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Electrochimica Acta 60 (2012) 177– 183

Contents lists available at SciVerse ScienceDirect

Electrochimica Acta

jou rn al hom epa ge: www.elsev ier .com/ locate /e lec tac ta

apacitive and faradic charge components in high-speed carbon nanotubectuator

ablo Giméneza, Ken Mukaib, Kinji Asakab, Kenji Hatac, Hideaki Oiked, T.F. Oteroa,∗

Center for Electrochemistry and Intelligent Materials (CEMI), ETSII, Universidad Politécnica de Cartagena, Paseo Alfonso XIII, Aulario II, 30203 Cartagena, SpainHealth Research Institute, National Institute of Advanced Industrial Science and Technology (AIST), 1-8-31 Midorigaoka, Ikeda, Osaka 563-8577, JapanNanotube Research Center, National Institute of Advanced Industrial Science and Technology (AIST), Central 5, 1-1-1 Higashi, Tsukuba, Ibaraki 305-8565, JapanDepartment of Organic and Polymer Materials Chemistry, Tokyo University of Agriculture and Technology, 2-24-16 Nakacho, Koganei, Tokyo 184-8588, Japan

r t i c l e i n f o

rticle history:eceived 1 September 2011eceived in revised form 8 November 2011ccepted 8 November 2011vailable online 18 November 2011

eywords:arbon nanotubeshronoamperogramstretched exponentialapacitive chargearadic charge

a b s t r a c t

When submitted to square-wave potentials of ±2 V, single-walled carbon nanotube films with an ionicliquid, taking part of an actuator, show high-frequency electromechanical responses (up to 100 Hz), withanodic current evolutions showing two maxima. Similar anodic chronoamperometric responses havebeen obtained from films of conducting polymers exchanging balancing anions with the electrolyte dur-ing reaction, being described by two stretched exponential functions deduced on physico-chemical bases:oxidation under nucleation–relaxation structural control and oxidation/swelling completion under dif-fusion control. Now by adding a third stretched function, describing a greater contribution now of thecharge of the electrical double layer, a good mathematical fit of the chronoamperometric response ofthe carbon nanotube films was carried out. By recovering the original physico-chemical meaning of theelectrochemical stretched functions, capacitive and structural faradic components of the chronoampero-metric charge were quantified as a function of the applied frequency (1–10 Hz). The capacitive component

of the charge ranges with frequency between 8.6% and 12.2% of the involved charge. The faradic (reac-tive) component ranges between 91.4% and 87.8%, being the main contributor to the volume variationsin the actuating films. The order of magnitude of the diffusion coefficients was 10−6 cm2 s−1, in goodagreement with the fast response of the reactive actuators constructed with those materials. A good sep-aration of capacitive and faradic components will allow a better design of electrochemical applicationsof single-walled carbon nanotube films.

. Introduction

Recently, much attention has been focused on electromechani-al polymer actuators, which can work quickly and softly driveny low voltage, and thus can be used as artificial muscle-likectuators for various bio-medical and human friendly applications1]. In previous papers [2,3], we reported the dry actuator thatan be fabricated simply by layer-by-layer casting, using ‘buckyel’ [4], a gelatinous room-temperature ionic liquid (IL) contain-ng single-walled carbon nanotubes (SWNTs). Our actuator (theucky-gel actuator) has a bimorph configuration with a polymer-upported internal ionic liquid electrolyte layer sandwiched byolymer-supported ‘bucky gel’ layer (bucky-gel electrode layer),

hich allows large and long-lived operation in air at low applied

oltage.

∗ Corresponding author. Tel.: +34 968 325519; fax: +34 968 325433.E-mail address: toribio.fotero@upct.es (T.F. Otero).

013-4686/$ – see front matter © 2011 Elsevier Ltd. All rights reserved.oi:10.1016/j.electacta.2011.11.032

© 2011 Elsevier Ltd. All rights reserved.

The supporting polymer has been utilized to provide materi-als with an easy fabricating property and a structural stability.On the other hand, an insulating property of the supporting poly-mer results in a lowering of electric conductivity. The supportingpolymer itself prevents a movement of ions in the electrode andthe electrolyte layers. Those issues could suppress the originalperformance of SWNT actuators: moving ions are responsible forstructural swelling/shrinking processes in the SWNT films originat-ing the macroscopic bending movement of the actuator.

