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Electrochemistry Communications 10 (2008) 190–194

Use of Butler–Volmer treatment to assess the capabilityof the voltammetric ion sensors: Application to a PPy/DBS film

for cations detection

Manuel Cano a, Rafael Rodrıguez-Amaro a, Antonio J. Fernandez Romero b,*

a Department of Physical-Chemistry and Applied Thermodynamics, Universidad de Cordoba, Campus de Rabanales, Edf. C-3, 14014 Cordoba, Spainb Laboratory of Electrochemistry, Intelligent Materials and Devices (CEMI), ETSII, Campus de Alfonso XIII,

Universidad Politecnica de Cartagena, 30203 Cartagena, Spain

Received 19 October 2007; received in revised form 21 November 2007; accepted 21 November 2007Available online 21 December 2007

Abstract

In this work, the Butler–Volmer formalism has been used to obtain a new equation to assess the calibration of voltammetric ion sen-sors. This new method postulates a direct relationship between the mid point reversible potential, ER, and the logarithm of the electrolyteconcentration. In the same way as the other relationships based on the Nernst equation, a positive slope is expected for a cationicexchanging system, and a negative one for an anionic sensor. However, the theoretical slope proposed in this work includes the elec-tron-transfer coefficient, which allows us to explain the slopes frequently reported in the literature non coincident with the ideal valueestimated from the Nernst equation: 2.303RT/nF. Also, comments are made on results from other literature with respect to the new equa-tion, and an application of this method to PPy/DBS films as a cation sensor is carried out.� 2007 Elsevier B.V. All rights reserved.

Keywords: Ion sensor; Butler–Volmer equation; Voltammetric detection; Conductive polymer; Cation selectivity

1. Introduction

The electrochemical sensors, including potentiometric,voltammetric/amperometric, and those using resistancechanges measurements are very attractive to practicalapplications because they are associated with small-size,portability, low energy consumption, and low cost [1–3].Voltammetric sensors have some advantages: they dispensewith the need to prepare one electrode per ion; the current–potential–time curves generated provide more analyticallyuseful information than single equilibrium potential curvesobtained under potentiometric conditions; also, the revers-ible potential can be calculated from data obtained underdynamic conditions [4].

1388-2481/$ - see front matter � 2007 Elsevier B.V. All rights reserved.

doi:10.1016/j.elecom.2007.11.025

* Corresponding author. Tel.: +34 968 325580; fax: +34 968 325931.E-mail address: antonioj.fernandez@upct.es (A.J. Fernandez Romero).

Actually, the expressions used to characterize ion-selec-tive electrodes are based on the Nersnt relationship. Bondand co-workers [4,5] adapted this equation for cation andanion voltammetric sensors, respectively

ER ¼ E00 þ S log½MþA� ð1Þ

ER ¼ E00 � S log½X�� ð2Þ

where jMþAj and jX�j are the cations and anions concentra-

tions, respectively, and ER is the reversible potential, de-fined by

ER ¼Ered

p þ Eoxp

2ð3Þ

Eredp is the reduction peak potential and Eox

p is the oxidationpeak potential. These equations were applied recently tocheck a TTF-TCNQ/PVC composite as ion-selective elec-trode [6].

M. Cano et al. / Electrochemistry Communications 10 (2008) 190–194 191

Eqs. (1) and (2) demonstrate a direct relationship betweenER and the logarithm of the electrolyte concentration, whereS is the slope derived from the plot, which has positive ornegative values for cationic or anionic exchanging, respec-tively. Moreover, ideally S will be equal to 2.303RT/nF.

Application of conducting polymers in chemical andbiochemical sensors has been extensively studied since themid-1980s. Polymers as polypyrrole (PPy), polyaniline(PANI), or Polythiophene (PTH) offer great possibilitiesto improve the selectivity, partly changing the chemicalstructure of the polymer backbone, and partly from themany possible counterions or neutral molecules that canbe trapped inside the polymer [2,3,7].

Moreover, for electrochemical ion sensors based onpolymeric materials, linear relationships between potentialand the logarithm of electrolyte concentration have beenreported. This behavior has been frequently explained onthe basis of the Nernst equation [8–12]. However, a treat-ment based in the Butler–Volmer expression has recentlybeen reported to explain the direct evolution of the poten-tial with respect to the logarithm of the electrolyte concen-tration [13].

2. Experimental

Pyrrole monomer (Fluka, >97%) was distilled undervacuum before use. Sodium dodecylbenzene sulfonate(Aldrich), LiClO4, NaClO4, and KClO4 (Merck) were usedas received. Millipore water with resistivity of >18 MX cmwas used.

