Anal. Chem. 2009, 81, 6830–6836
Electrocatalytic Responses at Mediator Modified Electrodes with Several Cyclic Step and Cyclic Sweep Potential Techniques. Application to the Oxidation of Ascorbate at a Ferrocene-Monolayer Modified Gold Electrode A. Molina,* C. M. Soto, and J. Gonza´lez Departamento de Quı´mica Fı´sica, Universidad de Murcia, Espinardo 30100, Murcia, Spain Analytical expressions for the current-potential and charge-potential curves of an electrocatalytic process taking place at redox mediator modified electrodes corresponding to the application of cyclic staircase or cyclic sweep potentials are presented. Simple equations for cyclic voltammetry and cyclic voltcoulometry curves have been also deduced for the usual experimental case corresponding to high catalytic rate constants, showing that whereas the current reach an stationary behavior, the charge always depend on time. The value of the rate constant of the chemical step can be easily determined from the plateau of the voltammogram or from the linear anodic region of the charge potential curves. The theoretical predictions have been tested with the electrocatalytic oxidation of ascorbate mediated by a mixed 6-(ferrocenyl)hexanethiol-butanethiol monolayer at a disk gold electrode, with an excellent agreement between theory and experiments. A catalytic rate constant 3440 M-1s-1 has been obtained, which is higher than those previously reported for this system with longer alkanethiol chains. One of the most fruitful trends in the comprehension and control of electrochemical reactions kinetics and catalysis has been the development of modified electrodes to achieve redox mediation of solution processes.1-6 This strategy is based on the electrochemical activation (through the application of an electrical perturbation to the electrode) of different sites at a modified surface. These sites will then oxidize or reduce other redox agents in the adjacent solution for which the direct electrochemical process at the naked surface is inhibited or cannot take place.1,5,7 * To whom correspondence should be addressed. E-mail:
[email protected]. (1) Encyclopedia of Electrochemistry; Bard, A. J., Stratmann, M., Fujihira, M., Rusling, J. F., Rubinstein, I., Eds.; Willey-VCH: Weinheim, 2007; Vol. 10. (2) Bard, A. J.; Faulkner, L. R. Electrochemical Methods, Fundamental and Applications, 2nd ed.; Wiley: New York, 2001. (3) Laviron, E. In Electroanalytical Chemistry; Bard, A. J., Ed.; Marcel Dekker: New York, 1982. (4) Bartlett, P. N. Bioelectrochemistry, Fundamentals, Expermiental Techniques and Applications; Wiley: Chichester, 2008. (5) Save´ant, J. M. Chem. Rev. 2008, 108, 2348–2378. (6) Laviron, E.; Roullier, L. J. Electroanal. Chem. 1980, 115, 65–74. (7) Durst, R. A.; Barmmer, A. J.; Murray, R. W.; Buck, R. P.; Andrieux, C. P. Pure Appl. Chem. 1997, 69, 1317–1323.
