Anal. Chem. 2010, 82, 935–941
Electrochemical Surface Plasmon Resonance: Basic Formalism and Experimental Validation Shaopeng Wang,† Xinping Huang,†,‡ Xiaonan Shan,† Kyle J. Foley,† and Nongjian Tao*,† Center for Bioelectronics and Biosensors, Biodesign Institute, Arizona State University, 1001 South McAllister Avenue, P.O. Box 875801, Tempe, Arizona 85287-5801, and Department of Chemistry, Lanzhou University, Lanzhou 730000, People’s Republic of China A quantitative formalism of electrochemical surface plasmon resonance (EC-SPR) was developed for studying electrochemical reactions. The EC-SPR signal from the reactions was found to be a convolution function of electrochemical current, and therefore, EC-SPR is a powerful tool that can provide information similar to the conventional current-based electrochemical techniques. As an example, potential-sweep EC-SPR was analyzed in details and was found to provide a new way to measure convolution voltammetry without the need of numerical integration. In addition to the benefits provided by the conventional convolution voltammetry, the EC-SPR has several unique advantages, including (1) spatial resolution that is particularly attractive for studying heterogeneous reactions, (2) optical properties of the reactions species that may assist identification of reaction mechanisms, and (3) high surface sensitivity for studying surface binding of the reaction species. Experiments and numerical simulations were carried out for a model system, hexaammineruthenium(III) chloride. The simultaneously measured electrochemical current and SPR response confirmed the relationship between the two quantities, and the numerical simulations were in excellent agreement with the measurements. Surface plasmon resonance (SPR) technique is highly sensitive to various processes taking place on a metal film. It has emerged as a powerful label-free method to study molecular binding processes taking place on a surface. Another important but less explored area of applications is electrochemical SPR (EC-SPR) for studying local electrochemical reactions on electrode surfaces.1 One of the first SPR studies of electrochemical reactions was based on detecting local surface potential.2 Other approaches include detection of surface-bound redox species,3-9 redoxinduced conformational changes in surface-bound proteins,7 * To whom correspondence should be addressed. E-mail:
[email protected]. Fax: (480) 965-9457. † Arizona State University. ‡ Lanzhou University. (1) Wang, S.; Boussaad, S.; Tao, N. J. In Biomolecular Films: Design, Function, And Applications; Rusling, J. F., Ed.; Marcel Dekker: New York, 2003; pp 213-251. (2) Hanken, D. G.; Corn, R. M. Anal. Chem. 1997, 69, 3665–3673. (3) Iwasaki, Y.; Horiuchi, T.; Morita, M.; Niwa, O. Surf. Sci. 1999, 428, 195– 198. (4) Wang, S. P.; Forzani, E. S.; Tao, N. J. Anal. Chem. 2007, 79, 4427–4432. (5) Wang, S.; Boussaad, S.; Tao, N. J. Rev. Sci. Instrum. 2001, 72, 3055–3060. 10.1021/ac902178f 2010 American Chemical Society Published on Web 01/04/2010
potential-controlled DNA melting, electrochemical polymerization,10,11 and anodic stripping and detection of metal ions.4 These studies are mainly focused on adsorption/desorption processes or changes in the adsorbed species. SPR is also sensitive to the charge density in the metal film,12 which has been employed recently by us to develop a surface impedance imaging technique.13 In addition to applications based on the SPR dependence on the intrinsic dielectric properties of the metal films and molecular adsorption on the metal films, SPR measures local refractive index in the bulk solution near the metal film. The latter is largely responsible for the observed electrochemical reaction of Fe(CN)63-/4- reported in literature.3 Despite of the promising applications of SPR in electrochemistry, a basic and quantitative formalism has not yet been developed for EC-SPR, which is the focus of the present work. We establish a quantitative relationship between the EC-SPR signal and the current measured by conventional electrochemical methods. As an example, we apply the formalism to the most widely used electrochemical method, potential-sweep measurements. Furthermore, by considering diffusion-controlled reversible redox reactions, we obtain explicit expressions of the EC-SPR signal in terms of important electrochemical parameters as a function of potential and time. Finally, we carry out simultaneous measurements of electrochemical current and EC-SPR of the redox reaction of hexaammineruthenium(III) chloride and show excellent agreement between the theory and experiments. THEORY SPR measures (1) molecular binding onto a metal film, (2) bulk refractive index changes near the metal film, and (3) dielectric property changes of the metal film. The first property is best known and widely applied to affinity studies of biomolecules. We will focus here the second and third properties, which are, as we will show below, directly related to faradic current and double layer charging current, respectively. (6) Wang, S.; Boussaad, S.; Wang, S.; Tao, N. J. Anal. Chem. 2000, 72, 4003– 4008. (7) Boussaad, S.; Pean, J.; Tao, N. J. Anal. Chem. 2000, 72, 222–226. (8) Kang, X. F.; Cheng, G. J.; Dong, S. J. Electrochem. Commun. 