Voltammetric Properties of the Reductive Desorption of Alkanethiol

Langmuir 2002, 18, 5231-5238

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Voltammetric Properties of the Reductive Desorption of Alkanethiol Self-Assembled Monolayers from a Metal Surface Takashi Kakiuchi,* Hideyuki Usui, Daisuke Hobara, and Masahiro Yamamoto Department of Energy and Hydrocarbon Chemistry, Graduate School of Engineering, Kyoto University, Kyoto 606-8501, Japan Received October 16, 2001. In Final Form: January 23, 2002 The current peak that appears on a linear-scan voltammogram for the reductive desorption of alkanethiol self-assembled monolayers (SAMs) from a gold surface in an aqueous alkaline solution exhibits intriguing features: the narrow full width at half-maximum (fwhm) of the peak, e.g., 20 mV for dodecanethiol SAMs, the saturation of fwhm in the SAM composed of long-chain alkanethiols, an asymmetric shape, the shift of the peak potential with increasing the alkyl chain length, and the peak area that is greater than what is expected from the (x3 × x3)R30° structure of adsorbed alkanethiols on Au(111). A Pade´ approximant expression for the adsorption isotherm proposed by Blum and Huckaby based on the two-dimensional Ising model, in combination with the semi-infinite linear diffusion of desorbed species, well explains these salient features of the reductive desorption behavior. The double-layer charging current can amount to one-third of the charge calculated from the area of the peak of the reductive desorption, explaining the discrepancy between the adsorbed amount of an alkanethiol calculated from the peak area and that expected from the (x3 × x3)R30° structure.

Introduction Voltammetry of the electrochemical reduction of alkanethiol self-assembled monolayers (SAMs) from a metal surface in an aqueous alkaline solution first reported by Porter and co-workers1,2 has been widely used to diagnose the state of SAMs3-34 and to engineer SAMs.35-41 In contrast to its frequent use, however, what is understood about the fundamental features of cyclic voltammograms * To whom correspondence may be addressed. TEL: (81)-75753-5528. FAX: (81)-75-753-3360. E-mail: [email protected]. (1) Widrig, C. A.; Chung, C.; Porter, M. D. J. Electroanal. Chem. 1991, 310, 335-359. (2) Walczak, M. M.; Popenoe, D. D.; Deinhammer, R. S.; Lamp, B. D.; Chung, C.; Porter, M. D. Langmuir 1991, 7, 2687-2693. (3) Weisshaar, D.; Walczak, M. M.; Porter, M. D. Langmuir 1993, 9, 323-329. (4) Rojas, M. T.; Ko¨niger, R.; Stoddart, J. F.; Kaifer, A. E. J. Am. Chem. Soc. 1995, 117, 336-343. (5) Everett, W. R.; Welch, T. L.; Reed, L.; Fritsch-Faules, I. Anal. Chem. 1995, 67, 292-298. (6) Calvente, J. J.; Kova´cˇova´, Z.; Sanchez, M. D.; Andreu, R.; Fawcett, W. R. Langmuir 1996, 12, 5696-5703. (7) Yang, D.-F.; Wilde, C. P.; Morin, M. Langmuir 1996, 12, 65706577. (8) Zhong, C.-J.; Porter, M. D. J. Electroanal. Chem. 1997, 425, 147153. (9) Zhong, C.-J.; Zak, J.; Porter, M. D. J. Electroanal. Chem. 1997, 421, 9-13. (10) Yang, D.-F.; Wilde, C. P.; Morin, M. Langmuir 1997, 13, 243249. (11) Yang, D.-F.; Al-Maznai, H.; Morin, M. J. Phys. Chem. B 1997, 101, 1158-1166. (12) Nishizawa, M.; Sunagawa, T.; Yoneyama, H. J. Electroanal. Chem. 1997, 436, 213-218. (13) Zhang, H.; Xia, H.; Li, H.; Liu, Z. Chem. Lett. 1997, 721-722. (14) Hobara, D.; Ota, M.; Imabayashi, S.; Niki, K.; Kakiuchi, T. J. Electroanal. Chem. 1998, 444, 113-119. (15) Peanasky, J. S.; McCarley, R. L. Langmuir 1998, 14, 113-123. (16) Oyamatsu, D.; Nishizawa, M.; Kuwabata, S.; Yoneyama, H. Langmuir 1998, 14, 3298-3302. (17) Oyamatsu, D.; Kuwabata, S.; Yoneyama, H. J. Electroanal. Chem. 1999, 473, 59-67. (18) Azehara, H.; Yoshimoto, S.; Hokari, H.; Akiba, U.; Taniguchi, I.; Fujihira, M. Electrochemistry 1999, 67, 1227-1230. (19) Azehara, H.; Yoshimoto, S.; Hokari, H.; Akiba, U.; Taniguchi, I.; Fujihira, M. J. Electroanal. Chem. 1999, 473, 68-74.

