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Langmuir 2006, 22, 4420-4428
Electric Field Driven Protonation/Deprotonation of Self-Assembled Monolayers of Acid-Terminated Thiols Ian Burgess, Brian Seivewright, and R. Bruce Lennox* Department of Chemistry and Centre for Self-Assembled Chemical Structures, McGill UniVersity, 801 Sherbrooke Street W, Montreal, QC, H3A 2K6, Canada ReceiVed October 13, 2005. In Final Form: February 7, 2006 Using electrochemical impedance spectroscopy (EIS), we provide an explanation for the pH dependence of the voltammetric peak height for the electric-field-driven protonation and deprotonation of carboxylic acid-terminated thiol self-assembled monolayers (SAMs). The current flowing through the interface can be divided into a purely capacitive current and a protonation/deprotonation current that is directly related to the rate of change of the SAM’s protonation (or deprotonation). We demonstrate that at applied potentials close to those corresponding to halfionization of the SAM and pHs near the pK1/2, the equivalent circuit describing the interface consists of a Helmholtz film capacity in parallel with a “protonation/deprotonation” impedance which is further shown to be a series combination of a resistor, Rp, and capacitor Cp. Explicit expressions for Rp and Cp are derived in terms of the rate constants for the forward (protonation) and reverse (deprotonation) reactions. Simulated EIS data demonstrate the agreement between our model of the interface and experimental impedance and voltammetric data.
Introduction Owing to their ability to electrostatically and chemically mediate substrate adhesion, surfaces modified with ω-functionalized self-assembled monolayers (SAMs) are versatile substrates for anchoring important biomolecules for different applications.1-3 Carboxylic acid-terminated thiols are particularly well suited for these purposes because adjusting the pH of the bathing solution can toggle adsorption by switching the surface’s hydrophilicity/ hydrophobicity or by tuning the electrostatic linkage between a carboxylate terminus and a positively charged molecule.2,4-7 For this reason, carboxylic acid-terminated thiol monolayers such as 16-mercaptohexadecanoic acid (MHA),8-13 11-mercaptoundecanoic acid (MUA),14-17 and 3-mercaptopropanoic acid (MPA)18-20 have been used as substrates for protein adsorption and biological sensing purposes. However, these application * To whom correspondence should be addressed. E-mail: bruce.lennox@ mcgill.ca. (1) Prime, K. L.; Whitesides, G. M. Science 1991, 252, 1164-7. (2) Jordon, C. E.; Frey, B. L.; Kornguth, S.; Corn, R. M. Langmuir 1994, 10, 3642-8. (3) Xu, X.-H.; Bard, A. J. J. Am. Chem. Soc. 1995, 117, 2627-31. (4) Frey, B. L.; Jordan, C. E.; Kornguth, S.; Corn, R. M. Anal. Chem. 1995, 67, 4452-7. (5) Nordera, P.; Dalla Serra, M.; Menestrina, G. Biophys. J. 1997, 73, 14681478. (6) Clark, S. L.; Hammond, P. T. Langmuir 2000, 16, 10206-10214. (7) Barrias, C. C.; Martins, M. C. L.; Miranda, M. C. S.; Barbosa, M. A. Biomaterials 2005, 26, 2695-2704. (8) Frederix, F.; Bonroy, K.; Laureyn, W.; Reekmans, G.; Campitelli, A.; Dehaen, W.; Maes, G. Langmuir 2003, 19, 4351-4357. (9) Wang, H.; Castner, D. G.; Ratner, B. D.; Jiang, S. Langmuir 2004, 20, 1877-1887. (10) Clark, R. A.; Bowden, E. F. Langmuir 1997, 13, 559-565. (11) Hildebrandt, P.; Murgida, D. H. Bioelectrochemistry 2002, 55, 139-143. (12) Tarlov, M. J.; Bowden, E. F. J. Am. Chem. Soc. 1991, 113, 1847-9. (13) Song, S.; Clark, R. A.; Bowden, E. F.; Tarlov, M. J. J. Phys. Chem. 1993, 97, 6564-72. (14) Kasmi, A. E.; Wallace, J. M.; Bowden, E. F.; Binet, S. M.; Linderman, R. J. J. Am. Chem. Soc. 1998, 120, 225-226. (15) Arnold, S.; Feng, Z. Q.; Kakiuchi, T.; Knoll, W.; Niki, K. J. Electroanal. Chem. 1997, 438, 91-97. (16) Kepley, L. J.; Crooks, R. M.; Ricco, A. J. Anal. Chem. 1992, 64, 3191-3. (17) Malem, F.; Mandler, D. Anal. Chem. 1993, 65, 37-41. (18) Giz, M. J.; Duong, B.; Tao, N. J. J. Electroanal. Chem. 1999, 465, 72-79. (19) Li, J.; Cheng, G.; Dong, S. J. Electroanal. Chem. 1996, 416, 97-104. (20) Zhao, Y.-D.; Pang, D.-W.; Hu, S.; Wang, Z.-L.; Cheng, J.-K.; Dai, H.-P. Talanta 1999, 49, 751-756.