2001, 3, 489– 493. (9) Wang, J. L.; Wang, F.; Chen, H. J.; Liu, X. H.; Dong, S. J. Talanta 2008, 75, 666–670. (10) Schweiss, R.; Lubben, J. F.; Johannsmann, D.; Knoll, W. Electrochim. Acta 2005, 50, 2849–2856. (11) Kienle, S.; Lingler, S.; Kraas, W.; Offenhausser, A.; Knoll, W.; Jung, G. Biosens. Bioelectron. 1997, 12, 779–786. (12) Kotz, R.; Kolb, D. M.; Sass, J. K. Surf. Sci. 1977, 69, 359–364. (13) Foley, K. J.; Shan, X.; Tao, N. J. Anal. Chem. 2008, 80, 5146–5151.
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Electrochemical Reactions. We consider an important family of electrochemical reactions in which neither reactants nor products bind to the electrode surface. In this case, SPR measures the reaction-induced changes in the bulk refractive index near the electrode. The SPR response (e.g., resonance angle shift) can be described in terms of the reactant and product concentrations, CO and CR, and given by θ(t) ) B
∫
∞
0
[ROCO(z, t) + RRCR(z, t)]e-z/l d(z/l)
(1) kf
where RO and RR are the changes in the local refractive index per unit concentration for the oxidized and reduced molecules, respectively. The constant, B, in eq 1 measures the sensitivity of the SPR angle to a change in the bulk index of refraction, which can be calibrated for a given SPR setup and reaction species. The exponential term in the integral is the decay of the evanesce field from the metal into the solution phase, where the decay length, l, is on the order of 200 nm. Note that, in principle, l is also a function of CO and CR, but to a first order of approximation one can regard l as a constant. For a given set of boundary and initial conditions, CO and CR can be readily determined by solving the diffusion/rate equations. If the electrochemical reaction is the rate-limited process, then CO and CR are determined by the reaction rate. On the other hand, if the reaction is diffusion-limited, CO and CR can be determined from the diffusion equation. So SPR measures local reaction kinetics, and this unique capability is ideal for studying heterogeneous chemical reactions, taking advantage of the spatial resolution of SPR imaging. Equation 1 can be simplified if the time scale of measurement is slower than the diffuse time of the reaction species over a distance of l ∼ 200 nm. In this case, eq 1 is replaced by θ(t) ≈ B[ROCO(z, t)|z)0 + RRCR(z, t)|z)0]
(2)
where CO(x, y, z, t)|z)0 and CR(x, y, z, t)|z)0 are the concentrations of the oxidized and reduced molecules near the electrode. For most ions and molecules in dilute solutions, with diffusion coefficient in the range of 10-9 to 10-11 m2/s,14 the diffusion time given by l2/(2D) is less than a millisecond, so eq 2 holds well for most electrochemical measurements. According to eq 2, SPR directly measures the local concentrations of oxidized and reduced species on the electrode surface. In contrast, conventional electrochemical methods measure current density versus potential or time, which is related to CO and CR according to15 I ) nFDO
∂CO ∂z
|
z)0
) -nFDR
∂CR ∂z
O + ne S R kb
where kf and kb are forward and backward reaction rates. If assuming one-dimensional (along the z-axis) and semi-infinite geometry, the diffusion equation of O is ∂CO ∂2C ) DO 2 ∂t ∂z
(4)
where CO(z, t) and DO are the concentration and diffusion coefficient of O. Performing Laplace transform on eq 4, we have
0 ˜ O(z, s) - CO sC ) DO
˜ O(z, s) ∂2C
(5)
∂z2
˜ O(z, s) is the Laplace transform of CO(z, t) and CO0 is where C the initial concentration of O, which is assumed to be a constant. The solution of eq 5 is 0 ˜ O(z, s) ) s-1CO C + A(s) exp[-(s/DO)1/2z]
(6)
where A(s) is a function to be determined from boundary conditions at the electrode surface. To relate the concentrations to current density, we perform Laplace transform on eq 3 and combine it with eq 6, which leads to 0 ˜ O(0, s) ) s-1CO C - (nFDO1/2)-1s-1/2˜I (s)
(7)
Inverse Laplace transform of eq 715 gives 0 CO(0, t) ) CO - [nF(πDO)1/2]-1
∫ i(t')(t - t') t
-1/2
0
dt' (8)
Using the same procedure, we obtain the concentration for the reduced species, R, on the electrode surface, given by
|
(3) z)0
where n is number of electrons transferred per reaction, F is the Faraday constant, and DO and DR are the diffusion coefficients of the reaction species. Comparing eqs 1 and 3, we know that both SPR and current measurements are related to the concentra(14) Flick’s Law of diffusion. URL: http://en.wikipedia.org/wiki/Fick%27s_ law_of_diffusion, accessed on September 28, 2009. (15) Bard, A. J.; Faulkner, L. R. Electrochemical Methods: Fundamentals and Applications, 2nd ed.; Wiley: New York, 2001.