for this reduction process is limited. Widrig et al. systematically studied the voltammetry for a series of alkanethiols and suggested the importance of the penetration of counterions into the monolayer in the reductive desorption.1 By analogy with the Angelstein-Kozlowska’s model for oxidative adsorption,42 Imabayashi et al. referred to the role of the intermolecular interaction between (20) Yoshimoto, S.; Yoshida, M.; Kobayashi, S.; Nozute, S.; Miyawaki, T.; Hashimoto, Y.; Taniguchi, I. J. Electroanal. Chem. 1999, 473, 8592. (21) Nishiyama, K.; Kie, T. T.; Taniguchi, I. Chem. Lett. 1999, 753754. (22) Byloos, M.; Al-Maznai, H.; Morin, M. J. Phys. Chem. B 1999, 103, 6554-6561. (23) Hobara, D.; Ueda, K.; Imabayashi, S.; Yamamoto, M.; Kakiuchi, T. Electrochemistry 1999, 67, 1218-1220. (24) Kanayama, N.; Kitano, H. Langmuir 2000, 16, 577-583. (25) Kakiuchi, T.; Sato, K.; Iida, M.; Hobara, D.; Imabayashi, S.; Niki, K. Langmuir 2000, 16, 7238-7244. (26) Chi, Q.; Zhang, J.; Nielsen, J. U.; Friis, E. P.; Chorkendorff, I.; Canters, G. W.; Andersen, J. E. T.; Ulstrup, J. J. Am. Chem. Soc. 2000, 122, 4047-4055. (27) Mohtat, N.; Byloos, M.; Soucy, M.; Morin, S.; Morin, M. J. Electroanal. Chem. 2000, 484, 120-130. (28) Zhang, J.; Chi, Q.; Nielsen, J. U.; Friis, E. P.; Andersen, J. E. T.; Ulstrup, J. Langmuir 2000, 16, 7229-7237. (29) Wong, S.-S.; Porter, M. D. J. Electroanal. Chem. 2000, 485, 135143. (30) Kawaguchi, T.; Yasuda, H.; Shimazu, K.; Porter, M. C. Langmuir 2000, 16, 9830-9840. (31) Hobara, D.; Kakiuchi, T. Electrochem. Commun. 2001, 3, 154157. (32) Munakata, H.; Kuwabata, S.; Ohko, Y.; Yoneyama, H. J. Electroanal. Chem. 2001, 496, 29-36. (33) Sawaguchi, T.; Sato, Y.; Mizutani, F. J. Electroanal. Chem. 2001, 496, 50-60. (34) Kakiuchi, T.; Iida, M.; Gon, N.; Hobara, D.; Imabayashi, S.; Niki, K. Langmuir 2001, 17, 1599-1603. (35) Weisshaar, D.; Lamp, B. D.; Porter, M. D. J. Am. Chem. Soc. 1992, 114, 5860-5862. (36) Imabayashi, S.; Hobara, D.; Kakiuchi, T.; Knoll, W. Langmuir 1997, 13, 4502-4504. (37) Imabayashi, S.; Gon, N.; Sasaki, T.; Hobara, D.; Kakiuchi, T. Langmuir 1998, 14, 2348-2351. (38) Hobara, D.; Sasaki, T.; Imabayashi, S.; Kakiuchi, T. Langmuir 1999, 15, 5073-5078. (39) Oyamatsu, D.; Kanemoto, H.; Kuwabata, S.; Yoneyama, H. J. Electroanal. Chem. 2001, 497, 97-105.

