Anal. Chem. 2007, 79, 7580-7587
Square Wave Voltcoulometry: A Tool for the Study of Strongly adsorbed Redox Molecules Joaquı´n Gonza´lez, Angela Molina,* Nuria Abenza, Carmen Serna, and Marie´n M. Moreno
Departamento de Quı´mica Fı´sica, Universidad de Murcia, Espinardo 30100, Murcia, Spain
A new multipotential pulse technique called square wave voltcoulometry (SWVC), based on the analysis of the difference of converted charge signals obtained between two successive half-cycles when a square wave potential is applied, is developed to study charge-transfer processes taking place in electroactive monolayers. The use of SWVC presents the advantage of giving rise to a peak-shaped response, which evolves to a charge plateau at high square wave pulse amplitudes, from which the total surface excess and the formal potential can be immediately measured for quasi-reversible and reversible processes. This characteristic represents its main advantage versus other multipotential step techniques, which lead to a negligible current under reversible conditions. The formal potential of the electroactive systems can be measured from the peak potential of the SWVC curves, even for quasi-reversible behavior. Moreover, the non-faradic effects on the response can be easily evaluated and avoided as is demonstrated in this paper. Experimental verification of the theoretical predictions is given for reversible and quasi-reversible systems. The main advantage derived from the use of discrete nature potential perturbations in the study of electroactive monolayers is their inherent ability to decouple faradic responses from nonfaradic ones.1-4 Among the different multipotential perturbations, the square wave one presents the advantage that it minimizes most of the nondesired effects because the registered signal, which corresponds to the current in square wave voltammetry (SWV), is related to the difference of signals obtained between successive half-cycles.1,2,4,5 This technique has been used in the electrochemical study of monolayers since it allows for a very efficient level of data analysis over a very wide range of frequencies. Moreover, an increase in the square wave pulse amplitude gives rise to an accurate measure of the surface rate constants of electrode * Corresponding author. E-mail:
[email protected]. Tel: +34 968 367524. Fax: +34 968 364148. (1) Bard, A. J.; Faulkner, L. R. Electrochemical Methods, 2nd ed.; Wiley: New York, 2001. (2) Brett, C. M. A.; Oliveira Brett, A. M. In Encyclopedia of Electrochemistry; Bard, A. J., Stratmann, M., Unwin, P., Eds.; Wiley-VCH: Weinheim, 2003; Vol. 3, Section 2.2. (3) Vos, J. G.; Forster, R. J.; Keyes, T. E. Interfacial Supramolecular Assemblies; Wiley: Chichester. 2003. (4) Galus, Z. Fundamentals of Electrochemical Analysis, 2nd ed.; Horwood E.: Chichester, 1994. (5) Osteryoung, J.; O’Dea J. J. In Electroanalytical Chemistry; Bard A. J., Ed.; Marcel Dekker: New York, 1986; Vol. 14.
7580 Analytical Chemistry, Vol. 79, No. 19, October 1, 2007
processes.6-13 Despite the above, the SWV technique also presents an important disadvantage due to the discrete potential perturbation applied, i.e., the fact that typical reversible processes, such as those corresponding to a great number of electroactive adsorbates (i. e., redox-active proteins and dendrimers, redox quinones and thiol derivatives, etc.), lead to a practically null faradic current, and high values of the square wave frequency must be used in order to transform the response to quasireversible, and nonidealities and non-faradic effects are enhanced under these conditions.1,6-10 In this paper, we propose an interesting alternative to SWV: the square wave voltcoulometry technique (SWVC), which is based on the analysis of the difference of converted faradic charge signals obtained between two successive half-cycles when a square wave potential is applied. We present analytical expressions corresponding to SWVC (Qsw/E curves) and SWV (Isw/E curves), which are applicable to quasi-irreversible charge-transfer processes, in order to compare both techniques. These expressions have been deduced from previously reported charge-potential and current-potential responses, which are valid for any multipotential sequence.14 The use of SWVC presents the advantage that it gives rise to an easily manageable response for reversible processes, which for extreme values of the square wave amplitude behaves in a formally similar way to that corresponding to the Isw/E curve obtained for a soluble solution redox species. From these limit situations, the total surface excess and the formal potential can be immediately measured. For quasi-reversible processes, kinetic parameters of the process can be obtained by