Electrochemical Impedance Study of Tl+ Reduction through

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Langmuir 1999, 15, 3672-3678

Electrochemical Impedance Study of Tl+ Reduction through Gramicidin Channels in Self-Assembled Gramicidin-Modified Dioleoylphosphatidylcholine Monolayers on Mercury Electrodes M. Rueda,* I. Navarro, G. Ramirez, F. Prieto,† C. Prado, and A. Nelson‡ Department of Physical Chemistry, University of Sevilla, c/Prof. Garcı´a Gonza´ lez s/n, Sevilla 41012, Spain Received November 4, 1998. In Final Form: February 12, 1999 Impedance measurements for the reduction of Tl+ on gramicidin-modified dioleoylphosphatidylcholinecoated mercury electrodes have been performed. The frequency dependence of the admittance data fits well to a Randles circuit, and the Warburg coefficient, σ, and the irreversibility coefficient, p′, can be obtained at every dc potential from the frequency analysis conforming to this circuit. However, the potential dependence of the Warburg coefficient is different from the one expected for a simple electron transfer. Instead, the σ-E data can be analyzed conforming to a mechanism including preceding and following homogeneous chemical steps to the electron transfer (CEC mechanism). In addition, from the irreversibility coefficient, p′, a value of the standard rate constant for the electron transfer of 0.035 cm s-1 and a potential independent value for the transfer coefficient, R, of close to 0.5 are obtained. The possibility that the CEC mechanism originates partly from nonlinear diffusion is considered, and the results are discussed in comparison with those given in the literature for Tl+ reduction on pure mercury.

1. Introduction There has always been much interest in electrochemistry concerning the interpretation of biological processes. Examples of these are the processes of ion transport and electron transfer through the biological membrane. To apply the electrochemical methods of modeling to biological membrane processes, some electrode systems have been proposed.1 Recently, a phospholipid-coated mercury electrode has been developed,2,3 following the pioneering work of Miller.1 It is obtained by spreading a solution of the lipid in a suitable solvent on the surface of an aqueous electrolyte, allowing the solvent to evaporate, and then immersing the hanging mercury electrode into the electrolyte through this surface. This results in an adsorbed monolayer that can be used as a biomimetic membrane analogously to the bilayer lipid membranes (BLM) that have been extensively employed as models of biological membranes. In the case of a lipid-coated mercury electrode, the film consists of half a bilayer with the polar heads directed toward the electrolyte solution.2 This supported monolayer system offers some advantages over BLM. Thus, the electric potential and the flux of electroreducible metal ions across the monolayer can be controlled more directly and accurately. The film is provided with an inherent mechanical stability and resistance to high electric fields so that after voltammetric exploration or potential pulses in a wide potential range the film remains unaltered. The use of mercury as the metal substrate * To whom correspondence should be addressed. Fax: 34-954233765. Tel: 34-954-556733. E-mail: [email protected]. † Present address: Departamento de Ingenieria Quı´mica, Quı´mica Fı´sica y Quı´mica Orga´nica, Universidad de Huelva, Spain. ‡ On leave from Plymouth Marine Laboratory, Citadel Hill, Plymouth PL1 2PB, U.K. (1) Miller, I. R. In Topics in Bioelectrochemistry and Bioenergetics; Milazzo, G., Ed.; John Wiley and Sons: Chichester, U.K., 1981; Vol. 4, pp 161-224. (2) Nelson, A.; Benton, A. J. Electroanal. Chem. 1986, 202, 253. (3) Nelson, A.; Aufret, N. J. Electroanal. Chem. 1988, 244, 99; 1988, 248, 167.

instead of solid electrodes represents also a major advantage because of the liquid state of mercury, which provides a perfectly smooth and defect-free support to the film. The permeability of the monolayer to electroreducible metal ions and the influence of incorporated proteins or ionophores have been extensively investigated.4-6 The habitual techniques in these studies have been cyclic voltammmetry and chronoamperometry, while differential capacity measurements have been used to characterize the monolayer. Moncelli et al.7-10 have used differential capacity and chronocoulometry measurements to calculate the charge density on lipid monolayers. The high accuracy attained in these experiments made it possible to obtain valuable information about the lipid-coated mercury electrolyte interface such as to test the validity of the Gouy-Chapman theory, to determine the intrinsic pKa of the phospholipids in the monolayer, and to study the adsorption of lipophilic ions. Despite the large amount of work that has been carried out on this membrane model system, electrochemical impedance measurements have not been used to study electron-transfer processes at these interfaces. This technique can give detailed information on the different steps (transport, electron transfer, chemical reactions, adsorption, etc.) involved in an electrode reaction, allowing the determination of the reaction mechanism.11,12 Because of this, it is intended to extend the impedance analysis previously performed on electrode (4) Nelson, A.; van Leeuwen, H. P. J. Electroanal. Chem. 1989, 273, 183 and 201. (5) Nelson, A. J. Electroanal. Chem. 1991, 303, 221. (6) Nelson, A.; Auffret, N.; Borlakoglu, J. Biochim. Biophys. Acta 1990, 1021, 205. (7) Moncelli, M. R.; Guidelli, R. J. Electroanal. Chem. 1992, 326, 331. (8) Moncelli, M. R.; Becucci, L.; Guidelli, R. Biophys. J. 1994, 66, 1969. (9) Moncelli, M. R.; Becucci, L.; Herrero, R.; Guidelli, R. J. Phys. Chem. 1995, 99, 9940. (10) Beccuci, L.; Guidelli, R.; Moncelli, M. R. J. Electroanal. Chem. 1996, 413, 187.

