- Email: [email protected]
The effect of the interfacial potential distribution on the reduction of adsorbed methylene blue at a mercury electrode
Journal of Electroanalytical Chemistry 445 (1998) 63 – 69
The effect of the interfacial potential distribution on the reduction of adsorbed methylene blue at a mercury electrode Michael J. Honeychurch a,b,* a
Department of Molecular Sciences, James Cook Uni6ersity of North Queensland, Towns6ille 4811, Queensland, Australia b Department of Chemistry, Uni6ersity of Hawaii, 2545 The Mall, Honolulu, Hawaii 96822, USA Received 6 May 1997
Abstract The constant current chronopotentiometric reduction of methylene blue adsorbed on a HMDE at fractional coverages of MB + of u 51 is reported and the results interpreted in terms of both an EE mechanism and the interfacial potential distribution (IPD) model of Smith and White (Anal. Chem., 64 (1992) 2398). Derivative chronopotentiometric (DCP) peaks were broader than expected for a two electron transfer under Langmuir isotherm conditions and shifted positively with increasing fractional coverage. Whilst the EE model satisfactorily accounted for the peak shape and was in general agreement with previously reported work (Zutic et al., J. Electroanal. Chem., 177 (1984) 253) it was not possible to account for the shift in the DCP peak. Calculated DCPs based on the IPD model had peak shapes consistent with the experimental DCPs and shifted positively with increasing fractional coverage in the manner of the experimental DCPs. © 1998 Elsevier Science S.A. All rights reserved. Keywords: Methylene blue; Interfacial potential distribution; Mercury electrode
1. Introduction The study of the electrochemical reduction of methylene blue, MB + , to leucomethylene blue, LMB, has been the subject of many studies over the years [1,2]. The reduction in solution at different electrodes and also following adsorption on mercury have been studied. In studies of the reduction of adsorbed MB + it is generally observed that linear sweep voltammograms are broader than expected for a two electron reversible reduction of an adsorbed molecule under Langmuir isotherm conditions. Likewise polarograms and chronocoulograms are broader than would be expected under such conditions. Pergola et al. [1] observed broad chronocoulograms for the reduction of adsorbed MB + on mercury and * Corresponding author. Current address: Inorganic Chemistry Laboratory, University of Oxford, South Parks Road, Oxford OX1 3QR, UK. E-mail:[email protected] 0022-0728/98/$19.00 © 1998 Elsevier Science S.A. All rights reserved. PII S 0 0 2 2 - 0 7 2 8 ( 9 7 ) 0 0 5 3 1 - 7
proposed that they were due to interactions between adsorbed molecules and used a Frumkin isotherm model analogous to that of Laviron [3] to determine the interaction parameters. Wopschall and Shain [4] found evidence to suggest that the reduction of MB + adsorbed on mercury was not a simple two electron reversible charge transfer but proceeds in two steps via the relatively stable semiquinone radical intermediate with a fast protonation of the intermediate. They managed to fit the experimental peak to a one step reversible mechanism by assuming non-integer values of n and found good agreement for napp of 1.66. The electron transfer kinetics of the MB + /LMB couple at mercury electrodes have also been studied by Zutic et al. [2] by double potential step chronocoulometry in 1 M KNO3. They concluded, from analysis of Tafel type slopes, that the reduction of adsorbed MB + involved two consecutive reversible one electron transfers (reversible EE mechanism) with a 16 mV separa-
M.J. Honeychurch / Journal of Electroanalytical Chemistry 445 (1998) 63–69
64
tion between the half wave potentials of the two single electron steps according to the following scheme MB + + e − ? MB ·
(1)
MB · +H + e ? LMB
(2)
+
−
At low bulk concentrations and fractional coverages of u B 1 only one chronocoulometric wave, corresponding to this reduction, is present. At higher coverages i.e. u \ 1 a second chronocoulometric wave appears which is due to the reduction of a second layer of adsorbed MB + through the adsorbed LMB layer [2,5]. In a recent paper [6], the constant current chronopotentiometric (CCCP) reduction of flavin adenine dinucleotide (FAD) was reported in which the shape of the derivative chronopotentiometric (DCP) reduction peak was consistent with the model that had been adapted for an EE reduction of a species adsorbed under Langmuir isotherm conditions. It, therefore, seemed appropriate to use this model to test the proposition that the MB + reduction is an EE mechanism although another possibility exists. Smith and White [7] have developed a general model to describe the reversible voltammetric response of electrodes with electroactive molecular films based on the interfacial potential distribution (IPD model). This model uses many of the concepts developed by Frumkin which were used to correct rate constants of irreversible reactions involving soluble reactants [8], and later employed by Lane and Hubbard [9] in a study of the kinetics of electroactive adsorbates. The work of Smith and White has since been extended to include the effects of surface immobilized acid or base groups [10,11], ion pairs [12] and discreteness of charge effects [11,13,14]. In the IPD model, when the oxidized and reduced adsorbed molecules have different charges, the resultant voltammogram may display apparent non-Langmuir behavior. Since there is a charge difference between MB + and LMB this explanation has also been examined. In this paper the constant current chronopotentiometric reduction of adsorbed methylene blue at fractional coverages of MB + of u5 1 is reported and the results interpreted in terms of an EE mechanism and the IPD model.
2. Experimental Constant current chronopotentiometry was performed using a Radiometer PSU-20 potentiometric stripping unit (Radiometer A/S, Copenhagen, Denmark). The PSU-20 was controlled with Tap2 3.0 software (Radiometer A/S, Copenhagen, Denmark) on an IBM compatible 286 computer. The potential vs. time
transient was measured at a frequency of 30 Hz in potential intervals of 2 mV with the output being a derivative chronopotentiogram of the form dt/dE. In order to obtain t vs. E plots raw data was converted to an ASCII file and curves were integrated with KALEIDAGRAPH 3.0 (Synergy Software) on an Apple Power Macintosh 7200/120 computer. The working electrode was a E410 hanging mercury drop electrode (HMDE) (Metrohm, Herisau, Switzerland) of surface area 0.0296 9 0.0011 cm2. All potentials were measured with respect to a saturated calomel electrode (SCE). Methylene blue (Sigma Aldrich, Castle Hill, Australia) stock solutions of 1.4× 10 − 3 M were made up in 0.1 M phosphate buffer (pH 7.4). The solution was purged for 30 min with nitrogen that had passed sequentially through a solution of vanadous chloride and then the supporting electrolyte. Solutions were blanketed with nitrogen during analysis. MB + was accumulated on the HMDE potentiostatically for 60 s at 0 mV from 0.4 to 3.5 mM solutions. After the completion of the adsorptive accumulation period MB + was a reduced by applying a −11.6 mA current to the cell. All measurements were made at 23°C.