comparing experimental results with the general equations given here. It is important to highlight that, at high enough values of the square wave amplitude, both reversible and quasi-reversible conditions give rise to a well-defined plateau in the Qsw/E curve, (6) Lovric M.; Komorsky-Lovric, S.; Murray, R. W. Electrochim. Acta 1988, 33, 739-744. (7) O’Dea, J. J.; Osteryoung, J. Anal. Chem. 1993, 65, 3090-3097. (8) Reeves, J. H.; Song, S.; Bowden, E. F. Anal. Chem. 1993, 65, 683-688. (9) O’Dea, J. J.; Ribes, A.; Osteryoung, J. J. Electroanal. Chem. 1993, 345, 287-301. (10) Komorsky-Lovric, S.; Lovric, M. J. Electroanal. Chem. 1995, 384, 115122. (11) Jeuken, L. J. C.; McEvoy, J. P.; Armstrong, F. A. J. Phys. Chem. B 2002, 106, 2304-2313. (12) Zhang, J.; Guo, S.-X.; Bond, A. M.; Honeychurch, M. J.; Oldham, K. B. J. Phys. Chem. B 2005, 109, 8935-8947. (13) Fleming, B. D.; Barlow, N. L.; Zhang, J.; Bond, A. M.; Armstrong, F. A. Anal. Chem. 2006, 78, 2948-2956. (14) Gonza´lez, J.; Abenza, N.; Molina, A. J. Electroanal. Chem. 2006, 596, 7486. 10.1021/ac071006a CCC: $37.00
© 2007 American Chemical Society Published on Web 08/29/2007
which allows an immediate measure of the total surface excess of the monolayer. Finally, and in contrast to SWV, the SWVC technique does not present a significant response for totally irreversible processes. In this case, the square wave frequency should be decreased as indicated in refs 6, 7, 9, 10, and 15 or SWV should be used. Moreover, the non-faradic effects on the Qsw/E curve can be easily evaluated and avoided as is demonstrated in this paper. In order to verify theoretical predictions for SWVC, we have analyzed the electrochemical behavior of monolayers of the system anthraquinone-2-carboxylic acid 10 µM in two different aqueous media: HClO4 1.0 M (pH ) 0) and HClO4 0.1 M/NaClO4 0.2 M solution (pH ) 1), and we study both reversible and quasireversible responses, respectively. Quinone monolayers behave almost ideally in agreement with refs 14 and 16-19 and nowadays there is a growing interest in these compounds because of their different applications such as chemical assemblies,20 photosynthetic electrochemical cells,21 hybrid films,22 spectroelectrochemical investigations,23 and biomimetics nanostructured electrocatalysts.24
Scheme 1. (a) General Potential-Time Waveform Corresponding to SWVC,a (b) Q/t Curve Obtained by Integrating the I/t Response Corresponding to the Application of the Perturbation Given in (a), (c) Qsw/E Curve (with Qsw ) Qf - Qr) of a Reversible Process for Different Limit Cases of Square Wave Amplitude Pulsesb
EXPERIMENTAL SECTION Materials and Procedures. Ethanol, NaH2PO4, Na2HPO4 (Merck, reagent grade), HClO4, and the anthraquinone-2-carboxylic acid (2-AQCA) (Aldrich, reagent grade) were used as received. 2-AQCA was dissolved in ethanol and then diluted with water until the final proportion of ethanol was 1%. 2-AQCA was adsorbed at the mercury surface at a rest potential Erest ) 0.150 and -0.200 V versus reference (at pH ) 0 and 1, respectively), for 30 s prior to measurements. Apparatus. SWVC, SWV, and chronoamperometry were performed by using a computer-driven potentiostat-galvanostat designed and constructed by Quiceltron. A three-electrode cell was employed in the experiments. A homemade static mercury drop electrode (SMDE) served as working electrode. 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. Solutions were prepared with distilled deionized water (Milli-Q filtering system), and nitrogen gas was passed through solutions for deaeration for 30-40 min prior to measurements, with a nitrogen atmosphere maintained over the solution during all the experiments. All the kinetic and thermodynamic values obtained for the 2-AQCA systems correspond to series of five essays. The results obtained are the mean of the five experimental values. The errors correspond to the standard deviation. (15) (16) (17) (18) (19) (20) (21) (22) (23) (24)
Komorsky-Lovric, S.; Lovric, M. Anal. Chim. Acta 1995, 305, 248-255. Forster, R. J. J. Electrochem. Soc. 1997, 144, 1165-1173. Forster, R. J.; O’Kelly, J. P. J. Electroanal. Chem. 2001, 498, 127-135. Molina, A.; Gonza´lez, J.; Abenza, N. Electrochim. Acta 2007, 52, 43514362. Molina, A.; Gonza´lez, J. Langmuir 2003, 19, 406-415. Katz, E.; Willner, I.; Electrochem. Commun. 2006, 8, 879-882. Lam, K. B.; Irwin, E. F.; Healy, K. E.; Lin L. Sens. Actuators, B 2006, 117, 480-487. Lin, K. C.; Chen, S. M. J. Electroanal. Chem. 2006, 589, 52-59. Noll, G.; Kozma, E.; Grandori, R.; Carey, J.; Schodl, T.; Hauska, G.; Daub, J. Langmuir 2006, 22, 2378-2383. Calvo, E. J.; Rothacher, M. S.; Bonazzola, C.; Wheeldon, I. R.; Salvarezza, R. C.; Vela, M. E.; Benitez, G. Langmuir 2005, 21, 7907-7911.