6830
Analytical Chemistry, Vol. 81, No. 16, August 15, 2009
The modification of the electrode surface can be carried out by different routes, with the covalent attachment of redox species forming an electroactive monolayer, which is one of the most used.1,4,8-11 Of the different species which can be immobilized, those derived from alkanethiols with pendant redox groups such as ruthenium, osmium, or ferrocene, have been of particular interest since, there is a broad variety of simple methods for chemical synthesis of these thiols and the monolayers thus formed present good stability, few defects, and ideal or nearly ideal voltammetric behavior (mainly when the thiol with a pendant redox group is diluted with an electroinactive alkanethiol).10-12 Moreover, these ferrocene-modified electrodes show excellent electrocatalytic responses to the oxidation of several interesting biomolecules or enzymes such as ascorbate or glucose oxidase.4,8,13 This property makes them very suitable for use as sensors or biosensors. The mediated electron transfer of solution species at these monolayer modified surfaces can be studied by using different electrochemical techniques such as cyclic voltammetry, multipulse chronoamperometry, or rotating disk voltammetry.1,2,4,14 Multipotential pulse techniques are also powerful tools in the characterization of the electrochemical responses of species immobilized on the electrode surface.2,15-20 In a previous paper we deduced an analytical expression for the current of an electrocatalytic process at mediator modified (8) Zanello, P. Inorganic Electrochemistry: Theory, Practise and Application; Royal Society of Chemistry: Cambridge, 2003. (9) Tammeveski, K.; Kontturi, K.; Nichols, R. J.; Potter, R. J.; Schiffrin, D. J. J. Electroanal. Chem. 2001, 515, 101–112. (10) Chidsey, C. E. D. Science 1991, 251, 919–922. (11) Flinkea, H. O. Electroanalytical Chemisty; Bard, A. J. Rubinstein, I., Eds.; Marcel Dekker: New York, 1996. (12) Alleman, K. S.; Weber, K.; Creager, S. E. J. Phys. Chem. 1999, 100, 17050– 17058. (13) Heller, A.; Feldman, B. Chem. Rev. 2008, 108, 2482–2505. (14) Myland, J. C.; Oldham, K. B. Electrochem. Commun. 2005, 7, 282–287. (15) Heering, H. A.; Mondai, M. S.; Amstrong, F. A. Anal. Chem. 1999, 71, 174. (16) Komorsky-Lovric, S.; Lovric, M. J. Electroanal. Chem. 1995, 384, 115– 122. (17) Forster, R. J.; Faulkner, L. R. J. Am. Chem. Soc. 1994, 116, 5453–5461. (18) Gonza´lez, J.; Abenza, N.; Molina, A. J. Electroanal. Chem. 2006, 596, 74– 86. (19) Abenza, N.; Gonza´lez, J.; Molina, A. Electroanalysis 2007, 19, 936–944. (20) Gonza´lez, J.; Molina, A.; Abenza, N.; Serna, C.; Moreno, M. M. Anal. Chem. 2007, 79, 7580–7587. 10.1021/ac901090g CCC: $40.75 2009 American Chemical Society Published on Web 07/14/2009
electrodes for any multipotential pulse technique.21 In this paper we will apply the above-mentioned equation to the study of the current-potential (I-E) and of the converted charge-potential (Q-E) responses obtained when a cyclic staircase or cyclic sweep potential is applied. This last case corresponds to cyclic voltammetry (CV) and cyclic voltcoulometry (CVC) techniques. We have compared the Q-E curves obtained with a cyclic staircase potential and a cyclic linear sweep potential and we have checked that they do not differ, even for pulse amplitude values of 10 mV. From these equations we have deduced a very simple independent of time expression for the CV curves corresponding to high catalytic rate constants or low sweep rates, whatever the reversibility of electrochemical step. We have also found easy equations for the CVC curves, showing that the catalytic chargepotential curves are dependent on time whatever the value of the catalytic rate constant, i. e., they never reach a stationary behavior. Moreover, the rate constant of the chemical step can be easily obtained from the current plateau of the I-E curve or by carrying out a linear regression of the Q-E curve at enough anodic potentials. In order to check the validity of the expressions deduced here, we have analyzed the electrocatalytic oxidation of sodium ascorbate mediated by a mixed 6-(ferrocenyl)hexanethiol-butanethiol monolayer on gold by using CV and CVC. From our results we have observed a nearly ideal reversible electrochemical step, and we have easily obtained the following value for the catalytic