Voltage attenuation along the electrodes of ionic polymer metal composites

Introduction

Ionic polymer metal composites (IPMCs) are electroactive materials that are composed of an ionomeric membrane sandwiched between two metal electrodes (Jo et al., 2013; Shahinpoor and Kim, 2001). A modest voltage applied across the metal electrodes causes remarkable mechanical deformation, and, in turn, an imposed mechanical deformation induces a measurable voltage difference across the electrodes (Jo et al., 2013; Shahinpoor and Kim, 2001). Due to these features, IPMCs are gaining momentum as actuators (Najemet al., 2012; Xiao et al., 2014), sensors (Brunetto et al., 2011; Chen et al., 2007), and energy harvesters (Cha et al., 2013b; Tiwari and Kim, 2013).

A variety of manageable equivalent circuit models have been proposed in the literature to support the use of IPMCs across a wide range of applications (Aureli and Porfiri, 2013; Bao et al., 2002; Bonomo et al., 2006; Chen et al., 2007; Kanno et al., 1995; Paquette et al., 2003; Porfiri, 2008; Punning et al., 2007; Shahinpoor and Kim, 2000). Such models can offer important insight into IPMC chemoelectromechanical behavior, greatly assist in the design of new IPMC-based devices, and support the refinement of new fabrication methods.

While the circuit models proposed by many authors (Bao et al., 2002; Bonomo et al., 2006; Kanno et al., 1995; Paquette et al., 2003; Punning et al., 2009, 2007; Shahinpoor and Kim, 2000) are based on phenomenological observations of IPMC response, the models established in Aureli and Porfiri (2013), Cha et al. (2013a), Chen et al. (2007), and Porfiri (2008) are derived from rigorous physics-based models of IPMC chemoelectromechanical behavior. Specifically, in Cha et al. (2013a), we have put forward a new physics-based distributed linear circuit model derived from the solution of a Poisson-Nernst-Planck system. The framework incorporates “composite layers” to describe the effect of metal particles between the ionomer and the metal electrodes (Tiwari and Kim, 2010; Wang et al., 2007) on charge transport within the IPMC. The model has been validated through a series of experiments on the impedance of patterned IPMCs, measured by systematically varying the portion of the electrode surface covered by external electrodes.

Here, we adapt the model proposed in Cha et al. (2013a) to study voltage attenuation along the length of an IPMC. We specifically seek to understand and predict electric losses associated with the electrode surface resistance. Our study shares similarities with Punning et al. (2009, 2007), where voltage attenuation was studied using a distributed circuit model consisting only of resistances and capacitances. Different from Punning et al. (2009, 2007), our model considers the effect of a Warburg impedance along the IPMC thickness, which is associated with the presence of composite layers. We experimentally and theoretically investigate IPMC response to both voltage step and sinusoidal inputs to elucidate the phenomenon of voltage attenuation across a wide frequency range.

Materials and methods

The IPMC sample used in the experiment is fabricated in-house from Nafion membrane N117 through electroless chemical reduction with one cycle of secondary platinum plating (Kim and Shahinpoor, 2003; Shahinpoor and Mojarrad, 2000). After fabrication, the sample is stored in a sodium chloride solution to promote counterion exchange. The IPMC is 13mm wide and 50mm long ( L = 50 mm ) with a nominal thickness of 0.2mm, see Figure 1(a).

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Figure 1.

(a) IPMC sample in a Petri dish and (b) schematic of fixtures and copper electrodes for measuring voltage attenuation along the IPMC.

We characterize the IPMC impedance using the “AC Impedance” technique on a CH Instruments 760D potentiostat (Cha et al., 2012). In the impedance measurement, the IPMC is fully covered by copper electrodes. We use a Fluke 175 true RMS digital multimeter to measure the IPMC surface resistance – for further details see Cha et al. (2013a).

To measure the surface voltage attenuation across the IPMC electrodes, we realize two dedicated fixtures from ABS plastic using a Stratasys Dimension Elite 3D printer. Copper electrodes with surface dimensions 1 . 7 × 13 m m 2 are embedded in each fixture at x = 0 , L / 4 , L / 2 , 3 L / 4 , and L, see Figure 1(b). We apply an input voltage V i ( t ) across the outermost pair of electrodes as a function of time t. We consider two inputs at x = 0 , namely: i) a step input of 1V and ii) a sinusoidal input of amplitude 1V and varying frequency f from 1 to 10Hz with a step of 1 Hz . The former is generated using the potentiostat, and the latter through an Agilent 33210A function generator with a power amplifier Kenwood KAC-6202. We measure the voltage across each pair of copper electrodes, V s ( x , t ) , using a National Instruments data acquisition (DAQ) board 9229 with a sampling rate of 1 . 613 kHz . We consider only the four electrode pairs at x = 0 , L / 4 , L / 2 , and L, since the DAQ board can measure four signals in total. We note that V s ( 0 , t ) = V i ( t ) . During the experiments, the IPMC is immersed in a tank with dimension of 406 × 210 × 274 m m 3 , filled with tap water at room temperature. The measurement uncertainty from the DAQ board is within ±1%, due to internal gains and offset errors.