10.1021/la981557j CCC: $18.00 © 1999 American Chemical Society Published on Web 04/17/1999

Electrochemical Impedance Study of Tl+ Reduction

processes of organic compounds at mercury electrodes13 to study electron-transfer processes at the phospholipidcoated electrodes. In this respect, the reduction of aqueous Tl+ ions through the gramicidin channels on gramicidin-modified phospholipid-coated mercury electrodes is an interesting system because it involves the transfer of only one electron and the ion passes through the gramicidin channels. The system has been previously studied with dc electrochemical techniques in a wide variety of conditions (different phospholipids, incorporated bioactive compounds, etc).14-16 Cyclic voltammetry and chronoamperometry results support the existence of a mechanism in which the electroactive species is generated in a preceding homogeneous chemical step (CE mechanism). This preceding step was identified as the translocation of the ion in the channel, and the rate constant obtained from the electrochemical methods was identified as a permeability rate constant. The electrochemical impedance method is a powerful tool to characterize electrode mechanisms with coupled chemical reactions, by combining the frequency and the potential analysis of the impedance data.17 In a previous paper18 experimental procedures were used to obtain impedance data for Tl+ reduction in gramicidin-modified dioleoylphosphatidylcholine (DOPC)-coated mercury electrodes. It was observed that the results in dynamic experiments depend on the previous history of the electrode film, so step-bystep experiments with the Fourier transformation method were recommended to perform the frequency analysis. It was also observed that the reduction on gramicidinmodified DOPC-coated mercury electrodes is slower than that on uncoated mercury electrodes. In the latter case, impedance and demodulation voltammetric experiments19,20 showed that thallium ions adsorb weakly at mercury and the reduction is so fast that only a secondorder technique such as the demodulation voltammetry can give kinetic information.20 It is the purpose of this paper to take advantage of the possibilities of the impedance analysis to characterize mechanisms with coupled homogeneous chemical steps in order to understand the reduction of Tl+ through the gramicidin channels in self-assembled gramicidin-modified DOPC monolayers on mercury. 2. Theory The CEC mechanism can be formulated as ka

kb

A {\ } O + ne S R {\ }B k k -a

-b

The mass transport of O and R species is not purely diffusional because they are supplied or removed by the (11) Rueda, M. In Research in Chemical Kinetics; Compton, R. G., Hancock, G., Eds.; Blackwell Science: Oxford, U.K., 1997; Vol. 4, pp 31-96. (12) Sluyters, J. H.; Sluyters-Rehbach, M. In Comprehensive Treatise of Electrochemistry; Bockris, J. O’M., Ed.; Plenum Press: New York, 1984; Vol. 9, pp 177-292. (13) Sluyters, J. H.; Sluyters-Rehbach, M. In Comprehensive Chemical Kinetics; Bandfor, C. H., Compton, R. G., Eds.; Elsevier: Amsterdam, The Netherlands, 1986; Vol. 26, pp 203-345. (14) Nelson, A. J. Chem. Soc., Faraday Trans. 1993, 89, 2799. (15) Nelson, A. Langmuir 1996, 12 (8), 2058. (16) Nelson, A. Langmuir 1997, 13, 5644. (17) Sluyters-Rehbach, M.; Sluyters, J. H. J. Electroanal. Chem. 1969, 23, 457; 1970, 26, 237. (18) Rueda, M.; Navarro, I.; Ramirez, G.; Prieto, F.; Nelson, A. J. Electroanal. Chem. 1998, 454, 155. (19) Sluyters-Rehbach, M.; Timmer, B.; Sluyters, J. H. Recl. Trav. Chim. Pays-Bas 1963, 82, 553. (20) Blankenborg, S. G. J.; Sluyters-Rehbach, M.; Sluyters, J. H. J. Electroanal. Chem. 1993, 349, 255.