a Dashed line corresponds to the index potential (see eq 3). (I)|Esw| < 10 mV, (II)(10 < |Esw| < 100) mV, and (III) |Esw| > 100 mV. Peak heights and half peak widths values corresponding to limit cases I and III are shown in the figure. Black and dark gray dots in (a) and (b) correspond to the values of forward and reverse potentials and charges, respectively, at the end of each pulse.
b
Time constant and resistance for the system 2-AQCA 10 µM + HClO4 0.1 M/NaClO4 0.2M (pH ) 1) have been obtained from multipulse potential chronoamperometry measures by following the procedure described in ref 14. Analytical Chemistry, Vol. 79, No. 19, October 1, 2007
7581
THEORY General Solutions for Square Wave Voltcoulometry (Qsw/E Curves) and Square Wave Voltammetry (Isw/E Curves). In this paper, we present a new multipotential pulse electrochemical technique called SWVC, in which, the potential sequence applied is that corresponding to square wave techniques, which is given by1,2,5
[ (p +2 1) - 1]|∆E | + (-1) |E p
Ep ) Einitial - Int
s
sw|;
[
Isw ) QMAX
θ2p-1 -
∑ j)1
1
θ2p + 1 + eη2p 2p-1(1 - θ ) 2p j θl θl η j)1 1 + e j l)j+1 1 + eηj l)j+1 p ) 1, 2, ..., np (5)
1+e 2p-2(1 - θ ) 2p-1 j η2p-1
∑
∏
]
∏
with
p ) 1, 2, ..., np (1)
with |∆Es| and |Esw| being the staircase and square wave pulse amplitudes, respectively, Int(x) is the integer part of the argument x and np the total number of potential pulses of the sweep. The sequence of applied potentials can be considered as an staircase of pulse amplitude |∆Es| on which a square wave of height 2|Esw|1,2,5 is superimposed (See Scheme 1). The signal is measured at the end of each potential pulse, and the net response is the difference between the signal corresponding to a pulse with odd index (forward) and the signal of the following pulse with even index (reverse), with all the potentials having the same time length, τ. In this new technique, we will apply the square wave potential sequence to the analysis of the converted charge in an electroactive monolayer where the electron-transfer process O + nekf {\ kb} R is taking place. We have considered that the adsorption follows the Langmuir isotherm in such a way that there are no interactions between adsorbates, and no desorption is observed in the time scale of the experiment. Thus, we will obtain the Qsw/E curves of this process with,
Qsw ) Q2p-1 - Q2p ) Qf - Qr;
1
(6)
kT,p ) kf,p + kb,p
(7)
ηp )
nF (E - E0) RT p
(8)
QMAX ) nFAΓT
(9)
In the above equations, kf,p and kb,p are the first-order heterogeneous rate constants (s-1) at potential Ep, for the electroreduction and electrooxidation reactions, respectively, and E0 is the formal potential of the surface process. In the following, we have supposed that the charge-transfer process can be described by a Butler-Volmer kinetics1-3 although the consideration of more complex models such as the Marcus one is straightforward.25 Simplified Solution for Reversible Processes (k0 f ∞, kf,pf ∞, kb,pf ∞). (a) Square Wave Voltcoulometry (Qsw/E Curves). Under reversible conditions, the θp terms, which appear in the expressions of the charge Qsw, given by eq 4, become null and the SWVC response takes the following simpler form:
(
Qsw)rev ) QMAX
p ) 1, 2, ..., (np/2) (2)
instead of the usual Isw/E curves corresponding to square wave voltammetry (with Isw ) I2p-1 - I2p ) If - Ir). The Qsw/E curves present an intense signal for reversible processes from which they can be completely characterized, whereas the Isw/E curves are not obtained under reversible conditions.1,7,10,14,18 Both Qsw and Isw signals are plotted versus the index potential, defined as an intermediate potential value between each pair of consecutive pulses (see dashed line in Scheme 1),
θp ) exp( -kT,pτ)
)
1 1 η2p-1 1+e 1 + eη2p
(10)
with η2p-1 ) η2p + (2nF/(RT))|Esw|. This response presents a peak whose potential and height are given by 0 Epeak index ) E
Qpeak sw ) QMAX tanh
(11)
(
)
nF|Esw| 2RT
(12)
Finally, the half-peak width takes the value
Eindex,p ) Ep + ( - 1)p+1|Esw|
(3)
The analytical, fully explicit, and easily manageable expressions of the charge-potential and the current-potential curves corresponding to electroactive monolayers when a square wave potential is applied are the following (see eq 1 in ref 14):
[
1
Qsw ) QMAX
1
(1 - θ2p) + 1+e 1 + eη2p 2p-2(1 - θ ) 2p-1 2p-1(1 - θ ) 2p j j θl θl p ) 1, 2, ..., np (4) η η j)1 1 + e j l)j+1 j)1 1 + e j l)j+1
∑
7582
(1 - θ2p-1) -
η2p-1
∏
∑
∏
]
Analytical Chemistry, Vol. 79, No. 19, October 1, 2007
Wrev 1/2 )
(
RT ln nF
)
1 + e2ηsw + 4eηsw + x(1 + e2ηsw + 4eηsw)2 - 4e2ηsw
1 + e2ηsw + 4eηsw - x(1 + e2ηsw + 4eηsw)2 - 4e2ηsw
(13)
Note that the peak potential given by eq 11 does not depend on the characteristics of the square wave sequence, whereas the (25) (a) Finklea H. O. In Electroanalytical Chemistry; Bard A. J., Rubinstein, I., Eds.; Marcel Dekker: New York, 1996; Vol. 19. (b) Finklea H. O. In Encyclopedia of Electrochemistry, Modified Electrodes; Bard, A. J., Stratmann, M., Fujihira, M., Rusling, J. F., Rubinstein, I., Eds.; Wiley-VCH: Weinheim, 2007; Vol. 10.