rate constant: kc′ ) (3440 ± 200) M-1 s-1. This value is higher than those previously reported for this system with longer alkanethiol chains.22 EXPERIMENTAL SECTION Reagents and Chemicals. Ethanol (Merck), 6-(ferrocenyl)hexanethiol (C6H22FeS), 1-butanethiol (C4SH), NaClO4, L(+) ascorbic acid sodium salt (C6H7NaO6), and buffer solution of pH 9 (Na2B4O7/HCl) (Sigma-Aldrich) were reagent grade and used as received. Electrochemistry. Cyclic staircase voltammetry (CSV) and voltcoulometry (CSVC), and CV) and CVC were performed using a computer-driven potentiostat-galvanostat designed and constructed by Quiceltron. A three-electrode cell was employed in the experiments with a gold disk electrode of diameter 0.01 cm as working electrode. The counter electrode was a Pt foil, and the reference electrode was a saturated calomel electrode (SCE). Solutions were prepared with distilled deionized water (Milli-Q filtering system). Nitrogen gas was passed through solutions for deaeration for 20 min prior to measurements, with nitrogen atmosphere maintained over the solution during all the experiments. All the kinetic and thermodynamic values obtained for the ascorbate system correspond to series of five assays. The results are the mean of the five experimental values. The errors correspond to the standard deviation. The coverages of ferrocene moiety have been calculated by numerical intergration of the baseline corrected voltammograms (21) Gonza´lez, J.; Soto, C. M.; Molina, A. Electrochim. Acta 2009, doi: 10.1016/ j.elecacta.2009.05.068. (22) Kazakeviciene, B.; Valincius, G.; Niaura, G.; Talaikyte, Z.; Kazemekaite, M.; Razumas, V.; Plausinaitis, D.; Teiserskiene, A.; Lisauskas, V. Langmuir 2007, 23, 4965–4971.
Scheme 1
of freshly prepared monolayers in an aqueous solution 1.0 M NaClO4 (pH 9). The roughness factor of the gold electrode, defined as the ratio fr ) Sr/Sg with Sr and Sg being the real surface and geometrical areas, has been determined from the integration of the reduction peak recorded in a 1.0 M H2SO4 solution with a sweep rate v ) 0.050 V s-1, by assuming a value of 400 µC cm-2 for a monolayer of chemisorbed oxygen at a polycrystalline gold electrode.23 From these measurements we have obtained fr ) 5.91. To avoid transport effects in the catalytic response, a magnetic stirrer with a constant rotation rate was placed close to the electrode surface, so a constant agitation was maintained during the whole experiment. By proceeding in this way we have checked that the values of the catalytic pseudo first order rate constant obtained do not depend on the ascorbate concentration. Preparation of the Mixed Ferrocene Modified Gold Electrode. Monolayers of ferrocene were formed by the self-assembling technique on gold substrates. The gold electrode was mechanically polished on alumina slurry (0.05 µm, Buehler), washed and electrochemically cleaned by cycling the potential between 0 and -1.4 V (vs SCE) in 2.0 M NaOH and then between 1.6 and 0.4 V (vs SCE) in 1.0 M H2SO4 until a stable voltammogram was obtained. It was then washed with ethanol and water, and after that the electrode was immersed in mixed solution 2 mM 6-(ferrocenyl)hexanethiol + 2 mM 1-butanethiol in a ratio 1:20 (V:V) respectively, for 48 h at room temperature. Upon removal from the deposition solution, the electrode was thoroughly rinsed with ethanol and water to remove the physically adsorbed species. THEORY Current and Charge of an Electrocatalytic Process at a Mediator Modified Electrode Corresponding to the Application of a Sequence of Pulse Potentials. Let us consider the following catalytic reaction scheme in which A and B refer to strongly adsorbed reduced and oxidized species, respectively, and C and D to species in solution. In Scheme 1, kox and kred are the heterogeneous rate constants for the oxidation and reduction of the adsorbed mediator couple A/B, respectively, and k′c is the rate constant for the chemical step. We will consider that there are no interactions between adsorbates, and no desorption is observed in the time scale of the experiment. Moreover, we assume that the surface concentrations of species C and D are constant and equal to their bulk values (c*C and c*, D respectively), so we can define a pseudo first order rate constant, kc ) k'cc*C
(1)
(23) Trasatti, S.; Petrii, O. A. Pure Appl. Chem. 1991, 63, 711–734.