Ppy/DBS films were generated by electrochemical oxida-tion on Pt foil electrodes. A potential of +0.8 V vs. Ag/AgCl was applied for 60 s in aqueous solutions of 0.1 Mpyrrole and 0.1 M DBS. Afterwards, the modified electrodewas taken out of the solution, washed with water, dried,and stored at 4 �C.

The electrochemical polymerization and the voltammet-ric measurements were performed with a PAR 273A poten-tiostat/galvanostat. A three electrodes cell composed of Ptfoil working electrode (area 1 cm2), an Ag/AgCl referenceelectrode, and a Pt wire as the auxiliary electrode, wereused. All the solutions were purged with N2 gas for 15 min.

With the aim of preventing an ohmic distortion, a vol-tammetric iRu compensation of 50 X – which was calcu-lated to be the mean for the different solutions used – hasbeen applied to our voltammetric measurements.

Each experimental potential (ER) was determined fromat least five measurements. All results were virtually identi-cal, which testifies to the high reproducibility of the PPy/DBS modified electrode.

3. Results and discussion

3.1. Butler–Volmer treatment

For the theoretical treatment we will consider the oxida-tion/reduction process of a PPy/DBS film using an aqueous

solution of MClO4 0.1 M, where M is an alkaline cation. Inthis case, DBS� anions will remain fixed inside the poly-meric material making it necessary that the electrolyte ionsare exchanged during the redox process. Thus, two basicredox reactions for the prevailing interchange of cationsor anions, respectively, could be proposed

PPy0DBS�Mþ¢ PPyþDBS� þMþ þ e� ðScheme IÞ

PPy0DBS� �Mþ þ ClO�4 ¢ PPyþDBS� �Mþ � ClO�4 þ e�

ðScheme IIÞIn the simplest approximation and considering an equi-

librium condition, the electrochemical potential for thesereactions could be described by the Nernst equation

E ¼ E00 þ RTnF

lnjPPyþDBS�jjMþjjPPy0DBS� �Mþj

¼ E00 þ RTnF

lnjPPyþDBS�j

jPPy0DBS� �Mþjþ RT

nFln jMþj ð4Þ

E ¼ E00 þ RTnF

lnjPPyþDBS� �Mþ � ClO�4 jjPPy0DBS� �MþjjClO�4 j

¼ E00 þ RTnF

lnjPPyþDBS� �Mþ � ClO�4 jjPPy0DBS� �Mþj

� RTnF

ln jClO�4 j

ð5Þ

These equations describe a semi-logarithmic increase in thepotential with electrolyte concentration when a cationic ex-change prevails, whereas a negative slope is predicted whenthe interchange of perchlorate anions prevails [8–12].

We consider that the Butler–Volmer formalism is moreappropriate for describing kinetic processes as this one.As regards the anodic part of the general process,R MO + ne� and considering that only oxidation occursin this branch of the voltammogram, the Butler–Volmerequation can be expressed by [14,15]

ia ¼ nFAk0 � CR � eð1�aÞnsf ðEa�E00 Þ ð6Þor

Ea ¼ E00 þ 1

ð1� aÞnsfln

ia

nFAk0� 1

ð1� aÞnsfln CR ð7Þ

where, ia, Ea, E00, a, k0, ns and CR are the anodic current,the anodic potential, the standard potential, the transfercoefficient, the standard rate constant, the n value of therate-determining step, and the reactive compounds concen-tration, respectively.

On the other hand, considering that in the cathodic partonly reduction is presented, the cathodic intensity, ic, canbe expressed by

ic ¼ nFAk0 � CO � e�ansf ðEc�E00 Þ ð8Þor

Ec ¼ E00 � 1

ansfln

ic

nFAk0þ 1

ansfln CO ð9Þ

where, Ec, and CO are the cathodic potential and the prod-uct compounds concentration, respectively.

192 M. Cano et al. / Electrochemistry Communications 10 (2008) 190–194

Considering that solid-state phases confined on the elec-trode surface (such as PPy+DBS� and PPy0DBS�M+) haveactivity values equal to unity, the Eqs. (7) and (9) can beexpressed for Scheme I by

Ec ¼ E00 � 1

ansfln

ic

nFAk0þ 1

ansfln Mþj j ð10Þ

Ea ¼ E00 þ 1

1� að Þnsfln

ia

nFAk0ð11Þ

Alternatively, previous studies reported changes in themid point reversible potential, ER, with the electrolyte con-centration [4–6]. Hence, ER could be given by Eq. (1) orEq. (2), which provide direct relationships between ER

and the cation or anion concentration for cationic or anio-nic exchange systems, respectively.