rev peak charge, Qpeak sw , and the half-peak width, W1/2, depend on the square wave amplitude according to eqs 12 and 13. These parameters present the following limiting values (see Scheme 1):
peak W rev 1/2 ) 90/n mV Qsw )
nF|Esw| QMAX for 2RT
|nEsw| < 10 mV
(14) W rev 1/2
) 2|Esw|
Qpeak sw
) QMAX
for
with Ru being the resistance of the cell, ∆Ep being the potential step applied (∆Ep ) 2|Esw| + |∆Es|) in the case of forward pulses and ∆Ep ) 2|Esw| for reverse pulses), and Cnf(E) being the nonfaradic capacitance of the electroactive monolayer. Therefore, by considering the interface with the parallel capacitors model introduced by Damaskin,30 the non-faradic capacitance, Cnf, can be written as
|nEsw| > 120 mV
Cnf ) CmOfO(τ) + CmR(1 - fO(τ))
From these limiting expressions, it is evident that the square wave Qsw/E curves corresponding to strongly adsorbed molecules behave in a similar way to the Isw/E curves observed for a soluble solution reversible redox process in square wave voltammetry when an ultramicroelectrode is used (i. e., when steady-state conditions are attained), if we take into account the analogous role played by Qsw (adsorbed species) and Isw (soluble solution species), and also QMAX (eq 9) and Id, with Id being the steadystate diffusion-limited current; see refs 1, 26, and 27. This analogy can be made because the normalized converted charge in a surface reversible electrode process is proportional to the difference between the initial surface concentration (ΓT) and that corresponding at potential Ep, (Q/QMAX) ∝ (ΓT - ΓO), and in electrochemical systems under mass-transfer control, the voltammetric normalized current is proportional to the difference between the bulk (cO*) and surface concentration (csO) at potential Ep, (I/Id) ∝ (cO* - csO(E)). Second, both types of systems fulfill
(17)
with CmO and CmR being the non-faradic capacitance at fO ) 1 and fO ) 0, respectively, which can be considered as practically constant, and fO(τ)( ) ΓO(τ)/ΓT) is the surface coverage of oxidized species at time τ. By taking into account the relationship between the coverage and the faradic charge Q (see eq 3 in ref 31), we can rewrite eq 17 in the following way:
Cnf ) CmO + (CmR - CmO)(Q/QMAX)
(18)
with Q being the expression of the faradic converted charge corresponding to the pth potential pulse given by eq 8 in ref 14. By solving eq 16 by taking into account the expression of Cnf(E) given by eq 18 we obtain for any potential pulse:
Qnf,p )
|∆Ep| -P(τ) e Ru
P(t) )
Ap + Bpe-kT,pt t 1 + ln Ap kT,pAp Ap + B p
(20)
kf,p Ap ) RuCmO + Ruδ kT,p
(21)
∫
τ
0
eP(t) dt + Qnf,p-1
(19)
with,
ΓT - ΓO(E) cO* - csO(E) 1 ) ) ΓT cO* 1 + eη
(15)
with η ) nF (E - E0)/(RT). Note also that, for low values of |nEsw|, the expressions of Wrev 1/2 and peak height given by eq 14 are analogous to those corresponding to LSV (if we change |Esw|/2 by v/4, with v being the sweep rate; see eqs 14.3.13 and 14.3.14 in ref 1). (b) Square Wave Voltammetry. For reversible chargetransfer processes (i. e. for (k0τ) g5), no significant current is observed (see eq 5), and therefore, this technique is not appropriate.7,10,14,18,28 Expression of the Non-Faradaic Charge of an Electroactive Monolayer in SWVC. The measured experimental converted charge when a potential Ep is applied can be considered as the sum of a pure faradic contribution, given by eq 9 in ref 14, and a non-faradic one, Qnf,p. The expression for Qnf,p can be obtained by taking into account the analogy between the interface and an RC circuit,1,29 so we must solve the following differential equation:
dQnf,p Qnf,p - ∆Ep + ) dt Ru RuCnf(E)
(16)
(26) Oldham K. B. In Microelectrodes: Theory and Applications; Montenegro, M. I., Queiros, M. A., Daschtach, J. L., Eds.; Kluwer Academic Publishers: Dordrecht, 1991. (27) Molina, A.; Serna, C.; Camacho, L. J. Electroanal. Chem. 1995, 394, 1-6. (28) Abenza, N.; Gonzalez, J.; Molina, A. Electroanalysis 2007, 19, 936-944. (29) Nahvi, M.; Edminister, J. A. Outline of theory and problems of Electric Circuits, 4th ed.; Mc Graw-Hill: New York, 2003.