3. Theory In the chronopotentiometric experiment the total number of adsorbed molecules at time t is equal to the number initially adsorbed (at t= 0) plus the total amount brought to, or removed from, the electrode by diffusion after the commencement of the experiment (t\ 0). For accumulation on a HMDE of radius ro by an adsorptive preconcentration procedure the mass balance equation is GMB + (t)+ GLMB(t)
& &
= GT + DMB +
t
0
t
+ DLMB
0
(cMB + (r,t) (r
(cLMB + (r,t) (r
.(t r = ro
.(t
(3)
r = ro
where Di is the diffusion coefficient of i; ci (r, t) is the concentration of i; Gi (t) is the surface excess of i; and GT is the total surface excess at t= 0. In the experiments reported below the time allowed for accumulation of MB + on the HMDE is much greater than the chronopotentiometric transition time (tB50 ms). Since all experiments were carried out in dilute solutions the amount of MB + accumulated during the preconcentration procedure was always much greater than the amount accumulated during the constant current reduction. Under these conditions GMB + (t)+ GLMB(t)= GT
(4)
M.J. Honeychurch / Journal of Electroanalytical Chemistry 445 (1998) 63–69
65
If it is assumed that only the oxidized form is present initially then GMB + (0) = GT. At the transition time t= t and the reduction of MB + is complete, therefore GMB + (t) = 0 and GLMB(t) =GT. In the absence of a diffusion reaction, the chronopotentiometric transition time, t, is given by
Substituting DG o = − nFE o, E= (fM − fHg), and the liquid junction potential ELJ = (fs(b) − fs(a)) into Eq. (10) gives
t = 2FGLMB/j
(5)
t= 2FGT /j
(6)
t −t =2FGMB + /j
(7)
Taking the potential of the solution (a) as a zero reference, defining an apparent adsorption formal poo S 2 S tential E o% a = E − ELJ + (RT/2F) ln[(a Cl − ) a H + ], and + taking the activities of MB and LMB at the plane of electron transfer as their surface concentrations GMB + and GLMB, and substituting into Eq. (11) gives
where j is the current density. Fig. 1 shows a diagram of the potential profile with MB + adsorbed on the electrode. The electrochemical cell for the system is + P
Hg(l) MB ,LMBP,K2HPO4(aq), KH2PO4(aq), KCl(aq) Hg2Cl2(s) Hg(l)
=m
P LMB
Hg Hg
+m
(11)
(12)
(13)
sM = (E o% a − Epzc − (fP/2)+ (RT/2F) ln[ f/(1− f )]) ×eoem/d
At equilibrium +2m
E= E o% a + (fP/2)+ (RT/2F) ln[GMB + /GLMB]
sM = (fM − fP)eoem/d
(b)
m
+ (RT/2F) ln[a PMB + (a S(b) )2a S(a) /a PLMB] Cl − H+
The charge densities at the metal, the plane of electron transfer and the diffuse layer can be related to the interfacial potential with the following equations [7,15]
(a)
P MB +
E= E o + (fP − fs(a))/2 −ELJ
+ 2m
Hg2Cl2 Hg2Cl2
S(b) Cl −
+2m
+ 2m
M e−
+m
Hg e−
P H+
sdiff = {2000eoesRT % ci [exp(− zi FfP/RT)− 1]}1/2 (9)
where m is the electrochemical potential of species i in phase j. The subscripts P, S and M indicate the plane of electron transfer, the solution and the HMDE, respectively. Following the procedure of Smith and White [7], the thermodynamic definitions (m ij =m oi +RT ln(a ij )+ zi Ff j; a ij = the activity of i in phase j; m PH + =m S(a) H+ = o o m oH + +RT ln(a S(a) )+ z Ff ; and DG =S 6 m , where + i s(a) i i i H 6i is the stoichiometric coefficient) were substituted into Eq. (9) to give j i
2F(fM −fHg)− F(fP −fs(a)) +2F(fs(b) −fs(a)) +DG o 2 S(a) P = RT ln[a PMB + (a S(b) Cl − ) a H + /a LMB]
(14)
(10)
(15) sP = FGm f
(16)
sdiff = − (sM + sP)
(17)
where eo is the permittivity of free space, em is the dielectric of the adsorbed layer of thickness d, es the dielectric of water with a supporting electrolyte containing ci ions of charge zi, Epzc is the potential of zero charge in the absence of specific adsorption, Gm is the surface concentration of MB + at monolayer (GT = uGm) and f= GMB + /GT. Eq. (14) applies only to the part of the surface that is covered by adsorbate. The capacitance of the adsorbed layer is Cm = eoem/d
(18)
and the total capacitance in the presence of a monolayer coverage is [7] CT = Cm(1−(fP/(E)
u= 1
(19)
At submonolayer coverages the capacitance can be estimated using Frumkin’s parallel capacitor model [16] CT = Cm(1−(fP/(E)u+ Co(1−u)
uB1
(20)
where Co is the capacitance in the absence of adsorption. The capacitative component of dt/dE is (dt/dE)c = CT /j
(21)
The faradaic component of dt/dE can be obtained from Eq. (22) Fig. 1. Diagram showing the potential profile used in the derivation of the IPD model. ‘P’ represents the plane of electron transfer.
j= − 2FdGMB + /dt = − 2FGT df/dt
(22)
M.J. Honeychurch / Journal of Electroanalytical Chemistry 445 (1998) 63–69
66
Table 1 Experimental data for the chronopotentiometric reduction of adsorbed MB+ on a HMDE following accumulation at 0 mV versus SCE (current −11.6 mA) u
slopea/mV
(r)
napp
Ep/mV (9 2 mV)
W1/2/mV
0.12 0.25 0.50 0.55 0.65 0.77 0.91
35.0 36.8 37.1 36.4 36.4 37.1 37.8
(0.9986) (0.9989) (0.9993) (0.9994) (0.9992) (0.9992) (0.9994)
1.68 1.59 1.58 1.61 1.62 1.58 1.55
−189 −185 −180 −179 −176 −172 −169
63 66 63 63 63 63 64
a
Slope of the log[(t−t)/t] vs. E plot.