studies have largely preceded a clear description of the factors that influence the acid/base properties of surface confined monolayers. For example, it is widely known that the surface pKa of acidic monolayer systems are significantly different than the solution-state pKa. These differences may be attributable to effects such as field-dependent or solvent-dependent (de)stabilization of the acid or base forms. This would be an intrinsic pKa change. Changes in the pKa can also arise from changes in the proton concentration at/near the acid group. This is an apparent pKa shift rather than an intrinsic one. The balance between these two effects is highly system specific and can rarely be separated. For example, experimental molecular force measurements have determined the surface pKa of MPA to be around 7.7.21 Schweiss et al.22 used streaming potential and streaming current measurements to monitor the adsorption of ions on both MUA and MHA SAMs and obtained pKa values of 5.15 and 5.20, respectively. Using cyclic voltammetry of an electroactive probe, Dai et al determined the pKa of MUA and MHA SAMs to be 7.3 and 7.9, respectively.23 Kakiuchi et al determined the values of MUA and 7-heptanoic acid SAMs to be 10.3 and 9.2 using double-layercapacitance titrations.24 Smalley et al.25 used laser-induced temperature jump studies to measure an ionic strength-dependent pKa for MUA SAMs ranging between 5.7 and 4.4. The observed range of the surface pKa of ω-acid-functionalized SAMs in the literature suggests that a more detailed understanding of the factors that control the surface pKa is needed. In many studies employing acid-terminated thiol SAMs, the state of the carboxylic acid group is assumed to be invariant with potential under conditions of constant pH. However, as shown in the model of Smith and White (SW)26 and its refinement by Fawcett and co-workers,27,28 the degree of surface charge on (21) Hu, K.; Bard, A. J. Langmuir 1997, 13, 5114-5119. (22) Schweiss, R.; Welzel, P. B.; Werner, C.; Knoll, W. Langmuir 2001, 17, 4304-4311. (23) Dai, Z.; Ju, H. Phys. Chem. Chem. Phys. 2001, 3, 3769-3773. (24) Kakiuchi, T.; Iida, M.; Imabayashi, S.-i.; Niki, K. Langmuir 2000, 16, 5397-5401. (25) Smalley, J. F.; Chalfant, K.; Feldberg, S. W.; Nahir, T. M.; Bowden, E. F. J. Phys. Chem. B 1999, 103, 1676-1685. (26) Smith, C. P.; White, H. S. Langmuir 1993, 9, 1-3. (27) Fawcett, W. R.; Fedurco, M.; Kovacova, Z. Langmuir 1994, 10, 2403-8. (28) Andreu, R.; Fawcett, W. R. J. Phys. Chem. 1994, 98, 12753-8.
10.1021/la052767g CCC: $33.50 © 2006 American Chemical Society Published on Web 04/01/2006
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the acid thiol monolayer (i.e., the degree of deprotonation) is dependent not only on the pH of the electrolyte but also on the electric field present at the interface. Using cyclic voltammetry, White et al.29 demonstrated that their model qualitatively explained observed experimental data for a mixed decanethiol/ MUA SAM on Ag(111) in that the potential of the voltammetric peak attributed to the protonation/deprotonation of the MUA shifted as a function of pH. However, they unexpectedly observed that the voltammetric peak height was also dependent on the pH, a phenomena that is unexplained by either the SW or the Fawcett models. White et al. plotted the voltammetric charge passed versus the solution pH and assigned the maximal charge to the pK1/230 of the MUA SAM. It is important to emphasize that the authors noted that their thermodynamic model offered no theoretical basis for this interpretation and that their assignment of pK1/2 was based solely on the similarity of their pH of maximal voltammetric signal with reported literature pKa values. The models of SW and Fawcett are based on thermodynamic equilibria and neglect the kinetics of the surface acid protonation/ deprotonation. In this paper, we use a kinetic approach to provide an explanation of the dependence of the voltammetric peak height on the electrolyte pH. Furthermore, we derive analytical expressions relating the results of electrochemical impedance spectroscopy (EIS) measurements to the forward and reverse rate constants for the protonation/deprotonation of surface-bound acid monolayers. Successful evaluation of these kinetic parameters would make it possible to determine the surface pK1/2 values as a function of the electrical potential applied to the SAM-modified electrode. Overview of Thermodynamic Models of the Ionizable Interface. Using equilibrium conditions to describe the interface of an ionizable monolayer and the bulk solution, Smith and White derived the following relationship between the solution pH, the local electrical potential at the plane of dissociation of the acid headgroups, Ψ, and the fraction of ionized molecules in the film;
dependent on the potential applied to the metal substrate. The effect of the electrode potential on the surface acid-base properties has been experimentally observed for carboxylic acid SAMs,31 amine-terminated SAMs32,33 and noncovalently bound adsorbed layers such as benzoic acid and pyridine derivatives on mercury.34-37 In the SW model, the total differential capacity of the interface is divided into contributions from the film, the ionizable headgroups, and the diffuse part of the double layer. For simplicity, we will use the equation describing the total interfacial capacity derived by SW rather than Fawcett’s more complicated expression, though we note that the latter model more accurately describes experimental data. Smith and White show that
1 1 1 ) + CT CF CS + C(θ)
(3)