(
(
Bp ) Ruδ
p-1 k f,j
∑k
)
kf,p
p-1
(1 - θj)
j)1 T,j
∏θ - k l
l)j+1
T,p
)
δ ) CmR - CmO
(22) (23)
The net non-faradic charge, which corresponds to the difference Qsw,nf ) Q2p-1,nf - Q2p,nf ) Qf,nf - Qr,nf, is given by (see eq 19),
Qsw,nf )
2|Esw| -P(τ) e Ru
∫
τ
0
eP(t) dt
(24)
Equation 24 has been obtained by considering that the pulse time length τ is much greater than the time constants (RuCmO) and/or (RuCmR). Note that, in agreement with eq 24, the non-faradic contribution to the Qsw/E response is only due to the potential jump (equal to 2|Esw|). This behavior is due to the differential character of the Qsw,nf/E response. (30) Damaskin, B. B.; Petriiand, O. A.; Batrakov, V. V. Adsorption of organic compounds on electrodes, 1st ed.; Plenum Press: New York, 1971. (31) Gonza´lez, J.; Molina, A. J. Electroanal. Chem. 2003, 557, 157-165.
Analytical Chemistry, Vol. 79, No. 19, October 1, 2007
7583
Under reversible conditions, the θp terms which appear in eqs 19-22 tend to zero, and therefore, the following simplified expression for the net non-faradic charge is obtained,
(
Qsw,nf ) 2|Esw| CmO +
)
δ 1 + eη2p
(25)
Note that eq 25 can be also obtained by considering that for reversible processes the non-faradic capacitance given by eq 18 is only dependent on the potential (see eq 3 in ref 31). Therefore, the expression of the non-faradic charge corresponding to a pulse Ep, due to the discrete nature of the potential, can be written as p
Qnf,p )
∑(C
nf(Ei)∆Ei)
(26)
i)1
with ∆Ei ) Ei - Ei-1. By calculating Qsw,nf from eqs 2 and 26, we obtain again the expression of the non-faradic charge given by eq 25. This equation indicates that Qsw,nf gives rise to a baseline for which Ep > E0 2|Esw|CmO. This expression can be considered as valid for dimensionless rate constants of the order of (k0τ) g1. For smaller k0τ values, the general expression of Qsw,nf, given by eq 24 must be used. Finally, note that when CmO = CmR ) Cm, the non-faradic charge logically takes the constant value 2|Esw|Cm, whatever the value of (k0τ) was. RESULTS AND DISCUSSION We have studied the influence of the reversibility of the electrode process on the forward and reverse theoretical chargepotential responses (Qf/QMAX) versus (Ein - E0) and (Qr/QMAX) versus (Ein - E0) curves; see solid and dashed lines, respectively, in Figure 1), and also on the net charge-potential one ((Qsw/ QMAX) versus (Ein - E0) curves; see Figure 2). These curves have been calculated from eqs 1 and 4 in this paper and eq 8 in ref 14 for n ) 1, |∆Es| ) 5 mV, different values of the square wave amplitude (|Esw|)25, 50, 100, and 150 mV), and three values of the dimensionless surface rate constant ((k0τ) ) 10, 0.25, and 0.01), which correspond to reversible, quasi-reversible, and totally irreversible behavior. Thus, we can see that for a reversible process (see Figures 1a and 2a for (k0τ) ) 10), the (Qf/QMAX) versus (Ein - E0) and (Qr/ QMAX) versus (Ein - E0) curves are well-defined sigmoids, which are shifted toward more positive and negative potentials, respectively, as |Esw| increases. Therefore, the (Qsw/QMAX) versus (Ein - E0) curves present a well-defined peak centered around the formal potential (dotted line) whose height and half-peak width increase also with |Esw| (in line with eqs 12 and 13), until, for |nEsw| > 100 mV‚s, the peak becomes a broad plateau whose height coincides with QMAX. The above behavior can be also observed for the quasireversible case shown in Figures 1b and 2b, although in this case, the shift in the (Qf/QMAX) versus (Ein - E0) and (Qr/QMAX) versus (Ein - E0) curves caused by an increase of |Esw| is much lower, a fact that leads to a smaller increase of the net charge curves in Figure 2b in such a way the plateau is not obtained for the values 7584 Analytical Chemistry, Vol. 79, No. 19, October 1, 2007
Figure 1. Theoretical SWVC (Qf/QMAX) versus (Ein - E0) (solid lines) and (Qr/QMAX) versus (Ein - E0) (dashed lines) curves calculated from eq 8 in ref 14 and eq 1 of this paper. The values of |Esw| and of the dimensionless rate constant (k0τ) are shown in the figure. |∆Es| ) 5 mV, T ) 298.15 K, and n ) 1. Ein is the index potential (see eq 3).