Analytical Chemistry, Vol. 81, No. 16, August 15, 2009
6831
In a previous reference, we have deduced the following analytical easily manageable expression for the current of the process given in Scheme 1, valid for any multipotential pulse technique:21 Ip QMAX
p-1
∑
) -(kT,p - kc)
j)1
(
)
p kox,j (1 - θj) θl + kT,j l)j+1
∏
kox,p kox,p (k - kc)θp + kc kT,p T,p kT,p
(2)
with θp ) exp(-kT,pτ)
{
kT,p ) kE,p + kc kE,p ) kred,p + kox,p
(3)
}
(4)
The current Ip in eq 2 corresponds to the pth potential pulse applied of a general sequence E1, E2, ..., Ep, in which all the pulses have the same length, τ. Moreover, QMAX ) nFSΓT, with S being the electrode area and ΓT the total electroactive surface excess. In this paper we will deduce the expression of the transformed charged, Qp, corresponding to the pth potential pulse applied in the following way: Qp ) Qmax
∫
tp
0
Ip dt Qmax p
(5)
By taking into account eqs 2 and 5 we obtain: Qp )QMAX
p
∑ j)2
((
1-
) ∑( (
)
kc (1 - θj)fB,j-1 + kT,j p
j)1
(
kox,j kc k τ + (1 - θj) 1 kT,j c kT,j
)))
kox,p (1 - θp) kT,p
p-1
∑ j)1
(
)
p kox,j (1 - θj) θl kT,j l)j+1
∏
(7)
If we consider a Butler-Volmer kinetics for the charge transfer of the adsorbed electrochemical mediator, the heterogeneous rate constants corresponding to the pth potential pulse are2,18
{
kred,p ) k0e-Rηp kox,p ) eηpkred,p
}
(8)
∑
p kox,j Qp kox,p ) + kcτ QMAX kT,p k j)1 T,j
∑
nF (E - E0) RT p
( )
Analytical Chemistry, Vol. 81, No. 16, August 15, 2009
(9)
(11)
For a reversible charge transfer step (i.e., for kE,p > > kc, see eq 4), eq 11 becomes eq 10. CV and CVC. Explicit expressions can also be deduced for CV and CVC by making ∆E e 0.1 mV and ∆E e 10 mV in the expressions for the current and charge given by eqs 2 (CV) and 6 (CVC), respectively. The expressions corresponding to the current in CV for the above particular cases are given in ref 21 (see eqs 16 and 19). Moreover, under these conditions the sums that appear in the Q-E curves (eqs 6, 10, and 11), can be transformed into integrals, from which is possible to obtain the following Q-E expressions for CVC in the case of a reversible charge transfer step (see eq 10),
QMAX
ηp )
(10)
where ηp is given by eq 9. Note that under these conditions the I-E expression given by eq 2 takes a simpler form which is only dependent on the last potential pulse, Ip/QMAX ) kceηp/(1 + eηp), and it reaches a stationary behavior, as is discussed in ref 21. Fast Catalytic Reaction kc > > 1 s-1, (i.e., θp f 0). When a high value of the catalytic rate constant kc is considered, we obtain very different behaviors for the I-E and Q-E curves, independently of the values of the electrochemical rate constants kred and kox. The expression for the current obtained under these conditions presents a very simple form (Ip/QMAX ) kckox,p/kT,p), which is analyzed in section 3.1 of ref 21. However, the corresponding Q-E curve does not have a simple form and, as we will discuss below, it cannot reach the steady state. By making θp f 0 in eq 6 we obtain the following expression for the Q-E curve:
Q
with
6832
p Qp eηj eηp ) + k τ c η ηj p QMAX 1+e j)1 1 + e
(6)
with fB,p being the expression of the surface coverage of oxidized species B corresponding to Ep (see eqs 3 and 12 in ref 21):
fB,p )
where n is the number of transferred electrons. k0, R, and E0 are the heterogeneous rate constant, the charge transfer coefficient and formal potential of the surface couple, respectively. In the following we will consider that the potential perturbation is a cyclic staircase potential (between the limit values Einitial and Efinal), in which all the pulses have the same height ∆E (whose sign may be positive or negative according to the potential sweep).2 The characteristic parameter for this perturbation is the sweep rate, given as v ) ∆E/τ. In these conditions the current-potential (I-E) and the converted charge-potential (Q-E) responses correspond to CSVand CSVC, respectively. Particular Cases. Reversible Charge Transfer Step k0 f ∞ (kred f ∞, kox f ∞). Under these conditions, the θj terms of eq 6 become null (see eqs 3 and 4), and we deduce that the converted charge is only dependent on the catalytic rate constant and on the different potential pulses of the sequence,