where CT is the total interfacial (i.e., experimentally measurable) capacity, CF is the capacity of the alkyl chains of the film, which can be modeled as a Helmholtz capacitor, CS is the diffuse layer capacity, and C(θ) is the capacity associated with the plane of dissociation and is therefore a function of the degree of ionization of the acidic headgroups. According to the models of SW26 and Fawcett,27,28 the total differential capacity of the interface should exhibit a peak at potentials close to those where the acidic headgroups in the SAM are half-ionized. Furthermore, at constant ionic strength, the potential corresponding to the maximum in the total differential capacity should shift cathodically with increasing pH but the maximum value of the capacity should be independent of the pH of the electrolyte solution. Materials and Methodology
Both models predict that a positive (negative) shift in the electrode potential causes a positive (negative) shift in Ψ. Consequently, the surface pKa of an ionizable SAM should be
The working electrodes in these experiments were polycrystalline gold beads formed by melting gold wire (99.99% Alfa Aesar) with a propane torch. The gold bead at the end of the gold wire was immersed in aqua regia (3:1 HCl/HNO3) to remove surface impurities and then remelted. This procedure was repeated iteratively until the molten gold displayed no visible contaminants. The electrodes were then electrochemically polished in 50 mM KClO4 (Aldrich, 2× recrystallized) by cycling through the surface oxidation/oxide stripping peaks (-0.8 V < E < 1.25 V vs SCE). Electrochemical measurements were performed in an all-glass sealed cell, which was connected to an external reference electrode (SCE) via a salt bridge. All glassware was heated in a mixture of H2SO4 and HNO3 (2:1 by volume) and then copiously washed with Millipore water (Millipore >18.2 MΩ) prior to every daily experiment. The counter electrode was a loop of flame-annealed gold wire. The electrolytes were prepared from NaF (Aldrich 99.99%), KOH (Sigma, 99.99% Semiconductor Grade), and HClO4 (70%, Aldrich). The aqueous electrolyte solution was thoroughly degassed with argon for a minimum of 30 min before the experiments were performed. An argon blanket was maintained over the electrolyte throughout the duration of the experiments to ensure an oxygen-free environment. Prior to every experiment, the working electrodes were cleaned in Piranha solution (3:1 H2SO4/H2O2), rinsed, flame-annealed, and quenched in Millipore water. These bare gold surfaces were then electrochemically characterized in 50 mM NaF to ensure their cleanliness. SAMs were electrochemically deposited, 0.2 V vs SCE
(29) White, H. S.; Peterson, J. D.; Cui, Q.; Stevenson, K. J. J. Phys. Chem. B 1998, 102, 2930-2934. (30) In an effort to avoid confusion, we wish to clearly define the difference between surface pKa and pK1/2. Both of these terms describe acidic monolayers and represent the pH of a solution in which the concentration of deprotonated surface species is equal to the concentration of protonated surface species (i.e., θ ) 1/2). The difference arises in that pK1/2 corresponds to a film in the presence of an interfacial potential, whereas surface pKa is a unique instance of pK1/2 when Ψ ) 0.
(31) Sugihara, K.; Shimazu, K.; Uosaki, K. Langmuir 2000, 16, 7101-7105. (32) Cao, X.-W. J. Raman Spectrosc. 2005, 36, 250-256. (33) Bryant, M. A.; Crooks, R. M. Langmuir 1993, 9, 385-7. (34) Dojlido, J.; Dmowska-Stanczak, M.; Galus, Z. J. Electroanal. Chem. 1978, 94, 107-22. (35) Opallo, M.; Dojlido, J. J. Electroanal. Chem. 1981, 127, 211-17. (36) Galus, Z.; Dojlido, J.; Chojnacka-Kalinowska, G. Electrochim. Acta 1972, 17, 265-70. (37) Mairanovskii, S. G. J. Electroanal. Chem. 1977, 75, 387-97.
log
θ FΨ ) pH - pKa + 1-θ 2.303RT
(1)
where R and T have their usual meanings, θ is the fraction of ionized molecules (i.e., ΓA-/(ΓA- + ΓHA) with Γi being the surface coverage of species i), and pKa is the surface pKa of the bound acid thiol molecules in the absence of any interfacial electric fields. Smith and White assumed that Ψ is equal to the potential drop across the diffuse layer. Fawcett and co-workers extended the SW model to include a more realistic Stern layer27 and accounted for discreetness of charge effects,28 which leads to a more complex relation between the potential applied to the electrode and Ψ. As eq 1 is applicable to both models, one can use it to relate pKa to pK1/2 by setting θ ) 0.5,
pK1/2 ) pKa - FΨ/2.303RT
(2)
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Figure 1. pH-dependent CVs of a Au bead electrode coated with an MUA SAM. (a) Plot of the anodic CV peak potential vs pH (scan rate: 20 mV s-1). (b) Plot of maximum anodic peak current vs pH. for 15 min, in a separate cell from a sonicated aqueous solution of 1 mM MUA, (Aldrich, 97%) and 0.1 M NaF. Electrochemical experiments (cyclic voltammetry and EIS) were performed using a Solartron 1287 potentiostat and a 1255B frequency response analyzer. Cyclic voltammograms (CVs) were recorded using CorrWare software (Scribner Associates), and the impedance measurements using ZPlot/ZView (Scribner Associates). The supporting electrolyte for these experiments was 50 mM NaF (pH ≈ 8.7), the pH of which was adjusted using dilute solutions of KOH and HClO4. The pH of the electrolyte was monitored using a pH meter (Accumet 910). For the EIS measurements, the range of frequencies of the 5 mV rms amplitude, ac perturbation was 3000 Hz to 0.5 Hz. Higher frequencies were avoided due to the stray capacitance of the salt bridge. Using an internal reference electrode
alleviated this problem but introduces the possibility of chloride contamination in the working cell. Fitting of the experimental EIS data and simulation of EIS curves was performed using ZView/ ZPlot.