10.1021/la011560u CCC: $22.00 © 2002 American Chemical Society Published on Web 05/22/2002

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adsorbed species in determining the peak potential.43 Hatchett et al. later pointed out using Ag(111) electrodes the importance of the difference in the adsorption Gibbs energy of alkanethiolates in the peak shift with the alkyl chain length.44 The appearance of double peaks on the voltammograms has been ascribed to the two different adsorption sites9,8,29,45 or the difference in the adsorbed states, that is, physisorption and chemisorption.22,27 On the other hand, chronoamperometry, a complementary electrochemical approach, has revealed the nucleation and growth processes at the onset of the reductive desorption.6,27,46-49 The initial gradual rise in the current resulting in a peak in the chronoamperometric transients is clearly seen in the case of the desorption of short-chain alkanethiolates, but the initial slow rise of the current becomes less discernible in SAMs having longer alkyl chains. This is consistent with an in situ observation of the reductive desorption of alkanethiol SAMs.50 Interestingly, the reductive desorption of sulfur atoms from Au(111) also exhibits a similar peak in the current transient,51,52 suggesting that the initial nucleation-growth process may not well reflect the properties related to the intermolecular interaction between the alkyl chain parts of the monolayers. Despite these foregoing efforts, there remain intriguing features in the current peak in voltammograms to be explained: an asymmetric shape, that is, a gradual increase followed by a sudden decrease after the peak potential, the narrowing full-width at half-maximum (fwhm) of the peak with the increase in the alkyl-chain length, and its leveling off at about 20 mV for SAMs composed of longer alkanethiolates. In voltammetric characterization of SAMs, a moderate scan rate, usually less than 100 mV, has been used. In the time scale of more than seconds for recording such voltammograms, the characteristics associated with the nucleation and growth are likely to be hidden by the voltammetric features described above. To explain such slow voltammetric behavior, it seems more attractive to invoke an adsorption isotherm that properly takes into account the intermolecular interactions. The observed narrow fwhm strongly suggests that the desorption is a cooperative process under the influence of the strong lateral interaction between adsorbed molecules. The Frumkin adsorption isotherm53 has been employed in explaining desorption transients to take account of the lateral interaction of adsorbed thiols.6,54

The Frumkin isotherm based on the mean-field approximation is not, however, appropriate to explain characteristic voltammetric features such as the narrow peak width, as it gives a large fwhm value of about 60 mV even when the attractive interaction is strong enough to induce the phase transition.55 In the case of the twodimensional lattice models of adsorbed layers, it is known that the better the approximation, the sharper the phase transition.56 It is therefore necessary to use an adsorption isotherm that can describe the sharper phase transition. In the present study, we used an analytical expression for the adsorption on a triangular lattice, which was formulated by Blum and Huckaby and was successfully applied to describe the underpotential deposition of Cu2 + ions on Au(111) in the presence of sulfate ions.57,58 The coexistence line of this isotherm is proportional to the eighth power of the fugacity of the adsorbate, while that of the Frumkin isotherm is the second.57 We will show that calculated voltammograms using the Blum and Huckaby isotherm well reproduce the main features of experimental voltammograms for the reductive desorption of a series of alkanethiol SAMs. Further, the contribution of the charging current to the reduction peak current was examined. The area under the voltammetric peak for the reductive desorption has been used for estimating the adsorbed amount of thiols on the electrode. The area is usually significantly greater2,7 than that expected from the (x3 × x3)R30° structure of alkanethiolates on Au(111).59,61 The reduction accompanies the change in the surface coverage of the thiol, which gives rise to the charging current composed of static and dynamic parts. The former is due to the fact that the double layer capacitance becomes higher after the desorption. The latter is associated with the change in the surface coverage with time in the course of the desorption. A proper estimation of this latter contribution is decisive in evaluating the adsorbed amount of thiols from the voltammogram. This in turn requires a proper model for the mechanism of the desorption as well as the potential of zero charges in both the absence and presence of the adsorption. Numerically calculated voltammograms based on the Blum and Huckaby isotherm were used to estimate the dynamic contribution. We will show that this contribution is far from negligible in estimating the adsorbed amount of thiols from the peak area.