Results and discussion

Figure 2 displays the voltage measured across the four electrode pairs for both the step and the sinusoidal inputs. Similar to Punning et al. (2007), we observe a remarkable attenuation of the voltage along the IPMC span. For the step response shown in Figure 2(a), the voltage after 1s reaches 79, 62, and 51% of the input voltage at x = L / 4 , L / 2 , and L, respectively. In addition to amplitude attenuation, Figure 2(b) displays a marked phase shift in the voltage signal, whereby we find that the voltage lags 31, 53, and 94 ∘ at x = L / 4 , L / 2 , and L with respect to the input signal, respectively.

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Figure 2.

Voltage across the IPMC electrodes produced by a (a) step input and (b) sinusoidal input at 10Hz. Black, red, green, and blue colors refer to x = 0 , L / 4 , L / 2 , and L, respectively. Solid and dashed lines indicate experimental results and theoretical predictions, respectively.

To predict the voltage across the electrodes as a function of x and t, we adapt the distributed circuit model proposed in Cha et al. (2013a). Therein, each element across the IPMC length is described as a two-port T network, in which the line elements correspond to the surface resistance and the through-the-thickness impedance consists of a resistance associated with charge transport in the ionomer, a capacitance related to the electrical double layers, and a Warburg impedance modeling charge diffusion in the composite layers (Cha et al., 2013a).

By specializing the analytical solution established in Cha et al. (2013a) to V s ( 0 , t ) = V i ( t ) and open-circuit boundary condition at x = L , the voltage across the electrodes in the Laplace domain becomes

where L [ · ] is the unilateral Laplace transform, s is the Laplace complex variable, r s is the electrode surface resistance per unit IPMC length, and z ( s ) is the through-the-thickness impedance per unit IPMC length. We comment that r s includes the surface resistances from the both the electrodes. The through-the-thickness impedance can be written as 1 + rw s + r γ s w s + γ s , where r is the through-the-thickness resistance per unit IPMC length, γ is the capacitance per unit IPMC length, and w is the Warburg impedance per unit IPMC length. Following Cha et al. (2013a), the circuit parameters are identified by separately measuring the surface resistance and the overall through-the-thickness impedance (covering the whole IPMC electrodes) as r s = 5875 Ω m − 1 , r = 0 . 171 Ω m , γ = 0 . 00696 F m − 1 , and w = 0 . 103 s 1 / 2 Ω − 1 m − 1 .

The temporal evolution of the voltage is obtained by numerically evaluating the inverse Laplace transform of Eq. (1) using Mathematica (www.wolfram.com) for the considered voltage inputs. Theoretical predictions in Figure 2 are in good agreement with experimental observations. The limited discrepancy between experiments and theoretical findings may be due to the fact that both the through-the-thickness impedance and surface resistance are taken as constant, independent of x.

To further elaborate on the accuracy of the model, in Figure 3 we display the transfer function L [ V s ] ( x , s ) / L [ V i ] ( s ) in the frequency domain by setting s = I ( 2 π f ) , where I is the imaginary unit. As the frequency of the input voltage increases, the magnitude of the transfer function decreases and the phase lag increases for every value of x. The dependence of the voltage attenuation on the frequency should be related to the frequency dependence of the through-the-thickness impedance. Specifically, as the frequency increases the reactive part of the through-the-thickness impedance decreases, resulting into a robust decrease of the impedance magnitude (Cha et al., 2012, 2013a; Farinholt and Leo, 2008). Such a decrease results in an increase in the current through the thickness of the IPMC, which ultimately magnifies the losses on the IPMC electrodes. Theoretical predictions in Figure 3 successfully anticipate the frequency dependence of the transfer function for all values of x.

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Figure 3.

Transfer function ((a) magnitude and (b) phase) of L [ V s ] ( x , s ) / L [ V i ] ( s ) . Red, green and blue colors refer to x = L / 4 , L / 2 , and L, respectively. Markers and dashed lines indicate experimental results and theoretical predictions, respectively.

To assess the individual role of each of the elements in the distributed circuit model, we perform a sensitivity analysis on the magnitude of the transfer function at 10 Hz and x = L by increasing each of the nominal values of the circuit elements by 10%. When the surface resistance r s increases by 10%, the magnitude decreases by 16%, while a 10% increase in the through-the-thickness resistance r causes a modest increase of only 1%. By increasing the capacitance γ and Warburg impedance w, the magnitude of the frequency response is reduced by 4% and 11%, respectively. This analysis suggests that the surface resistance is the most influential parameter on voltage attenuation, followed by the Warburg impedance. Both these quantities can be controlled during IPMC fabrication, by adjusting the number of plating layers (Cha et al., 2012, 2013a; Onishi et al., 2001) and the electrode composition (Akle and Leo, 2008; Cellini et al., 2015; Yang et al., 2012).

Conclusion

In this note, we have studied electric attenuation along the length of IPMCs. We have demonstrated that a distributed circuit model can predict voltage attenuation for different input voltages across a wide frequency range. The model only requires the measurement of the overall IPMC impedance and the electrode surface resistance, and thus offers a valuable tool in the design of IPMC sensors, actuators, and energy harvesters. Our results indicate that the surface resistance and the Warburg impedance are key determinants of voltage attenuation, suggesting that the fabrication of IPMC actuators should seek to reduce both these parameters.