Results Cyclic Voltammetry. Figure 1 shows the results of the pH dependence of CVs of an MUA SAM on polycrystalline gold. The results closely correspond to those reported by White et al. for a mixed decanethiol/MUA SAM on Ag(111).29 We observe that the peak attributed to the protonation/deprotonation shifts
Protonation/Deprotonation Kinetics of Acid SAMs
cathodically with increasing pH. As shown in inset (a) of Figure 1, the peak position shifts linearly with pH at a rate of 67 mV/ decade. From eq 1, the expected slope of the line should be 59 mV/decade. The measured value is close to that predicted by SW’s equation, and the discrepancy may arise from the fact that we are plotting the applied electrode potential rather than the local potential, Ψ. Inset (b) in Figure 1 plots the voltammetric peak current versus pH and displays a maximum value at pH ≈ 8.9. This is in very good agreement with White et al. who reported a maximum voltammetric peak current at pH ≈ 8.5 for a mixed MUA/C12SH on Ag(111).38-42 The voltammetric scan rate dependence of the protonation/deprotonation peak, Figure S1 of the Supporting Information, shows that the peak current increases linearly with scan rate. This often corresponds to a surface redox couple. However, as initially detailed by SW and Fawcett and further developed here, the voltammetric (and EIS) signals are due to the non-Faradaic process of protonation and deprotonation. The observed voltammetric scan-rate dependence arises because the equivalent circuit used to describe this process is coincidentally identical to the equivalent circuit associated with surface redox electrochemistry. To reiterate, SW’s model (and Fawcett and co-workers’ refinement) explains the potential shift in the voltammetric peak with changing pH but does not account for the dependence of the peak height on pH. Below we present an explanation for this latter observation based on kinetic considerations. Electrochemical Impedance Spectroscopy. To further characterize the interface, we performed EIS measurements with DC potentials ranging from -500 to 0 mV. According to both the SW and Fawcett models, the equivalent circuit describing the interface should consist of a solution resistance in series with a capacitor to describe the total interfacial capacitance (see eq 3). Figure 2 presents the results of EIS studies on an MUA monolayer formed on a polycrystalline gold electrode as a function of the applied DC potential. The pH of the electrolyte was 8.5. The EIS data are rendered in a Bode phase angle diagram which plots the negative of the phase angle, - φ ) arctan(Zimg/Zreal), versus the frequency of the ac perturbation. For DC potentials < -300 or > -200 mV the Bode phase angle plots show high values of the phase angle for all frequencies above a characteristic roll-off point. For a resistor in series with a capacitor-like element, the phase angle should approach -90° at frequencies lower than the roll-off point and essentially remain independent of the ac frequency. This is exactly what is observed in Figure 2 for E < -300 mV and E > -200 mV. In our fitting analysis, a constant phase element (CPE) was used rather than a pure capacitor. The impedance of a CPE is a power law-dependent capacity, ZCPE ) A(jω)-R and accounts for the roughness of solid electrodes, which leads to frequency dispersion. The closer the value of R (38) The well-pronounced peak in both our and White et al.’s CVs allows us to determine the influence of the metal substrate on E1/2. Given the large differences in the points of zero charge of polycrystalline gold (ca -70 to -40 mV vs SCE39,40) and Ag(111) (-700 mV vs SCE41), one might expect a large difference of E1/2 between the two systems. Correcting for the saturated Hg/HgSO4 reference electrode used by White et al. (+400 mV vs SCE42), we estimate a formal peak potential of -225 mV vs SCE for White et al.’s experiment conducted in 0.1 M NaF, pH 8.5. A formal peak potential of -243 mV vs SCE (0.05 M NaF, pH 8.5) is obtained here. Given that the two experiments were performed in slightly different conditions (electrolyte strength, SAM composition, and scan rate), this small difference establishes that E1/2 is not dependent upon the metal substrate. (39) Clavilier, J.; Nguyen Van Huong, C. J. Electroanal. Chem. 1977, 80, 101-14. (40) Clavilier, J.; Nguyen Van Huong, M. C. R. Seances Acad. Sci., Ser. C 1969, 269, 736-9. (41) Hamelin, A.; Vitanov, T.; Sevastyanov, E. S.; Popov, A. J. Electroanal. Chem. 1983, 145, 225-64. (42) Bard, A. J.; Faulkner, L. R. Electrochemical Methods: Fundamentals and Applications, 2nd ed.; John Wiley and Sons Inc.: New York, 2001.