) CVC
(
kc RT 1 + eη eη ln + v nF 1 + eηi 1 + eη
)
(12)
and in the case of a fast catalytic reaction with irreversible charge transfer step (kc > > 1 s-1, kox , kred for E , E0, cathodic sweep,
Figure 1. Theoretical I-E (1a and 1c) and Q-E curves (1b and 1d) calculated from eqs 2 and 6 in cyclic staircase voltammetry and voltcoulometry, respectively, for a catalytic mechanism. The values of kc and of the dimensionless heterogeneous rate constant (k0τ) are on the curves. ∆E ) 5 mV, τ ) 10 ms, Einitial ) -400 mV, Efinal ) 400 mV, T ) 298 K, R ) 0.5, and n ) 1. In Figures 1b and d we have also included the Q-E curves obtained in cyclic voltcoulometry calculated from eqs 12 and 13 for v ) 0.5 V s-1.
and kox . kred for E . E0, anodic sweep, see Eqs. (4, 8 and 11),
( ) Q
QMAX
) CVC
(
kox + kc kox kc RT ln + kox + kc v (1 - R)nF kox,i + kc
) (13)
with ηi ) nF(Einitial - E0)/RT and kox,i ) k0exp {(1 - R)ηi}. RESULTS AND DISCUSSION Theoretical Results. Figure 1 shows the theoretical I-E and Q-E curves, calculated from eqs 2 and 6, respectively, for different values of the catalytic rate constant kc, and corresponding to a cyclic staircase potential with ∆E ) 5 mV and τ ) 10 ms (i.e., v ) 0.5 V s-1). We have considered two values of the dimensionless heterogeneous rate constant (k0τ) ) 2 and 0.02, which refer to reversible (1a and 1b) and totally irreversible (1c and 1d) electrochemical behavior. From Figures 1a and c we can see that, when the catalytic rate constant kc increases, the I-E response changes its feature from two peak-shaped curves (with more separate peaks the smaller reversibility degree of the charge transfer), to a single sigmoidal one (stationary state). The kc limit necessary for reaching this stationary behavior increases as the value of the heterogeneous rate constant k0 decreases (note that in Figure 1c the steady state has not been reached for kc ) 20 s-1).
The Q-E curves of Figures 1b and d clearly show that, according to eqs 6, 10, and 11, a stationary behavior cannot be reached in any case. From the first sweep of these curves we can also observe that the converted charge is null until potentials close to E0, from which it increases with the potential, with this increase becoming linear for anodic enough values. For the second sweep, the Q-E curves present an opposite behavior, i.e., they increase linearly until they reach a constant value (charge plateau) for enough cathodic potentials. It is important to highlight that the cyclic Q-E curves shown in Figures 1b and d are independent of the pulse amplitude for ∆E e 10 mV, i. e., the results obtained in CV are identical to those of CSV under these conditions. We have included in these Figure the Q-E curves obtained in CVC calculated from eqs 12 and 13 and they are perfectly superimposable on those obtained in CSVC. Moreover, for CVC the above behavior can be characterized when the charge transfer step is reversible (1b) or totally irreversible (1d). Reversible Charge Transfer Step k0 f ∞ (kred f ∞, kox f ∞). Under these conditions, if we consider anodic potentials, E . E0, we obtain from eq 12
( ) Q QMAX
CVC
)1(
kc (E - E0) v
Analytical Chemistry, Vol. 81, No. 16, August 15, 2009
(14) 6833
Figure 2. Theoretical Q-E curves calculated from eq 6 for a catalytic mechanism in Cyclic Staircase Voltcoulometry. kc ) 20 s-1. The values of the dimensionless heterogeneous rate constant (k0τ) are on the curves. Other conditions as in Figure 1.