In a previous paper [5], we reported that a freestanding elec-trode film can be made from ‘bucky-gel’ without any supportingpolymers by using ‘supergrowth’ millimeter-long single-walledcarbon nanotubes (SG-SWNTs), which were synthesized by awater-assisted chemical vapour deposition ‘supergrowth’ method[6]. The uniquely large dimension of SG-SWNTs is supposed toenhance the entanglements of carbon nanotubes, which contribute

to the successful fabrication of the freestanding electrode films bysupporting fast swelling/shrinking volume changes under anodicor cathodic current flow. With this electrode film in hand, we havedeveloped a high-performance bimorph actuator that shows in air a

1 himica Acta 60 (2012) 177– 183

votoc(gca(ccftaib

twcrstpcetarliavbpirtpab

2

2

owarbbC(d

2

cU((

Fig. 1. Experimental three-layered actuator composed of the two SG-SWNT elec-trodes sandwiching an electrolyte layer (PVdF/EMITFSI), one electrode connectedto the working electrode and the second to the counter electrode terminal of thepotentiostat. The electrolyte film of PVdF/EMITFSI is longer than the two electrodesand is connected to a silver film through the PVdF/EMITFSI/AgTFSI electrolyte: this

78 P. Giménez et al. / Electroc

ery large bending motion in quick response under high-frequency,ver 100 Hz, applied square-wave voltage of ±2 V. We concludedhat this quick response can be achieved by the contribution ofxidation-reduction (redox) reaction of SWNTs in addition to theapacitive charging/discharging process of the electric double layerEDL) around the dispersed conductive nano-particles in the bucky-el electrode layers [7]. The capacitive component related to theharge of the EDL has been considered to be the key factor ofctuating and charge storage devices based on carbon nanotubeCNT) in the literature [8,9]. Here, we try to clarify if the electro-hemical response, origin of the mechanical actuating properties,an be fitted by a capacitive describing function or if a mixture ofaradic and capacitive functions should fit better the experimen-al results. A good separation of the charge components will allow

better understanding of the electrochemical responses support-ng the technological improvement of actuators, supercapacitors,atteries, membranes and other devices based on SWNTs.

In this paper, we further analyze the electric current responses ofhe SG-SWNT films from bimorph actuators to consecutive square-ave voltages of various frequency, in order to decompose the

ontribution of the charge components. The chronoamperomet-ic responses of the SG-SWNT bimorph actuators submitted toquare-wave voltage of ±2 V are similar (requiring a shorter time)o those obtained for the potentiostatic oxidation of conductingolymers [10–15], historically named “anomalous electrochemi-al results”, “memory effect”, “relaxation effect” or “asymmetricffect”. Based on physico-chemical principles, a theoretical equa-ion, constituted of two stretched exponential functions, wasttained allowing a good description of the chronoamperometricesults from conducting polymers by the electrochemically stimu-ated conformational relaxation, ESCR, model [16–20]. This modelncludes quantitative expressions of the conformational relaxationnd conformational compaction structural processes, which driveolume variations (swelling and shrinking) and actuation. Here,y using those stretched exponential functions and its structuralhysico-chemical background, we will try to develop a theoret-

cal description and quantification of the chronoamperometricesponses and its components from SG-SWNT bimorph actua-ors. Mathematical stretched exponential functions (without anyhysico-chemical background) have been used in literature to fit

range of relaxation behaviors in disordered and non-equilibriumiological and physical systems [21–24].

. Experimental

.1. Materials

Long (millimeter-scale) SG-SWNTs were supplied by Nan-tube Research Center, AIST, which were synthesized byater-assisted chemical vapor deposition, ‘supergrowth’ method,

s reported elsewhere [6]. Other reagents were used aseceived from Sigma–Aldrich Co. (1-ethyl-3-methylimidazoliumis(trifluoromethanesulfonyl) imide (EMITFSI), propylene car-onate (PC), and methyl isobutyl ketone (MIBK)), Arkemahemicals Inc. (poly (vinylidene fluoride-co-hexafluoropropylene)PVdF-HFP):Kynar Flex 2801®), Kishida Chemicals Co. (N,N-imethylacetamide (DMAc)).

.2. Preparation of the SWNT electrode film

A mixture of the SG-SWNTs (15 mg) in DMAc (3 mL) was soni-

ated for 10 min using a horn-type ultrasonic probe (a Nissei modelS-50 ultrasonic generator, 28 kHz, 50 W), and diluted with DMAc

6 mL), and then an aliquot (1 mL) was cast on a Teflon mold10 mm × 25 mm), which was heated at 50 ◦C and allowed to dry

is a Ag/Ag+ reference electrode, being connected to the reference electrode termi-nal of the potentiostat. The evolution of the working electrode potential is followedduring electrochemical control of the three layers actuator.

the solvent for one day. And then, a portion (1 mL) of a mixtureof EMITFSI (30 mg) in DMAc (9 mL) was cast, which was heated at50 ◦C and allowed to dry the solvent for one day. Then, the electrodefilm was dried to remove the trace solvent (DMAc) under reducedpressure at 80 ◦C for three days, thus affording an electrode film.The thickness of the electrode film was 17 �m.

2.3. Preparation of electrolyte layer

A mixture of EMITFSI (300 mg), PVdF-HFP (300 mg) and PC(750 mg) in MIBK (9 mL) was stirred overnight at 70 ◦C. Then, a por-tion of the resulting gelatinous mixture was cast on an aluminummold (25 mm × 25 mm) preheated at 35 ◦C for 2 h and heated at80 ◦C for 4 h. Then, the electrolyte film was dried under a reducedpressure at 80 ◦C for 3 days, affording a soft film. The thickness ofthe electrolyte film was 17.5 �m.

