Cyclic Reciprocal Derivative Chronopotentiometry with Power Time

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Langmuir 2003, 19, 406-415

Cyclic Reciprocal Derivative Chronopotentiometry with Power Time Currents Applied to Electrodes Coated with Electroactive Molecular Films. Influence of the Reversibility Angela Molina* and Joaquin Gonzalez Departamento de Quı´mica Fı´sica, Facultad de Quı´mica, Universidad de Murcia, Espinardo, 30100, Murcia, Spain Received April 17, 2002. In Final Form: August 14, 2002 The theory of reversible, quasi-irreversible, and totally irreversible charge-transfer reactions between adsorbed molecules in cyclic reciprocal derivative chronopotentiometry with power currents of the form I(t) ) (I0tu (CRDPC) is presented. For certain values of u, it is possible to set the peak heights to increase when the reversibility of the process decreases. This possibility represents an enormous advantage of this electrochemical technique in the characterization of nonreversible processes, since it is the only technique for which this behavior is observed. The use of programmed currents is advantageous versus constant currents (used in the usual reciprocal derivative chronopotentiometry) since in this last case peaks are not obtained for totally irreversible processes. CRDPC presents, as compared to cyclic voltammetry, higher and narrower peaks. Moreover, the signals obtained in CRDPC are also narrower than those corresponding to cyclic reciprocal derivative exponential chronopotentiometry. The theoretical predictions have been proved by applying CRDPC to the study of adsorption of quinizarine (reversible behavior) and azobenzene (irreversible behavior) systems on mercury in aqueous media.

Introduction Reciprocal derivative chronopotentiometry (RDC) with constant current, introduced by Jagner,1,2 is a derivative technique which has enjoyed wide use in recent years for the study of different electrode processes. This is because the technique, which is based on the plotting of the reciprocal of the time derivative of the chronopotentiogram versus the measured potential (dt/dE vs E), presents a characteristic peak that is quantitatively related to the kinetic and thermodynamic parameters of the electrode process which remain almost unaffected by the capacitive effects.3,4 At present, this technique, also known as potentiometric stripping analysis (PSA),5 is widely used in the collection of analytically useful data and in the diagnosis of electrochemical reactions,3,4,6-12 including the study of electrodes coated with molecular films.13 In a previous paper, we introduced cyclic reciprocal derivative exponential chronopotentiometry (CRDEC), in which exponential currents of the form I(t) ) (I0eωt are applied instead of constant currents.14 This new technique * To whom correspondence should be addressed. E-mail: [email protected]. Tel: 34 968 36 75 24. Fax: 34 968 36 41 48. (1) Anderson, L.; Jagner, D.; Josefson, M. Anal. Chem. 1982, 54, 1371. (2) Jagner, D. Trends Anal. Chem. 1983, 2, 53. (3) Molina, A.; Gonzalez, J.; Saavedra, F.; Abrantes, L. M. Electrochim. Acta 1999, 45, 761. (4) Gonzalez, J.; Molina, A.; Lopez-Tenes, M.; Serna, C. J. Electrochem. Soc. 2000, 147, 3429. (5) Fogg, A.; Wang, J. Pure Appl. Chem. 1999, 71, 891. (6) Wang, J.; Tian, B. Anal. Chem. 2000, 72, 3241. (7) Wang, J.; Rivas, G.; Jiang, M.; Zhang, H. Langmuir 1999, 15, 6541. (8) Wang, J.; Cai, X.; Wang, J.; Jonsson, C. Anal. Chem. 1995, 67, 4065. (9) Tomschik, M.; Jelen, F.; Havran, L.; Trnkova´, L.; Nielsen, P. E.; Palecˇek, E. J. J. Electroanal. Chem. 1999, 476, 71. (10) Bi, S.; Yu, J. J. Electroanal. Chem. 1996, 405, 51. (11) Abrantes, L. M.; Molina, A.; Gonzalez, J.; Saavedra, F. Electrochim. Acta 1999, 45, 457. (12) Kizek, R.; Trnkova´, L.; Palecˇek, E. Anal. Chem. 2001, 73, 4801. (13) Honeychurch, M. J. J. Electroanal. Chem. 1998, 445, 63.

greatly improves RDC with constant current in the study of adsorbed molecules exhibiting irreversible behavior, since the response in CRDEC (the deωt/dE vs E curve) presents peaks whatever the reversibility of the process, whereas in RDC with constant current the responses do not present peaks when totally irreversible systems are analyzed.14 In this paper, we study the use of successive current time functions which vary with a power of time u of the form I(t) ) (I0tu in order to introduce cyclic reciprocal derivative power chronopotentiometry (CRDPC). This technique greatly improves the results obtained in CRDEC when studying the response of electrodes coated with electroactive irreversible molecular films. This is because a comparison of the sensitivity and resolution of the signals obtained in reversible and irreversible electrode processes in any electrochemical technique (with potential controlled14,15 or current controlled included CRDEC3,4,11,14-17) reveals that the signal for a totally irreversible process always presents less sensitivity and resolution than that obtained for a reversible one. However, whenever CRDPC is applied in the study of irreversible processes, we observe that there are values of the power of time u in the applied current for which the peaks corresponding to irreversible processes are higher and narrower than those corresponding to reversible processes. Such a possibility represents, without doubt, an enormous advantage of this technique over other electrochemical techniques, and as far as we know, it is the only technique for which this type of behavior is observed. The comparison between the CRDPC responses and the cyclic voltammetry (CV) currents for nonreversible pro(14) Gonzalez, J.; Molina, A. Langmuir 2001, 17, 5520. (15) Bard, A. J.; Faulkner, L. R. Electrochemical Methods, 2nd ed.; Wiley: New York, 2001. (16) Galus, Z. Fundamentals of electrochemical analysis, 2nd ed.; Ellis Horwood: New York, 1994. (17) Molina, A.; Gonzalez, J.; Moreno, M. M. Electroanalysis 2002, 14, 281.