with the upper sign referring to the first sweep and the lower to the second one. From this linear relationship between the charge and the potential, kc can be easily deduced from the anodic slopes of both sweeps. The expression of the reversible cathodic charge plateau can also be deduced from eq 12 by imposing E f -∞ in the second cathodic sweep,
(
Qplateau QMAX
)
)1+
CVC
2kc (E - E0) |v| f
(15)
with Ef being the reversal potential. Irreversible Charge Transfer Step. In this case, on introducing E . E0 into eq 13 it can be immediately deduced
( ) Q
QMAX
)1(
CVC
()
kc kc RT k0 ln ( (E - E0) v (1 - R)nF kc v (16)
Concerning the irreversible cathodic charge plateau, by making E f -∞ in the expression of the charge for the second sweep we obtain:
(
Qplateau QMAX
)
CVC
)1+
()
2kc 2kc RT k0 ln (E - E0) + |v| (1 - R)nF kc |v| f (17)
Note that in agreement with eqs 14 and 16, the absolute value of the slope of these linear regions does not depend on the reversibility degree of the charge transfer step and its measurement will allow us to obtain the catalytic rate constant. This behavior can be clearly observed in Figure 2, where we have plotted the theoretical Q-E curves calculated from eq 6 for a catalytic mechanism in CSVC with v ) 0.5 V s-1 for a catalytic rate constant kc ) 20 s-1 and different values of the dimensionless heterogeneous rate constant (k0τ). 6834
Analytical Chemistry, Vol. 81, No. 16, August 15, 2009
Figure 3. Theoretical I-E (a) and Q-E (b) curves calculated from eqs 2 and 6, respectively, for a catalytic mechanism in CV and CVC (∆E ) 0.01 mV), with v ) 0.5 V s-1, k0 ) 200 s-1 and kc ) 5 s-1. The values of the sweep rate v are on the curves. Other conditions as in Figure 1.
Note also that, for the value of Ef used in this Figure, the cathodic charge plateau of these curves decreases the more irreversible the charge transfer is, in line with eqs 15 and 17 (in the case Ef > . E0, the Qplateau does not depend on the electrochemical rate constant since the last term in eqs 15 and 17 becomes dominant). In Figure 3 we have studied the effect of the sweep rate on the theoretical I-E (3a) and Q-E (3b) curves obtained in CV and CVC and calculated with eqs 2 and 6 (with ∆E ) 0.01 mV), for a catalytic mechanism with kc ) 5 s-1 and k0 ) 200 s-1. From the curves in Figure 3a it can be seen that the decrease of the sweep rate v leads to a decrease of the current and to a stationary I-E curve. Nevertheless, the current reaches the value kc at anodic potentials, independently of the sweep rate. Concerning the Q-E curves of Figure 3b, no stationary behavior is obtained in any case. According to eqs 14-17, both the slope of the linear zone and the height plateau depend on 1/v and therefore, the charge value increases as v decreases. Experimental Results. We have carried out the experimental verification of the above predictions by analyzing the cyclic voltcoulograms of a ferrocene-containing monolayer on a gold electrode in presence of sodium ascorbate. Self-assembled monolayers with pendant ferrocenes have been widely used in studies on long-range electron transfer, electro-