2.4. Preparation of the actuator strip for potentiotaticexperiments

Electrolyte film, with dimensions 15 mm × 2 mm width, wassandwiched by 11 mm × 1.5 mm-wide two electrode films, andsubsequently placed between hot-press plates of a screw-typesmall hot-pressing apparatus, heated at 70 ◦C for 3 min, and thenpressed (80 N) for 3 min at the same temperature, to accomplishadherence of the three layers. Finally, actuator strips were trimmedaway 10 mm × 1 mm size. The electrolyte film is longer than bothelectrodes and through a film of PVdF/EMITFSI and 0.1 M Ag TFSIis connected to a Silver film acting as reference electrode (Ag/Ag+).The ensamble is depicted by Fig. 1. This experimental setup allowsto adjust the potential of the working SG-SWNT electrode bysupplying the required current, chronoamperometric response,required by capacitive, or capacitive and faradic, processes duringthe polarization time.

2.5. Characterization

The details of the electric current response of the actuator whenapplying voltages were measured by using potentio/galvanostat(BioLogic Science Instruments model VSP).

3. Results and discussion

Fig. 2a shows five consecutive anodic/cathodic chronoamper-

ometric responses of the SG-SWNT working electrode when theactuator was submitted to ±2 V square-wave voltage at 10 Hz.The anodic branches present two maxima, an unexpected resultfor a capacitive process. The cathodic response only shows one

P. Giménez et al. / Electrochimica

Fig. 2. (a) Five consecutive anodic and cathodic current/time responses of the SG-Sva

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WNT working electrode when the actuator was submitted to ±2 V square-waveoltage at 10 Hz. (b) Current curves of the SG-SWNT actuator during +2 V domain atpplied square-wave voltages from 1 Hz to 10 Hz.

aximum and, after 0.15 s the processes (the current) still goesn. Similar choroamperometric responses could be attributed to aery slow discharge of the EDL or to a film reduction under counte-ion diffusion kinetic control. Fig. 2b shows the stationary, after 30onsecutive cycles, anodic (at +2 V) chronoamperometric responsest different frequencies ranging from 1 Hz to 10 Hz: all the anodicranches show two maxima.

The initial sharp maximum at shorter times than 40 ms can bettributed to a capacitive component: the charge of the electrical

ouble layer, as described in Fig. 3. The second maximum is inde-endent of that of the initial capacitive charge and must be due to

different process. The increase of the current up to the maximum

ig. 3. Anodic chronoamperogram from the SG-SWNT electrode showing the fourinetic controlling processes according to the four processes described by the elec-rochemically stimulated conformational relaxation (ESCR) model for the responsesf conducting polymer films [14,15,17].

Acta 60 (2012) 177– 183 179

is attributed in electrochemistry (electrodeposition) to nucleationprocesses. By analogy with chronoamperometric responses of con-ducting polymers [16,19,20], it can be attributed, in an initialapproach, to the oxidation (reaction (1)) of the nanotubes undernucleation–relaxation kinetic control. The main difference is thatbending movements indicate a prevalent exchange of cations at anypotential: the material swells by reduction and shrinks by oxida-tion:

SG-SWNTn+(TFSI−)n + n(EMI+) + ne

→ SG-SWNT∗(TFSI−)n(EMI+)n (1)

where SG-SWNT* represents the active centers on the neutral car-bon nanotubes, those participating in the oxidation reaction bystoring a positive charge at the end of the oxidation reaction, andTFSI− is the anion attached to the SG-SWNT and EMI + representsthe cation exchanged between the nanotube films and the elec-trolyte for charge balance.

By oxidation, the nanotube salt [SG-SWNTn+ (TFSI−)n] is gener-ated. That means that attraction forces between neighbor swollenreduced structures, SG-SWNT* (TFSI−)n(EMI+)n, are strongest thaninteraction between neighbor oxidized, SG-SWNTn+(TFSI−)n, andshrunken structures. Most toughness reduced structures requiressome time to nucleate the separation–relaxation and confor-mational rearrangement of neighbor SG-SWNT* (TFSI−)n(EMI+)n,structures to allow the expulsion of cations. This could sup-pose a higher order in the reduced material, related to that ofthe oxidized material, to be checked in subsequent studies. Thechronoamperometric responses are similar to those obtained dur-ing oxidation by nucleation–relaxation from films of conductingpolymers [17,25,26]. At the maximum, the nuclei coalesce and theentire geometrical surface is relaxed allowing the coions (cations)to diffuse. The oxidation/shrinking is completed under diffusionkinetic control. Due to the relaxed structure and to the low inter-action between the oxidized, SG-SWNTn+(TFSI−)n, neighbors thereduction–swelling with penetration of cations occurs uniformlyacross the material under diffusion control.