10.1021/la020369x CCC: $25.00 © 2003 American Chemical Society Published on Web 12/12/2002

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Langmuir, Vol. 19, No. 2, 2003 407

cesses reveals higher and better defined peaks in CRDPC. These peaks are also narrower and higher than those obtained in CRDEC.14 We have analyzed the influence of the exponent u in the applied current and of the kinetic parameters k0 (rate constant of the surface electrochemical reaction, in s-1) and R and (1 - R) (charge-transfer coefficients of the cathodic and anodic surface reactions, respectively) on the CRDPC curves, and we have proposed methods for calculating kinetic parameters of the charge-transfer reaction k0 and R and the interfacial standard potential for the Langmuir isotherm E0. The above methods have been applied to the study of the adsorption of quinizarine (reversible) and azobenzene (irreversible) systems on mercury in aqueous media. From the measurement of the peak potentials and peak heights, we have obtained accurate values for the kinetic and thermodynamic parameters of both systems. In the case of the azobenzene system, for a u value of 0.075 we obtain CRDPC peaks which are =1.7 times higher and half peak widths that are =50% smaller than those of CV. The greater sensitivity and resolution of the signals obtained, the lower influence of capacitive and ohmic drop effects,3,4,14,17,18 and its higher versatility as compared to that of CV make CRDPC one of the best electrochemical methods both in the detection of trace levels and in the characterization of the electrochemical behavior of molecular films.

Peak potentials and peak heights in CRDPC were measured from the fitted differentiated curves without further analysis. All the kinetic and thermodynamic values obtained for the quinizarine and azobenzene systems correspond to series of five essays. The results obtained are the mean of the five experimental values, while the errors correspond to the standard deviation. Chemical Reagents. K2HPO4, KH2PO4, KNO3, HClO4, ethanol (Merck, reagent grade), quinizarine, and azobenzene (Aldrich, reagent grade) were used as received. Azobenzene and quinizarine were dissolved in ethanol and then diluted with water until the final proportion of ethanol was 1% (azobenzene and quinizarine concentrations were 3 × 10-5 and 10-5 M, respectively). In the case of azobenzene solutions, K2HPO4 and KH2PO4 were used to fix the pH at 6.74 (with KNO3 0.1 M as the supporting electrolyte). Azobenzene and quinizarine were adsorbed at the mercury surface at a potential of -0.60 and -0.40 V, respectively, for 30 s prior to measurements. Water was bidistilled, and nitrogen gas was passed through solutions for deaeration for 15 min prior to measurements.

Experimental Section

To obtain the equations for the response corresponding to CRDPC, we assume for the adsorbate monolayer that the Langmuir isotherm is obeyed. The adsorption coefficients of both electroactive species and the maximum surface coverage are independent of the potential. In a chronopotentiometric experiment, the potential time response (E vs t curve) is given by14,22

Apparatus. A computer-driven potentiostat-galvanostat was designed and constructed by QUICELTRON (Spain). Pulse and waveform generation and data acquisition were performed using i-SBXDD4 and DAS16-330i (ComputerBoards, USA) boards, respectively. All computer programs were written in our laboratory. In the cyclic chronopotentiometric experiments, the current switch was performed when the potential attained a prefixed value (cathodic or anodic) at which we supposed that the transition time had already been reached. The necessary comparison was carried out by means of an interrupt service routine using the clock of the personal computer. Electrodes. A three-electrode cell was employed in the experiments. A static mercury drop electrode (SMDE) served as working electrode. The SMDE was constructed using a dropping mercury electrode (DME), EA 1019-1 (Metrohm), to which a homemade valve was sealed. The electrode radius of the SMDE was determined by weighing a large number of drops. The counter electrode was a Pt foil, and the reference electrode was a Ag/AgCl, KCl 1.0 M electrode. Signal Processing. In the experimental measurements of the potential-time curves, we have used different digital noise filters of the instrument supported software. The experimental E versus t curves were then smoothed by applying the moving average smoothing procedure proposed by Savitzky and Golay19 and transformed to the corresponding tu+1 versus E curves. The experimental tu+1 versus E curves obtained for the quinizarine system were fitted with a sigmoidal regression. In the case of the curves corresponding to the azobenzene solution, we programmed theoretical equations for the totally irreversible tu+1 versus E curves in order to carry out the regressions. In both cases, we used the SigmaPlot program,20 and the fitted curves obtained were numerically differentiated by using a finite differences formula of the fifth degree21 so as to obtain the dtu+1/dE versus E curves (CRDPC). (18) Smith, C. P.; White, H. S. Anal. Chem. 1992, 64, 2398. (19) Savitzky, A.; Golay, M. J. E. Anal. Chem. 1964, 36, 1627. (20) Sigma Plot for Windows, version 5.0; Jandel Scientific: Corte Madera, CA, 1999. (21) Maron, M. J. Numerical Analysis: A Practical Approach; Collier McMillan: London, 1982.

