; Aida, T. Electrochim. Acta 2008, 53, 5555–5562. (4) Fukushima, T.; Kosaka, A.; Ishimura, Y.; Yamamoto, T.; Takigawa, T.; Ishii, N.; Aida, T. Science 2003, 300, 2072–2074. (5) Takeuchi, I.; Asaka, K.; Kiyohara, K.; Sugino, T.; Terasawa, N.; Mukai, K.; Fukushima, T.; Aida, T. Electrochim. Acta 2009, 54, 1762– 1768. (6) de Levie, R. Electrochim. Acta 1963, 8, 751–780. (7) de Levie, R. Electrochim. Acta 1964, 9, 1231–1245. (8) Candy, J.-P.; Fouilloux, P. Electrochim. Acta 1981, 26, 1029–1034. (9) Paasch, G.; Micka, K.; Gersdorf, P. Electrochim. Acta 1993, 38, 2653–2662. (10) Bisquert, J.; Garcia-Belmonte, G.; Fabregat-Santiago, F.; Ferriols, N. S.; M.Yamashita, M.; Pereira, E. C. Electrochem. Commun. 2000, 2, 601–605. (11) Song, H.-K.; Jung, Y.-H.; Lee, K.-H.; Dao, K. H. Electrochim. Acta 1999, 44, 3513–3519.

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JP1018185

Electrochemical Impedance Spectroscopy and Electromechanical

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