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tions of the reactant and product, but they are not identical. SPR is detecting the concentration changes near the working electrode surface, whereas current measures the concentration gradient. We develop below first a quantitative relationship between SPR signals and the current, and then consider a more specific example, reversible redox reactions. Relationship between Current and SPR Signals. Let us consider a redox reaction
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CR(0, t) ) C0R + [nF(πDR)1/2]-1
∫ i(t')(t - t') t
-1/2
0
dt' (9)
Substituting eqs 8 and 9 into eq 2, we have θ(t) ) θ0 + B(RRDR-1/2 - RODO-1/2)(nFπ1/2)-1 ×
∫ i(t')(t - t') t
0
-1/2
dt'
(10)
where θ0 ) ROCO0 + RRCR0 is the SPR signal at t ) 0. Equation 10 can be written in a more convenient form as ∆θ(t) ) B(RRDR-1/2 - RODO-1/2)(nFπ1/2)-1 ×
∫ i(t')(t - t') t
-1/2
0
dt'
∂CO(0, t) ∂CR(0, t) ) -DR ∂z ∂z
(12)
Combining the Laplace transform of eq 12 with the solutions of the diffusion equations (eq 6 for O and a similar express for R), we have 0 ξCO(0, t) + CR(0, t) ) ξCO + C0R
(13)
where ξ ) (DO/DR)1/2. In order to determine the SPR signal using eq 2, we need both CO(0, t) and CR(0, t), which requires another boundary condition at the electrode surface. Reversible Reactions. If we assume that the reaction is fully reversible, then the forward and backward reaction rates are large, and the Nernst law CO(0, t) nF ) exp (E(t) - E0) CR(0, t) RT
[
]
(14)
holds, where R is the molar gas constant, T is temperature, and E0 is the standard potential. Combining eqs 13 and 14, we can determine CO(0, t) and CR(0, t), and substituting them into eq 2, we obtain
θ(E) )
(ξCO0 + CR0)(ROS(E) + RR) 1 + ξS(E)
where S(E) ) exp[((nF)/(RT))(E - E )]. 0
E(t) ) Ei - vt
(11)
where ∆θ ) θ(t) - θ0 measures the shift in the SPR signal. Equation 11 provides a quantitative relation between the EC-SPR signal and the electrochemical current density measured by conventional electrochemical methods. It is important to note that the SPR signal is a convolution function of current, according to eq 11. Imbeaux and Saveant16 have developed convolution voltammetry by numerically computing the convolution integral in eq 11. In comparison with the more traditional voltammetry that is based on the analysis of peak currents and potentials, the convolution voltammetry has many advantages but is not directly measured and thus less convenient.15 An important conclusion from the above analysis is that SPR measures the convolution voltammetry directly without the need of performing numerical computation. Equation 11 provides a quantitative relationship between SPR and current signals. We now aim at a more explicit expression of the SPR signal in terms of important diffusion, thermodynamic, and kinetic parameters, as a function of potential and time. This requires one to define the boundary conditions. The semi-infinite geometry implies that the concentrations of O and R far away from the electrode surface are fixed at the initial values. At the electrode surface, flux balance (steady state) requires that
DO
Linear Potential-Sweep Measurements. Similar to cyclic voltammetry (CV), one can measure SPR response while cycling the electrode potential. The SPR signal versus potential is given by eq 15 by simply replacing E in the equation with for 0 < t < (Ef - Ei)/v
(16)
and E(t) ) Ef + vt
for (Ef - Ei)/v < t < 2(Ef - Ei)/v (17)
where Ei and Ef are the upper (initial) and lower limits of the potential, and v is the potential sweep rate. According to eq 15, the EC-SPR signal is independent of the potential sweep rate. If CR0 ) 0, then the EC-SPR signal is simply proportional to the initial concentration of O. Double Layer Charging Contribution. The above discussion did not consider the potential-induced change in the dielectric properties of the metal film. This change occurs because the potential changes the charge density of the metal film and thus the surface plasmon resonance frequency. We have shown previously13 that the corresponding SPR signal is proportional to the double layer charging current density and given by ∆θ )