Theory We will consider the subsequent reductions and oxidations between adsorbates that take place when several successive programmed power time currents of the form I(ti) ( I0 tiu (with u > -1) are applied. The surface electrode process considered is given by kred

O(absorbed) + ne- {\ } R(absorbed) k ox

I0tu ) ( (kredΓA(t) - koxΓB(t)) nFA

(1)

with the sign “+” referring to cathodic currents and the sign “-” to anodic ones and

kred ) k0η-R

(2)

kox ) k0η1-R

(3)

η ) exp

nF (E - E )] [RT 0

(4)

Taking into account that the total adsorbate excess, ΓT, is constant during the experiment,

ΓT ) ΓA,0 + ΓB,0 ) ΓA(t) ) ΓB(t)

(5)

we deduce the expressions of the surface excesses of both species, and by imposing the condition Γi(t ) τ) ) 0 (with i ) A for cathodic currents and i ) B for anodic ones) we obtain the following expressions for the transition times:3

τu+1 )

(u + 1)nFAΓA,0 I0 for the first power current applied (6)

(22) Laviron, E. In Electroanalytical Chemistry; Bard, A. J., Ed.; Marcel Dekker: New York, 1982; Vol. 12.

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(u + 1)nFAΓT I0 for the second, third, etc. power currents applied (7)

τu+1 )

In eqs 1-7, ΓA,0 and ΓB,0 are the initial values of the surface excesses of the oxidized and reduced species, respectively, A is the electrode area (cm2), and n, F, R, and T have their usual meanings. By introducing eqs 2-7 in eq 1 and by making the following change of variable,

T ) (t/τ)u+1

(8)

we deduce

u + 1 u/(u+1) R T η ) 1 - T - η(ΓB,0/ΓA,0) - ηT τk0 first power time current applied (9)

of successive current steps (u ) 0), eqs 14 take the following explicit form:

dT dE

)

dT dE

)

Cyclic Reciprocal Derivative Power Chronopotentiometry for Totally Irreversible Processes. For a totally irreversible process (k0 , 1 s-1), eqs 9-11 are simplified to the following form:14-17

1-T RT RT ln(τk0) + ln RnF RnF (u + 1)T(u/u+1) cathodic (12)

E - E0 )

RT ln(τk0) E-E )(1 - R)nF 1-T RT ln (1 - R)nF (u + 1)T(u/u+1)

,u)0 )

anodic

Note that in these equations, the E versus t response given by eq 1 has been transformed into the E versus T response (with T being the dimensionless time given by eq 8). This presents interesting advantages, as will be shown in the following sections. By differentiating eqs 12 and 13 with respect to the potential, we deduce the analytical expressions for the cathodic and anodic dT/dE versus E curves (CRDPC responses) corresponding to an irreversible cathodic, dT/dE)cathodic, or anodic, dT/dE)anodic, process for any value of u,

dT dE

)

dT dE

)

2

)cathodic

) anodic

(2u+1)/(u+1) R

η RnF (u + 1) T 0 RT T + u τk

(14)

(1 - R)nF (u + 1)2 T(2u+1)/(u+1)η-(1-R) RT T+u τk0

for u * 0 Equations 14 are not explicit expressions of the potential E(t). However, for the particular case of the application

(15)

(1 - R)nF 1 -(1-R) η RT τk0

Peak Parameters. The expressions for the peak heights and peak potentials corresponding to the dT/dE versus E curve can be easily obtained from eqs 14 by carrying out the second derivative of these equations with respect to the potential and by making d2T/dE2 ) 0. We must also take into account that the power of time u must fulfill u > 0, since for u e 0, peaks are not obtained. Hence, we deduce

dT dE

)

dT dE

)c,peak

)

)

a,peak

RnF(u + 1) Gu RT

(16)

(1 - R)nF(u + 1) Gu RT

for u > 0 for the cathodic and anodic peak heights and

Ec,peak ) E0 + Ea,peak ) E0 -

RT RT ln(τk0) + F RnF RnF u

(17)

RT RT ln(τk0) F (1 - R)nF (1 - R)nF u

for u > 0 for the cathodic and anodic peak potentials, with

Gu )

0

anodic (13)

RnF 1 R η RT τk0

for u ) 0

u + 1 u/(u+1) R T η ) 1 - T - ηT τk0 third, fifth, etc. power time currents applied (10) u + 1 u/(u+1) R T η ) -T + η(1 - T) τk0 second, fourth, etc. power time currents applied (11)

,u)0 ) -

cathodic

Fu ) ln

Hu - Hu2 u + Hu

(18)

1 - Hu (u + 1)Hu(u/u+1)

Hu ) xu(u + 1) - u From eqs 16 and 17, we can immediately obtain the ratio between peak heights, |dT/dE)c,peak/dT/dE)a,peak|, and the difference between peak potentials, ∆Epeak ) |Ec,peak - Ea,peak|, given by

|

dT/dE)c,peak

|

dT/dE)a,peak

∆Epeak )

)

R 1-R

RT 1 (ln(τk0) + Fu) nF R(1 - R)

(19) (20)

Equations 16-20 for the peak parameters are valid for u > 0 since for the case u ) 0, peaks are not obtained from eqs 15. Another interesting feature of the response of the CRDPC technique is the half peak width of the dT/dE versus E curves, defined as the difference between the potentials at which a value of the CRDPC curve equal to the half peak height (dT/dE)peak/2) is obtained. We have found that the half peak width for this technique is a


Langmuir, Vol. 19, No. 2, 2003 409

function of the power of time u and is given by (see eqs 14 and 16)