chemical rectification, electrocatalytic processes, and the development of new sensors and biosensors.1,8,10-13 Ideal or nearly ideal voltammetric behavior can be obtained with these monolayers when the ferrocene thiol is diluted with an alkanethiol.10-12 In our case, we have formed a 6-(ferrocenyl)hexanethiol-butanethiol (FcC6SH-C4SH, 1:20) mixed monolayer, and the redox reaction of the ferrocene moiety as electrochemical mediator has been investigated in the presence of sodium ascorbate as reducing agent. Thus, the ferrocenium formed at anodic potentials is reduced to ferrocene by the ascorbate in solution and the whole process turns into a surface catalytic reaction, in agreement with the following Scheme: kred
FcC6SH {\} Fc+C6SH + ekox
kc
Fc+C6SH + Asred 98 FcC6SH + Asox
(II)
As-red and Asred are the abbreviated form of oxidized and reduced sodium ascorbates, respectively. We have formed the FcC6SH-C4SH mixed monolayers by following the procedure described in the Experimental Section and we have evaluated their electrochemical behavior with CV in a solution 1.0 M NaClO4 (pH 9). Practically reversible I-E curves have been observed in these conditions with a ferrocene excess (taking into account the roughness factor fr ) 5.91) of Γferrocene ) (9.1 ± 0.1) × 10-11 mol cm-2. This result is in line with those previously reported by Creager at al.24 To obtain the catalytic rate constant of this process, we carried out CV with different sweep rates in an aqueous solution 1.0 M NaClO4 (pH 9) with sodium ascorbate in a concentration 10 mM. The corresponding I-E and Q-E curves have been plotted in Figures 4a and b, respectively, with the sweep rates being indicated on the curves. The CV curves in Figure 4a show a sigmoidal feature which is typical of stationary or nearly stationary behavior (see Figure 1). The increase of the sweep rate moves the response away from the stationary limit, in agreement with the theoretical results shown in Figure 3. From these experimental voltammograms, a not well-defined plateau can be observed which is independent of the sweep rate with a current increase of 5% when v goes from 0.06 to 0.2 V s-1 (see Figure 4a). These deviations let us conclude that, from the measurement of the CV current plateaus, only an estimation of the catalytic rate constant kc can be made. In the case of the Q-E curves of Figure 4b, it can be seen that no stationary behavior has been reached, as we have discussed above (see Figures 1 and 3). The experimental transformed charges increase as the sweep rate decreases and they show a clear linear region at potentials above 0.150 V. The slope of these linear zones should be equal to (kcQMAX)/v, whatever the reversibility degree of the charge transfer step (see eqs 14 or 16 and the above discussion). We have carried out the linear regression of these zones for different values of v in the range 0.020-0.200 V s-1, and the slopes obtained have been plotted vs the inverse of the sweep rate (see Figure 4c). An excellent linearity with practically coincident plots for the two (24) Rowe, G. K.; Creager, S. E. Langmuir 1991, 7, 2307–2312.
Figure 4. Experimental I-E (a) and Q-E (b) curves obtained in CV and CVC for a mixed ferrocene monolayer (FcC6SH-C4SH) adsorbed on a disk gold electrode of radius r0 ) 0.01 cm in an aqueous solution 1 M NaClO4 (pH 9) with sodium ascorbate 10 mM. The values of the sweep rate v (in V s-1) are 0.06 (black circles), 0.09 (white circles) and 0.2 (solid lines). T ) 298 K. In Figure 4c we have plotted the values of slopes for the anodic (black dots) and cathodic (white squares) sweeps, and also the charge plateaus (gray triangles) of the Q-E curves in the range v ) 20-200 mVs-1 vs 1/v.