1 c∆E R
(18)
where R is a constant, c is the interfacial capacitance per unit area, and ∆E is potential change. For a bare gold surface, we have determined that R ∼ 47 C · m-2 · deg-1.13 Time derivative of eq 19 yields 1 dθ ) id dt R
(19)
where id is the polarization or double layer charging current. Equation 19 shows that EC-SPR also measures the double layer charging current, and the time derivative of the SPR signal is directly proportional to the double layer charging current. The relation is different from the faradic current, which is related to the SPR signal via a convolution integral (eq 11). The double charging effect is relatively small compared with the bulk index of refraction changes arising from the redox reactions. However, it dominates the SPR signal (and also the current measured by the conventional electrochemical techniques) when no electrochemical reactions take place on the electrode. In general the double layer charging contribution to the EC-SPR signal may vary with the potential due to the dependence of the interfacial capacitance on the potential and molecular adsorption.17 By analyzing the double layer charging-induced SPR signals, one can determine interfacial capacitance information indirectly by measuring SPR response versus potential. MATERIALS AND METHODS Chemicals. All chemicals were purchased from Sigma-Aldrich and were used without further purification. The 0.5 M pH 7
(15) (16) Imbeaux, J. C.; Saveant, J. M. J. Electroanal. Chem. 1973, 44, 169–187. (17) Shi, Z.; Lipkowski, J.; Gamboa, M.; Zelenay, P.; Wieckowski, A. J. Electroanal. Chem. 1994, 366, 317–326.
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Figure 1. (A) Schematic illustration of the SPR setup. (B) SPR images in 11.78 mM Ru(NH3)63+ dissolved in phosphate buffer (0.5 M pH 7) at -0.1 and -0.3 V (vs Ag/AgCl reference electrode), as well as the difference of the two images. Bare gold and SAM-coated areas used for data extraction and processing are indicated by yellow squares.
phosphate buffer was prepared by dissolving 1:1 molar ratio of Na2HPO4 and NaH2PO4 in deionized water. The 0.6, 2, 6, and 20 mM hexamineruthenium(III) chloride (Ru(NH3)6Cl3) solutions were prepared by dissolving the correct amount of Ru(NH3)6Cl3 in the prepared phosphate buffer. Instrumentation. We used the Kretschmann configuration for our SPR imaging setup,18 and the thickness and/or dielectric properties of adsorbed layers can be resolved spatially with subnanometer vertical resolution.19 The lateral resolution of SPR imaging is close to diffraction limit with a recently reported objective-based approach.20 Figure 1A illustrates the prism-based SPR imaging setup used for all experiments described in this paper. A BK7 triangle prism was used with a collimated p-polarized red LED (Hamamatsu L7868-01, central wavelength 670 nm, Japan) as light source and a high-speed CCD camera (Pike F-032B from Allied Vision Technologies, Newburyport, MA 01950) as detector. A gold-coated microscope coverslip was placed on top of the prism using index match fluid and used as the SPR sensing surface. An electrochemical cell (cut from a flexiPERM 8-well removable and reusable TC Chamber, USA Scientific, Ocala, FL) was placed on top of the gold film for holding the reaction solution. Pt wire counter electrode and Ag/AgCl reference electrode (Cypress systems, Chelmsford, MA 01824) were inserted to the electrochemical cell from the top opening. A microAutolab type III potentiostat was used for controlling the potential and recording the potential and current. To synchronize the SPR imaging with the electrochemical measurement, we recorded the analog outputs of the potential and current from the potentiostat at a high speed (2 kHz) via a national instrument A/D board along with the open shutter trigger signal from the CCD camera, using a Labview program. In this way, the potential and current were synchronized with the corresponding SPR images. (18) Kretschmann, E. Z. Phys. 1971, 241, 313–324. (19) Rothenhausler, B.; Knoll, W. Nature 1988, 332, 615–617. (20) Huang, B.; Yu, F.; Zare, R. N. Anal. Chem. 2007, 79, 2979–2983.