Wc1/2 )

u/(u+1) RT (1 - T2)T1 ln RnF (1 - T )T u/(u+1) 1

Wa1/2 )

(21)

2

(1 - T2)T1u/(u+1) RT ln (1 - R)nF (1 - T1)T2u/(u+1)

with T1 and T2 being

-(Gu - 2) + x(Gu - 2)2 - 8uGu T1 ) 4

(22)

-(Gu - 2) - x(Gu - 2)2 - 8uGu T2 ) 4 and Gu given in eqs 18. Equations 16-22 have been obtained from eqs 14 corresponding to totally irreversible processes. In the case of quasi-irreversible processes, it is not possible to use any simplification in the theoretical equations for the potential time response (eqs 9-11) and their derivatives. The kinetic parameters of the surface electrochemical process in this last case can be obtained by fitting the experimental results with theoretical curves calculated for different sets of values of the rate constant, the charge-transfer coefficients, and the interfacial standard potential. Cyclic Reciprocal Derivative Power Chronopotentiometry for Reversible Processes. For a reversible process (k0 f ∞), eqs 9-11 are transformed into23

E(t) ) E0 +

1-T RT ln nF ΓB,0/ΓA,0 - T first power time current applied (23)

RT 1 - T ln nF T second, third, etc. power time currents applied

E(t) ) E0 (

with T given in eq 8. By differentiating eqs 23 with respect to the potential, we obtain the analytical expressions for the dT/dE versus E curves (CRDPC responses) corresponding to a reversible electrode process,23

| |

nF η dT )dE RT (1 + η)2

cathodic and anodic

(24)

From eqs 23 and 24, it can be deduced immediately from this model that the cathodic and anodic responses corresponding to a reversible process possess the same peak potential; this, ideally, will be equal to E0 (i.e., Ec,peak ) Ea,peak ) E0), and therefore ∆Epeak ) |Ec,peak - Ea,peak| is equal to zero.23 Moreover, the peak heights, dT/dE)peak, and the ratio dT/dE)/dT/dE)peak are given by

dT dE

)

peak

nF )4RT

(25)

dT/dE) η )4 dT/dE)a,peak (1 + η)2 cathodic and anodic Thus, in this case the ratio dT/dE)/dT/dE)peak is only dependent on η and is identical to that corresponding to

Figure 1. Theoretical normalized (E - E0) vs T (a) and dT/dE vs (E - E0) curves (b) for a reversible surface charge-transfer process obtained from eqs 23 and 24, respectively. T ) (t/τ)u+1. I(t) ) I0tu . I0/(nFAΓA,0) ) 1.0 s-(u+1), n ) 1, T ) 298 K. The values of the power of time u in the applied current are on the curves.

cyclic voltammetry (see eq 68 in ref 22). Moreover, it is fulfilled that |dT/dE)c,peak/dT/dE)a,peak| ) 1. Finally, the half width of reversible peaks can be obtained in the same way as described above for an irreversible process. Thus we obtain the following value for cathodic and anodic curves: W1/2 = 3.53 RT/(nF), which is not dependent on the experimental conditions and is identical to the half width value obtained in cyclic voltammetry for a reversible surface process.22 Results and Discussion Theoretical Results. In Figure 1, we have plotted the normalized E versus T curves with T ) (t/τ)u+1 (Figure 1a) and the dT/dE versus E curves (Figure 1b), corresponding to the application of a programmed current I0tu to a reversible process for three different values of u. As can be deduced from these figures, both plots give rise to a single response which is independent of the experimental conditions. The behavior of the d(t/τ)u+1/dE versus E curves shown in Figure 1b presents great advantages over the signal usually obtained in reciprocal derivative chronopotentiometry, that is, the d(t/τ)/dE versus E curve, since in this last case the reversible response depends on the value of the power of time u (see Table 2 in ref 3) and, therefore, we do not obtain a unique curve as in the case of the d(t/τ)u+1/dE versus E curves.

410


Molina and Gonzalez Table 1. Values of the Ratio between the Cathodic and Anodic Peak Heights for Irreversible and Reversible Processes, RCRDPC and RCRDPC , Given by Equations 26 and c a 27, and of the Cathodic and Anodic Half Peak Widths, c a W1/2 and W1/2, Obtained from Equations 21 and 22a u

RCRDPC , c RCRDPC a

RCRDPC ) RCRDPC c a for R ) (1-R) ) 0.5

Wc1/2, Wa1/2

0.075 0.10 0.20 0.25 0.50 0.75 1.00

2.503ξ 2.361ξ 2.022ξ 1.910ξ 1.607ξ 1.461ξ 1.373ξ

1.251 1.180 1.011 0.955 0.804 0.730 0.686

1.31RT/(ξnF) 1.40RT/(ξnF) 1.68RT/(ξnF) 1.79RT/(ξnF) 2.16RT/(ξnF) 2.39RT/(ξnF) 2.55RT/(ξnF)

a ξ ) R for a cathodic (c) process, and ξ ) 1 - R for an anodic (a) one.

of this technique due to the fact that, as far as we know, this is the only electrochemical technique for which such behavior is observed. The reason for this higher sensitivity for irreversible processes lies in the fact that peak heights obtained in CRDPC are functions of the value of u. Hence, the ratio between peak heights corresponding to a totally irreversible process and a reversible one for a cathodic or anodic applied current is given by (see eqs 16 and 25)

RCRDPC ) c

irrev dT/dE)c,peak rev dT/dE) c,peak

) 4R(u + 1)Gu cathodic peaks (26)

and

Figure 2. Theoretical normalized (E - E0) vs T (a) and dT/dE vs (E - E0) curves (b) for a totally irreversible surface chargetransfer process obtained from eqs 12-13 and 14, respectively. T ) (t/τ)u+1 . I(t) ) I0tu . k0 ) 0.1 s-1, R ) 0.5. The values of the power of time u in the applied current are on the curves. Other conditions are as in Figure 1.