The time ranges of the SG-SWNTs film responses are shorterthan those of conducting polymers films.

3.1. Mathematical fitting, physical and chemical meaning

Based on physico-chemical principles, a theoretical descriptionof the anodic chronoamperometric responses was attained for con-ducting polymers [16,19,20]. The attained function is constitutedby two stretched exponential functions that, being deduced frombasic principles, does not include any adjustable parameter, all thecomponents having well defined physical and chemical meaning.Now those mathematical functions and their physical and chemicalmeaning will be used to adjust and describe processes in SWNTs.The stretched exponential functions have been used for long timein physical and biological science to adjust responses from sys-tem having a distribution of relaxation times due to different localenvironments, local orders or comprising different molecular orstructural lengths or dimensions [21–26].

The general stretched exponential function for electrochemicalresponses involving currents can be described[19,24] as:

I = I0e(−t/�)ı; 0 < ı < 1 (2)

where I is the current, I0 is the initial current, � is a relaxation time,t is the elapsed time, and ı is the stretching coefficient.

It should be noted that when ı = 1, such a fit corresponds to any

part of the chronoamperogram occurring in the absence of con-formational relaxation control [17]. Inside the nanotube’s film thatmeans under diffusion kinetic control of the EMI+ coions. In thatcase, Eq. (2) becomes the current evolution under diffusion kinetic

1 himica Acta 60 (2012) 177– 183

cd

I

wcccso

l

tpc

b

wberswsst

sc

I

Etccasur

(1Tbfo

I

E(wq

k

2

2

Fig. 4. Experimental anodic I/t response when the SG-SWNT electrode was submit-ted to ±2 V square-wave potential at a frequency of 2 Hz. Dotted line: capacitivecharge of the electrical double layer (EDL). Dash-dotted line: oxidation underrelaxation–nucleation kinetic control. Short dotted line: oxidation under diffusion

80 P. Giménez et al. / Electroc

ontrol Id(t) of the charge balance coions inside the SG-SWNT filmeduced by the ESCR model:

d(t) = bQde−b (3)

here Qd is the oxidation charge obtained by integration of thehronoamperometric response, I0 = bQd and � = 1/b. Under thoseonditions (diffusion kinetic control) the oxidation experimentalharge consumed at any oxidation time, t, Q(t) after the potentialtep obtained by integration, until that time, of the chronoamper-gram and the total oxidation charge Qd are related [17] by:

n[

1 − Q (t)Qd

]= −bt (4)

The apparent diffusion coefficient, D, of the coions from the solu-ion across the partially oxidized material from the film oxidationoint of the nanotube in the relaxed structure (dynamic structuralonditions) is included in the coefficient b:

= 2D

h2(5)

here h is the thickness of the SG-SWNT film. The constant b cane obtained (Eq. (4)) by plotting ln [1 − Q(t)/Qd] versus t from thexperimental chronoamperogram; Q(t) is the chronoamperomet-ic experimental charge at the time t after the potential step. Thelope obtained from the linear part corresponding to the regionhere the diffusion is the kinetic controlling process is the con-

tant b. The diffusion coefficient, D, of the coions across the relaxedtructure (diffusion under dynamic structural conditions) duringhe oxidation process is obtained from Eq. (5).

The chronoamperometric responses of conducting polymershowing two maxima are described, as deduced from basic physico-hemical principles [16,17], by the equation:

(t)=2aQrt exp(−at2)+2abQdexp(−bt)

∫ t

0

t′ exp(bt′−at′2)dt′ (6)

q. (6) includes two stretched exponential functions. The firsterm describes the oxidation under nucleation/relaxation kineticontrol, Ir(t). The second term describes the oxidation/shrinkingompletion including coion diffusion kinetic control. After relax-tion completion the structure is open and t′ becomes zero [17]: theecond term becomes Eq. (3), describing the oxidation completionnder diffusion kinetic control at the end of the chronoamperomet-ic response.

The fraction of the charge involved in the sharp initial peakFig. 2b) of the nanotube responses, oxidation times lower than0 ms, can be attributed to the charge of the electrical double layer.he charge evolution of the EDL after potential step to 2 V cane described by a third stretched function [27]. In this way, theunction describing all the processes included in the chronoamper-metric response of SG-SWNT films should become:

(t) = kQEDL exp(−kt) + 2aQrt exp(−at2) + bQde−bt (7)

q. (7) is expected to describe the anodic chronoamperogramsFig. 2b) of the electric response of the SG-SWNT actuators (Fig. 2a)hen submitted to square-wave potentials (±2 V) of different fre-

uencies (Fig. 2). It includes three different components:Charge of the electrical double layer [26]:

QEDL exp(−kt) (8)

Oxidation under nucleation/relaxation control:

aQrt exp(−at2) (9)

Oxidation/shrinking completion:

abQd exp(−bt)

∫ t

0

t′ exp(bt′ − at′2)dt′ (10)

kinetic control of the coions through the nanotube film. Dashed line: simulatedresponse obtained by addition of the three components. Similar fits for (a) 1 Hz, (b)4 Hz (c) 5 Hz, (d) 8.04 Hz, (e) 10 Hz are depicted at the supplementary information.