Langmuir, Vol. 22, No. 9, 2006 4423
Figure 2. Bode plots (phase angle vs frequency) for MUA SAM on polycrystalline Au for potentials -500 mV e E e 0 mV vs SCE. Electrolyte was 50 mM NaF, pH adjusted to 8.5.
approaches unity, the more the element behaves as an ideal capacitor43 and the value of A becomes equivalent to the inverse of the capacity, C. In all our fitting analyses, the values of R were 0.98 or larger for this CPE. Data for the fitting results (R, A ) 1/C, and the goodness of fit parameter, χ2) are presented in Table S1 of the Supporting Information. As expected, the fitting of the EIS curves with a simple model of an R-CPE series circuit gives excellent fits for E < -300 mV and E > -200 mV. In contrast, in the region of DC potentials close to the observed peak in the cyclic voltammetry (-300 mV e E e -200 mV), the Bode phase angle plots display a characteristic “dip” at intermediate frequencies (ca. 1 Hz < f < 100 Hz) where the phase angle is significantly lower than 90°. The dip is most strongly pronounced at potentials that correspond to the formal peak potential in the CV. Thus, the interface cannot be modeled as a simple R-CPE series circuit at the protonation/deprotonation potentials. The influence of pH on the EIS data is as pronounced as it is for the cyclic voltammetry data. Figure 3 displays threedimensional plots of the phase angle as function of potential and frequency for different solution pH values. At both high and low pH, the dip is completely absent, indicating that the interface mimics an R-CPE series circuit. It is only when the pH of the electrolyte is close to 9 and the DC potential applied to the electrode corresponds to the peak observed in the voltammetry that the characteristic dip is apparent in the Bode phase angle plots.
Discussion Explanation of Experimental EIS Data. An explanation of the observed EIS data at DC potentials corresponding to the peak in the CV is as follows. Consider the reaction kf
H+ + A- {\ } HA k
(Reaction 1)
b
where HA denotes surface-bound, protonated molecules and Arepresents the bound, conjugate base. The degree of charge at the plane of dissociation plus the excess charge in the diffuse part of the double layer will be balanced by the surface charge density, σm, on the electrode. At constant pH, σm is a function (43) Brug, G. J.; Van den Eeden, A. L. G.; Sluyters-Rehbach, M.; Sluyters, J. H. J. Electroanal. Chem. 1984, 176, 275-95.
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Figure 4. (a) RC model circuit for a nonionizing SAM consisting of a solution resistance and a film capacity in series. (b) Model circuit for an ionizing SAM consisting of a generic impedance, Zp, in parallel with the film capacitance, Cc. (c) Model circuit for an acid-terminated SAM consisting of a protonation/deprotonation resistance and capacitance in parallel with the film capacitance
Differentiating eq 4 with respect to time provides an expression for the current flowing through the interface
i)
( ) ∂σm ∂E
( )
∂σm dE + θ dt ∂θ
E
dθ dt
(5)
The first term in eq 5 describes the capacitive current arising from charging the interface under conditions of constant composition, whereas the contribution to the total current due to the rate of change in the degree of ionization is provided by the second term. Although the current is not experimentally separable, the total current can be mathematically divided into a purely charging current and a current due to the kinetics of the surface acid chemistry described in Reaction 1. The current that arises due to the protonation/deprotonation reaction under the condition of constant total coverage is
ip ) λ
Figure 3. 3D electrochemical impedance spectra of an MUA SAM on a Au bead electrode as a function of potential and various pHs.
of both the applied potential (E) and the degree of ionization of the carboxylic acid functionalities (θ). The relationships between these variables can be written in terms of a complete differential.
σm ) f(E,θ)
dσm )
( ) ∂σm ∂E
θ
dE +
( ) ∂σm ∂θ
E
dθ
(4)
dθ dt
(6)
where λ is (∂σm/∂θ)E. Although λ might appear to be related to the electrosorption valency,44 γ′ ) (1/F)(∂σm/∂Γi)E, it should not be confused with the charge flowing to the electrode per adsorbed MUA molecule because the partial derivative in eq 6 is with respect to the fractional coverage of the acid and not the surface coverage, Γ. In instances where there is no change in the degree of ionization of the SAM, (i.e., dθ/dt ) 0), the protonation/deprotonation current does not exist and the observed current arises solely from the capacitive charging of the interface. This occurs at DC potentials far removed from the peak in the CV and/or at pHs well-removed from the pK1/2. Under these conditions, one should be able to successfully model the interface as a capacitor, Cc, in series with the electrolyte resistance, Rs (see Figure 4a). This is experimentally observed. On the other hand, when dθ/dt is appreciable, a generic parallel impedance, Zp, associated with the protonation/deprotonation must be introduced (see Figure 4b). (44) IUPAC prefers using the notation “formal partial charge number” and the symbol l.