Langmuir, Vol. 15, No. 10, 1999 3673

chemical reactions. The corresponding flux equations can be solved by Laplace transformation, and the faradic impedance be deduced as explained in11

[

]

Kb Ka λ λ s-1/2 + Ka + 1 O Kb + 1 R λR λO (s + ka′)-1/2 (s + kb′)-1/2 (1) Rct Ka + 1 Kb + 1

ZF ) Rct + Rcf

[

]

where the rate constants ki′ and the equilibrium constants Ki are defined as

ki′ ) ki + k-i; Ka ) ka/k-a; Kb ) k-b/kb

(2)

the parameters Rct and λi are defined as usual11,12

Rct )

( )

( )

∂jF ∂jF 1 ;λ)1/2 ∂E ci ∂ci nFD i

(3)

E,cj

and s is related to the complex number i ) x-1 by s ) iω with ω as the frequency of the ac perturbation in radians. The first two terms of the summation in eq 1 imply the same frequency dependence as that observed for a simple electron-transfer process. The third term, which has been identified as a Gerischer impedance ZG,11,12 introduces a more complicated frequency dependence. However, two limiting cases can be distinguished: (i) The high-frequency limit results when ki′ , ω. Then, it is clear that the latter summation can be simplified and the faradaic impedance attains Randles behavior, characterized by two parameters, the charge-transfer resistance, Rct, and the Warburg coefficient, σ:

ZF ) Rct + (σO + σR)s-1/2 ) Rct + σs-1/2

(4)

σi ) (λiRct/(2)1/2

(5)

with

The plus sign pertains to oxidized species and the minus sign to reduced species. (ii) The low-frequency limit when ki′ . ω gives

[

]

λO λR k ′ -1/2 k ′ -1/2 + Ka + 1 a Kb + 1 b Kb Ka λ λ s-1/2 ) (Rct)app + (σ)apps-1/2 Rct Ka + 1 O Kb + 1 R (6)

ZF ) Rct + Rct

[

]

which represents a pseudo-Randles behavior with frequency having an apparent transfer resistance, (Rct)app, and an apparent Warburg coefficient, (σ)app. It can be thought at first sight that only case ii or the complete eq 1 can give information on the chemical steps, but even if they do not show up in the frequency dependence, the potential dependence of σ and Rct is determined by ki′ and Ki values implicit in the potential dependence of the surface concentrations cO and cR, which appear in the definition of Rct and σ:

Rct )

RT 1 2 Rc + (1 R)cR exp(φ) n F kf O 2

(7a)

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Rueda et al.

DO-1/2 + DR-1/2 exp(φ) RT n2F2(2)1/2 RcO + (1 - R)cR exp(φ)

σ)

(7b)

where kf is the potential-dependent forward rate constant of the electron-transfer step, R is the transfer coefficient, and φ is related to the standard potential of this step, E°, as φ ) (nF/RT)(E - E°). In ref 17 the guidelines were given to derive the potential dependence of cO and cR in the case of coupled homogeneous chemical reactions in the scope of Jacq’s diffusion layer theory.21 Following them, the expressions for cO and cR at the interface in the case of the CEC mechanism can be derived. After substitution in eq 7b and assuming that the electron-transfer step is “Nernstian” under dc conditions, it can be written that

(σCEC)rev )

(

La RT exp(j) + +1+ 1/2 1/2 * L n F (2) DO cO b La exp(-j) (8) Lb 2

2

)

where the function Li represents the influence of the chemical reactions, as is defined in Jacq’s reaction layer treatment for the mass transfer in the mechanism21

Li )

KiF(li) + 1

(9)

(Ki + 1)F(li)

with the function F(li) given by 1/2

F(li) ) π

Γ[1 + li2/π]

(10)

Γ[1/2 + li2/π)]

In this equation Γ stands for the gamma function and li ) δi(ki′/DO)1/2, where δi is the thickness of the diffusion layer. The standard potential for the electron-transfer step is implicit in eq 8 in the potential-dependent function, j:

j)

nF nF (E - Erev (E - E0) + ln(DO/DR)1/2 1/2 ) ) RT RT

rev ) σmin,CEC

[

(

) )]

Ka La RT exp(-j) + 1 + 1/2 * K + 1 L n F (2DO) cO a b K b La + exp(j) (12) Kb + 1 Lb 2

2

(

In Figure 1 are shown some of the σ vs E plots obtained with eqs 8 and 12. They have been calculated with typical values for the different coefficients and compared with what is expected for a simple electron transfer:

σrev )

exp(j) + 2 + exp(-j) RT 2 1/2 n F (2) DO1/2c*O + DR1/2c*R 2

(13)

The σ-E curves for these three cases have a minimum value, σmin, at a potential Emin. For instance, eq 8 for the high-frequency limit yields (21) Jacq, J. Electrochim. Acta 1967, 12, 1.