Eq. (10) becomes Eq. (3) for t′ = 0 that means in absence of thenucleation–relaxation component, or after nucleation–relaxationcompletion.

Coefficients a and b [20] are:

a → a�N0�2

�20 A

exp(−2�H

RT

)(11)

b → b = 2D

h2(5)

� → Length of an elemental segment (average length of the SG-SWNT here).N0 → Number of oxidation nucleus initiated under each definedexperimental condition.�0 → pre-exponential factor of the relaxation time.A → total film area.D → diffusion coefficient.h → film thickness (17.5 �m here).

�H = �H∗ + �Hc − �He → �H = �H∗ + zc�c − zr� (12)

zc → cathodic polarization coefficient (experimental determina-tion): charge consume to compact by electrochemical reduction1 mol of nanotubes.�H* → conformational energy in the absence of external electricfields.�c → cathodic overpotential (−2 V).� → anodic overpotential (2 V).Qr → relaxation charge (obtained below).zr → electrochemical relaxation coefficient (experimental deter-mination): charge required to relax by electrochemical oxidation1 mol of reduced and compacted SWNTs.T → temperature.

Using the MATLAB program we have simulated the differentcomponents of the anodic chronoamperometric response to ±2 Vat a frequency of 2 Hz (Fig. 4). See Supplementary information fordifferent experimental frequencies. For every frequency, QEDL, Qd,

Qr, a, b, k and D were determined.

This approach provides a good fitting of the experimentalresponses from films of SG-SWNTs and ionic liquid (EMITFSI). Theresponse includes the fast charge of the electrical double layers

P. Giménez et al. / Electrochimica Acta 60 (2012) 177– 183 181

Table 1Charges consumed by the three constituent processes obtained by integration ofthe stretched exponential functions at each frequency: QEDL, charge of the electricaldouble layer; Qr, oxidation–relaxation charge; Qd, oxidation–diffusion charge; k, aand b, coefficients of the stretched functions.

Hz QrmC QdmC QEDLmC b s−1 a kcm2 s−1

1 2.60 5.30 0.74 2.49 62.82 36.202 2.46 5.20 0.66 6.93 522.8 122.44 1.90 4.73 0.64 9.42 1976 199.85 1.75 4.43 0.66 14.49 4238 312.9

(Sns

ipicto

3

pdao(

talCtttf(

Fnwt

Fig. 6. Charges consumed for oxidation completion under diffusion kinetic control(Qd) of the coions through the relaxed-open structure of carbon nanotubes as a func-

8.04 1.42 3.93 0.64 19.42 9410 410.810 1.26 3.50 0.66 23.9 13,680 474.8

physical process) and the oxidation (chemical process) of theG-SWNTs. This oxidation includes two terms: oxidation underucleation–relaxation kinetic control and oxidation under diffu-ion kinetic control.

Table 1 shows the three components of the decomposed exper-mental charge. The charge of the electrical double layers, QEDL,resents minor changes with frequency. Lower fractions of packed

nitial structures, require lower relaxation charges and higherharges are consumed to complete the oxidation–swelling (reac-ion (1)) of the SG-SWNTs film under diffusion kinetic control (Qd)f the counterions inside the film.

.2. The relaxation charge, Qr

After separation of the different components of the chronoam-erometric charges consumed by the SG-SWNTs film underifferent frequencies, oxidation–relaxation charges were plottedgainst the applied frequency. Fig. 5 shows an exponential decreasef the attained relaxation charges as a function of the reduction timehalf of the square potential wave).

With increasing frequencies, lower times are available for reduc-ion at −2 V with insertion of charge balance coions (reaction (1)),nd conformational packing of the SG-SWNTs film. The result is aess packed nanotube’s structure at the end of the reduction time.ompaction and relaxation are opposed processes so, charge andime spent after potential step to +2 V to relax the packed struc-ure must decrease at increasing frequencies. As shown in Fig. 5,

he relaxation charge Qr decreases with increasing frequencies (�),ollowing a exponential expression: Qr = 2.10exp(−�/5.83) + 0.89r2 = 0.99). Lower fractions of the film SWNTs having a packed

ig. 5. Charges consumed to relax (Qr) by partial oxidation of the packed reducedanotube structures as a function of the frequencies of the applied ±2 V square-ave potentials. Square symbols are relaxation charges obtained by integration of

he simulated relaxation current. The dashed line is the exponential fit.

tion of the frequencies of the applied ±2 V square-wave potentials. Square symbolsare diffusion charges obtained by integration of the simulated diffusion current. Thedashed line is the linear fit.

structure at increasing frequencies requires, shorter times to berelaxed after potential step to 2 V: the oxidation–relaxation max-imum appears at shorter times (Fig. 2a). The ESCR model gives agood description of the experimental results from SG-SWNT films.