(40) Imabayashi, S.; Hobara, D.; Kakiuchi, T. Langmuir 2001, 17, 2560-2563. (41) Hobara, D.; Uno, Y.; Kakiuchi, T. Phys. Chem. Chem. Phys. 2001, 3, 3437-3441. (42) Angerstein-Kozlowska, H.; Klinger, J.; Conway, B. E. J. Electroanal. Chem. 1977, 75, 45-60. (43) Imabayashi, S.; Iida, M.; Hobara, D.; Feng, Z. Q.; Niki, K.; Kakiuchi, T. J. Electroanal. Chem. 1997, 428, 33-38. (44) Hatchett, D. W.; Stevenson, K. J.; Lacy, W. B.; Harris, J. M.; White, H. S. J. Am. Chem. Soc. 1997, 119, 6596-6606. (45) Walczak, M. M.; Alves, C. A.; Lamp, B. D.; Porter, M. D. J. Electroanal. Chem. 1995, 396, 103-114. (46) Yang, D.-F.; Morin, M. J. Electroanal. Chem. 1997, 429, 1-5. (47) Yang, D.-F.; Morin, M. J. Electroanal. Chem. 1998, 441, 173181. (48) Vinokurov, I. A.; Morin, M.; Kankare, J. J. Phys. Chem. B 2000, 104, 5970-5796. (49) Mulder, W. H.; Calvente, J. J.; Andreu, R. Langmuir 2001, 17, 3273-3280. (50) Hobara, D.; Miyake, K.; Imabayashi, S.; Niki, K.; Kakiuchi, T. Langmuir 1998, 13, 3590-3596. (51) Lamp, B. D.; Hobara, D.; Porter, M. D.; Niki, K.; Cotton, T. M. Langmuir 1997, 13, 736-741. (52) Martin, H.; Vericat, C.; Andreasen, G.; Creus, A. H.; Vela, M. E.; Salvarezza, R. C. Langmuir 2001, 17, 2334-2339. (53) Frumkin, A. N. Z. Phys. Chem. 1925, 116, 466-484. (54) Calvente, J. J.; Kova´cˇova´, Z.; Andreu, R.; Fawcett, W. R. J. Chem. Soc., Faraday Trans. 1996, 92, 3701-3708.

Reagents. 1-Propanethiol (Tokyo Kasei Kogyo), 1-pentanethiol (Aldrich), 1-octanethiol (Wako Pure Chem.), 1-decanethiol (Aldrich), 1-dodecanethiol (Aldrich), and 1-tetradecanethiol (Tokyo Kasei Kogyo) were used after the purification with a silica gel column. Water was distilled and purified with a Milli-Q system (Millipore Co.). All other chemicals used were of reagent grade. Methods. Gold (99.99%) was vapor-deposited on freshly cleaved mica sheets at a reduced pressure, 3.57 The value of s is 0.001 when g2 > 3 and (3.001 - g2)/5 when g2 < 3. The pairwise interaction energy between the adsorbed alkanethiolate molecules, w, is related to g2 through

g2 ) exp(-w/kBT)

(8)

where kB is the Boltzmann constant. We assumed that the dependence of B k′ and A k′ on the applied potential is expressed by the Butler-Volmer-type equations

B k ′ ) k0′ exp[-(1 - R)(F/RT)(E - E0′)]

(9)

A k ′ ) k0′ exp[R(F/RT)(E - E0′)]

(10)

and

where k0′ is the apparent standard rate constant, R is the transfer coefficient, E is the electrode potential, and E0′ is the formal potential for the reduction of the adsorbed alkanethiolates at the limit of θ f 0. After the desorption, long-chain alkanethiolates tend to form micelles or aggregates and remain on the electrode surface, while shorter-chain alkanethiolates seem to dissolve into the aqueous phase.11,22,50 In the present model, we assumed for simplicity the semi-infinite linear diffusion (72) Huckaby, D. A.; Blum, L. J. Chem. Phys. 1990, 94, 2646-2649.