When a totally irreversible process is considered (see Figure 2), the temporal dependence of the response cannot be eliminated, and it is not possible to obtain a single E versus T curve (Figure 2a). As a consequence, the dT/dE ()d(t/τ)u+1/dE) curves depend on the value of u (Figure 2b). This dependence and the absence of peaks in these curves for u e 0 can be considered as criteria for identifying a totally irreversible process. In general, when we compare the signal obtained in reversible and irreversible electrode processes in electrochemical techniques with potential controlled or current controlled, it is observed that the signal corresponding to a totally irreversible process presents a lower sensitivity than that obtained for a reversible one.14,15 Thus, in differential pulse voltammetry (DPV),24 CV,25 derivative voltammetry (DV),26 or even in CRDEC,14 it is observed that the peak heights always decrease when the reversibility of the process decreases. However, when we apply power currents of the form (I0tu and the reciprocal derivative of the E versus T curve is obtained, there are values of the power of time u for which the peak heights corresponding to irreversible processes are higher than those corresponding to reversible ones. This possibility represents an enormous advantage (23) Molina, A.; Gonzalez, J. J. Electroanal. Chem. 2000, 493, 117. (24) Birke, R.; Kim, M. H.; Strassfeld, M. Anal. Chem. 1981, 53, 852. (25) Nicholson, R. S.; Shain, I. Anal. Chem. 1964, 36, 706. (26) Kim, M. H.; Smith, V. P.; Hong, T. K. J. Electrochem. Soc. 1993, 140, 712.

RCRDPC a

)

irrev dT/dE)a,peak rev dT/dE) a,peak

) 4(1 - R)(u + 1)Gu anodic peaks (27)

with Gu given in eqs 18, in such a way that for a value of R ) (1 - R) ) 0.5 it is fulfilled that 4R(u + 1)Gu > 1 for u < 0.20, whereas 4R(u + 1)Gu < 1 for u g 0.20; that is, the peak heights of the cathodic or anodic curves corresponding to an irreversible process are greater than those corresponding to a reversible one if u < 0.20 (see Table 1). To illustrate the behavior discussed above, Figure 3a,b shows the influence of the surface rate constant k0 on the normalized dT/dE versus E curves deduced from eqs 9-11 for two different values of the power of time u in the applied currents I(t) ) (I0tu (u ) 0.50, Figure 3a, and u ) 0.10, Figure 3b). From these figures, it can be observed that as k0 decreases, the cathodic and anodic curves are shifted toward negative and positive directions, respectively, thus increasing the difference between both peak potentials. In relation to the peak heights, Figure 3a, corresponding to u ) 0.5, shows a typical electrochemical behavior. Both cathodic and anodic peak heights decrease in absolute value when k0 decreases, until the limit values given in eqs 16 are reached. However, in Figure 3b, obtained for u ) 0.1, we can observe that the heights of both peaks increase in absolute value as k0 decreases, until the limit values given in eqs 16 are reached. We can conclude that the interest of the dT/dE versus E curves for values of u e 0.20 should be apparent since, as Figure 3b shows, irreversible processes provide, in this case, more sensitive signals than do reversible ones. As compared to cyclic voltammetry, CRDPC is much more advantageous for the characterization of irreversible charge-transfer reactions of adsorbed molecules due to the lower influence of capacitive and ohmic


Langmuir, Vol. 19, No. 2, 2003 411

Figure 3. Theoretical dT/dE vs (E - E0) curves obtained from eqs 9-11 corresponding to the application of two successive power time functions. I(t) ) I0tu and I(t) ) -I0tu. T ) (t/τ)u+1. The values of the power of time u in the applied currents are u ) 0.5 (a) and u ) 0.1 (b). I0/(nFAΓA,0) ) 2.0 s-(u+1), R ) 0.5. The values of k0 (in s-1) are on the curves. Other conditions are as in Figure 1.

drop effects3,4,14,17,18 and also because the peaks obtained in CRDCP are much higher and narrower than those obtained in CV. For comparison, both voltammetric and chronopotentiometric signals should be given in V-1; hence the voltammetric current should be converted to V-1 by dividing it by (nFAΓA,0v). Thus, the ratio between peak heights for totally irreversible processes obtained in CRDPC and CV is given by (see eq 16 of this paper and eqs 18 and 19 in ref 27)

dT/dE)peak ψCV peak

) 2.72(u + 1)Gu

cathodic and anodic (28)

-1 where the peak current, ψCV peak (in V ), and the half peak 27 , for CV are given by width, WCV 1/2

WCV 1/2 = 2.43RT/(ξnF)

(29)

CV |ΨCV peak| ) |Ipeak/(nFAΓA,0v)| ) ξnF/(2.72RT)

ξ ) R or ξ ) 1 - R From eqs 28 and 29, we deduce that for values of the (27) Laviron, E. J. Electroanal. Chem. 1979, 101, 19.