of |Esw| used, and a higher square wave amplitude than that used in the figure is needed in order to obtain it. Nevertheless, even for this low value of the dimensionless rate constant, the peak potential of the (Qsw/QMAX) versus (Ein - E0) curves coincides with the formal potential. This coincidence can be observed for this value of (k0τ) for values of |nEsw| g10 mV. The irreversible behavior is shown in Figures 1c and 2c. In this case, the (Qf/QMAX) versus (Ein - E0) and (Qr/QMAX) versus (Ein - E0) curves are very close, and for low values of |Esw|, they actually change their position in such a way that a negative net charge appears (see the (Qsw/QMAX) versus (Ein - E0) curve with |Esw| ) 25 mV in Figure 2c). An increase of the square wave pulse amplitude causes both forward and reverse to tend to separate in
Figure 2. Theoretical SWVC (Qsw/QMAX) versus (Ein - E0) curves calculated from eq 4. Dotted lines mark the formal potential position. Other conditions as in Figure 1.
such a way that a positive, growing peak is observed in the (Qsw/ QMAX) versus (Ein - E0) curve, with its peak potential being shifted up to values close to that corresponding formal potential (see curve with |Esw| > 150 mV in Figure 2c). Thus, clear criteria of reversibility can be established from these results: Reversible Conditions ((k0τ) > 5). The Qsw/E curve will reach a plateau for square wave pulse amplitude values of |nEsw| g100 mV (with a deviation less than 5%). In contrast, the Isw/E curve will be null. Quasi-Reversible Conditions (5 > (k0τ) > 0.05). The Qsw/E signal will achieve the plateau for higher square wave pulse amplitude values than in the reversible case (where a greater |nEsw| value is necessary the smaller (k0τ) is). Under these conditions, the Isw/E response is not null and it shows a clear
Figure 3. Black dots: experimental cathodic SWVC Qsw/E curves c versus E curves (b) of (a) and corrected faradic SWVC cathodic Qsw the 2-AQCA 10 µM + HClO4 1 M adsorbed on a mercury electrode. |∆Es| ) 5 mV and τ ) 5 ms. The values of the square wave pulse amplitudes (in mV) are shown in the figure. Solid lines: theoretical c Qsw/E (a) and Qsw /E (b) curves for the above system calculated from eqs 10 and 25 corresponding to reversible processes with E0 ) 0.017 V, QMAX ) 119 nC, and the values of CmO and CmR shown in Table 1. Einitial ) 0.100 V. r0 ) 0.03445 cm, n ) 2, and T ) 298 K. Inset: experimental Isw/E curve for the 2-AQCA system corresponding to τ ) 5 ms, |∆Es| ) 5 mV, and |Esw|) 40 mV. Dotted line marks the formal potential position.