Figure 5. Calculated voltammograms at g2 ) 1 (curve 1), 2 (curve 2), 2.9 (curve 3), 3.1 (curve 4), 3.3 (curve 5), 3.5 (curve 6), and 4.0 (curve 7). Other parameters are as follows: k0′ ) 100 s-1, K ) 1, and δE ) 0.2 mV.

for the mass transport of desorbed thiolates in the solution and numerically calculated cyclic voltammograms from eqs 4, 6, 9, and 10, using the explicit finite difference method.73 In each iteration, we determined a value of z corresponding to a given value of θ by interpolation using eq 6. The dimensionless current we calculated, Φ, was defined as

Φ)-

iF 1 FA (DvF/RT)1/2 bc

(11) Rd

where D is the diffusion coefficient of the alkanethiolate in solution and v is the scan rate. On the other hand, iF is related to dΓ/dt (eq 3). From eqs 3 and 11

-

iF L ) Γm Φ × K FA tk

(12)

where L defines the number of digitization of simulated time tk and K is a constant, which was always set to unity in the present numerical calculation. Figure 5 illustrates calculated voltammograms at several different values of g2 when E° ′ ) 0, v ) RT/F s-1, k0′ ) 100 s-1, and the increment of E, δE ) 0.2 mV. With increasing g2, the peak becomes sharper and shifts to the negative direction. Moreover, the shape of the peak is asymmetric and the fwhm narrows down to 20 mV when g2 > 3. The further increase in g2 beyond the critical value does not change the fwhm, while Ep continues to shift to the negative direction of the potential. These features well agree with experimentally observed trends shown in Figures 3 and 4. (73) Feldberg, S. W. In Electroanalytical Chemistry; Bard, A. J., Ed.; Marcel Dekker: New York, 1969; Vol. 3, p 199.

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Figure 6. Fitting of calculated fwhm (solid line) to experimental points (a) and the comparison of theoretical prediction of the shift of Ep (dotted line) with experimental data (b). Parameters for calculation are as follows: k0′ ) 104 s-1, K ) 1, and δE ) 0.2 mV.

A theoretical dependence of fwhm on w obtained from the voltammograms calculated for k ) 105 s-1 and the increment of the potential being 0.2 mV is well fitted to the experimental plot of fwhm on n (Figure 6a). In the fitting, we assumed that the point of the inflection at -w/kbT ) 1.10 (g2 ) 3) in the theoretical fwhm vs w plot agrees with the point of the inflection experimentally observed at n ) 9 (Figure 4a) and that the theoretical variation of fwhm with w when -w/kbT < 1.10 is fitted to the experimental points. Figure 6a supports an intuitive expectation that n is proportional to the interaction energy between adsorbed alkanethiolates. Another important point in Figure 6a is that the present model explains why the fwhm levels off beyond n ) 9. When the attractive interaction is strong enough to cause the phase transition in the adsorbed monolayer, the shape of the adsorption isotherm, or, more precisely, the sharpness of the phase transition, becomes insensitive to the value of g2 when g2 > 3.58 In other words, the appearance of the point of inflection suggests the occurrence of the phase transition in the course of the desorption. This prediction of the presence of the point of inflection distinguishes the present model from a recent theoretical approach using a lattice statistics in combination with the potential-dependent probability of the defect formation that predicts the narrowing of fwhm down to zero as w increases.74 The critical value of w at the point of inflection corresponds to 2.7 kJ mol-1 at 25 °C. We note that this value obviously reflects not only the magnitude of the lateral interaction (74) Aoki, K.; Kakiuchi, T. J. Electroanal. Chem. 1998, 452, 187192.