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Derivation of the Protonation/Deprotonation Impedance. The derivation of the protonation impedance follows in an analogous fashion to the derivation of the Faradaic impedance for a surface redox reaction given by Gabrielli et al.45 from which we borrow heavily. We stress that this impedance is not due to a Faradaic reaction (such as hydrogen evolution) but rather stems from the change in the electrode’s surface charge density due to changes in the degree of ionization at the plane of dissociation. We start with the assumption that Reaction 1 follows a Langmuir isotherm
is to induce a corresponding fluctuation in the degree of ionization which causes a change in the protonation/deprotonation current.
dθ ) kb(1 - θ) - kfθ[H+] dt
dθ ) f(θ,E) dt
kf ) kf exp[-bf(E - E )]
(8)
kb ) kb exp[bb(E - E )]
(9)
0
0
0
E(t) ) Es + dE(t) ip(t) ) ip,s + di(t)
(14)
Inspection of eqs 7-11 reveals that
(7)
where kf and kb are the rate constants for the forward (protonation) and reverse (deprotonation) reactions. It is further assumed that, at constant electrolyte pH, the reaction is controlled by the applied potential (as shown by SW, Fawcett, and Figure 1 of the current work) and the relationship between the applied potential, E, and the measured rate constants (kf and kb) is given by a modified form of the Tafel equation.42 0
θ(t) ) θs + dθ(t)
(15)
where
f ) (1 - θ)k0 exp[bb(E - E0)] - θ[H+]k0 exp[-bf(E - E0)] (16) and similarly
ip ) g(θ,E)
(17)
where
g ) λ{(1 - θ)k0 exp[bb(E - E0)] θ[H+]k0 exp[-bf(E - E0)]} (18)
where,
bf )
Rλ RTΓtot
(10)
We can relate the quantities θ, E, ip by taking the full derivatives of eqs 15 and 17
(dθdt ) ) (∂E∂f ) dE(t) + (∂θ∂f ) dθ(t) ∂g ∂g d(i (t)) ) ( ) dE(t) + ( ) dθ(t) ∂E ∂θ
and
d
bb )
(1 - R)λ RTΓtot
(11)
The parameter λ/(RTΓtot)(where Γtot ) ΓA- + ΓHA) represents the number of charge units transferred to the electrode in the protonation/deprotonation reaction, and R is the transfer coefficient (0 < R < 1). This modified Tafel equation has been previously used by Parsons46 to describe the specific adsorption of a redox-inactive adsorbate on Ag(111). The parameters kf0 and kb0 are the rate constants for a chosen reference potential, E0, and have units of M-1 s-1 and s-1, respectively. The current that flows due to the protonation/deprotonation reaction is arrived at by combining eqs 6 and 7. +
ip ) λ(kb(1 - θ) - kfθ[H ])
(12)
In the steady state, the forward reaction balances the backward reaction, and by setting the left-hand side of eq 7 equal to zero, we achieve
θs )
kb +
kf[H ] + kb
(13)
θ
p
V
θ
V
(19) (20)
Explicitly evaluating the partial derivatives of eqs 16 and 18 provides the following;
(dθdt ) ) {a} dE(t) - {b} dθ(t)
(21)
d(ip(t)) ) λ[{a} dE(t) - {b} dθ(t)]
(22)
a ) (1 - θ)kbbb + θ[H+]kfbf
(23)
b ) kb + [H+]kf
(24)
d
where
and
the former which can be rewritten using eq 13 to yield
a)
kfkb[H+]
[bb + bf]
kf[H+] + kb
(25)
where the subscript s denotes the steady-state conditions. Now consider a small perturbation, dE(t), being superimposed upon the steady-state potential, Es. The effect of this perturbation
If dθ˜ (ω), dV ˜ (ω), and dı˜p(ω)are the Fourier transforms of dθ(t), dV(t), and dip(t), respectively, then the Fourier transforms of eqs 21 and 22 are as follows;
(45) Gabrielli, C.; Huet, F.; Keddam, M.; Haas, O. Electrochim. Acta 1988, 33, 1371-81. (46) Jovic, V. D.; Parsons, R.; Jovic, B. M. J. Electroanal. Chem. 1992, 339, 327-37.
jω dθ˜ (ω) ) {a} dV ˜ (ω) - {b} dθ˜ (ω)
(26)
˜ (ω) - {b} dθ˜ (ω)) dı˜p(ω) ) λ({a} dV
(27)
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Figure 5. Fit of equivalent circuit (Figure 4C), solid line, to experimental Nyquist plot of MUA in pH 9.0 at -0.275V vs SCE, square points. Inset: Bode angle plot of MUA SAM in pH 9.0 at -0.275V vs SCE, square points, and equivalent circuit fit, solid line.
Finally, by combining eqs 26 and 27 to eliminate dθ˜ (ω), we arrive at an expression for the impedance of the protonation/ deprotonation reaction.
Zp(ω) )
dV ˜ (ω) b 1 1+ ) jω dı˜p(ω) aλ
[
]
(28)
Equation 28 demonstrates that the protonation impedance consists of both a real valued quantity and an imaginary quantity which corresponds to a series combination of a resistor and a capacitor. Explicit expressions for the values of Rp and Cp are readily obtained by substituting eqs 24 and 25 into 28
Re[Z] ) Rp )
[
+
kf[H ] + kb 1 λ k k [H+][b + b ] f b b f
]
(29)
and recalling that Zcapacitor ) 1/jωC
Img[Z] ) Cp )
1 Rp(kb + kf[H+])
(30)
Figure 4c shows the equivalent circuit needed to model the interface at conditions where the protonation/deprotonation reaction is appreciable. The generic protonation/deprotonation impedance has been replaced with a series combination of a resistor and a capacitor. Parsons and co-workers used an equivalent circuit identical to that in Figure 4c to model the adsorption of acetate ions on Ag(111),47 implying that the protonation/deprotonation of acid thiol SAMs is fundamentally equivalent to the partial charge transfer concept used to treat the specific adsorption of anions on metal electrodes. We tested the adequacy of our model by fitting the EIS spectra shown in Figure 2, as well as the EIS bode phase angle curves that displayed the “dip” in Figure 3, to the equivalent circuit of Figure 4c. As shown in Figure 5, other than having to replace the pure capacitors with CPEs, our equivalent circuit provides excellent fits to the experimental data. Parameters of the best fit results are shown in Table S1 of the Supporting Information. Nature of the pH Dependence on Voltammetric/EIS Data. The expressions for the protonation/deprotonation resistance and capacitance can be used to provide insight into the apparent pH dependence of the voltammetric peak and the “dip” in the EIS. We do this by simulating the EIS spectra at the potential (47) Jovic, V. D.; Jovic, B. M.; Parsons, R. J. Electroanal. Chem. 1990, 290, 257-62.