Substituting f=GMB + /GT into Eq. (12), differentiating with respect to t, solving for df/dt and substituting into Eq. (22) gives the faradaic component of dt/dE [7] (dt/dE)f =(4F 2/RTGT f(1 − f )(1 − (fP/(E)/j
(23)
Adding Eqs. (23) and (21) gives the equation for the DCP dt/dE = [{(4F 2/RT)GT f(1 − f )(1 − (fP/(E)} +CT ]/j (24) After substituting Eq. (6) into Eq. (24), the equation for the DCP can be rewritten as
K 1/2 =
4h − 16h 2 − [4(h 2 − 6h +1)(h − h 3/2 − h 1/2)] 2(h − h 3/2 − h 1/2) (27)
h= exp[− (2F/RT)(E − E o% a )]
(28)
and the value of h at the half peak height can be obtained from W1/2 = (RT/F) ln h
(29)
Substituting the value for W1/2 into Eqs. (27) and (29) gives a value of K of 0.839 0.03. For KB 16 only one peak is observed experimentally and the DCP peak occurs at Ep = E o% a and is given by [6]
dt/dE =[(2F/RT)tf(1 −f )(1 − (fP/(E)] +(CT /j ) (25)
4. Results and discussion The experimental data are summarized in Table 1. Plots of log[(t −t)/t] versus E for the experimental peaks at various fractional coverages were linear with slopes of 36.790.8 mV (Table 1). The magnitude of the slope equates to an apparent number of electrons transferred, napp, of 1.60 which is in close agreement to the non-integer value of n obtained from linear sweep voltammetry by Wopschall and Shain [4]. Integration of the DCPs, assuming a linear baseline, gave the maximum charge as 18.39 0.8 mC cm − 2, in agreement with the value of 18.1 9 0.3 mC cm − 2 reported previously [2]. The DCPs were symmetrical with peak widths at half peak height, W1/2, of approximately 63 mV. No variation in W1/2 with fractional coverage was observed. Assuming the reduction to be an EE mechanism then the equation for the DCP is expressed in terms of a semiquinone formation constant K K= G 2MB · /GMB + GLMB
(26)
the relationship between W1/2, and K for the DCP is [6,17]
Fig. 2. Experimental DCP (——) of 2.67 mM MB + in 0.1 M phosphate buffer, pH 7.40, following 60 s adsorptive accumulation at 0 mV vs. SCE, and calculated DCP with E o% a =180 mV and () K= 0.52 and (- - -) K =0.83.
dt dE
=− p
M.J. Honeychurch / Journal of Electroanalytical Chemistry 445 (1998) 63–69
n
Ft 1 RT (2+ K 1/2)
(30)
A plot of (dt/dE)p versus t was linear (r = 0.9995) passing through the origin with slope −14.41 V − 1 from which K was determined as being 0.529 0.08. The DCP response was calculated from these two values for K using the methods described previously [6]. An excellent fit with the experimental peak was obtained for K= 0.52 (Fig. 2). This value of K can then used to estimate the separation in the reduction potentials for the two individual reduction steps since they are related to K by [6] o% (E o% 1 −E 2 )F/RT= ln K
(31)
A separation of 17 mV is predicted which is in agreement with the value obtained by Zutic et al. [2] Despite the good agreement with previous work and the excellent correlation between the experimental and calculated DCPs there are some apparent anomalies in the experimental data which are not explained by the proposed EE model. Table 1 shows that the peak potential of the DCPs varied with fractional coverage. The variation was linear (r =0.993) with slope 25.1 mV and intercept − 192 mV. A shift in the half wave potential was also reported by Pergola et al. [1] and seemed to be present in the chronocoulograms of Zutic et al. [2] although not discussed. Whilst the shape of the DCP is invariant at all fractional coverages this shift in peak potential is not accounted for with the EE model. Lateral interactions between adsorbed species are known to produce a dependence of the peak potential on fractional coverages [3]. Laviron assumed that adsorption followed a Frumkin isotherm and derived an equation in which the peak shape and peak potential were dependent on the interactions between adsorbates [3]. The magnitude of the interactions is given by an interaction coefficient, a, which is positive for attraction and negative for repulsion. The peak potential is dependent on (aOO −aRR), where aOO and aRR, are interaction coefficients for interactions between oxidized adsorbates and between reduced adsorbates respectively. The peak shape is dependent on (aOO +aRR − 2aOR), where aOR is the interaction coefficient for interactions between oxidized and reduced adsorbates. Following Laviron’s formalism our observations of a peak potential shift would imply that (aOO −aRR)" 0, however, the lack of any change in the shape of the DCP peak with varying coverage does not imply (aOO +aRR −2aOR)= 0 since the peak shape then becomes the same as for a Langmuir isotherm and this would require W1/2 to be a constant value of 45 mV for a two electron transfer. Pergola et al. [1] used a Frumkin isotherm model analogous to Laviron’s to explain their observations of
67
chronocoulometric wave broadening and a shift in the half wave potential with fractional MB + coverage and found both (aOO + aRR − 2aOR)" 0 and (aOO − aRR)" 0. However, these authors used a high concentration of chloride ion in their experiments which produces a steep region at the beginning of the chronopotentiogram (chronocoulogram) due to the oxidation of the electrode. Under such conditions it would appear that the adsorbed MB + molecules adopt a different orientation on the electrode since these authors reported a maximum charge of 25 mC cm − 2 which is considerably higher than that reported here and by Zutic et al. [2]. A different orientation on the electrode may account for different forces between adsorbed molecules resulting in different experimental observations. Therefore, the results of Pergola et al., which included an estimation of the lateral interaction coefficients, cannot be directly extrapolated to this study. The effect of lateral interaction on EE reductions have been considered by others [18]. An assumption that all the lateral interaction parameters are equal was necessary in order to provide a workable model. Following such an assumption the equation reduced to that for a Langmuir isotherm (no interactions). Therefore, while the EE model for Langmuir adsorption adequately describes the DCP peak shape, a model analogous to that presented by Kakutani and Senda [18] for ac voltammetry, that combines the two one electron steps and allows for lateral interactions between the adsorbed molecules (oxidized, reduced and radical intermediate), would seem necessary in order to account for the progressive peak shift with increasing coverage of MB + . This has not been attempted due to the difficulties in obtaining workable solutions, which has been discussed elsewhere [18]. In seeking an explanation for the experimental observations, let us consider the effect of the interfacial potential difference on the reduction in terms of the IPD model of Smith and White [7] which is adapted to the MB + /LMB system. DCPs were calculated by the following sequence of steps using a spreadsheet with values of f in the initial column. To solve Eqs. (12)–(25), it is necessary to have values for the three unknowns in the set of equations, E o% a , Epzc, and em/d. Pergola et al. [1] determined the formal potential of the MB + /LMB couple at pH 7.9, in the absence of adsorption, to be − 2489 2 mV versus the SCE which equates to 219 mV at pH 7.4. When adsorption occurs the formal potential for the reduction will be shifted by an amount equal to (RT/2F) ln(bR/bO), where bR and bO are the adsorption coefficients of LMB and MB + respectively. Notwithstanding that it seems likely that MB + and LMB were oriented differently in the experiments of Pergola et al. compared this work, as a first approximation their value of (bR/bO), which
68
M.J. Honeychurch / Journal of Electroanalytical Chemistry 445 (1998) 63–69
Fig. 3. Experimental DCPs of MB + (——) and DCPs calculated using the IPD model (- - -). Coverages u= 0.12, 0.55, 0.77 and 0.91.