splitting for high enough |Esw| values.7,10 For example, for (k0τ) ) 0.25, values of |nEsw| g 180 mV and g140 mV must be used to reach a well-defined charge plateau and a splitting of the current response, respectively. In the Qsw/E curves corresponding to (k0τ) > 0.25, the peak potential will coincide with the formal potential of the system for values of |nEsw| g10 mV. Thus, if we increase the pulse time length τ, both E0 and QMAX can be accurately measured from the Qsw/E curves for a reversible and even quasi-reversible process. Once these values are known, we can calculate the kinetic parameters R and (k0τ) from the comparison between theoretical and experimental curves. The experimental verification of the theoretical predictions for a reversible behavior can be seen in Figure 3, in which we have plotted the Qsw/E curves (see symbols in Figure 3a) corresponding to the system 2-AQCA 10 µM in HClO4 1.0 M and obtained Analytical Chemistry, Vol. 79, No. 19, October 1, 2007
7585
Table 1. Experimental Values the Non Faradaic Capacitance of the Monolayer Due to the Reduced and Oxidized Molecules (CmR and CmO, Respectively), Obtained in SWVC for the System Anthraquinone-2-carboxylic Acid (2-AQCA) 10µM in Aqueous Solutions of HClO4 1.0M (pH)0) and HClO4 0.1M/NaClO4 0.2M (pH)1). |∆Es| ) 5 mV. pH ) 0, τ ) 5 ms
pH ) 1, τ ) 0.5 ms
Esw/ mV
CmR/µF cm-2
CmO /µF cm-2
Esw/mV
CmR/µF cm-2
CmO/µF cm-2
20 30 40 50 70
3.35 ( 0.01 6.71 ( 0.01 5.87 ( 0.01 4.03 ( 0.01 2.40 ( 0.01
11.74 ( 0.01 7.83 ( 0.01 7.55 ( 0.01 8.05 ( 0.01 16.78 ( 0.01
30 40 50 60 100
8.95 ( 0.01 9.23 ( 0.01 9.39 ( 0.01 9.51 ( 0.01 10.07 ( 0.01
11.18 ( 0.01 11.74 ( 0.01 12.08 ( 0.01 12.86 ( 0.01 15.10 ( 0.01
different values of the square wave pulse amplitude and a constant pulse time length τ ) 5 ms for a staircase pulse amplitude |∆Es| ) 5 mV. This system, according to the literature, presents a dielectronic reversible reduction under these conditions.16 In order to prove this, we have measured the surface rate constant by employing multipotential pulse chronoamperometry in the way discussed in ref 14, and we have obtained a value of k0 ) 5500 ( 10 s-1, which leads to a dimensionless rate constant of (k0τ) ) 27.5 under our experimental conditions, corresponding to a reversible behavior. Further verification of this fact can be seen in the inset in Figure 3a, which clearly shows that this process leads to a null square wave faradic current; i.e., the current corresponding to this system cannot be distinguished from the background values. According to this behavior, a broad plateau, independent of the value of the square wave pulse amplitude, should be seen in the experimental reversible Qsw/E curves at values of |nEsw| g100 mV, in agreement with eq 13. However, we can clearly see that, although the curves corresponding to the highest |Esw| values in Figure 3a present this plateau, it increases with |Esw|. This is due to the contribution of the non-faradic charge to the whole response (also responsible for the asymmetric non-faradic baseline that can be clearly observed), which changes with the square wave pulse amplitude, in line with eq 25. This non-faradic contribution to the charge-potential curves of Figure 3a can be easily quantified and eliminated. Thus, first we must obtain the experimental values of the non-faradic capacitance of the interface due to the oxidized and reduced adsorbed molecules, CmO and CmR, as the constant charge values at potentials far way from the peak potential divided by 2|Esw| (see eq 25). The values of CmO and CmR corresponding to the different values of |Esw| used in this figure appear in Table 1. The value of E0 has been obtained from the peak potential, so we find E0 ) 0.017 ( 0.002 V. Once CmO, CmR, and E0 are known, the corrected Qcsw/E curves can be easily obtained by using eq 25, i.e., by subtracting the Qsw,nf response from the experimental Qsw values in the way Qcsw ) Qsw - Qsw,nf, such that QMAX is given by the height of the corrected plateau, i.e., QMAX ) Qsw)plateau - 2|Esw|CmO (note that at the charge plateau η2p-1 f 0, and therefore, it is fulfilled that 1/(1 + eη2p) = 1/(1 + enF|Esw|/(RT)) = 0, according to eqs 3 and 25), obtaining QMAX ) 119 ( 5 nC. Thus, the corrected Qcsw/E curves of the 2-AQCA system are shown in Figure 3b (symbols), which now show that the charge plateau is independent of the square wave pulse amplitude (see curves |nEsw| g100 mV). The fact that the charge plateau is attained at these square waves pulse amplitudes is an additional confirmation of the reversibility of the electrode process, in 7586 Analytical Chemistry, Vol. 79, No. 19, October 1, 2007
agreement with the discussion above (see Figure 2a). Note that the QMAX value obtained gives rise to a surface excess of ΓT ) (4.1 ( 0.1) × 10 - 11 mol cm-2, in line with results in ref 16. In Figure 3a and b, we have also plotted the theoretical total ((Qsw + Qnf,sw) versus E) and corrected (Qsw/E) faradic curves, respectively, calculated from eqs 4 and 25 (solid lines), which show a very good agreement with the experimental ones. In Figure 4a, we have plotted the Qsw/E curves corresponding to the system 2-AQCA 10 µM in a HClO4 0.1M solution with NaClO4 0.2 M as supporting electrolyte (pH ) 1), obtained for a staircase pulse amplitude |∆Es| ) 5 mV, different values of the square wave pulse amplitude, and a constant pulse time length τ ) 0.5 ms (symbols). The increase of the pH and the subsequent smaller availability of protons in solution cause a decrease of the surface rate constant and a shift