3.3. Oxidation–diffusion charge, Qd

Once the packed structure was relaxed, the oxidation/shrinkingof the open SG-SWNT structure is completed (reaction (1)) underdiffusion kinetic control (Qd) of the balancing coions through therelaxed/open structure towards the new positive charges gener-ated by electron extraction at the active centers of the SG-SWNT.This diffusion charge decreases with increasing frequencies, fol-lowing a linear expression: QD = 5.40 − 0.19�, where � is thefrequency (Hz), as shown in Fig. 6. Lower reduction times at−2 V, for increasing frequencies, give less reduced structures. Thechronoamperometric responses present increasing currents at theend of the polarization time (Fig. 2a). The consequence is that lowercharges are consumed during the subsequent oxidation process, asdepicted by Fig. 6.

3.4. Apparent diffusion coefficients

As stated in Eq. (5), the coefficient, b includes the apparent diffu-sion coefficient of coions during oxidation inside the relaxed stateof the shrinking film of nanotubes. The representation of Eq. (4)from the experimental results obtained at the different studiedfrequencies, the b coefficients were obtained (See Fig. 2, supple-mentary information). Fig. 7a shows a linear variation of b withfrequency, b = 2.50 + 0.70�, r2 = 0.97; b and � dimensions are (s−1).With increasing frequencies, the reduction–packing time is lowerand from less packed initial structures allow a faster diffusion coef-ficient during the subsequent oxidation, as can be seen in Fig. 7b:D = 2.01 + 3.5� (r2 = 0.97).

The attained D (cm2 s−1) values range between 3.81 × 10−6 and36.6 × 10−6 cm2 s−1 are 4 to 3 orders of magnitude higher thanthose obtained from conducting polymer films [20,21,28]. Thosehigh D values indicate the unique combination between carbon

natotubes and the ionic liquid (EMITFSI) being the origin of the fastelectrochemical based devices like actuators and artificial muscles[5,7]. A clarification of the physical origin of those high apparent dif-fusion coefficients for only some mixtures of nanotubes and ionic

182 P. Giménez et al. / Electrochimica Acta 60 (2012) 177– 183

Fig. 7. (a) Calculated b coefficients from the stretched functions for the oxidationcompletion under diffusion kinetic control at different frequencies; (b) diffusioncoefficients, D, of the coions through the relaxation state of the shrinking nanotubefifi

lha

3

umi(

�

Ttpaeb

c

comitant oxidation charges (Table 2). The total theoretical charge(QTh) is obtained by the sum of those three components. Thecharge percentage of the capacitive (%QEDL) and faradic compo-nents, related to the total charge, were obtained and presented in

Table 2Experimental and theoretical charges obtained by the sum of the three theoreti-cal components, together with capacitive and faradic charges at each frequency:QT, total experimental charge; QTh, total theoretical charge obtained by thesum of the three theoretical components: electrical double layer charge (QEDL),oxidation–relaxation charge (QR), and oxidation diffusion charge (QD); %QEDL,percentage of the capacitive component; %QR + QD, percentage of the faradiccomponents.

Hz QTmC QTh (QEDL + QR + QD)mC QR + QDmC %QR + QD %QEDL

1 5.36 8.64 7.9 91.4 8.62 7.15 8.32 7.66 92.1 7.94 5.49 7.27 6.63 91.2 8.8

lm for the oxidation completion at different frequencies. Dashed lines are the linearts.

iquids requires a subsequent study. Similar fast responses alsoave been found with some combinations of conducting polymersnd ionic liquids [11,29–31].

.5. Coefficient a

Eq. (11) describes this coefficient, for experiments performednder constant pressure, as a function of different experimentalagnitudes and the enthalpy variation along the processes. Accord-

ng to the electrochemically stimulated conformational relaxationESCR) model, this enthalpy includes three terms [14,15]:

H = �H∗ + �Hc − �He → �H = �H∗ + zc�c − zr� (12)

he first term, �H*, is a mechanical component. The seconderm, zc�c, is the conformational energy (CV) required to com-act 1 mol of carbon nanotubes by cathodic reduction–packingt the cathodic overpotential of �c. The third term, zr�, is thenergy required to relax 1 mol of packed nanotube conformations

y oxidation–relaxation at the anodic overpotential �.

The second term includes zc (charge required to reduce andompact 1 mol of CNTs). This charge is predicted to increase for

Fig. 8. Square points are calculated a coefficients from the nucleation–relaxationstretched functions at different frequencies for the oxidation initiation, and a dashedcurve is an exponential fit.

rising reduction time, or wait time tw [28], at a constant reductionpotential:

zc = z0c + RT˛

�cln(tw) (13)

Fig. 8 shows that the attained values of the coefficient a forthe oxidation of the SG-SWNTs increases linearly with frequency:a = −3081.18 + 588.42�, (r2 = 0.99). At higher frequencies the reduc-tion potential of −2 V is applied for shorter times (tw): from Eq.(13) lower values of zc are expected. Considering the influence ofzc in Eq. (12), lower values of �H should be obtained giving (Eq.(11)) increasing values of a. As a partial conclusion the ESCR modelalso allow a good qualitative description of the variation of a withfrequency.

