Anal. Chem. 2000, 72, 5567-5575
Spectroelectrochemical Sensing Based on Multimode Selectivity Simultaneously Achievable in a Single Device. 5. Simulation of Sensor Response for Different Excitation Potential Waveforms Andrew F. Slaterbeck, Michael L. Stegemiller, Carl J. Seliskar, Thomas H. Ridgway,* and William R. Heineman*
Department of Chemistry, University of Cincinnati, P.O. Box 210172, Cincinnati, Ohio 45221-0172
The simulation of the optical response in spectroelectrochemical sensing has been investigated. The sensor consists of a sensing film coated on an optically transparent electrode (OTE). The mode of detection is attenuated total reflection. Only species that partition into the sensing film, undergo electrochemistry at the potentials applied to the OTE, and have changes in their absorbance at the wavelength of light propagated within the glass substrate of the OTE can be sensed. A fundamental question arises regarding the excitation potential waveforms employed to initiate the electrochemical changes observed. Historically, selection has been based solely upon the effectiveness of the waveform to quickly electrolyze any analyte observable by the optical detection method employed. In this report, additional requirements by which the waveform should be selected for use in a remote sensing configuration are discussed. The effectiveness of explicit finite difference simulation as a tool for investigating the applicability of three different excitation potential waveforms (square, triangle, sinusoid) is demonstrated. The simulated response is compared to experimental results obtained from a prototype sensing platform consisting of an indium tin oxide OTE coated with a cation-selective, sol-gel-derived Nafion composite film designed for the detection of a model analyte, tris(2,2′-bipyridyl)ruthenium(II) chloride. Using a diffusion coefficient determined from experimental data (5.8 × 10-11 cm2 s for 5 × 10-6 M Ru(bipy)32+), the simulator program was able to accurately predict the magnitude of the absorbance change for each potential waveform (0.497 for square, 0.403 for triangular, and 0.421 for sinusoid), but underestimated the number of cycles required to approach steady state. The simulator program predicted 2 (square), 3 (triangle), and 5 cycles (sinusoid), while 5 (square), 15 (triangle), and 10 (sinusoid) cycles were observed experimentally. A new sensor designed to improve selectivity by combining electrochemistry, spectroscopy, and selective partitioning through 10.1021/ac991460h CCC: $19.00 Published on Web 10/21/2000
© 2000 American Chemical Society
an applied thin film has been demonstrated.1-7 Future applications for the sensor include the monitoring of underground waste storage facilities, which would require the ability to operate the sensor remotely. In electrochemistry, it is generally appreciated that long connections between the electrodes and the potentiostat increase noise and raise concerns of potential instability. Recent work by Wang et al. has shown that when stripping voltammetry is performed, reasonably noise-free communication between the potentiostat and a solid gold electrode was achieved by use of long, shielded cables.8 In spectroelectrochemical sensing, the optical constraints imposed upon the system typically require a very thin (optically transparent), resistive working electrode with a relatively large surface area. A working electrode with this geometry is itself prone to noise pickup and uneven potential distribution across its surface. Making long connections to such an electrode, even with low-resistance, shielded cable, greatly increases the likelihood of signal degradation. In spectroelectrochemical sensing the analytical signal is optical; therefore, one does not need to continuously monitor the current at the working electrode. Consequently, one could position the potentiostat very near the sensing region, using on-board batteries and optical control to eliminate the possibility of noise and instability resulting from power and communication wires. In this configuration, current demand placed upon the unit should be kept as low as possible to minimize power consumption. There (1) Slaterbeck, A. F.; Shi, Y.; Seliskar, C. J.; Ridgway, T. H.; Heineman, W. R. In Proceedings of the Symposium on Chemical and Biological Sensors and Analytical Electrochemical Methods; Ricco, A. J., Butler, M. A., Vanysek, P., Horvai, G., Silva, A. F., Eds.; The Electrochemical Society, Inc.: Pennington, NJ, 1997; Vol. 97-19, pp 50-60. (2) Shi, Y.; Slaterbeck, A. F.; Seliskar, C. J.; Heineman, W. R. Anal. Chem. 1997, 69, 3679-3686. (3) Shi, Y.; Seliskar, C. J.; Heineman, W. R. Anal. Chem. 1997, 69, 48194827. (4) Seliskar, C. J.; Heineman, W. R.; Shi, Y.; Slaterbeck, A. F.; Aryl, S.; Ridgway, T. H.; Nevin, J. H. Proc. SPIE-Int. Soc. Opt. Eng. 1998, 3258, 56-65. (5) Seliskar, C. J.; Shi, Y.; Gao, L.; Clager, M. R.; Slaterbeck, A. F.; Heineman, W. R. Proc. SPIE-Int. Soc. Opt. Eng.. 1998, 3258, 66-74. (6) Hu, Z.; Slaterbeck, A. F.; Seliskar, C. J.; Ridgway, T. H.; Heineman, W. R. Langmuir 1999, 15, 767-773. (7) Slaterbeck, A. F.; Ridgway, T. H.; Seliskar, C. J.; Heineman, W. R. Anal. Chem. 1999, 71, 1196-1203. (8) Wang, J.; Larson, D.; Foster, N.; Armalis, S.; Lu, J.; Rongrong, X.; Olsen, K.; Zirino, A. Anal. Chem. 1995, 67, 1481-1485.