of the formal surface potential of this system toward more negative values.16 Actually, the surface rate constant, measured by employing multipotential pulse chronoamperometry,14 has a value of k0 ) 1800 ( 100 s-1, which leads to a dimensionless rate constant of (k0τ) ) 0.9 under these conditions. Therefore, this system presents a quasi-reversible reduction, which involves two electrons. This behavior can be confirmed from the Isw/E curves shown in the inset Figure 4a. Thus, for |Esw| ) 30 mV, a broad current peak can be observed and a splitting of this curve, which is typical of quasi-reversible behavior, can be seen for |Esw| ) 50 mV.9,10 Note that the experimental Qsw/E curves of 2-AQCA increase with |Esw| and also present a well-defined charge plateau, but in this case, the square wave amplitude necessary for reaching it is higher than at corresponding to the reversible case (|nEsw| > 140 mV, curve not shown in this figure), in agreement with theoretical discussions carried out in Figure 2. The contribution of non-faradic charges is also present in curves of Figure 4a, leading to an asymmetric baseline (again with higher values in the anodic region) and to an increase of charge plateau values with |Esw| (see eq 24). In order to quantify the non-faradic charge and also to obtain the kinetic parameters of this system, we must proceed in the following way: first we obtain the CmO and CmR values from the curves in this figure from the constant anodic and cathodic baselines divided by 2|Esw|. The values of these capacitances are shown in Table 1. Second, in agreement with theoretical results of Figure 2b, the formal potential can be obtained from the peak potential since it remains unaffected by the different square wave pulse amplitude used, being Epeak ) E0 ) -0.017 ( 0.002 V (see dotted line). Once we have obtained these parameters, and given the nonavailability of theoretical expressions for the peak parameters
QMAX ) 0.135 µC, with the theoretical Qsw/E curves being plotted in Figure 4a (solid lines). The value of the total faradic charge obtained in this case gives rise to a surface excess of ΓT ) (4.7 ( 0.1) × 10-11 mol cm-2, which is slightly higher than the reversible one. In Figure 4b, we have plotted the experimental corrected Qcsw ( ) Qsw - Qsw,nf) versus E curves for this system (symbols), and also the theoretical faradic ones calculated from eq 4, and again it is seen that a charge plateau independent of the square wave pulse amplitude is reached.
Figure 4. Black dots: experimental SWVC cathodic Qsw/E (a) and c /E curves (b) of the system corrected faradic SWVC cathodic Qsw 2-AQCA 10 µM + HClO4 0.1M/NaClO4 0.2 M (pH ) 1) adsorbed on a mercury electrode. τ ) 0.5 ms and |∆Es| ) 5 mV. Solid lines: theoretical Qsw/E curves calculated from eqs 4 and 24 for the above system with Einitial ) 0.1500 V and Ru ) 150 Ω. Inset: experimental Isw/E curve for the 2-AQCA system corresponding to τ ) 0.5 ms, |∆Es| ) 5 mV, and two values of the square wave pulse amplitudes, which are shown in the figure (in mV). Other conditions as in Figure 3.
of quasi-reversible processes, we must generate theoretical Qsw/E curves, by employing general eqs 4 and 24 corresponding to the faradic and non-faradic charges, respectively, for different sets of values of (k0τ), R and QMAX in order to compare them with experimental ones. In this calculus, we can introduce as the initial value of the faradic charge QMAX that calculated from the charge plateau values by using eq 25 corresponding to reversible behavior in a similar way to the previous case. In this way, by using eqs 4 and 24, we have obtained the best fittings for the following parameters: (k0τ) ) 0.9, R ) 0.5, and
CONCLUSIONS A new multipotential pulse technique called SWVC has been developed to study the charge-transfer process taking place in electroactive monolayers. Obtaining an intense and easily manageable response for reversible processes is the main advantage of SWVC over other multipotential pulse techniques based on the recording of currents such as SWV, which lead to negligible signals under these conditions. At high enough values of the square wave pulse amplitude, a well-defined plateau is obtained in the Qsw/E curves, both in reversible and quasi-reversible conditions, which allows an immediate measure of the total faradic charge of the monolayer. This charge plateau is very sensitive to the influence of other processes in the response like successive electron transfers or chemical complications. The formal potential of the electroactive systems coincides with the peak potentials of the Qsw/E curves for high values of square wave pulse amplitude, even for quasi-reversible behavior. The expression of the non-faradic charge has been deduced whatever the reversibility of the charge-transfer process, pointing out that this contribution to the experimental SWVC response can be easily eliminated, even when a potential dependent non-faradic capacitance is considered. The theoretical predictions for SWVC have been verified by means of the system anthraquinone-2-carboxylic acid in two different aqueous media. ACKNOWLEDGMENT The authors greatly appreciate the financial support provided by the Direccio´n General de Investigacio´n Cientı´fica y Te´cnica (Project CTQ2006-12552/BQU), and the Fundacio´n SENECA (Project 03079/PI/05). N.A. thanks the Ministerio de Educacio´n y Ciencia for the grant received.
Received for review May 17, 2007. Accepted July 20, 2007. AC071006A
Analytical Chemistry, Vol. 79, No. 19, October 1, 2007
7587