In subsequent studies, activation energies and conformationalpacking energies could be calculated for the oxidation SG-SWNTsfilms from chronoampeometric results designed according with theESCR model.

3.6. Capacitive and faradic charges

By integration of the anodic experimental responses (Fig. 3),the total experimental charge (QT) in Table 2, as a function of theapplied frequency (for different oxidation times) is obtained. Thestretched exponential functions describing current components(EDL, relaxation and diffusion) can be integrated giving the con-

5 5.52 6.84 6.18 90.3 9.78.04 4.52 5.99 5.35 89.3 10.7

10 4.06 5.42 4.76 87.8 12.2

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P. Giménez et al. / Electroc

he table. The capacitive percentage ranges between 8.6% and 12.2%nd the faradic component between 91.4% and 87.8%. We can con-lude that, according to the ESCR model, the charge involved inhe anodic branches of the chronoamperometric responses of SG-WNT should be constituted by the capacitive charge of the EDLnd two faradic charges driving structural changes required forhe actuation mechanism: oxidation under nucleation relaxationinetic control and oxidation/shrinking under diffusion kinetic con-rol of the coions trough the shrinking SG-SWNT film.

The described theoretical adjust presents a great potentialityo identify, understand and quantify both physical and chemicalomponents of the chronoamperometric responses. By recoveringhe original electrochemical methodology from the ESCR model17] using a standard three-electrode system, the results of whichill be reported in the next paper, we are now obtaining spe-

ific constants: zc, zr; the conformational energies for structuralhanges and volume increment or volume elimination, �Hc, �Hr;he mechanical component of the energy, �H* for SG-SWNT filmn IL electrolyte by systematic variation of the involved variablestemperature, anodic and cathodic potential for the potential step,re-polarization time or electrolyte concentration). Experimentalesults will be compared with those here attained by mathematicalt. Most of the literature considers that those voltammetric results

rom CNT not showing specific maximums are uncontroversial evi-ences of exclusive capacitive processes [32–35]. In a next papere will show how those materials respond to different concentra-

ions (>0.1 M) of electrolyte or different overpotentials as predictedy electrochemical reaction kinetics giving results that cannot beredicted from usual capacitive models.

. Conclusions

The chronoampeormetric responses of SG-SWNTs films toquare potential waves can be fitted by three stretched exponentialunctions corresponding to: the charge of the EDL, the beginningf the SG-SWNT oxidation under nucleation–relaxation kineticontrol, and the oxidation completion under diffusion control ofalancing coions in the film. Functions and results are concordantith the ESCR model obtained for conducting polymers, keeping

imilar structural meaning for the faradic processes. Capacitiverocesses linked to the charge of EDL consume between 8% and2% of the involved charge. Faradic processes consume between2% and 88% of the involved charge. Despite the presence of com-action and relaxation processes, the mixture SG-SWNTs/EMITFSIrovides apparent diffusion coefficients (under swelling dynamiconditions) ranging from 10−6 to 10−7 cm2 s−1, close to thosef ions and molecules in liquid electrolytes (10−5–10−6 cm2 s−1).hose high diffusion coefficients of the balancing counterionsequired for charge balance of the faradic process support the fastending responses from electrochemomechanical actuators con-tructed using those carbon nanotubes up to voltage frequenciesigher than 100 Hz. In this way, carbon nanotubes must be con-idered as reactive (from an electrochemical point of view) andiomimicking materials. Electric pulses promote faradic reactionsith generation of positive charges, the subsequent restruc-

uration of double bonds that gives conformational movements,harge storage, free volume generation and exchange of coions

or charge balance. Volume changes (electro-chemo-mechanical);harge storage; changes in porosity, storage and delivery of bal-ncing coions, moreover good biocompatibility are switchableiomimetic properties linked to, and controlled by, the consumed

[[[[

Acta 60 (2012) 177– 183 183

charge (the electrochemical reaction). The capacitive componentof the charge should participate as a complementary componentfor charge storage or electro-mechanical properties. A good sep-aration and quantification of capacitive and faradic charges fromSG-SWNTs films will allow most precise designs and technologi-cal development of electrochemical devices as: actuators, batteriesfor fast charge/discharge proposals, smart membranes (of electro-chemical adjustable porosity), smart drug and chemical deliverydevices or electron/ion reactive transducers.

Acknowledgments

We acknowledge financial support from Spanish Government(MCI) Projects MAT2011-24973 and CTQ2007-60459, Seneca Foun-dation Project 08684/PI/08, Consejería de Educación de Murcia, andPlan Regional de Ciencia y Tecnología 2007–2010.