Figure 6. Simulated values of Rp (a) and Cp (b) vs pH for potentials corresponding to the maximum protonation/deprotonation current.
corresponding to the protonation/deprotonation at different values of the pH. At this potential, we choose kf to have a value of 109 M-1 s-1, set kb ) 1 s-1, and note that, as defined by Reaction 1, the equilibrium constant for the surface deprotonation, K1/2, is equal to kb/kf, so that the values we have chosen correspond to a SAM with a surface pK1/2 of 9. The value selected for λ was 10 µC cm-2 and is assumed to be constant with potential. This value was estimated from some preliminary chronocoulometric experiments, which we describe in detail in a follow-up publication. We further assume that the energetics of the reaction are symmetric, i.e., R ) 0.5 and that Γtot ) 8.0 × 10-10 mol cm-2. We used these values to simulate the values of Rp and Cp as a function of pH using eqs 29 and 30, the results of which are shown in Figure 6. The value of Rp is shown to increase rapidly with increasing pH, ranging from a value of ∼20 kΩ at pH 6 to 2 MΩ at pH 11. In contrast, Cp displays a peak dependence on the pH of the electrolyte, reaching a maximum value when the pH equals the pK1/2 (pH ) 9 in our example). We proceed further by using the values of Rp and Cp and the equivalent circuit of Figure 4c to construct simulated EIS bode phase angle plots for the protonation/deprotonation potential as a function of pH. We chose a value of 100 Ω for the electrolyte resistance and a value of 2 µF cm-2 for the charging capacitance, Cc. The latter value is obtained from the equation of a Helmholtz capacitor
Cc )
0 d
(31)
where is the relative permittivity of the hydrocarbon core of the SAM ( ≈ 3), o is the permittivity of vacuum (8.85 × 10-12 C2 J-1 m-1), and d is the thickness of the hydrocarbon layer (estimated to be ca. 1.3 nm on the basis of Tanford’s empirical
Protonation/Deprotonation Kinetics of Acid SAMs
Langmuir, Vol. 22, No. 9, 2006 4427
Figure 7. Simulated electrochemical impedance spectrum as a function of pH - pK1/2 at the potential corresponding to the maximum protonation/deprotonation current.
equation48). For convenience, we assume an electrode area of 1 cm2. We note that the contribution to the total interfacial capacitance from the diffuse part of the double layer has been purposely omitted, as its contribution to the total capacity is negligible in the presence of such a low value of Cc even at the potential of zero charge (see Supporting Information). Figure 7 shows a three-dimensional plot of the phase angle as a function of both the log of the ac perturbation frequency and the pK1/2normalized pH. The simulation reveals that the most pronounced phase angle “dip” occurs when the pH ) pK1/2. At pHs far removed from the pK1/2, the magnitude of the dip has been greatly attenuated. Qualitatively, the simulated results are in excellent agreement with the experimental results shown in Figures 2 and 3. The simulated data can also be used to explain the voltammetric behavior of the MUA films as a function of pH. The admittance modulus of the interface is given by the reciprocal of the impedance modulus |Y| ) |Z|-1 and is therefore directly proportional to the peak current in the cyclic voltammetry experiment. Figure 8a shows the admittance as a function of frequency for different pK1/2-normalized pHs. One can use the admittance data to simulate the cyclic voltammetric peak height dependence on pH by plotting the admittance versus the pK1/2normalized pH for one particular frequency. Examples shown in Figure 8b for frequencies 1, 0.5, and 0.1 Hz correspond to CV scan rates of 20, 10, and 2 mV/s, respectively. The peak shape dependence of the simulated voltammetric response on electrolyte pH, Figure 8b, corresponds to the experimental voltammetric peak heights of inset b in Figure 1. Interestingly, we note that the simulated voltammetric admittance does not necessarily reach its maximum value when the solution pH equals the surface pK1/2. According to Figure 8b, the pH corresponding to the maximum peak is dependent on the voltammetric scan rate. Rendering our experimental impedance results as an admittance plot (figure not shown) reveals qualitatively similar features to those of Figure 8a. However, constructing the equivalent plot to Figure 8b with the experimental data does not reveal a discernible frequency dependence on the position of the maximum admittance. A possible explanation for this apparent discrepancy might be that the pH increments employed in this study are too large to allow for the scan rate effect on admittance to be apparent. This observation highlights a cause for caution when using a single scan rate to estimate pK1/2 values when using DC voltammetry. Determining Surface Acid Dissociation Constants from Electrochemical Data. On the basis of the simulated data shown (48) Tanford, C. J. Phys. Chem. 1972, 76, 3020-4.