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between two adsorbed thiolate molecules but also other contributions including those from solvent molecules.58 By using the phenomenological correspondence between w and n in Figure 6a, we also compared in Figure 6b the theoretical dependence of Ep on w with experimental Ep vs n plot (Figure 4b). The comparison of experimental data for well-annealed SAMs with the theoretical curve in Figure 6b shows that the experimental shift in Ep is much greater than the theoretical prediction. For example, the theoretical prediction of the difference in Ep between n ) 2 and 9 is 0.05 V, while the experimental difference is about 0.28 V. This discrepancy indicates the importance of the adsorption Gibbs energy of alkanethiolates in determining the position of the reduction peak, as rightly pointed out by Hatchett et al.75 If we take the difference between experimental and theoretical values of Ep at n ) 9, 0.243 V or 23.4 kJ mol-1, as the contribution of the methylene units to the adsorption Gibbs energy of the thiolates, the contribution of one methylene unit is 2.6 kJ mol-1. This is comparable to the values of the transfer Gibbs energy of one methylene unit from water to a pure alkane (3.7 kJ mol-1) or to a nonionic micelle (2.9 kJ mol-1).76 A lesser degree of the variation of Ep with n when n > 9 (Figure 4b), where the desorption accompanies the phase transition of the monolayer, is then likely to be ascribed to the micelles or aggregates of alkanethiolates formed on the electrode surface after the desorption.11,22,50 When the desorbed species is in the form of such aggregates on the electrode surface, the value of the transfer Gibbs energy of the thiolates from the electrode surface to the aggregates would be much smaller than that into the bulk aqueous phase, giving rise to the smaller shift of the Ep with n. The effect of the magnitude of k0′ on Ep is illustrated in Figure 7. Curves 5 and 6 calculated for k0′ ) 103 and 104 s-1, respectively, agree with each other, showing the reversible behavior. A comparison of experimental values of fwhm with the results in Figure 7 suggests that the reductive desorption is dc reversible at v ) 20 mV s-1. This figure can also be interpreted as the one showing the effect of the magnitude of v on the voltammograms, as the rate constant used in the calculation is relativised with respect to v1/2. The Ep shifts to the negative direction with increasing v, as were seen experimentally (Figure 2b). Contribution of Charging Current. The peak area of the reductive desorption has been conveniently used to estimate the adsorbed amount of alkanethiolates.2,4,5,7,13,28 However, the charge under the peak is usually greater than that estimated from the (x3 × x3)R30° structure of adsorbed thiolates. The degree of the excess varies from 10% to 50%, the latter of which found in the present study far exceeds that predicted by the surface roughness, 1.11.2.3,77,78 The importance of the contribution of charging current to the area under the peak of the reductive desorption has been first emphasized by Schneider and Buttry.79 They estimated the contribution of the charging current from the difference between the double layer capacitance before and after the desorption and concluded that the measurement of the reductive desorption charge is not likely to be a reliable way to (75) Hatchett, D. W.; Uibel, R. H.; Stevenson, K. J.; Harris, J. M.; White, H. S. J. Am. Chem. Soc. 1998, 120, 1062-1069. (76) Israelachvili, J. N. In Intermolacular and Surface Forces; Academic Press: London, 1992; Chapter 16. (77) Rodriguez, J. F.; Mebrahtu, T.; Soriaga, M. P. J. Electroanal. Chem. 1987, 233, 283-289. (78) Schlenoff, J. B.; Li, M.; Ly, H. J. Am. Chem. Soc. 1995, 117, 12528-12536. (79) Schneider, T. W.; Buttry, D. A. J. Am. Chem. Soc. 1993, 115, 12391-12397.

Desorption of Alkanethiol SAMs

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Figure 8. Variation of surface coverage (curve 1) and the slope (curve 2) with applied potential in the course of the reductive desorption. Parameters for calculation are as follows: g2 ) 3.1, k0′ ) 104 s-1, K ) 1, and δE ) 0.2 mV.