Emin ) E0 +

(11)

Equally, by substitution of cO and cR into eq 6 for the case of the low-frequency limit, it can be written that

σrev CEC,app )

Figure 1. (a) Warburg coefficient as a function of potential for the CEC mechanism at the high-frequency limit calculated with eq 8, DO ) 10-5 cm s-1, cO ) 10-3 M, and La/Lb ) 3 (s) or La/Lb ) 0.33 (- - -). The dotted line represents the curve for a simple dc-reversible electron transfer calculated with the same parameters and eq 13. (b) CEC mechanism at the lowfrequency limit calculated with eq 12, Ka ) Kb ) 0.5, and La/Lb ) 3 (s), La/Lb ) 0.33 (- - -), or La/Lb ) 1 (- -). The dotted line is as in a.

( )

DR RT ln nF DO

1/2

() ( ())

+

La RT ln nF Lb

La RT 1+ 2 2 * 1/2 1/2 Lb n F cO(2) DO

1/2

(14a)

1/2 2

(14b)

As observed in Figure 1a, the σ-E curves for this case shift positively with respect to the reversible half-wave potential when La/Lb > 1 and negatively when La/Lb < 1. In the former situation σmin is higher than that for a reversible electron transfer, and in the latter it is lower. The low-frequency case also yields σ-E curves shifted positively or negatively with respect to the reversible halfwave potential depending on the La/Lb ratio, but the σmin value is always lower than expected for a reversible electron transfer. Even if the ratio La/Lb ) 1, low values of the equilibrium rate constants Ki also provide lower σmin values (see Figure 1b). 3. Experimental Section Supporting electrolytes formed by 0.1 mol dm-3 KCl aqueous solutions buffered with 0.01 mol dm-3 Na2HPO4/NaH2PO4 at pH 7.10 were used. Water was obtained from light mineral water by distilling it once from permanganate and subsequent deionization by an Elga system provided with an organex column and an UV lamp, to ensure the elimination of traces of organic impurities, even those of low boiling point. Thallium acetate and gramicidin D were from Sigma and DOPC was from Lipid Products (Nutfield,

Electrochemical Impedance Study of Tl+ Reduction U.K.). All of the other compounds were Merck reagent grade. Stock solutions of lipid 0.1% in pentane were prepared and stored at temperatures lower than -20 °C. Stock solutions of gramicidin, 2.13 × 10-3 mol dm-3, were prepared in methanol and those of thallium acetate, 0.1 mol dm-3, in water. All of the experiments were performed at 25 ( 0.05 °C under an inert argon atmosphere. Thallium ion concentrations in the cell were 5 × 10-5 and 1 × 10-4 mol dm-3. A hanging mercury drop electrode, HMDE (Methrom), was used as the working electrode either uncoated or modified with a gramicidin-DOPC adsorbed monolayer. The adsorbed monolayer on mercury was prepared as described by Nelson et al.,2,3 transferring the phospholipid film spread at the gas-solution interface onto the surface of the electrode by lowering the HMDE through it. Before the lipid solution in pentane was spread on the surface of the electrolyte solution, the latter was deaerated by purging with high-purity argon for no less than 30 min. The amount of lipid spread on the argon-solution interface corresponded to 2-3 monolayers. The hydrophobicity of mercury assured a stable monolayer of the lipid to be transferred in the way that the carbon tails approach the metal and the polar heads the electrolyte solution. This organization avoids multilayer formation when a second touch of the monolayer at the gaslipid interface takes place by repeating the immersion procedure, which is contrary to what was observed with gold electrode.22 In any case, only single touches have been used in this paper. The quality and stability of the film on the electrode were checked by capacity-potential experiments. A well-organized lipid film should give values for the minimum capacity at potentials at which the film is impermeable to ions (-0.2 to -0.8 V vs SCE) of around 1.75 µF/cm2 and pseudocapacitance peaks associated with phospholipid reorientation (at -0.9 and -1.1 V) of 50 ( 5 and 40 ( 5 µF/cm2, at a low frequency (ca. 70 Hz).23,24 To modify the phospholipid layers with gramicidin, a fraction of the stock solution of gramicidin was spiked into the electrolyte to a concentration 1.3 × 10-7 mol dm-3 in the cell and the gas-water interface was equilibrated with the gramicidin by stirring for 5 min. Subsequently, the modified lipid monolayer was deposited on the electrode as described above. A platinum electrode and a saturated calomel electrode were used as auxiliary and reference electrodes, respectively. An Autolab multifunctional electrochemical system (Echo Chemie, Utrecht, Holland) equipped with a frequency analyzer module (FRA) was used for the voltammetry and the impedance measurements. It was employed as either a single sine or a multisine Fourier transformation instrument. The amplitude of the ac perturbation was 0.01 V peak-to-peak, and the frequencies were varied in the range 50 Hz to 15 kHz. The ac perturbation was applied for five cycles before measurements in order to guarantee the steady-state conditions for the ac signal. The instrument provides the real and imaginary impedance components of the cell, Z′ and Z′′, respectively, or the corresponding admittance components, Y′ and Y′′.25 Potential scan experiments have been performed following procedure i in ref 18, in which the potential is varied on the same gramicidin-modified DOPC-coated drop in small potential increments and in single sine mode. These measurements have only been used to check the organization of the film and to detect the faradaic potential region for Tl+ reduction. However, to obtain impedance data suitable to perform the frequency and potential analysis, procedure iii in ref 18 was used. It consists of stepby-step experiments in which a pulse of frequencies is applied superimposed to a dc potential and the response analyzed in the Fourier transformation mode. A different coated drop was used for every dc potential within the faradaic region. The experiments were programmed in two sequences: first potentials were varied in increments of -20 mV along the wave on different drops and (22) Bizzotto, D.; Lipkowski, J. Prog. Colloid Polym. Sci. 1997, 103, 201. (23) Leermakers, F. A. M.; Nelson, A. J. Electroanal. Chem. 1990, 278, 53. (24) Nelson, A.; Leermakers, F. A. M. J. Electroanal. Chem. 1990, 278, 73. (25) Sluyters, J. H.; Sluyters-Rehbach, M. In Electroanalytical Chemistry; Bard, J. A., Ed.; Marcel Dekker: New York, 1970; Vol. 4, p 1.