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Figure 1. (a) Absorbance spectrum of 1 × 10-5 M Ru(bipy)32+ in 0.1 M KNO3, emission spectrum of arc lamp/monochrometer with 450 nm selected, and emission spectrum of Panasonic blue LED. Values were normalized for comparison. (b) Comparison of 1 mM Ru(bipy)32+ in 0.1M KNO3 at a bare ITO electrode with 1 × 10-5 Ru(bipy)32+ partitioned into Nafion-SiO2-coated ITO electrode. Potentials measured vs Ag/AgCl reference electrode. Current values normalized for comparison.
are two main sources of current demand from the potentiostat: faradaic processes, in which current is the result of charge transfer across the electrode-solution interface when species undergo electrochemical reactions at the electrode surface, and nonfaradaic processes, in which current occurs without charge transfer across the electrode-solution interface (roughly analogous to the charging of a capacitor). When analyte concentrations are low, the nonfaradaic processes place the greater demand upon the potentiostat. Nonfaradaic current results from the charge balance required when the electrode is polarized. Four factors contribute to its magnitude: the composition of the supporting electrolyte, the potential window, the surface area of the electrode, and the excitation waveform employed. In a “real” sensing application, the first three are fixed by the nature of the sample environment, the electrochemical behavior of the analyte, and (in this application) the constraints imposed upon the electrode geometry by the optical requirements. The one factor remaining that can be altered to minimize the nonfaradaic contributions is the excitation potential waveform. As described previously,7 there are three excitation potential waveforms that, when applied continuously, will approach the desired steady-state response needed to apply ensemble averaging techniques: square, triangle, and large amplitude sinusoid. The work presented in this paper compares the relative characteristics of these three waveforms and demonstrates that the sensor response to each of these waveforms can be simulated by use of an explicit finite difference program. EXPERIMENTAL SECTION Materials. The following chemicals were used in this work: tetraethoxysilane (TEOS, Aldrich), Nafion (5% solution in lower aliphatic alcohols and water, Aldrich), tris(2,2′-bipyridyl)ruthenium(II) chloride hexahydrate ((Ru(bipy)32+), Aldrich), hydrochloric acid, and potassium nitrate. All reagents were used without further purification. Ru(bipy)32+ solutions were made by dissolving the appropriate amounts in 0.1 M potassium nitrate solution (supporting electrolyte), prepared with deionized water from a Barnstead water purification system. Indium tin oxide (ITO) glass (11-50 Ω/square, 150-nm-thick film on 1.1-mm glass, Thin Film Devices) was cut into 1 in. × 3 in. slides, scrubbed with Alconox, 5568 Analytical Chemistry, Vol. 72, No. 22, November 15, 2000
rinsed thoroughly with deionized water, dried, and then allowed to equilibrate with air before using. Preparation of Sensing Films. The sensing films employed here were prepared as described previously.7 Briefly, 4 mL of deionized water, 2 mL of TEOS, and 0.1 mL of 0.1 M HCl were combined in a sealed 30-mL glass vial and stirred for 3 h. A clear, single-phase sol resulted. A 1.0-mL portion of this sol was immediately blended with 3.0 mL of Nafion. The resulting solution was spin-coated onto the ITO electrode using a Headway spincoater at 3000 rpm for 30 s. The ends of the ITO slide were masked with tape, leaving areas uncoated for prism coupling. The coated slide was allowed to air-dry overnight and then was submersed in supporting electrolyte overnight before use. The resulting films were ∼400 nm thick, determined with a HewlettPackard 8453 diode array spectrophotometer using an interference fringe method.9 Instrumentation. The instrumentation employed for these studies