By differentiating q with respect to E, we obtain Figure 7. Variation of voltammograms with the value of k0′: k0′ (s-1) ) 10 (curve 1), 20 (curve 2), 50 (curve 3), 102 (curve 4), 103 (curve 5), 104 (curve 6). Other parameters are as follows: g2 ) 3.1, K ) 1, and δE ) 0.2 mV.

measure surface coverage.79 A similar consideration has been made to correct the peak area allowing for the contribution of the charging current to estimate the surface coverage of alkanethiols.10 However, the difference in the capacitance before and after the desorption only partly explains the charging current component during the reductive desorption, as the rate of the change in the surface coverage in the desorption process can be considerable, particularly when the desorption accompanies the phase transition, that is, in the case of the sharp change of the surface coverage with the applied potential as illustrated in Figure 8. To estimate the magnitude of the charging current in the course of the desorption, a certain functional form relating θ and the surface charge density, q, is required. The charging current, ic, is then calculated by differentiating q with respect to t

-ic ) dq/dt ) vdq/dE

(13)

in the case of linear-scan voltammetry. The negative sign on the left-hand side is for the conformity with the convention of the faradaic current described above. One of the simplest models for q is Frumkin’s two-parallelplate capacitor model,80 which has been successfully used to describe the adsorption of organic molecules on electrodes,81

q ) q0(1 - θ) + q′θ

(14)

where q0 is the surface charge density of the uncovered part of the electrode and q′ is that covered with the SAM. (80) Frumkin, A. N. Z. Phys. 1926, 35, 792-802. (81) Damaskin, B. B.; Petrii, O. A.; Batrakov, V. V. Adsorption of Organic Compounds on Electrodes; Plenum Press: New York, 1971.

dθ dq ) C0(1 - θ) + C′θ + [(C′ - C0)φ - C′φN] (15) dE dE where C0 and C′ are the double-layer capacitances at θ ) 0 and θ ) 1, respectively, and are assumed to be independent of the applied potential. The potential in eq 15, φ, is referred to the potential of zero charge, pzc, at θ)0

φ ) E - Epzc,θ)0 and

φN ) Epzc,θ)1 - Epzc,θ)0 where Epzc,θ ) 1 is the pzc at θ ) 1 referred to the same reference electrode as Epzc,θ)0 refers to. An expression of q used recently for estimating the charging current for the desorption of SAMs into ethanol30 seems to be based on the same Frumkin model. The first two terms on the right-hand side of eq 15 represent the static part of the charging current, reflecting the change in the double layer capacitance before and after the desorption, whereas the third term represents the dynamic part or pseudocapacitance part involving dθ/ dE. Therefore

ic ) ic,static + ic,dynamic The presence of this dynamic term implies that the magnitude of this contribution depends on the sharpness of the desorption. To evaluate the latter contribution to ic, a functional form of dθ/dE is required as a function of E. In fact, ic,dynamic is proportional to iF, as can be seen from eqs 4 and 15. We used the calculated dθ/dE predicted by the model described above when k0 ) 104 cm s-1, g ) 3.1 and Γm ) 7.67 × 10-10 mol dm-2, and v ) 25.6926 mV s-1 as illustrated in Figure 8. We note that it is difficult to separately estimate iF and ic by changing v in linear-scan voltammetry, as dθ/dE does not depend on v, when k0′ is