sweeps can be seen in this Figure. From this data we have obtained (kcQMAX) ) (0.144 ± 0.002) µA. By taking into account the value of Γferrocene previously determined (which leads to a total charge QMAX ) 4.1 nC), we finally obtain kc ) (34.4 ± 2) s-1 for the first order catalytic rate constant which, in agreement with eq 1, leads to a rate constant k′c ) (3440 ± 200) M-1s-1. This value is higher than those previously reported for this system with longer alkanethiol chains.22 We have also plotted the values of the cathodic charge plateau versus 1/v, again obtaining a very good linearity (see Figure 4c). We have previously pointed out that the value of the charge plateau is strongly affected by the reversibility of the charge Analytical Chemistry, Vol. 81, No. 16, August 15, 2009
6835
a sweep rate v ) 0.050 V s-1 in an aqueous solution 1.0 M NaClO4 (pH 9) with sodium ascorbate 10 mM (solid lines). In this Figure we have included the theoretical I-E and Q-E curves calculated from eqs 16 of ref 21 and 12, which correspond to a catalytic process with reversible electrochemical mediator (symbols). To calculate the theoretical curves we have used: kc ) 33 s-1, QMAX ) 4.1 nC and E0 ) 0.116 V. The agreement between theoretical and experimental results confirms the validity of the supposition of reversible charge transfer step made above and also the accuracy of the experimental parameters deduced. These results allow us to conclude that CSV and CV are revealed as useful tools for carrying out a fast and accurate determination of the characteristic parameters of a catalytic mechanism in a very simple way. CONCLUSIONS
Figure 5. (solid lines) Experimental I-E (a) and Q-E (b) curves obtained in CV and CVC for a mixed FcC6SH-C4SH monolayer adsorbed on a disk gold electrode of radius r0 ) 0.01 cm in an aqueous solution 1 M NaClO4 (pH 9) with sodium ascorbate 10 mM.v ) 0.05 V s-1. (symbols) Theoretical I-E (a) and Q-E (b) curves calculated from eqs 16 in 21 and 12 by using the following parameters: E0 ) 0.116 V, kc ) 33 s-1, n ) 1, R ) 0.5, QMAX ) 4.1 nC and T ) 298 K.
transfer step (see eqs 15 and 17). If we suppose that the ferrocene oxidation can be considered as reversible under these conditions (and the voltammograms carried out in a solution 1.0 M NaClO4 clearly endorse this point), the linear dependence observed should be given by eq 15, with the slope being 2kcQMAX(Ef-E0). By combining the value obtained for the slope with that of kcQMAX calculated above, and by taking into account that Ef ) 0.300 V, we deduce the following value for the formal potential of the ferrocene/ferrocenium couple: E0 ) (0.115 ± 0.002) V vs SCE. We will check the validity of this result below. To check the goodness of the data obtained from the Q-E curves in Figure 4b, in Figure 5 we have plotted the experimental I-E and Q-E curves obtained in CV and CVC, respectively, for
6836
Analytical Chemistry, Vol. 81, No. 16, August 15, 2009
In this paper we present analytical expressions for the current and charge of an electrocatalytic process taking place at a redox mediator modified electrode when a cyclic staircase or a cyclic sweep potential is applied. In the usual experimental case for which the catalytic rate constant is very high, we have deduced very simple expressions for the I-E and Q-E curves. It must be highlighted that under these conditions, the current shows a sigmoidal feature independent of the sweep rate which clearly points to its stationary nature, whereas the charge never reaches a stationary behavior and its value is strongly dependent on the sweep rate. Also, the Q-E curves obtained when potential steps or potential sweeps are applied are practically coincident for pulse amplitude values ∆E e 10 mV. Moreover, the catalytic rate constant kc can be obtained easily from the anodic plateau of the I-E curves or by carrying out a linear regression of the anodic zone of the Q-E curves. The theoretical predictions for CV and CVC have been verified by analyzing the electrocatalytic oxidation of sodium ascorbate mediated by a mixed 6-(ferrocenyl)hexanethiol-butanethiol monolayer in gold. ACKNOWLEDGMENT We greatly appreciate the financial support provided by the Direccio´n General de Investigacio´n Cientı´fica y Te´cnica (Project Number CTQ2006-12552/BQU), and the Fundacio´n SENECA (Project Number 08813/PI/08). C.M.S thanks the Ministerio de Educacio´n y Ciencia for the grant received.
Received for review May 19, 2009. Accepted June 29, 2009. AC901090G