Continuing with the Butler–Volmer treatment, we canobtain the ER value taking Ec and Ea from Eqs. (10) and(11) as Ered

p and Eoxp , respectively

ER ¼Ered

p þ Eoxp

2� Ec þ Ea

2ð12Þ

Note that in this method we assume that at anodic orcathodic peak potentials only oxidation or reduction pro-cesses occur, respectively. This approximation is in accor-dance with Fig. 1, where the peaks are widely separated(DEp P 400 mV), making the error very low. In the sameway, voltammograms reported in Refs. [4–6] present peakssufficiently separated; therefore, the same hypothesis couldbe applied to them.

For the Scheme I, introducing Eqs. (10) and (11) in thisequation, one obtains

ER ¼ E00 þ 1

2

1

1� að Þnsfln

ia

nFAk0� 1

ansfln

ic

nFAk0

� �

þ 1

2ansfln Mþj j ð13Þ

For clarity, the second term can be designed by Z, andthus this equation would be transformed into

Fig. 1. Voltammograms recorded for a PPy/DBS film immersed in 0.01 M aqucarried out changing the potential from �1.1 V to 0.5 V. Scan rate = 10 mV s

ER ¼ E00 þ Z þ 1

2ansfln Mþj j ð14Þ

Comparing this expression with Eq. (1) it should benoted that they are very similar. Moreover, a direct rela-tionship between ER and the cation concentration isobtained experimentally, as it will be shown below forPPy/DBS polymer, and as it has been reported for differentsystems [4–6]. Hence, Z has to be a constant term, and thisequation can thus be transformed into

ER ¼ H þ 1

2ansfln Mþj j ð15Þ

where H is the origin ordinate constant.On the other hand, the cathodic and anodic peak cur-

rents do not maintain similar values with the electrolyteconcentration. However, a relationship between ic and iahas to exist to make the Z term constant with the electro-lyte concentration.

With respect to Scheme II, where anion exchangeprevails, and considering again that solid-state phases con-fined on the electrode surface (such as PPyþDBS�MþClO�4and PPy0DBS�Mþ) have activity values equal to unity, theEqs. (7) and (9) can be expressed by

Ec ¼ E00 � 1

ansfln

ic

nFAk0ð16Þ

Ea ¼ E00 þ 1

ð1� aÞnsfln

ia

nFAk0� 1

ð1� aÞnsfln ClO�4�� �� ð17Þ

In this case, we will use Eqs. (16) and (17) to obtain ER

ER ¼ E00 þ 1

2

1

1� að Þnsfln

ia

nFAk0� 1

ansfln

ic

nFAk0

� �

� 1

2 1� að Þnsfln ClO�4�� �� ð18Þ

Note that in this equation the second term is identical tothat designed by Z in Eq. (13) for Scheme I. Again, in thesame way, this term will be included inside the constant, H,resulting

eous solutions of LiClO4, NaClO4, and KClO4. The voltammograms were�1.

M. Cano et al. / Electrochemistry Communications 10 (2008) 190–194 193

ER ¼ H � 1

2 1� að Þnsfln ClO�4�� �� ð19Þ

Furthermore, substituting f by its value and using deci-mal logarithm, Eqs. (15) and (19), for Scheme I and II,respectively, could be expressed by

ER ¼ H þ 2:303RT

2ansFlog Mþj j ð20Þ

ER ¼ H � 2:303RT

2 1� að ÞnsFlog ClO�4�� �� ð21Þ

It is further worth noting that these equations are verysimilar to Eqs. (1) and (2) reported by Bond et al. [4,5],where the only changes are the slope and the origin ordi-nate constant. Thus, for cationic exchange the slope isequal to S/2a, and for anionic movement the slope is equalto �S/2(1-a), while the origin ordinate is E00 + Z. Note alsothat, for a system where a = 1�a = 0.5, the resulting slopesare in accordance with those of Bond equations. Moreover,in systems where ic is equal, in absolute value, to ia the ori-gin ordinate constant in Eqs. (20) and (21) will be equal toE00. Hence, in systems where jicj = jiaj and a = 1�a = 0.5the equations obtained using the Butler–Volmer formalismwill coincide exactly with those derived by Bond from theNernst equation.

In addition, in Ref. [5] Bond et al. obtained for aTCNQ0/� system a S value of 44.4 mV/dec, which is notcoincident with 58.5 mV/dec, predicted by the Nernst equa-tion at 22 �C. Knowing that during the redox process of theTCNQ0/� system an interchange of cations is produced aswell as Scheme I, Eq. (20) can be applied for this system.From this equation and considering ns = 1, a value of aequal to 0.66 could explain the 44.4 mV/dec slope valuereported.