was estimated to be 4.75, was used to calculate the adsorption formal potential, which gives E o% a 200 mV. This value was used in subsequent calculations. In the absence of specific adsorption the potential of zero charge of mercury is − 430 mV versus SCE therefore Epzc = − 430 mV was used in all calculations. Finally em/d was varied so as to provide the best fit between the experimental and the calculated DCPs. ˚ − 1. The Best results were obtained using em/d = 6 A + thickness of MB , if it were to be lying flat on the ˚ [5]. If it is assumed electrode, is approximately 3.25 A that the plane of electron transfer is between 1.6 and ˚ then one obtains a dielectric constant for MB + 3.25 A of 10–20. At a given coverage of MB + , Eqs. (16), (14) and (17) were solved in that order to give the value of sdiff, which was then multiplied by u. Since a non-symmetrical electrolyte was used in these experiments, fP was determined by first plotting fP as a function of sdiff, for fP B 100 mV, in a 0.1 M phosphate buffer using Eq. (15). It was found that the relationship between fP and sdiff could be described by a 6th order polynomial (r = 0.9999)
and shape of experimental and calculated DCPs across the range of fractional coverages. The calculated baselines were generally of the magnitude of the experimental baseline. At lower coverages (uB 0.25), the calculated baseline had a steeper slope than the experimental baseline. A dip is present in all the calculated baselines with a minimum corresponding to the region of the
fP = 0.91707sdiff − 6.0117s 2diff −24.062s 3diff −53.175s 4diff − 59.727s 5diff −26.562s 6diff
(32)
Having calculated sdiff, fP could then be determined using Eq. (32) and substituted into Eq. (12) to give E. (fP/(E was determined by numerical differentiation and calculations made using Eqs. (20), (21), (23) and (25)). Calculations using the IPD model are shown in Fig. 3. An excellent correlation is obtained between the size
Fig. 4. Experimental () and calculated () peak potentials for reduction of adsorbed MB + in 0.1 M phosphate buffer, pH 7.40.
M.J. Honeychurch / Journal of Electroanalytical Chemistry 445 (1998) 63–69
faradaic peak. This feature was present in some of the calculations of Smith and White. Peak areas (transition times) calculated by subtracting the calculated baseline were approximately 4% greater than when using a straight baseline. Fig. 4 shows a comparison between experimental and calculated peak potentials. A good correlation is obtained in that the shift in the calculated peak potential is the same magnitude as the experimental shift. The slight curvature in the plot of calculated peak potential versus fractional coverage does differ from the linearity of the experimental plot. Nevertheless these differences would appear to be relatively minor given the assumptions made in calculating the calculated DCPs and the relatively simple model used.
5. Conclusion In previous reports in the literature, the effects of lateral interactions between adsorbed molecules and a two step EE mechanism have been offered as explanations of the apparent non-ideal or non-Langmuir behavior of adsorbed MB + . In this paper a model which takes into account the effects of the interfacial potential distribution provides calculated DCPs which have peak shapes consistent with the experimental DCPs and which shift positively with increasing fractional coverage in the manner of the experimental DCPs. It is therefore possible to use this model to describe MB + behavior when adsorbed on mercury electrodes without the need to invoke non-ideal behavior of adsorbed molecules or more a complex mechanism than a direct two electron transfer.
.
69
Acknowledgements Part of this work was undertaken at James Cook University of North Queensland where the author would like to acknowledge the receipt of a James Cook University Department of Molecular Sciences scholarship.
References [1] F. Pergola, G. Piccardi, R. Guidelli, J. Electroanal. Chem. 83 (1977) 33. [2] V. Zutic, V. Svetlicic, M. Lovric, I. Ruzic, J. Chevalet, J. Electroanal. Chem. 177 (1984) 253. [3] E. Laviron, Voltammetric methods for the study of adsorbed species, in: A.J. Bard (Ed.), Electroanalytical Chemistry, vol. 12, Marcel Dekker, New York, 1982, p. 53 [4] R.H. Wopshall, I. Shain, Anal. Chem. 39 (1967) 1527. [5] V. Svetlicic, J. Tomaic, V. Zutic, J. Chevalet, J. Electroanal. Chem. 146 (1983) 71. [6] M.J. Honeychurch, M.J. Ridd, Electroanalysis 8 (1996) 362. [7] C.P. Smith, H.S. White, Anal. Chem. 64 (1992) 2398. [8] A.J. Bard, L.R. Faulkner, Electrochemical Methods, Wiley, New York, 1980, p. 540 [9] R.F. Lane, A.T. Hubbard, J. Phys. Chem. 77 (1973) 1413. [10] C.P. Smith, H.S. White, Langmuir 9 (1993) 1. [11] W.R. Fawcett, M. Fedurco, Z. Kovacova, Langmuir 10 (1994) 2403. [12] M. Ohtani, S. Kuwabata, H. Yoneyama, Anal. Chem. 69 (1997) 1045. [13] R. Andreu, W.R. Fawcett, J. Phys. Chem. 98 (1994) 12753. [14] R. Andreu, J.J. Calvente, W.R. Fawcett, M. Molero, Langmuir 13 (1997) 5189. [15] R.J. Hunter, Zeta Potential in Colloid Science Principles and Applications, Academic Press, London, 1981, p. 28 [16] A.N. Frumkin, B.B. Damaskin, Adsorption of Organic Compounds at Electrodes, in J. O’M. Bockris, B.E. Conway (Eds.), Modern Aspects of Electrochemistry, vol. 3, Butterworths, London, 1964, p. 149 [17] V. Plichon, E. Laviron, J. Electroanal. Chem. 71 (1976) 143. [18] T. Kakutani, M. Senda, Bull. Chem. Soc. Jpn. 53 (1980) 1942.