Figure 4. Experimental E vs t (a,b) and (t/τ)u+1 vs E curves (c) for the quinizarine 10 µM/HClO4 1.0 M system on a SMDE. I(t) ) (I0tu. Γquinizarine,0 ) (8.29 ( 0.2) × 10-11 mol cm-2, r0 ) 0.035 cm, n ) 2, T ) 295 K. The values of the power of time u in the applied currents are on the figure.

power of time u < 0.75, the peaks obtained in CRDPC are higher and narrower (see Table 1) than those obtained in CV (see also experimental results). For example, for u ) 0.1 the peaks obtained in CRDPC are 1.6 times higher and =47% narrower than those obtained in CV. Moreover, CRDPC peaks are also narrower than those obtained when an exponential current of the form I(t) ) -I0eωt is used (CRDEC14). Equations 12 and 13 for the potential time curves of a totally irreversible process are also valid for u e 0, and specifically for -1 e u e 0. But this last interval of values is not advisable for determining kinetic parameters of the charge transfer, since, in these conditions, the anodic and cathodic normalized dT/dE versus E curves do not present peaks. Nevertheless, due to the fact that this is a typical characteristic of irreversible processes, this behavior can be used for detecting its presence. Experimental Results. Reversible Behavior: Quinizarine in Aqueous Acidic Media. In the first place, we have applied the CRDPC technique to the study of the redox behavior of quinizarine (1,4-dihydroxyanthraquinone) in aqueous acidic solutions. This system is strongly adsorbed on mercury and behaves as reversible.28

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Figure 6. (Lines with symbols) Experimental dT/dE vs E curves for the quinizarine 10 µM/HClO4 1.0 M system on a SMDE. T ) (t/τ)u+1. I(t) ) I0tu and I(t) ) -I0tu. I0 ) 6.0 µA s-u. The values of u and τ (in ms) are as follows: (black circles) 0.075, 45.4; (white triangles) 0.10, 42.9. (Solid lines) Experimental cyclic voltammograms (ICV/(nFAΓquinizarine,0v) vs E curves) for the quinizarine 10 µM/HClO4 1.0 M system on a SMDE. Sweep rate v ) 5.0 V s-1. Γquinizarine,0 ) (8.29 ( 0.2) × 10-11 mol cm-2. Other conditions are as in Figure 4. Figure 5. Experimental dt1.075/dE vs E (a) and dT/dE vs E (b) curves for the quinizarine 10 µM/HClO4 1.0 M system on a SMDE. T ) (t/τ)1.075. I(t) ) I0t0.075, u ) 0.075. The values of I0 (in µA s-0.075) and τ (in ms) are as follows: 5, 59.9; 6, 48.8; 7, 42.2; 8, 36.3. Other conditions are as in Figure 4.

Figure 4 shows the chronopotentiometric E versus t curves (Figure 4a,b) and their corresponding (t/τ)u+1 vs E curves (Figure 4c), obtained for the quinizarine 10 µM/ HClO4 1.0 M system in an aqueous solution with 1% of ethanol. All these curves have been obtained for the application of 16 programmed currents of the form I(t) ) (I0tu to a SMDE and for two different values of the exponent of time u (0.075 and 0.20). From the E versus t curves, it can be deduced that the transition times for the reduction and oxidation are the same (i.e., anodic and cathodic E vs t curves are specular images, with the same transition time). It can be also observed from Figure 4c how the I(t) ) (I0tu versus E curves remain practically independent of the value of u, in accordance with theoretical predictions (eqs 23). From the chronopotentiometric curves shown in Figure 4, we have obtained the non-normalized reciprocal derivative curves (dtu+1/dE vs E curves, see Figure 5a) and the normalized derivative ones (dT/dE or d(t/τ)u+1/dE vs E curves, see Figure 5b) shown in Figure 5 for u ) 0.075 and for four different values of the current amplitude I0. From the non-normalized curves dtu+1/dE versus E curves in Figure 5a, it can be seen that for this system we obtain symmetrical curves for the anodic and cathodic processes in which Ec,peak ) Ea,peak ) E0, with E0 being the interfacial standard potential for the Langmuir isotherm.23 From the peak potentials in Figure 5a, we have obtained (28) Forster, R. J. Analyst 1996, 121, 733.

the following values for E0 from the cathodic and anodic curves, respectively: (-0.198 ( 0.001) V and (-0.197 ( 0.001) V versus Ag/AgCl, KCl 1.0 M. Moreover, the distance between the cathodic and anodic peak potentials of these curves is ∆Epeak = 0 mV with a maximum error of 2 mV in all the cases. These curves also fulfill that the ratio between cathodic and anodic peak heights is |dT/dE)c,peak/ dT/dE)a,peak| = 1.0 for any value of the current amplitude and with an error margin of less than 5%. The results for both peak potentials and peak heights indicate that this process behaves as a reversible surface charge transfer.23 It can also be observed in Figure 5a that the cathodic and anodic peak heights decrease in absolute value as I0 increases. The dependence of the peak heights on the current amplitude is given by the following equations:

)

dtu+1 dE

)

dtu+1 dE

)c,peak

a,peak

)

n2F2AΓquinizarine,0 u + 1 nF u+1 τ )4RT 4RT I0 (30)

2 2 nF u+1 n F AΓquinizarine,0 u + 1 τ ) (31) 4RT 4RT I0

with Γquinizarine,0 being the initial excess of quinizarine on mercury. Thus, by plotting the cathodic and anodic peak heights versus (u + 1)/I0, a linear dependence is found and we can easily obtain the initial surface excess of quinizarine. From the data shown in Figure 5a, we have obtained Γquinizarine,0 ) (8.29 ( 0.2) × 10-11 mol cm-2, which is in agreement with the value reported in ref 28, which is Γquinizarine,0 ) 1.1 × 10-10 mol cm-2 (obtained in a pure aqueous medium). Figure 5b shows the normalized dT/dE ()d(t/τ)u+1/dE) versus E curves obtained by dividing curves in Figure 5a