Langmuir, Vol. 15, No. 10, 1999 3675

Figure 2. Capacitance-potential plots obtained with DOPCcoated mercury elecrodes (‚‚‚) and with gramicidin-modified DOPC-coated mercury electrodes (s) in solutions containing 5 × 10-5 M Tl+ . The symbols represent the values obtained from dc analysis conforming to the Randles equation (16) at Tl+ concentrations: 5 × 10-5 (b) and 10-4 M (O).

Figure 3. In-phase impedance component as a function of potential obtained in a potential scan experiment with the DOPC-coated mercury electrode in the supporting electrolyte (‚‚‚) and in a solution containing 5 × 10-5 M Tl+ (- - -) and with the gramicidin-modified DOPC-coated mercury electrode in 5 × 10-5 M Tl+ solutions (s). The symbols represent data obtained with the gramicidin-modified DOPC-coated mercury electrode in step-by-step experiments on different coated drops at Tl+ concentration 5 × 10-5 M. then a second series at intercalated potential were performed in the same way, so that any deterioration of the electrolyte-gas film during the experiments could be noticed. The electrolysis time was 1 s.

4. Results and Analysis 4.1. Potential Scans on the Same GramicidinModified DOPC-Coated Drop. The reduction of Tl+ ions through the gramicidin-modified DOPC-coated electrode shows up both in the real and in the imaginary impedance or admittance components, registered as a function of potential at a fixed frequency. In Figure 2 the pseudocapacitance plots (Cs-E) can be observed. The Cs values have been determined by Cs ) Y′′/ω, where Y′′ is the imaginary admittance component and ω the frequency of the ac perturbation in radians. The two peaks in the region -0.9 to -1.1 V associated with the reorientation of the lipid23,24 are shown in the inset of the figure. Their heights in the absence of gramicidin indicate a well-organized lipid film. This is also characterized by the value of the minimum capacitance (in the -0.2 to -0.65 V region), which is 1.75 µF/cm2. The pseudocapacitance peak around -0.4 V is associated with the reduction of Tl+ ions, and it only appears when gramicidin has been added to the film. In Figure 3 the in-phase impedance component can be observed as a function of potential. Two peaks around the

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Rueda et al.

Figure 4. Frequency dependence of the real admittance component for Tl+ reduction at indicated potentials obtained with (a) gramicidin-modified DOPC-coated mercury electrodes in 5 × 10-5 M Tl+ solutions and (b) uncoated hanging mercury electrodes in 10-4 M Tl+ solutions. The lines represent the fitted results to the Randles equation (15).

same potentials as the pseudocapacitance peaks associated with the reorganization of the lipid film can be observed with DOPC-coated electrodes and Tl+ ions in solutions, which do not appear in the absence of the Tl+ ions. They most probably represent some interaction of the ion with the lipid polar heads which can affect the lipid reorientation. However, the peak around -0.4 V only appears when the DOPC layer is modified with gramicidin so Tl+ reduction takes place mainly through the gramicidin channels. Some results obtained in step-by-step experiments on different coated drops are also shown in Figure 3. The reproducibility in generating different drop films can be considered acceptable. 4.2. Analysis as a Function of the Frequency. The real components of the cell impedance were corrected for the ohmic resistance obtained at high frequencies at potentials outside the faradaic region and transformed together with the imaginary components into the interfacial admittance components, Y′el and Y′′el.25 The ω1/2/Y′el vs ω plots at some potentials along the wave are given in Figure 4a for modified electrodes and in Figure 4b for uncoated hanging mercury electrodes. The former fits well to the Randles equation

Y′el )