The effect of the interfacial potential distribution on the reduction of adsorbed methylene blue at a mercury electrode Michael J. Honeychurch a,b,* a
Department of Molecular Sciences, James Cook Uni6ersity of North Queensland, Towns6ille 4811, Queensland, Australia b Department of Chemistry, Uni6ersity of Hawaii, 2545 The Mall, Honolulu, Hawaii 96822, USA Received 6 May 1997
Abstract The constant current chronopotentiometric reduction of methylene blue adsorbed on a HMDE at fractional coverages of MB + of u 51 is reported and the results interpreted in terms of both an EE mechanism and the interfacial potential distribution (IPD) model of Smith and White (Anal. Chem., 64 (1992) 2398). Derivative chronopotentiometric (DCP) peaks were broader than expected for a two electron transfer under Langmuir isotherm conditions and shifted positively with increasing fractional coverage. Whilst the EE model satisfactorily accounted for the peak shape and was in general agreement with previously reported work (Zutic et al., J. Electroanal. Chem., 177 (1984) 253) it was not possible to account for the shift in the DCP peak. Calculated DCPs based on the IPD model had peak shapes consistent with the experimental DCPs and shifted positively with increasing fractional coverage in the manner of the experimental DCPs. © 1998 Elsevier Science S.A. All rights reserved. Keywords: Methylene blue; Interfacial potential distribution; Mercury electrode
1. Introduction The study of the electrochemical reduction of methylene blue, MB + , to leucomethylene blue, LMB, has been the subject of many studies over the years [1,2]. The reduction in solution at different electrodes and also following adsorption on mercury have been studied. In studies of the reduction of adsorbed MB + it is generally observed that linear sweep voltammograms are broader than expected for a two electron reversible reduction of an adsorbed molecule under Langmuir isotherm conditions. Likewise polarograms and chronocoulograms are broader than would be expected under such conditions. Pergola et al. [1] observed broad chronocoulograms for the reduction of adsorbed MB + on mercury and * Corresponding author. Current address: Inorganic Chemistry Laboratory, University of Oxford, South Parks Road, Oxford OX1 3QR, UK. E-mail:[email protected] 0022-0728/98/$19.00 © 1998 Elsevier Science S.A. All rights reserved. PII S 0 0 2 2 - 0 7 2 8 ( 9 7 ) 0 0 5 3 1 - 7
proposed that they were due to interactions between adsorbed molecules and used a Frumkin isotherm model analogous to that of Laviron [3] to determine the interaction parameters. Wopschall and Shain [4] found evidence to suggest that the reduction of MB + adsorbed on mercury was not a simple two electron reversible charge transfer but proceeds in two steps via the relatively stable semiquinone radical intermediate with a fast protonation of the intermediate. They managed to fit the experimental peak to a one step reversible mechanism by assuming non-integer values of n and found good agreement for napp of 1.66. The electron transfer kinetics of the MB + /LMB couple at mercury electrodes have also been studied by Zutic et al. [2] by double potential step chronocoulometry in 1 M KNO3. They concluded, from analysis of Tafel type slopes, that the reduction of adsorbed MB + involved two consecutive reversible one electron transfers (reversible EE mechanism) with a 16 mV separa-
M.J. Honeychurch / Journal of Electroanalytical Chemistry 445 (1998) 63–69
64
tion between the half wave potentials of the two single electron steps according to the following scheme MB + + e − ? MB ·
(1)
MB · +H + e ? LMB
(2)
+
−
At low bulk concentrations and fractional coverages of u B 1 only one chronocoulometric wave, corresponding to this reduction, is present. At higher coverages i.e. u \ 1 a second chronocoulometric wave appears which is due to the reduction of a second layer of adsorbed MB + through the adsorbed LMB layer [2,5]. In a recent paper [6], the constant current chronopotentiometric (CCCP) reduction of flavin adenine dinucleotide (FAD) was reported in which the shape of the derivative chronopotentiometric (DCP) reduction peak was consistent with the model that had been adapted for an EE reduction of a species adsorbed under Langmuir isotherm conditions. It, therefore, seemed appropriate to use this model to test the proposition that the MB + reduction is an EE mechanism although another possibility exists. Smith and White [7] have developed a general model to describe the reversible voltammetric response of electrodes with electroactive molecular films based on the interfacial potential distribution (IPD model). This model uses many of the concepts developed by Frumkin which were used to correct rate constants of irreversible reactions involving soluble reactants [8], and later employed by Lane and Hubbard [9] in a study of the kinetics of electroactive adsorbates. The work of Smith and White has since been extended to include the effects of surface immobilized acid or base groups [10,11], ion pairs [12] and discreteness of charge effects [11,13,14]. In the IPD model, when the oxidized and reduced adsorbed molecules have different charges, the resultant voltammogram may display apparent non-Langmuir behavior. Since there is a charge difference between MB + and LMB this explanation has also been examined. In this paper the constant current chronopotentiometric reduction of adsorbed methylene blue at fractional coverages of MB + of u5 1 is reported and the results interpreted in terms of an EE mechanism and the IPD model.
2. Experimental Constant current chronopotentiometry was performed using a Radiometer PSU-20 potentiometric stripping unit (Radiometer A/S, Copenhagen, Denmark). The PSU-20 was controlled with Tap2 3.0 software (Radiometer A/S, Copenhagen, Denmark) on an IBM compatible 286 computer. The potential vs. time
transient was measured at a frequency of 30 Hz in potential intervals of 2 mV with the output being a derivative chronopotentiogram of the form dt/dE. In order to obtain t vs. E plots raw data was converted to an ASCII file and curves were integrated with KALEIDAGRAPH 3.0 (Synergy Software) on an Apple Power Macintosh 7200/120 computer. The working electrode was a E410 hanging mercury drop electrode (HMDE) (Metrohm, Herisau, Switzerland) of surface area 0.0296 9 0.0011 cm2. All potentials were measured with respect to a saturated calomel electrode (SCE). Methylene blue (Sigma Aldrich, Castle Hill, Australia) stock solutions of 1.4× 10 − 3 M were made up in 0.1 M phosphate buffer (pH 7.4). The solution was purged for 30 min with nitrogen that had passed sequentially through a solution of vanadous chloride and then the supporting electrolyte. Solutions were blanketed with nitrogen during analysis. MB + was accumulated on the HMDE potentiostatically for 60 s at 0 mV from 0.4 to 3.5 mM solutions. After the completion of the adsorptive accumulation period MB + was a reduced by applying a −11.6 mA current to the cell. All measurements were made at 23°C.