Langmuir, Vol. 19, No. 2, 2003 413

Figure 8. Experimental dt1.1/dE vs E (a) and dT/dE vs E (b) curves for the azobenzene 30 µM in KNO3 0.1 M (pH ) 6.74) system, on a SMDE. T ) (t/τ)1.1. I(t) ) I0t0.1, u ) 0.10. The values of I0 (in µA s-0.10) and τ (in ms) are as follows: 6, 114.8; 8, 88.0; 10, 70.1; 12, 59.2. Other conditions are as in Figure 7.

Figure 7. Experimental E vs t curves (a,b) and (t/τ)u+1 vs E curves (c), for the azobenzene 30 µM in KNO3 0.1 M (pH ) 6.74) system, on a SMDE. I(t) ) (I0tu. Γquinizarine,0 ) (1.81 ( 0.2) × 10-10 mol cm-2, r0 ) 0.035 cm, n ) 2, T ) 295 K. The values of the power of time u in the applied currents are on the figure.

by τu+1. According to the theoretical results discussed above, in the case of a reversible surface electrode process we obtain a single response for the CRDPC curves (see eqs 23 for the potential time curves and eq 24 for the reciprocal derivative ones). Finally, we have demonstrated in a previous work that the responses obtained in CRDPC and CV techniques are identical for the case of an electrode coated with a molecular film of a reversible electroactive couple.23 In Figure 6, we have plotted the response obtained for the quinizarine system in cyclic voltammetry for a sweep rate of v ) 5 V s-1 (solid line) for which the capacitive effects have been corrected and in CRDPC for the application of two successive cathodic and anodic programmed currents, I(t) ) I0tu and I(t) ) -I0tu, respectively, with u ) 0.075 (black circles) and 0.10 (white triangles), with both voltammetric and chronopotentiometric signals being given in V-1. The curves in this figure clearly show the total analogy between CRDPC (d(t/τ)u+1/dE vs E) and CV (ICV/(nFAΓquinizarine,0v) vs E) techniques. The reason for this analogy has been extensively discussed in ref 23. Irreversible Behavior: Azobenzene in Aqueous Solution. We have also applied the CRDPC technique to the study

of the experimental system azobenzene 30 µM in KNO3 0.1 M (pH ) 6.74), which behaves as quasi-irreversible as a function of the pH.14,29,30 Figure 7 shows the experimental chronopotentiometric E versus t curves (Figure 7a,b) and their corresponding (t/τ)u+1 versus E curves (Figure 7c) obtained for this system by the application of six programmed currents of the form I(t) ) (I0tu to a SMDE with I0 ) 8.0 µA s-u and for two different values of the exponent of time u (0.075 and 0.20). These curves show the great asymmetry between reduction E versus t curves (which are shifted toward negative potential values) and oxidation E versus t ones (which are shifted toward positive potential values). Transition times, logically, remain unaffected by the reversibility of the surface process and are approximately the same in both cathodic and anodic responses. Figure 7c also shows that the (t/τ)u+1 versus E curves are dependent on the value of u, contrary to those obtained for a reversible process (see Figure 4c). Figure 8 shows the influence of the current amplitude I0 on the non-normalized dtu+1/dE versus E curves (Figure 8a) and on the normalized dT/dE ()d(t/τ)u+1/dE) versus E ones (Figure 8b) obtained for the azobenzene system for a fixed value of the power of time u ) 0.1 and for four values of I0. From these figures, we can conclude that when the value of I0 increases, the cathodic and anodic (29) Komorsky-Lovric, S.; Lovric, M. Electrochim. Acta 1995, 40, 1781. (30) Laviron, E.; Mugnier, Y. J. Electroanal. Chem. 1980, 111, 337.

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Figure 10. (Solid lines) Experimental dT/dE vs E curves for the azobenzene 30 µM in KNO3 0.1 M (pH ) 6.74) system, on a SMDE. T ) (t/τ)u+1. I(t) ) I0tu and I(t) ) -I0tu . I0 ) 12.0 µA s-u. The values of u are on the curves. The values of τ (in ms) are as follows: u ) 0.075, 54.7; u ) 0.10, 60.4; u ) 0.20, 89.8. (Dotted line) Experimental deωt/dE vs E curves for the azobenzene 30 µM in KNO3 0.1 M (pH ) 6.74) system, on a SMDE. I0 ) 1.5 µA, ω ) 10 s-1, τ ) 0.136 s. (Broken lines) Experimental cyclic voltammograms (ICV/(nFAΓA,0v) vs E curves) for the system azobenzene 30 µM in NO3K 0.1 M (pH ) 6.74), on a SMDE. Sweep rate v ) 2.0 V s-1. Other conditions are as in Figure 7.