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Preparation of the Sensing Surface. The 18 mm × 18 mm no. 1 BK7 glass microscopy coverslips (VWR no. 48366045) were first cleaned with deionized water and absolute ethanol, followed by 3 min of cleaning in an oxygen-plasma cleaner (Harrick Scientific Corporation). The cleaned coverslips were coated with 2 nm of chromium and 47 nm of gold by a sputter coater (Quorum Emitech Corporation, model K675X). Prior to each experiment, the gold film was cleaned with deionized water and absolute ethanol, blown to dry, and then briefly annealed with a hydrogen flame to remove possible surface contamination. A solution of 5 mM HS(CH2)15CH3 in absolute ethanol was prepared. The gold film surface was partially coated with a selfassembled monolayer (SAM) of 1-hexadecanethiol (CH3(CH2)15SH) to form two areas: a bare gold area for the redox reactions and a SAM-coated area to block the redox reactions (Figure 1B). The SAM coating was created using a 5 mM ethanol solution of 1-hexadecanethiol with a piece of poly(dimethylsiloxane) (PDMS) as stamp.21 The PDMS stamp was first submerged in the 5 mM thiol solution and dried out with nitrogen gas, and then was placed onto the gold surface for 5 min. SPR Imaging of Ruthenium Redox Reaction. After mounting the gold chip and electrochemical cell, 0.4 mL of 0.5 M PBS buffer was first introduced into the cell with a pipet. The incident light was adjusted to an angle slightly smaller than the resonance angle of bare gold surface so that both the SAM-coated and bare gold areas were within the linear detection range. The exposure time of the CCD camera was adjusted for maximum image intensity (to increase signal-to-noise ratio) while avoiding saturation. Next, CVs and SPR images were recorded while sweeping the potential. For each measurement, 16-bit grayscale SPR images were recorded at up to 640 fps. After the measurements for buffer completed, Ru(NH3)6Cl3 was added to the electrochemical cell for studying the redox reaction of the ruthenium complex. Data Extraction and Processing. Figure 1B shows typical SPR images at the oxidation and reduction potentials and the difference of the images between the two states. The raw SPR images were batch-converted to 16-bit tiff format files using a Matlab program. Average SPR intensity was calculated over the bare gold and SAM-coated area (rectangle areas marked by dash lines) for all images, using Image J software. The SPR intensity changes were calibrated to millidegree (mDeg) of SPR angle shift, θ, using 1% ethanol as standard. Calibration of Ruthenium Complex Optical Properties. In order to calculate SPR response using the theory developed here, we determined BRO and BRR, SPR angular shifts per unit concentration, for the oxidized and reduced forms of the ruthenium complex. This was carried out using a BI-2000 system (Biosensing Instruments, www.biosensingusa.com). First, the ruthenium complex in the oxidized state at each concentration was injected into the flow cell, and the SPR response was determined and used to calculate BRO. Second, in order to determine BRR, we converted the ruthenium complex to the reduced state by applying a negative electrode potential value (-0.3 V). BRR and BRO were found to be 2.5 and 5 mDeg/mM, respectively. (21) Kumar, A.; Biebuyck, H. A.; Whitesides, G. M. Langmuir 1994, 10, 1498– 1511.