3. Theory In the chronopotentiometric experiment the total number of adsorbed molecules at time t is equal to the number initially adsorbed (at t= 0) plus the total amount brought to, or removed from, the electrode by diffusion after the commencement of the experiment (t\ 0). For accumulation on a HMDE of radius ro by an adsorptive preconcentration procedure the mass balance equation is GMB + (t)+ GLMB(t)
& &
= GT + DMB +
t
0
t
+ DLMB
0
(cMB + (r,t) (r
(cLMB + (r,t) (r
.(t r = ro
.(t
(3)
r = ro
where Di is the diffusion coefficient of i; ci (r, t) is the concentration of i; Gi (t) is the surface excess of i; and GT is the total surface excess at t= 0. In the experiments reported below the time allowed for accumulation of MB + on the HMDE is much greater than the chronopotentiometric transition time (tB50 ms). Since all experiments were carried out in dilute solutions the amount of MB + accumulated during the preconcentration procedure was always much greater than the amount accumulated during the constant current reduction. Under these conditions GMB + (t)+ GLMB(t)= GT
(4)
M.J. Honeychurch / Journal of Electroanalytical Chemistry 445 (1998) 63–69
65
If it is assumed that only the oxidized form is present initially then GMB + (0) = GT. At the transition time t= t and the reduction of MB + is complete, therefore GMB + (t) = 0 and GLMB(t) =GT. In the absence of a diffusion reaction, the chronopotentiometric transition time, t, is given by
Substituting DG o = − nFE o, E= (fM − fHg), and the liquid junction potential ELJ = (fs(b) − fs(a)) into Eq. (10) gives
t = 2FGLMB/j
(5)
t= 2FGT /j
(6)
t −t =2FGMB + /j
(7)
Taking the potential of the solution (a) as a zero reference, defining an apparent adsorption formal poo S 2 S tential E o% a = E − ELJ + (RT/2F) ln[(a Cl − ) a H + ], and + taking the activities of MB and LMB at the plane of electron transfer as their surface concentrations GMB + and GLMB, and substituting into Eq. (11) gives
where j is the current density. Fig. 1 shows a diagram of the potential profile with MB + adsorbed on the electrode. The electrochemical cell for the system is + P
Hg(l) MB ,LMBP,K2HPO4(aq), KH2PO4(aq), KCl(aq) Hg2Cl2(s) Hg(l)
=m
P LMB
Hg Hg
+m
(11)
(12)
(13)
sM = (E o% a − Epzc − (fP/2)+ (RT/2F) ln[ f/(1− f )]) ×eoem/d
At equilibrium +2m
E= E o% a + (fP/2)+ (RT/2F) ln[GMB + /GLMB]
sM = (fM − fP)eoem/d
(b)
m
+ (RT/2F) ln[a PMB + (a S(b) )2a S(a) /a PLMB] Cl − H+
The charge densities at the metal, the plane of electron transfer and the diffuse layer can be related to the interfacial potential with the following equations [7,15]
(a)
P MB +
E= E o + (fP − fs(a))/2 −ELJ
+ 2m
Hg2Cl2 Hg2Cl2
S(b) Cl −
+2m
+ 2m
M e−
+m
Hg e−
P H+
sdiff = {2000eoesRT % ci [exp(− zi FfP/RT)− 1]}1/2 (9)
where m is the electrochemical potential of species i in phase j. The subscripts P, S and M indicate the plane of electron transfer, the solution and the HMDE, respectively. Following the procedure of Smith and White [7], the thermodynamic definitions (m ij =m oi +RT ln(a ij )+ zi Ff j; a ij = the activity of i in phase j; m PH + =m S(a) H+ = o o m oH + +RT ln(a S(a) )+ z Ff ; and DG =S 6 m , where + i s(a) i i i H 6i is the stoichiometric coefficient) were substituted into Eq. (9) to give j i
2F(fM −fHg)− F(fP −fs(a)) +2F(fs(b) −fs(a)) +DG o 2 S(a) P = RT ln[a PMB + (a S(b) Cl − ) a H + /a LMB]
(14)
(10)
(15) sP = FGm f
(16)
sdiff = − (sM + sP)
(17)
where eo is the permittivity of free space, em is the dielectric of the adsorbed layer of thickness d, es the dielectric of water with a supporting electrolyte containing ci ions of charge zi, Epzc is the potential of zero charge in the absence of specific adsorption, Gm is the surface concentration of MB + at monolayer (GT = uGm) and f= GMB + /GT. Eq. (14) applies only to the part of the surface that is covered by adsorbate. The capacitance of the adsorbed layer is Cm = eoem/d
(18)
and the total capacitance in the presence of a monolayer coverage is [7] CT = Cm(1−(fP/(E)
u= 1
(19)
At submonolayer coverages the capacitance can be estimated using Frumkin’s parallel capacitor model [16] CT = Cm(1−(fP/(E)u+ Co(1−u)
uB1
(20)
where Co is the capacitance in the absence of adsorption. The capacitative component of dt/dE is (dt/dE)c = CT /j
(21)
The faradaic component of dt/dE can be obtained from Eq. (22) Fig. 1. Diagram showing the potential profile used in the derivation of the IPD model. ‘P’ represents the plane of electron transfer.
j= − 2FdGMB + /dt = − 2FGT df/dt
(22)
M.J. Honeychurch / Journal of Electroanalytical Chemistry 445 (1998) 63–69
66
Table 1 Experimental data for the chronopotentiometric reduction of adsorbed MB+ on a HMDE following accumulation at 0 mV versus SCE (current −11.6 mA) u
slopea/mV
(r)
napp
Ep/mV (9 2 mV)
W1/2/mV
0.12 0.25 0.50 0.55 0.65 0.77 0.91
35.0 36.8 37.1 36.4 36.4 37.1 37.8
(0.9986) (0.9989) (0.9993) (0.9994) (0.9992) (0.9992) (0.9994)
1.68 1.59 1.58 1.61 1.62 1.58 1.55
−189 −185 −180 −179 −176 −172 −169
63 66 63 63 63 63 64
a
Slope of the log[(t−t)/t] vs. E plot.