Appendix A. Supplementary data

Supplementary data associated with this article can be found, inthe online version, at doi:10.1016/j.electacta.2011.11.032.

References

[1] F. Carpy, E. Smela, Biomedical Applications of Electroactive Polymer Actuators,1st ed., John Wiley & Sons Ltd., Chichester, 2009.

[2] T. Fukushima, K. Asaka, A. Kosaka, T. Aida, Angew. Chem. Int. Ed. 44 (2005)2410.

[3] K. Mukai, K. Asaka, K. Kiyohara, T. Sugino, I. Takeuchi, T. Fukushima, T. Aida,Electrochim. Acta 53 (2008) 5555.

[4] T. Fukushima, A. Kosaka, Y. Ishimura, T. Yamamoto, T. Takigawa, N. Ishii, T. Aida,Science 300 (2003) 2072.

[5] K. Mukai, K. Asaka, T. Sugino, K. Kiyohora, I. Takeuchi, N. Terasawo, D.N. Futoba,K. Hata, T. Fukushima, T. Aida, Adv. Mater. 21 (2009) 1582.

[6] K. Hata, D.N. Futaba, K. Mizuno, T. Namai, M. Yumura, S. Iijima, Science 306(2004) 1362.

[7] K. Mukai, K. Asaka, K. Hata, T.F. Otero, H. Oike, Electrochim. Acta 17 (2011)10965.

[8] S. Gupta, M. Hughes, A.H. Windle, J. Robertson, J. Appl. Phys. 95 (2004) 2038.[9] G.A. Snook, P. Kao, A.S. Best, J. Power Sources 196 (2011) 1.10] M. Kalaji, L.M. Peter, L.M. Abrantes, J.C. Mesquita, J. Electroanal. Chem. 274

(1989) 289.11] U. Makoto, J. Electrochem. Soc. 141 (1994) 3336.12] C. Odin, M. Nechtschein, Synth. Met. 43 (1991) 2943.13] C. Odin, M. Nechtschein, Synth. Met. 44 (1991) 177.14] Y. Tezuka, K. Aoki, J. Electroanal. Chem. 273 (1989) 161.15] Y. Tezuka, S. Ohyama, T. Ishii, K. Aoki, Bull. Chem. Soc. Jpn. 64 (1991) 2045.16] T.F. Otero, H. Grande, J. Rodriguez, J. Phys. Chem. B 101 (1997) 8525.17] T.F. Otero, H.J. Grande, J. Rodriguez, J. Phys. Chem. B 101 (1997) 3688.18] T.F. Otero, J. Mater. Chem. 19 (2009) 681.19] B.J. West, T.F. Otero, B. Shapiro, E. Smela, J. Phys. Chem. B 113 (2009) 1277.20] T.F. Otero, H. Grande, J. Rodriguez, Synth. Met. 85 (1997) 1077.21] T.F. Otero, J.G. Martinez, J. Solid State Electrochem. 15 (2011) 1169.22] K.C.B. Lee, J. Siegel, S.E.D. Webb, S. Leveque-Fort, M.J. Cole, R. Jones, K. Dowling,

M.J. Lever, P.M.W. French, Biophys. J. 81 (2001) 1265.23] F.D. Lin, Y.J. Wang, M. Lonergan, J. Appl. Phys. 104 (2008).24] A.M. Funston, T.A. Fadeeva, J.F. Wishart, E.W. Castner, J. Phys. Chem. B 111

(2007) 4963.25] T.F. Otero, I. Boyano, M.T. Cortes, G. Vazquez, Electrochim. Acta 49 (2004) 3719.26] T.F. Otero, I. Boyano, Chemphyschem 4 (2003) 868.27] M.H. Holzle, U. Retter, D.M. Kolb, J. Electroanal. Chem. 371 (1994) 101.28] H. Grande, T.F. Otero, Electrochim. Acta 44 (1999) 1893.29] T.N. Shoa, J.D.W. Madden, T. Mirfakhrai, G. Alici, G.M. Spinks, G.G. Wallace, Sens.

Actuators A: Phys. 161 (2010) 127.30] Y. Wu, G. Alici, G.M. Spinks, G.G. Wallace, Synth. Met. 156 (2006) 1017.31] S.W. John, G. Alici, G.M. Spinks, J.D. Madden, G.G. Wallace, Smart Mater. Struct.

18, 085007 (2009).

32] J.N. Barisci, G.G. Wallace, R.H. Baughman, J. Electroanal. Chem. 488 (2000) 92.33] J.N. Barisci, G.G. Wallace, R.H. Baughman, J. Electrochem. Soc. 147 (2000) 4580.34] P.W. Rutz, R. Kotz, A. Wokman, Electrochim. Acta 54 (2009) 4451.35] J.D.W. Madden, J.N. Barisci, P.A. Anquetil, G.M. Spinks, G.G. Wallace, R.H. Baugh-

man, I.W. Hunter, Adv. Mater. 18 (2006) 870.