Numerical Simulation. To verify our theory, we simulated the SPR and current response numerically. The concentrations for both the reactant and product were determined from the diffusion equation with appropriate initial and boundary conditions, as discussed in the Theory part. Taking into account of these boundary conditions, we simulated the concentration profiles versus time by using COMSOL software. Knowing the concentration profiles, and BRR and BRO for the ruthenium complex, we determined the SPR response using eqs 1 and 2. The current response was simulated by eq 3. RESULTS AND DISCUSSION CV of Hexaammineruthenium(III) Chloride at Different Potential Windows. Figure 2A shows the CVs of the ruthenium redox reaction at three different potential windows. For a potential window of 0.1 to -0.1 V, no ruthenium redox reaction occurs (blue dashed lines), and the current is small. When the potential window shifted negatively, the redox reaction takes place as shown by the large increase in the current. For a potential window of -0.1 to -0.3 V, a well-defined couple of reduction and oxidation peaks appear in the CV located at -0.27 and -0.17 V, respectively.15,22 However, the ruthenium redox reaction is expected to be fast,23 and the separation between the redox peaks should be smaller in the ideal case. The relatively large separation observed here, as we found, is mainly due to the solution resistance,15 which could be corrected and minimized. Nevertheless, in this work, we do not attempt to correct it, in order to show that the relation between the SPR signal and electrochemical current given by eq 11 is general and does not require the assumption of reversible ideal reactions. The simultaneously recorded SPR versus potential (or SPR voltammogram) is plotted in Figure 2B. The SPR signal is mainly caused by the refractive index difference between the reduced and oxidized forms of the ruthenium complex, but it also includes a small contribution from the double layer charging effect.13 The two different contributions are illustrated clearly in Figure 2B by measurements with different potential windows. When the potential scan window is outside of the redox reaction (e.g., between -0.1 and +0.1 V), the SPR changes slightly (2-3 mDeg), which is mainly due to the double charging effect described by eq 19. By shifting the potential scan window negatively to cover the redox reaction (e.g., between -0.3 and -0.1 V), we observed a large sigmoidal SPR signal. For comparison, we analyzed the SPR signals of SAM-covered area, and two observations are worth noting. First, the SPR signal change attributed to the double large charging effect (-0.1 to +0.1 V) becomes even smaller, which is expected due to the decrease in the interfacial capacitance. Second, the SPR signal change associated with the redox reaction (-0.3 to -0.1 V) also decreases significantly, due to the blockade of the redox reaction by the SAM. Relationship of Current and EC-SPR Signal. We now turn to the experimental validation of the theory presented earlier, especially the relationship between the SPR voltammetry and the conventional CV. One simple prediction of the theory is that the SPR voltammogram is independent of the potential scan rate. This (22) Demaille, C.; Brust, M.; Tsionsky, M.; Bard, A. J. Anal. Chem. 1997, 69, 2323–2328. (23) Sun, P.; Mirkin, M. V. Anal. Chem. 2006, 78, 6526–6534.
Figure 2. Measured conventional CVs and SPR voltammograms of 11.78 mM Ru(NH3)63+ at different potential windows: (A) conventional CVs; (B) SPR voltammograms of the bare gold area; (C) SPR voltammograms of the SAM-coated area. Potential scanning rate: 0.1 V/s.
is in contrast to the conventional CV, in which the redox peak current is proportional to the square root of the scan rate. Figure 3A plots the CVs at three different scan rates, 0.01, 0.1, and 1.0 V/s, showing that the peak current increases by ∼10 when the scan rate was increased from 0.01 to 1.0 V/s. The simultaneously recorded SPR voltammograms at different scan rates (Figure 3B) show little dependence of the total amount of SPR response on the scan rate. The most important prediction of the theory is that SPR voltammogram is simply a convolution integral of the current given by eq 11. Using eq 11 and independently calibrated BRR () 2.5 mDeg/mM), and BRO () 5 mDeg/mM), we calculated SPR voltammogram from the current shown in Figure 3A. The Analytical Chemistry, Vol. 82, No. 3, February 1, 2010