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sufficiently large (curves 5 and 6 of Figure 7), and a faster scan of the potential would invalidate the present approach resorting to the adsorption isotherm. The pzc of Au(111) in 0.1 mol dm-3 HClO4 is 0.42 V (vs Ag|AgCl|satd KCl).82 Although OH- ions specifically adsorb on Au(111),83 it is presumably negligible in the potential range where the reductive desorption takes place. We assumed therefore 0.42 V for Epzc,θ)0. On the other hand, our recent estimate of Epzc,θ)1 using the potentialdependent contact angle measurements84 is -0.49 V (vs Ag|AgCl|satd KCl) for the adsorption of undecanethiol, which agrees with an earlier estimate reported using a Wilhelmy plate method, -0.5 V (vs SCE) for a dodecanethiol SAM.85 It is difficult to obtain a reliable value of E0′ for the reductive desorption of an alkanethiolate. A plausible assumption would be to use a value of E0′ for S atoms adsorbed on Au(111) estimated from the extrapolation of Ep at v ) 0 to n ) -1, -0.64 V (vs Ag/AgCl/satd KCl),69 although, strictly speaking, E0′ to be used in the calculation is the value for the formal potential of the reduction of an isolated alkanethiol molecule adsorbed on Au(111), which is probably more negative than the value for the reduction of adsorbed S atoms. Assuming that E0′ ) -0.64 V, C0 ) 40,43 and C′ ) 2 µF cm-2,1 we calculated the charging current (Figure 9). The contribution of ic to the area under the peak is substantial. In this example, one can see from Figure 9 that the charge due to the charging current amounts to 42 µC cm-2, that is, one-third of the total charge, 116 µC cm-2. This charging current can well explain experimental values, (1.1-1.2) × 10-9 mol cm-2, for the adsorbed amount of thiolates formally obtained from the peak area for wellannealed SAMs of alkanethiols on Au(111)-rich surfaces.7,25,34 The contribution of the dynamic part is much larger that the static one, as shown in the inset of Figure 9. This clearly indicates that the evaluation of the dθ/dE is essential to estimate the contribution of the double layer charging in the reductive desorption. The dynamic part of the charging current explains why the area under the peak often gives the charge significantly greater than that expected from a close-packed monolayer and the roughness factor. Conclusion Intriguing features that have been observed in voltammetry of the reductive desorption of alkanethiolates have been satisfactorily explained by the model based on Blum and Huckaby’s adsorption isotherm that is capable of describing the phase transition of adsorbed layer in contact (82) Hamm, U. W.; Kramer, D.; Zhai, R. S.; Kolb, D. M. J. Electroanal. Chem. 1996, 414, 85-89. (83) Chen, A.; Shi, Z.; Bizzotto, D.; Lipkowski, J.; Pettinger, B.; Bilger, C. J. Electroanal. Chem. 1999, 467, 342-353. (84) Iwami, Y.; Hobara, D.; Yamamoto, M.; Kakiuchi, T. Manuscript in preparation. (85) Sondag-Huethorst, J. A. M.; Fokkink, L. G. J. Langmuir 1992, 8, 2560-2566.

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Figure 9. Illustration of the contribution of charging current, ic, to the voltammetric peak current of reductive desorption, i. Parameters for calculating iF are the same as those in Figure 8. See text for other parameters. Inset illustrates the relative contribution of ic,dynamic (curve 1) and ic,static (curve 2).

with a solution. Experimental voltammograms sometimes show more complicated structures, including the appearance of the double peaks8,27 or a hump after the main reduction peak,9,10,30 the latter of which may be related to the recent STM observation that, after the reductive desorption, the reconstruction of Au(111) to (x3 × 23) structure takes place with the time delay of a few minute.86 The present model does not embrace all these features. But, we believe that it seizes the salient features of the voltammetric behavior. The present study clearly shows that the slow-scan voltammetry of the reductive desorption reflects the molecular details of SAMs in equilibrium, such as intermolecular interactions, adsorption Gibbs energy, and aggregates formation, and, hence, will continue to be an invaluable tool to diagnose the state of the SAMs. Care must be exercised to evaluate the adsorbed amount of thiolates from the area under the peak of the reductive desorption, though it is a useful measure of the adsorption. Acknowledgment. This work was partially supported by a Grant-in-Aid for Scientific Research (No.10440220) and a Grant-in-Aid for Exploratory Research (No. 11875183) from the Ministry of Education, Science, Sports, and Culture, Japan, and CREST of JST (Japan Science and Technology). LA011560U (86) Hobara, D.; Yamamoto, M.; Kakiuchi, T. Chem. Lett. 2001, 374375.