ω1/2 p′ω1/2 + 1 σ (p′ω1/2 + 1)2 + 1

(15)

with p′, the irreversibility quotient, defined as p′ ) σ/Rct. However, the plots obtained with uncoated mercury electrodes are descendent as expected for a fast electrode reaction with reactant and/or product adsorption, which is in agreement with the results obtained with the dropping mercury electrode.19,20 Moreover, the imaginary electrode admittance components, Yω1/2/Y′′el, obtained in the case of coated electrodes fit well to the corresponding Randles equation

Y′′el )

ω1/2 i + Cdωi σ (p′ω1/2 + 1)2 + 1

(16)

so that the double-layer capacitance, Cd, can also be obtained. The σ and p′ values obtained for coated electrodes with the Randles analysis at potentials along the wave and at the two studied concentrations can be seen in Figures 5 and 6, respectively. The σ data at the two concentrations

Figure 5. Warburg coefficient as a function of potential for Tl+ reduction on gramicidin-modified DOPC-coated mercury electrodes Tl+ concentration: 5 × 10-5 (b) and 10-4 M (O). The lines represent calculated curves: with eq 8 for the CEC mechanism and La/Lb ) 3.53, E° ) -0.455 V (s); with eq 13 for a simple one electron transfer and DO ) 4.2 × 10-6 cm2 s-1, E° ) -0.463 V (_ _ _) and DO ) 1.82 × 10-5 cm2 s-1, E° ) -0.456 V (‚‚‚).

Figure 6. Experimental p′-E plots obtained at Tl+ concentrations: 5 × 10-5 (b) and 10-4 M (O). The line representd the calculated curve for the CEC mechanism and the parameters given in the text.

have been normalized by multiplying by the Tl+ concentration, and they can be seen to agree quite well. The Cd values can be seen in Figure 2. They seem to conform well to the line that can be extrapolated from the Cd-E behavior outside the faradaic region under the same experimental conditions. The small dispersion observed in the data can be considered quite acceptable because the data are obtained with a three-parameter fit procedure at potentials at which the faradaic process is more significant than the charge of the interface. The observed behavior indicates that Tl+ adsorption on gramicidin-modified DOPC-coated electrodes is negligible because weak adsorption will also conform to eq 16 but yields much higher Cd values.20 4.3. Analysis as a Function of Potential. A frequency dependence conforming to the Randles equations (15) and (16) does not necessarily represent that the mechanism consists of a simple electron transfer because other mechanisms can also give the same behavior under some limit conditions, although with different meaning for the reaction parameters σ and p′, as was shown for the CEC mechanism in section 2. These situations have been denoted as “pseudo-Randles behavior”.11,12 The potential dependence of the reaction parameters obtained in the frequency analysis has to be studied in order to detect these situations. The σ-E data have initially been

Electrochemical Impedance Study of Tl+ Reduction

Langmuir, Vol. 15, No. 10, 1999 3677

analyzed according to eq 13 for a simple electron-transfer reaction under dc Nernstian conditions. The impedance data given in this paper and the voltammograms obtained under similar conditions with gramicidin-modified DOPCcoated mercury electrodes in ref 5 indicate that these conditions are fulfilled. From the experimental σmin value the diffusion coefficient for Tl+ can be obtained, and from the Emin value the standard potential can be obtained. The diffusion coefficient DR of thallium in mercury was taken from the literature25 as 1.05 × 10-5 cm2 s-1. In Figure 5 it can be seen that the experimental normalized σ-E data at the two studied concentrations fit well eq 13 for a simple electron transfer with DO ) 4.2 × 10-6 cm2 s-1 and E0 ) -0.463 V. However, these values contrast with those given in the literature, obtained with uncoated mercury electrodes and the same electrolyte concentration, DO ) 1.82 × 10-5 cm2 s-1 and E0 ) -0.456 V, respectively.20 It can be observed in Figure 5 that the σ-E plot generated with these latter values is much lower than the experimental data and shifted negatively. This behavior is indicative of a CEC mechanism, as described in section 2. However, as lower DO values than expected for a simple electron-transfer process can also result from other mechanisms with coupled homogeneous reactions17 and, on the other hand, a CE mechanism has previously been proposed by one of the authors16 for Tl+ reduction through the gramicidin channels, it is important to discuss if both cases can be distinguished from the σ-E behavior. Effectively, the minimum potential of the σ-E curve for the CE mechanism is given by17

Emin ) E0 +

( )