Substituting f=GMB + /GT into Eq. (12), differentiating with respect to t, solving for df/dt and substituting into Eq. (22) gives the faradaic component of dt/dE [7] (dt/dE)f =(4F 2/RTGT f(1 − f )(1 − (fP/(E)/j
(23)
Adding Eqs. (23) and (21) gives the equation for the DCP dt/dE = [{(4F 2/RT)GT f(1 − f )(1 − (fP/(E)} +CT ]/j (24) After substituting Eq. (6) into Eq. (24), the equation for the DCP can be rewritten as
K 1/2 =
4h − 16h 2 − [4(h 2 − 6h +1)(h − h 3/2 − h 1/2)] 2(h − h 3/2 − h 1/2) (27)
h= exp[− (2F/RT)(E − E o% a )]
(28)
and the value of h at the half peak height can be obtained from W1/2 = (RT/F) ln h
(29)
Substituting the value for W1/2 into Eqs. (27) and (29) gives a value of K of 0.839 0.03. For KB 16 only one peak is observed experimentally and the DCP peak occurs at Ep = E o% a and is given by [6]
dt/dE =[(2F/RT)tf(1 −f )(1 − (fP/(E)] +(CT /j ) (25)
4. Results and discussion The experimental data are summarized in Table 1. Plots of log[(t −t)/t] versus E for the experimental peaks at various fractional coverages were linear with slopes of 36.790.8 mV (Table 1). The magnitude of the slope equates to an apparent number of electrons transferred, napp, of 1.60 which is in close agreement to the non-integer value of n obtained from linear sweep voltammetry by Wopschall and Shain [4]. Integration of the DCPs, assuming a linear baseline, gave the maximum charge as 18.39 0.8 mC cm − 2, in agreement with the value of 18.1 9 0.3 mC cm − 2 reported previously [2]. The DCPs were symmetrical with peak widths at half peak height, W1/2, of approximately 63 mV. No variation in W1/2 with fractional coverage was observed. Assuming the reduction to be an EE mechanism then the equation for the DCP is expressed in terms of a semiquinone formation constant K K= G 2MB · /GMB + GLMB
(26)
the relationship between W1/2, and K for the DCP is [6,17]
Fig. 2. Experimental DCP (——) of 2.67 mM MB + in 0.1 M phosphate buffer, pH 7.40, following 60 s adsorptive accumulation at 0 mV vs. SCE, and calculated DCP with E o% a =180 mV and () K= 0.52 and (- - -) K =0.83.
dt dE
=− p
M.J. Honeychurch / Journal of Electroanalytical Chemistry 445 (1998) 63–69
n
Ft 1 RT (2+ K 1/2)
(30)
A plot of (dt/dE)p versus t was linear (r = 0.9995) passing through the origin with slope −14.41 V − 1 from which K was determined as being 0.529 0.08. The DCP response was calculated from these two values for K using the methods described previously [6]. An excellent fit with the experimental peak was obtained for K= 0.52 (Fig. 2). This value of K can then used to estimate the separation in the reduction potentials for the two individual reduction steps since they are related to K by [6] o% (E o% 1 −E 2 )F/RT= ln K
(31)
A separation of 17 mV is predicted which is in agreement with the value obtained by Zutic et al. [2] Despite the good agreement with previous work and the excellent correlation between the experimental and calculated DCPs there are some apparent anomalies in the experimental data which are not explained by the proposed EE model. Table 1 shows that the peak potential of the DCPs varied with fractional coverage. The variation was linear (r =0.993) with slope 25.1 mV and intercept − 192 mV. A shift in the half wave potential was also reported by Pergola et al. [1] and seemed to be present in the chronocoulograms of Zutic et al. [2] although not discussed. Whilst the shape of the DCP is invariant at all fractional coverages this shift in peak potential is not accounted for with the EE model. Lateral interactions between adsorbed species are known to produce a dependence of the peak potential on fractional coverages [3]. Laviron assumed that adsorption followed a Frumkin isotherm and derived an equation in which the peak shape and peak potential were dependent on the interactions between adsorbates [3]. The magnitude of the interactions is given by an interaction coefficient, a, which is positive for attraction and negative for repulsion. The peak potential is dependent on (aOO −aRR), where aOO and aRR, are interaction coefficients for interactions between oxidized adsorbates and between reduced adsorbates respectively. The peak shape is dependent on (aOO +aRR − 2aOR), where aOR is the interaction coefficient for interactions between oxidized and reduced adsorbates. Following Laviron’s formalism our observations of a peak potential shift would imply that (aOO −aRR)" 0, however, the lack of any change in the shape of the DCP peak with varying coverage does not imply (aOO +aRR −2aOR)= 0 since the peak shape then becomes the same as for a Langmuir isotherm and this would require W1/2 to be a constant value of 45 mV for a two electron transfer. Pergola et al. [1] used a Frumkin isotherm model analogous to Laviron’s to explain their observations of
67
chronocoulometric wave broadening and a shift in the half wave potential with fractional MB + coverage and found both (aOO + aRR − 2aOR)" 0 and (aOO − aRR)" 0. However, these authors used a high concentration of chloride ion in their experiments which produces a steep region at the beginning of the chronopotentiogram (chronocoulogram) due to the oxidation of the electrode. Under such conditions it would appear that the adsorbed MB + molecules adopt a different orientation on the electrode since these authors reported a maximum charge of 25 mC cm − 2 which is considerably higher than that reported here and by Zutic et al. [2]. A different orientation on the electrode may account for different forces between adsorbed molecules resulting in different experimental observations. Therefore, the results of Pergola et al., which included an estimation of the lateral interaction coefficients, cannot be directly extrapolated to this study. The effect of lateral interaction on EE reductions have been considered by others [18]. An assumption that all the lateral interaction parameters are equal was necessary in order to provide a workable model. Following such an assumption the equation reduced to that for a Langmuir isotherm (no interactions). Therefore, while the EE model for Langmuir adsorption adequately describes the DCP peak shape, a model analogous to that presented by Kakutani and Senda [18] for ac voltammetry, that combines the two one electron steps and allows for lateral interactions between the adsorbed molecules (oxidized, reduced and radical intermediate), would seem necessary in order to account for the progressive peak shift with increasing coverage of MB + . This has not been attempted due to the difficulties in obtaining workable solutions, which has been discussed elsewhere [18]. In seeking an explanation for the experimental observations, let us consider the effect of the interfacial potential difference on the reduction in terms of the IPD model of Smith and White [7] which is adapted to the MB + /LMB system. DCPs were calculated by the following sequence of steps using a spreadsheet with values of f in the initial column. To solve Eqs. (12)–(25), it is necessary to have values for the three unknowns in the set of equations, E o% a , Epzc, and em/d. Pergola et al. [1] determined the formal potential of the MB + /LMB couple at pH 7.9, in the absence of adsorption, to be − 2489 2 mV versus the SCE which equates to 219 mV at pH 7.4. When adsorption occurs the formal potential for the reduction will be shifted by an amount equal to (RT/2F) ln(bR/bO), where bR and bO are the adsorption coefficients of LMB and MB + respectively. Notwithstanding that it seems likely that MB + and LMB were oriented differently in the experiments of Pergola et al. compared this work, as a first approximation their value of (bR/bO), which
68
M.J. Honeychurch / Journal of Electroanalytical Chemistry 445 (1998) 63–69
Fig. 3. Experimental DCPs of MB + (——) and DCPs calculated using the IPD model (- - -). Coverages u= 0.12, 0.55, 0.77 and 0.91.