Figure 9. Experimental dependence of Ec,peak and Ea,peak with ln(τ/s) (a) and of ∆Epeak with ln(τ/s) (b) for the azobenzene 30 µM in KNO3 0.1 M (pH ) 6.74) system, on a SMDE. I(t) ) I0t0.1, u ) 0.10. Other conditions are as in Figure 8.

curves are shifted toward more negative and positive potential values, respectively, and this causes the difference between peak potentials, ∆Epeak, to increase. The variation of the peak potentials, Ec,peak and Ea,peak, and also of ∆Epeak with the logarithm of transition time, is linear, as is shown in Figure 9. According to eqs 17 and 20, the linear dependence of Ec,peak, Ea,peak and ∆Epeak with ln τ is a typical feature of totally irreversible processes. Hence we can conclude that in these conditions, azobenzene behaves as totally irreversible and we can calculate the values of the kinetic and thermodynamic parameters of the charge transfer by using eqs 16-20. From non-normalized dtu+1/dE versus E curves in Figure 8a, we can conclude that, analogously to the behavior observed in the case of a reversible system, cathodic and anodic peaks heights decrease in absolute value as I0 increases. If we compare the normalized curves of Figure 8b with those obtained for a reversible system (Figure 5b), we can see that in the case of irreversible behavior we do not obtain a single cathodic and a single anodic curve, as we do in the reversible case. Note that in this figure all the anodic and cathodic peaks possess the same respective heights, since peak heights for totally irreversible processes are only dependent on the value of the exponent u and on the cathodic and anodic charge-transfer coefficients (eq 16). Therefore, from the measurement of cathodic and anodic peak heights, R and (1 - R) can be obtained immediately. Thus, from the curves in Figure 8b

we have obtained R ) (0.69 ( 0.02) and (1 - R) ) (0.28 ( 0.01). Moreover, once the charge-transfer coefficients are known, we can obtain the value of the rate constant k0 from the intercept of the linear plots of Figure 9. Thus, from Figure 9b (eq 20), we obtain the following value: log(k0/s-1) ) (0.20 ( 0.02); from Figure 9a, we deduce the following value of the interfacial standard potential E0: (-0.344 ( 0.002) V versus Ag/AgCl, KCl 1.0 M. These values are in line with those previously obtained by us with CRDEC in ref 14 (log(k0/s-1) ) (0.32 ( 0.02), R ) (0.63 ( 0.02), (1 - R) ) (0.35 ( 0.02), and E0 ) (0.336 ( 0.002) V versus Ag/AgCl, KCl 1.0 M). The difference between both sets of data is related to the difference in pH (6.60 in ref 14, 6.74 in the present work) and is in good agreement with data in the literature.30 The initial excess of azobenzene on mercury has also been determined from measurements of peak heights of the CRDPC curves corresponding to u ) 0.10. This value has been obtained by plotting cathodic and anodic peak heights of the dtu+1/dE curves in Figure 8a versus (u + 1)/I0 for different values of the current amplitude I0 (see eqs 6, 7, and 16). Thus, we have obtained Γazobenzene,0 ) (1.81 ( 0.02) × 10-10 mol cm-2, which is in agreement with the value Γazobenzene,0 ) 10-10 mol cm-2 reported in ref 31 by Wopschall and Shain and obtained with linear sweep voltammetry. Finally, Figure 10 shows the comparison between the experimental normalized CRDPC responses for the azobenzene system obtained for three values of the u exponent (0.075, 0.100, and 0.200) and a fixed value of the current amplitude I0 ) 12 µA s-u, the normalized cyclic voltammograms of this system obtained in the same conditions for a sweep rate of v ) 2.0 V s-1, and the CRDEC curves for the azobenzene system corresponding to the application (31) Wopschall, R. H.; Shain, J. Anal. Chem. 1965, 35, 1535.


of exponential currents of the form I(t) ) (I0eωt with ω ) 10 s-1 and ) I0 ) 1.5 µA. Voltammetric and chronopotentiometric curves are given in V-1 for comparison. It can be clearly observed from this figure that the signals corresponding to CRDPC present both higher and narrower peaks than those corresponding to CV or to CRDEC. This behavior is in agreement with theoretical predictions (see Table 1 in ref 14 and eq 28 and Table 1 in this work). Thus, according to eq 28, for u ) 0.1 the ratio dT/dE)peak/ψCV peak ) 1.60, and for u ) 0.075, dT/dE)peak/ψCV peak ) 1.70. From data in Figure 10, we obtain that the values for the ratio between peak heights obtained in CRDPC and CV are similar to theoretical values for the anodic peaks. In the case of the cathodic peaks, the CV experimental ratio dT/dE)peak/ψpeak is even greater than the values theoretically expected because of a strong distortion in the cyclic voltammograms, which is probably due to capacitive effects. This distortion mainly affects the voltammetric cathodic peak and strongly increases with the sweep rate.18 Nevertheless, CRDPC curves are

Langmuir, Vol. 19, No. 2, 2003 415

highly reproducible since the capacitive effects are negligible under these conditions. We have also measured the cathodic and anodic half peak widths in CRDPC curves and obtained the following values for the cathodic peaks: Wc1/2(u ) 0.075) ) 25 mV and Wc1/2(u ) 0.10) ) 27 mV, which are in good agreement with the theoretical ones (see Table 1). These values are, in all the cases, lower than those corresponding to CRDEC. From these results, we can conclude that, as compared to CV, the greater sensitivity, the lower values of the half peak widths, and the smaller distortion of the signal make CRDPC one of the best electrochemical methods for dealing with surface processes. Acknowledgment. The authors greatly appreciate the financial support provided by the Direccioń General de Investigacioń Cientı´fica y Tećnica (Project Number BQU2000-0231) and to the Fundacioń SENECA (Expedient Number 00696/CV/99). LA020369X

Cyclic Reciprocal Derivative Chronopotentiometry with Power Time

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