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allows us to perform convolution voltammetry without the need of numerical calculations. Furthermore, the spatial resolution of the EC-SPR technique makes it particularly attractive for studying heterogeneous electrochemical reactions. Theoretical Calculation of SPR Voltammograms. As we discussed in the Theory section, if we assume that the Nernst law holds, the SPR voltammograms can be calculated by eq 15 at different concentrations. The same assumption also allows us to calculate the conventional CVs.15 Figure 4 shows the measured (Figure 4A) and calculated (Figure 4B) CVs for the buffer and Ru(NH3)6Cl3 solution at different concentrations. The calculated CVs are in agreement with the measured CVs, except that the potential difference between the oxidation and reduction peaks is 57 mV, smaller than that in the measured CVs. The discrepancy indicates that the measured redox of Ru(NH3)6Cl3 is not an ideally reversible reaction, as we discussed earlier. Figure 4C shows the measured SPR voltammograms of buffer and Ru(NH3)6Cl3 at different concentrations. In the absence of the ruthenium complex (buffer alone), the SPR signal decreases with potential, which is at least partially due to the double layer charging effect discussed earlier. The presence of ruthenium complex causes an additional SPR response from the faradic current. This additional contribution is found to be proportional to the concentration as predicted by the theory (e.g., eq 15). Figure 4D shows calculated SPR voltammograms that include both the double layer charging effect and faradic current contribution, described by eqs 19 and 15, respectively. The calculated SPR voltammograms (Figure 4D) are in good overall agreement with the measured data (Figure 4C). One exception is that the calculated buffer data shows a smaller shift than the measured data. The reason for this difference is that the calculation for the buffer includes only the double layer charging effect. Within the potential window, there is a small amount side reaction, due to, e.g., reduction of dissolved oxygen, which leads to a small contribution to the SPR signal.24 The oxygen reduction contribution is expected to be small at more positive potential windows. Indeed, at the potential window of -0.1 to 0.1 V (Figure 2B, blue dashed line), the SPR voltammograms shows a smaller SPR shift, solely due to double layer charging effect. Figure 3. Relationship between current and SPR signals: (A) measured conventional CVs; (B) measured SPR voltammograms; (C) calculated SPR voltammograms using eq 11 and the conventional CVs shown in panel A as inputs. The electrolyte is 3 mM Ru(NH3)63+ in phosphate buffer, and the electrode is bare gold.
calculated SPR voltammograms (Figure 3C) are in good agreement, both in shape and values, with the measured data in Figure 3B. The agreement supports the theory and demonstrates that one can perform convolution voltammetry by measuring the SPR signals versus potential. The conventional voltammetry is based on the analysis of current and potential peaks, which discards much of the information, in particular, the shape of the voltammogram. The convolution voltammetry was introduced to overcome the limit of the conventional voltammetry,16 since the convolution voltammetry is directly related to the concentrations of reaction species; while the conventional voltammetry measures current that is related to the gradients of the concentrations, the former is often easier to interpret than the latter. Another advantage of the convolution voltammetry is that the electrolyte resistance can be easily accounted for. The SPR voltammetry 940
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CONCLUSION We have developed a quantitative formalism to describe ECSPR. Like the conventional current-based electrochemical methods, it has two major contributions, double layer charging and faradic current contributions. For the double charging contribution, the time derivative of the EC-SPR signal is proportional to the double layer charging current. The faradic current contribution measured by SPR is a convolution function of the current measured by the conventional electrochemical techniques. Potentialsweep EC-SPR (or SPR voltammetry) provides a new way to directly measure convolution voltammetry without the need of numerical calculations. In order to validate the theory experimentally, we have carried out simultaneously electrochemical current and SPR response measurements using hexaammineruthenium(III) chloride as a model system. We have calculated SPR voltammograms under (24) Wang, J. Stripping Analysis: Principles, Instrumentation, And Applications; VCH: Deerfield Beach, FL, 1985.
Figure 4. Measured and calculated conventional CVs and SPR voltammograms of Ru(NH3)63+ at different concentrations: (A) measured conventional CVs; (B) simulated conventional CVs; (C) measured SPR voltammograms; (D) simulated SPR voltammograms. Potential scanning rate: 0.1 V/s.
different conditions using the electrochemical current data as inputs, and the results confirm that SPR voltammetry measures the convolution voltammetry. We have also calculated the SPR voltammograms based on the diffusion equation and Nernst law directly without using the current data, and the results are also in good agreement with the experimental SPR voltammograms. In comparison with the conventional current-based electrochemical methods, EC-SPR is particularly attractive for studying heterogeneous reactions taking place on electrode surfaces, and for measuring optical properties of the reactions species, which may assist identification of reaction mechanisms. In addition, the
high surface sensitivity of SPR allows EC-SPR to detect surface binding of the reaction species.
ACKNOWLEDGMENT Financial support from NSF (CHE-0554786) is acknowledged.
Received for review September 28, 2009. Accepted December 7, 2009. AC902178F
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