Fig. 2. Calibration plots of reversible potential, ER, versus log [M+] for arate = 10 mV s�1.

Unwin et al.[16] have studied the reaction betweenTCNQ and FeðCNÞ4�6 at the interface between two immis-cible electrolyte solutions (ITIES), and they reported a avalue of 0.56 ± 0.04. This value is next to 0.66, the one cal-culated by our method, though there is a clear differencebetween this system and that used by Bond.

3.2. PPy/DBS film as a cation sensor

As has already been commented, equations derived fromthe Nernst or Butler–Volmer ones, provide a direct rela-tionship between ER and ion concentration, although theirconstants and slopes are different.

We have used a PPy/DBS modified electrode immersedin aqueous solutions of sodium, potassium, and lithiumperchlorate to examine the properties of this polymericmaterial as a voltammetric cation sensor. The redox reac-tion of this system is described by Scheme I, as it is deducedfrom the positive slope observed in Fig. 2. In this case theDBS� anions are fixed inside the polymer matrix, and theyare not exchanged during the redox process, as it has beenreported previously [17–19].

Thus, cyclic voltammograms of a PPy/DBS film wereobtained from �1.1 V to 0.5 V in different concentrationsof these electrolyte solutions (Fig. 1). A moderate scan rate(610 mV s�1) allowed us to maintain the polymeric modi-fied electrodes operational for a long period of time (nodeterioration was observed after five months of working).Moreover, the polymer was rapidly recycled (2–3 cycleswere sufficient to suppress any memory effect developingfrom contact with previous solutions).

ER values were calculated from these voltammograms,and a linear relationship between ER and log [M+] wasobtained for the three alkaline cations studied (Fig. 2). This

PPy/DBS modified electrode in aqueous solutions of MþClO�4 . Scan

194 M. Cano et al. / Electrochemistry Communications 10 (2008) 190–194

result, where increasing slopes are observed, is in accor-dance with Eq. (1), derived from Nernst and Eq. (20)obtained from Butler–Volmer.

The slopes obtained from Fig. 2 have very similar val-ues, ranging between 41 and 36 mV/dec. However, all ofthem differ from the ideal Nernstian value. Hence, we con-sider that it is more appropriate to use Eq. (20), whichcould explain these slope values. From this equation thevalue of the slope is defined by

S0 ¼ 2:303RT

2ansFð22Þ

From Fig. 2 we can estimate the values of factor a � ns

for the PPy+/0 couple when different cations were used:0.82 for K+, 0.76 for Na+, and 0.72 for Li+.

As for cation identity, it is demonstrated that on identicalcation concentrations in electrolyte solutions each cation ledto a different voltammetric peak pattern and hence differentreversible potential values for the PPy+/0 couple (Fig 2).Thus, the PPy/DBS system can be deemed as a voltammetricsensor analogue to a cation-selective electrode.

4. Conclusions

A new method based on the Butler–Volmer theory toassess the capability of the voltammetric cation and anionsensors has been proposed. Eqs. (20) and (21) are very sim-ilar to those proposed previously by Bond et al. derivedfrom the Nernst relationship, Eqs. (1) and (2). Also, in asystem where jicj = jiaj and a = 1 � a = 0.5 the equationsobtained using the Butler–Volmer formalism will be similarto those proposed by Bond, i.e., at systems with behaviorsimilar to Nernst the method proposed by us is still valid.Knowing that most of the redox systems studied do not ful-fill the Nernst conditions, it is essential to have a method atour disposal that is based on the Butler–Volmer equation,which could be used for systems out of equilibrium.

The new method allows us to explain the slopes reportedin the literature non coincident with the ideal value esti-mated from the Nernst equation: 2.303RT/nF. Moreover,from the slope value obtained experimentally a transfercoefficient can be proposed for the system studied.

In the end, the PPy/DBS modified electrode has provedto fulfill Eq. (20), and due to its different response to the

three alkaline cations analyzed, it can be deemed as a vol-tammetric cation sensor. The application of this newmethod to different polymeric cation and anion sensors isactually in progress in our laboratories.

Acknowledgements

M.C. and R.R.-A. wish to acknowledge funding bySpain’s Ministerio de Educacion y Ciencia within theframework CTQ2004-01677, and cofunding by FEDER.AJFR would like to thank the financial support from theSpanish government through grant BQU2001-0477, andfrom the Seneca Foundation through the project PI-25/00827/FS/01.

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