was estimated to be 4.75, was used to calculate the adsorption formal potential, which gives E o% a 200 mV. This value was used in subsequent calculations. In the absence of specific adsorption the potential of zero charge of mercury is − 430 mV versus SCE therefore Epzc = − 430 mV was used in all calculations. Finally em/d was varied so as to provide the best fit between the experimental and the calculated DCPs. ˚ − 1. The Best results were obtained using em/d = 6 A + thickness of MB , if it were to be lying flat on the ˚ [5]. If it is assumed electrode, is approximately 3.25 A that the plane of electron transfer is between 1.6 and ˚ then one obtains a dielectric constant for MB + 3.25 A of 10–20. At a given coverage of MB + , Eqs. (16), (14) and (17) were solved in that order to give the value of sdiff, which was then multiplied by u. Since a non-symmetrical electrolyte was used in these experiments, fP was determined by first plotting fP as a function of sdiff, for fP B 100 mV, in a 0.1 M phosphate buffer using Eq. (15). It was found that the relationship between fP and sdiff could be described by a 6th order polynomial (r = 0.9999)
and shape of experimental and calculated DCPs across the range of fractional coverages. The calculated baselines were generally of the magnitude of the experimental baseline. At lower coverages (uB 0.25), the calculated baseline had a steeper slope than the experimental baseline. A dip is present in all the calculated baselines with a minimum corresponding to the region of the
fP = 0.91707sdiff − 6.0117s 2diff −24.062s 3diff −53.175s 4diff − 59.727s 5diff −26.562s 6diff
(32)
Having calculated sdiff, fP could then be determined using Eq. (32) and substituted into Eq. (12) to give E. (fP/(E was determined by numerical differentiation and calculations made using Eqs. (20), (21), (23) and (25)). Calculations using the IPD model are shown in Fig. 3. An excellent correlation is obtained between the size
Fig. 4. Experimental () and calculated () peak potentials for reduction of adsorbed MB + in 0.1 M phosphate buffer, pH 7.40.
M.J. Honeychurch / Journal of Electroanalytical Chemistry 445 (1998) 63–69
faradaic peak. This feature was present in some of the calculations of Smith and White. Peak areas (transition times) calculated by subtracting the calculated baseline were approximately 4% greater than when using a straight baseline. Fig. 4 shows a comparison between experimental and calculated peak potentials. A good correlation is obtained in that the shift in the calculated peak potential is the same magnitude as the experimental shift. The slight curvature in the plot of calculated peak potential versus fractional coverage does differ from the linearity of the experimental plot. Nevertheless these differences would appear to be relatively minor given the assumptions made in calculating the calculated DCPs and the relatively simple model used.
5. Conclusion In previous reports in the literature, the effects of lateral interactions between adsorbed molecules and a two step EE mechanism have been offered as explanations of the apparent non-ideal or non-Langmuir behavior of adsorbed MB + . In this paper a model which takes into account the effects of the interfacial potential distribution provides calculated DCPs which have peak shapes consistent with the experimental DCPs and which shift positively with increasing fractional coverage in the manner of the experimental DCPs. It is therefore possible to use this model to describe MB + behavior when adsorbed on mercury electrodes without the need to invoke non-ideal behavior of adsorbed molecules or more a complex mechanism than a direct two electron transfer.
.
69
Acknowledgements Part of this work was undertaken at James Cook University of North Queensland where the author would like to acknowledge the receipt of a James Cook University Department of Molecular Sciences scholarship.
References [1] F. Pergola, G. Piccardi, R. Guidelli, J. Electroanal. Chem. 83 (1977) 33. [2] V. Zutic, V. Svetlicic, M. Lovric, I. Ruzic, J. Chevalet, J. Electroanal. Chem. 177 (1984) 253. [3] E. Laviron, Voltammetric methods for the study of adsorbed species, in: A.J. Bard (Ed.), Electroanalytical Chemistry, vol. 12, Marcel Dekker, New York, 1982, p. 53 [4] R.H. Wopshall, I. Shain, Anal. Chem. 39 (1967) 1527. [5] V. Svetlicic, J. Tomaic, V. Zutic, J. Chevalet, J. Electroanal. Chem. 146 (1983) 71. [6] M.J. Honeychurch, M.J. Ridd, Electroanalysis 8 (1996) 362. [7] C.P. Smith, H.S. White, Anal. Chem. 64 (1992) 2398. [8] A.J. Bard, L.R. Faulkner, Electrochemical Methods, Wiley, New York, 1980, p. 540 [9] R.F. Lane, A.T. Hubbard, J. Phys. Chem. 77 (1973) 1413. [10] C.P. Smith, H.S. White, Langmuir 9 (1993) 1. [11] W.R. Fawcett, M. Fedurco, Z. Kovacova, Langmuir 10 (1994) 2403. [12] M. Ohtani, S. Kuwabata, H. Yoneyama, Anal. Chem. 69 (1997) 1045. [13] R. Andreu, W.R. Fawcett, J. Phys. Chem. 98 (1994) 12753. [14] R. Andreu, J.J. Calvente, W.R. Fawcett, M. Molero, Langmuir 13 (1997) 5189. [15] R.J. Hunter, Zeta Potential in Colloid Science Principles and Applications, Academic Press, London, 1981, p. 28 [16] A.N. Frumkin, B.B. Damaskin, Adsorption of Organic Compounds at Electrodes, in J. O’M. Bockris, B.E. Conway (Eds.), Modern Aspects of Electrochemistry, vol. 3, Butterworths, London, 1964, p. 149 [17] V. Plichon, E. Laviron, J. Electroanal. Chem. 71 (1976) 143. [18] T. Kakutani, M. Senda, Bull. Chem. Soc. Jpn. 53 (1980) 1942.