DR RT ln nF DO

) Erev 1/2 +

1/2

RT ln(La)1/2 nF

+

RT ln(La)1/2 nF (17)

and because, in view of the definition of La in eq 9, it always has to be La < 1, the minimum potential is shifted negatively with respect to the reversible half-wave potential. This is opposite to that observed for Tl+ reduction on coated electrodes (Emin ) -0.450 V, while Erev 1/2 obtained from the experiments on uncoated mercury electrodes under the same conditions is -0.463 V). Instead, eq 14a for Emin in the case of a CEC mechanism can explain the experimental behavior when La > Lb. The ratio La/Lb can be obtained from the experimental σmin value and eq 14b for the CEC mechanism, adopting the DO value given in the literature20 (1.85 × 10-5 cm2 s-1) and without any assumption about the E° value. In this way, La/Lb ) 3.53 was obtained. Quite consistent with the model is that when this La/Lb value is inserted into eq 14a for Emin, the experimental value provides the same E° ) -0.455 V as obtained with uncoated mercury electrodes. In Figure 5 it can be seen that the σ-E curves calculated with these La/Lb and E° values and eq 12 for the CEC mechanism fit well the experimental data at the two studied Tl+ concentrations. Further information on the equilibrium and rate constants for the two chemical reactions is not feasible as the ratio La/Lb is a complex function of them (see eq 9), so it includes too many parameters to be obtained from only one set of data. On the other hand, the impedance data not only provide information about the mass-transfer processes but also are very sensitive to the kinetics of the electron-transfer steps. In previous dc experiments the standard rate constant for the electron-transfer step could not be determined because its high value is out of the accessible

Figure 7. Potential dependence of the forward rate constant for the electron-transfer step, obtained from the p′ values and E° ) -0.456 V and DO ) 1.82 × 10-5 cm2 s-1 at the two Tl+ concentrations. The line represents the calculated values for a Butler-Volmer electron transfer with R ) 0.45 and ks ) 0.035 cm s-1.

range for these techniques. However, even for dc-reversible electrode reactions, the rate constant for the heterogeneous electron transfer is included in the parameters Rct and p′ obtained with the impedance analysis. For the CEC mechanism at the high-frequency limit, eqs 7a and 7b for Rct and σ together with the definition of p′ give

p′ )

21/2DO1/2 1 kf 1 + (DO/DR)1/2 exp(φ)

(18)

with kf as the forward rate constant for the electrontransfer step. This expression is very interesting because it allows the determination of not only the rate constant for the electron-transfer step but also the kf values at every potential along the wave. The values obtained in this paper can be seen in Figure 7 in the form of ln kf-φ plots. The plots obtained at the two concentrations can be considered coincident and linear. This is a confirmation of the elemental nature of the electron-transfer step, so that it does not include further coupled chemical steps (curved ln kf-φ plots can result when the reduction is also controlled by heterogeneous chemical reactions such as protonations, desolvation, etc.11-13). The potentialindependent charge-transfer coefficient, R, that is obtained from the slope is 0.45, in agreement with that generally adopted for an elemental electron-transfer step. From the ordinate, the standard rate constant, ks ) 0.035 cm s-1, was obtained. This ks value is much lower than the value of 1.2 cm s-1, which is obtained with uncoated mercury electrodes.19,20 In Figure 6 the p′-E curves generated with eq 18 using the kf values calculated with the obtained R and ks values can be observed to be in agreement with the experimental values, within experimental errors. 5. Discussion The impedance analysis presented above has provided information on both the mass transfer to and from the interface and the reduction itself. The mass transfer conforms well to a CEC mechanism in which the concentrations of the Ox and Red species at the interface are related to the concentrations in the bulk of other nonelectroactive species, A and B, respectively, as formulated in the scheme in section 2. A CEC process can also be associated with nonlinear diffusion transport mechanisms coupled to electrode reactions. Thus, it is well-known that nonlinear diffusion to partially blocked electrodes can be formulated in terms of differential equations similar to the equations that describe the mass transfer in homo-

3678 Langmuir, Vol. 15, No. 10, 1999

Rueda et al.

geneous CEC mechanisms but with a different meaning for the constants ki and Ki.27-30 Such a model has previously been applied to describe the behavior of microarray electrodes31 and the blocking properties of monolayers containing active pinholes.32 The gramicidin-modified lipid film used in this paper could be represented by this type of system, with the gramicidin channels acting as pinholes embedded in an insulating lipid plane on the electrode. According to Amatore et al.,30 the mass transfer can still be formulated as in the scheme of section 2 but with the homogeneous rate and the equilibrium constants shown as

ka ) k-b and k-a ) kb, Ka ) Kb, k′ ) ka + k-a ) kb + k-b

(19)

Their meanings are expressed in a model consisting of regular disk-type active sites distributed into a blocking film:

K ) (1 - θ)/θ; k′ ) (DO/4R02)(θ/0.3)2(1 - θ)-1 (20) where θ is the coverage of the blocking layer and R0 is half the distance between two adjacent active sites. Evidently, in the scope of this model La and Lb should be equal so that La/Lb )1 and the σ-E curves should be identical with the one for a simple electron-transfer process. It is interesting that when considered at the molecular level, nonlinear diffusion processes to the gramicidin channel mouth of radius 2 Å cannot give the CEC behavior described in the paper. If 1 - θ is around 0.01 as previously speculated,15,16 then RO is 20 Å. These pore dimension values, which are approximately consistent with the maximum coverage that can be reached at the solution gramicidin concentration used in this study, would yield a very high value of k′ for the high-frequency limit to hold. As a result, only very substantial clustering of gramicidin molecules in the film could be compatible with a CEC mechanism originating from nonlinear diffusion processes alone. These considerations are commensurate with the observed asymmetry found in the CEC mechanism, which indicates that it cannot originate from nonlinear diffusion processes alone. According to previous suggestions by one of the authors,14-16 it is assumed that the preceding chemical step is associated with the Tl+ entry into the channel prior to Tl+ reduction. This could account for part of the first chemical step in the CEC mechanism elucidated in this study. Whether this is superimposed on nonlinear diffusion processes accounting for the transport of Tl+ to the channel mouth and the transport of Tl atoms from the channel base in the mercury is uncertain. Because of this, the origen of the second C step remains to be characterized. Further experiments with different gramicidin concentrations are in progress in order to clarify this point. (26) Stromberg, A. G.; Zakharova, A. E. Sov. Electrochem. 1965, 1, 922. (27) Gueshi, T.; Takuda, K.; Matsuda, H. J. Electroanal. Chem. 1978, 89, 247. (28) Gueshi, T.; Takuda, K.; Matsuda, H. J. Electroanal. Chem. 1979, 101, 29. (29) Takuda, K.; Gueshi, T.; Matsuda, H. J. Electroanal. Chem. 1979, 102, 41. (30) Amatore, C.; Saveant, J. M.; Tessier, D. J. Electroanal. Chem. 1983, 147, 39. (31) Aoki, K. Electroanalysis 1993, 5, 627. (32) Finklea, H. O.; Snider, D. A.; Fedyk, J.; Sabatani, E.; Gafni, Y.; Rubinstein, Y. Langmuir 1993, 9, 3660.

Probably, the conditions can be found in which only the first “chemical” step is significant, so its rate constant can be compared with the rate constant previously obtained in the scope of the CE mechanism.14-16 On the other hand, the impedance analysis in this paper has provided for the first time the ks value for the electron transfer through the gramicidin channels (0.039 cm s-1), enabling it now to be compared with the rate constant obtained on pure mercury (1.2 cm s-1 20). The lower value obtained in this study may indicate that the energetic situation for the tunnel electron transfer at a certain position within the channel is very different from that existing at the mercury-electrolyte interface. This is not surprising in the context of the energy barriers which are associated with the translocation of ions within the gramicidin channels.33-35 These include ion desolvation at the mouth of the channels, electrostatic interactions in the low dielectric medium surrounding the channel, and binding interactions with the peptide groups of gramicidin. The lower value of the rate constant can also be due to the decreased effective area of the electrode surface available for the electron transfer in the case of coated electrodes. The comparison between the experimental ks value and the one obtained with uncoated mercury electrodes yields a 1 - θ value of 0.03, which is consistent with earlier estimations.14-16 Moreover, it should be mentioned that specifically adsorbed anions on mercury enhance the reduction rate of cations such as Tl+.19,20 Because anion adsorption is absent on the gramicidin-modified DOPCcoated mercury electrode, the reduction rate is expected to be lower on these electrodes. It is planned that these effects will be considered in further experiments at different gramicidin concentrations. 6. Conclusions The faradaic impedance analysis for Tl+ reduction through gramicidin channels in self-assembled gramicidinmodified DOPC monolayers on mercury electrodes has clearly shown the implication of chemical steps, as previously indicated by dc experiments. However, the high sensitivity of the potential impedance analysis based on the σ-E curves allows the unambiguous assignation of a CEC mechanism instead of the previously proposed CE mechanism. The preceding chemical step in this mechanism is assumed to be the desolvation of Tl+ or its translocation through the channels, but whether this is superimposed on radial diffusion processes accounting for Tl+ and Tl transport is not certain. The electron transfer seems to be an elemental step because a potential independent transfer coefficient close to 0.5 is obtained, and the value for the standard rate constant for this electron-transfer step is lower than that on uncoated mercury electrodes. Acknowledgment. This work has been funded by the Spanish Council of Science and Education (DGICYT, Madrid Project PB94-1454) and the Andalusian Research Plan. A grant to A.N. from the Andalusian Research Plan and traveling support from the British Council are greatly acknowledged. LA981557J (33) Jordan, P. C. Biophys. J. 1984, 45, 1091, 1101; 1983, 41, 189. (34) Cai, M.; Jordan, P. C. Biophys. J. 1990, 57, 883. (35) Hill, B. Ionic Channels of Excitable Membranes; Sinauer Associates: MA, Sunderland, 1984; pp 289 and 291-314.