Figure 8. (a) Simulated admittance plot vs frequency for pK1/2normalized pHs at the potential corresponding to the maximum protonation/deprotonation current. (b) Simulated admittance plot vs pK1/2-normalized pHs for specific frequencies at the potential corresponding to the maximum protonation/deprotonation current.
in Figure 7, it is tempting to infer that the greatest “dip” in experimentally measured Bode phase angle plots occurs when the pH of the electrolyte corresponds to the surface pKa of the SAM. There are several subtle reasons why we hesitate to make this assertion. First, it is important to restate that the quantity evaluated is pK1/2 and not pKa, the two being related by eq 2. The former is clearly a function of the potential applied to the SAM-covered electrode, while the latter is specific to the condition of zero electric field at the plane of acid dissociation. The potential dependence of pK1/2 has been previously reported for SAMs.31-33 Second, we simulate the EIS data in Figure 7 for potentials corresponding to the voltammetric peak as a function of pH by assuming pH-independent rate constants such that pK1/2 equals 9. However, Figure 1 clearly shows that the voltammetric peak potential is a function of pH. Combining this observation with eqs 8 and 9, which state that the rate constants are dependent on potential, it becomes evident that the rate constants must be dependent on pH. Finally, the value of λ, (∂σm/∂θ)E, has also been assumed to be invariant with potential and/or pH. This may or may not be true, and it is unclear how a variable value of λ affects the simulations shown in Figure 7. We believe that a more exact means of evaluating pK1/2 values would be to use experimentally determined values of Rp and Cp and eqs 29 and 30 to directly evaluate the forward and reverse rate constants. A particularly appealing feature of this approach is that the influence of the potential on pK1/2 can be readily determined as long as Rp and Cp are extractable from the EIS data. This may be problematic if the rate constant for the protonation, kf, is large enough that the reaction is diffusion controlled. In such a case, the value determined from the EIS
4428 Langmuir, Vol. 22, No. 9, 2006
data will be an apparent rate constant that is less than the true protonation rate constant. Slevin and Unwin have recently used induced desorption mode SECM to determine a protonation rate constant of 2.5 × 107 M-1 s-1(after unit conversion) for stearic acid Langmuir monolayers.49 The rate constant for diffusionlimited proton transfer in water is on the order of 1010 M-1 s-1.50 Accurate determination of the protonation/deprotonation rate constants should be possible if the magnitudes of these variables extend to the current system.
Conclusions We have derived an analytical expression for the impedance of the protonation/deprotonation reaction of a surface-bound acidic SAM. Our treatment of the interface includes a contribution to the total current due to the kinetics of the change in the degree of dissociation of the COOH groups. To test our model, we have simulated the EIS spectra for the interface, and the results are in qualitative agreement with our experimental results on an MUA SAM on polycrystalline gold. Our model successfully predicts the observed pH dependence on the voltammetric peak height attributed to the electric field driven protonation/ deprotonation of the MUA SAM. This is not accounted for by the previous thermodynamic models of SW26 and Fawcett.27,28 This work demonstrates that electrochemical techniques, particularly EIS, can be used to determine the surface pK1/2 of acidic organic films on conductive surfaces. Unlike other techniques, it should be possible to use EIS to extract the rate constants for the surface acid chemistry. We know of no reports of these physical parameters for acid thiol SAMs.
Burgess et al.
It is interesting to consider the parameters that may influence the rate constants. Several reports31-37 have shown that an applied potential can change the surface pKa. These include a change in kf and/or kb, hydrogen bonding and local solvent structure, and ionic strength.25,51 However, attribution of changes in the pKa due to potential, solvent structure, etc. is beyond the scope of this paper. Furthermore, any attempt to do so would require an experimental means of determining kf and kb in order to verify the model’s merit. One requires a value of λ in order to proceed. Although we have outlined a methodology to extract the rate constants using EIS, an important quantity which needs to be evaluated before this is truly possible is λ. We are currently performing chronocoulometric and surface IR experiments toward this end which will allow us to extract the values of kf, kb, and K1/2 from EIS measurements. Finally, we wish to note that, although we have demonstrated the use of this approach for acidic monolayers, the formalism of the mathematics should be identical for monolayers containing basic functionalities. Acknowledgment. I.B. thanks both NSERC Canada and the Tomlinson Foundation of McGill for postdoctoral funding. B.S. thanks FQRNT for provision of a doctoral fellowship. NSERC and FQRNT provided funding for this research. Supporting Information Available: Contribution of the diffuse layer capacity to the total capacity and the fitting results of the equivalent circuit in Figure 4c; and scan-rate-dependence data of the voltammetric peak. This material is available free of charge via the Internet at http://pubs.acs.org. LA052767G
(49) Slevin, C. J.; Unwin, P. R. J. Am. Chem. Soc. 2000, 122, 2597-2602. (50) Eigen, M. Angew. Chem., Int. Ed. Engl. 1964, 3, 1-19.
(51) Smalley, J. F. Langmuir 2003, 19, 9284-9289.