was the same as described previously.7 Two light sources were employed: a xenon arc lamp/monochromator and a blue LED, λmax ) 460 nm (Panasonic, Digi-Key P390-ND). The arc lamp/monochromator provided a narrow wavelength range (∼10nm full width, half-maximum, fwhm) centered on the maximum absorbance of Ru(bipy)32+ while the LED gave a broad emission profile (∼63 nm fwhm) whose peak did not coincide with the maximum absorbance of Ru(bipy)32+ (Figure 1a). The choice of light source is discussed below. Light from either source was directly prism coupled into the ITO glass of the spectroelectrochemical cell with a Schott SF6 coupling prism (Karl Lambrecht). A high-viscosity refractive index standard fluid (Cargill, n ) 1.517) was used to span the gap between the prism and ITO glass. Light from the arc lamp was first passed through a 0.25-m monochromator (Bausch & Lomb) to select 450 nm before coupling into the ITO glass. After propagating through the ITO glass, light from either source was decoupled with another SF6 prism and focused onto a UV-enhanced photodiode (Photonic Detectors, Digi-Key PDB-V107). The signal from the detector was amplified with an op-amp follower-with-gain circuit and fed into a National Instru(9) Goodman, A. M. Appl. Opt. 1978, 17, 2779.
ments A/D, D/A card (PCI-MI0-16E-4) for further processing. The electrochemistry was performed with a conventional threeop-amp potentiostat built in our laboratory. All potential values were measured versus a Ag/AgCl reference electrode (3 M KCl). The excitation potential waveform was generated in code based on user-selected parameters and applied to the potentiostat by means of a D/A on the National Instruments card. A virtual instrument developed in Visual Basic and using controls from the National Instruments Component Works was employed to control the experimental parameters and also manipulate the data, which were ultimately plotted in Microsoft Excel.10 Absorbance spectra of Ru(bipy)32+ solutions and normal incidence absorbance spectra of the film-coated ITO glass were made with a diode array spectrophotometer (Hewlett-Packard 8453). The emission spectra of the arc lamp/monochromator and LED light sources were obtained with a 0.5-m spectrometer (SPEX 1870) using either a CCD detector (Spectrum One CCD model MTECCD-2000) or photomultiplier (Hamamatsu R928), respectively. Chemical System. The model analyte employed for this study was Ru(bipy)32+. Reversible electrochemistry accompanied by distinct spectral changes in the visible region made this couple ideal for our purposes.
Ru(bipy)32+ h Ru(bipy)33+ + e-
SiO2 film. This condition is analogous to a thin-layer electrochemical cell as all of the analyte was confined within ∼400 nm of the electrode surface. Unlike an electrochemical thin-layer cell, however, the boundary was not a “hard” surface. Typically, the outside wall of a thin-layer cell is glass or some other nonconductive substance on the far side of which are the reference and auxiliary electrodes. This results in large uncompensated solution resistance values (on the order of high kΩ) and therefore significant iR drop within the thin-layer cell. In our system, the attraction of the analyte for the sensing film was so strong that the film-solution interface behaves as an impermeable barrier to diffusion of the analyte out into bulk solution. Instead of the traditional nonconductive barrier, the boundary was the edge of the sensing film. The film used here had ionic conductance resulting in uncompensated resistance on the order of tens to hundreds of ohms.15 This comparatively low resistance simplifies the simulation relative to that for traditional thin-layer cells as described by Feldberg et al. in which iR compensation was a significant concern.11,16 Modeling a system of this sort via explicit finite difference simulation requires two modifications to the program and, in this instance, the decision to model only the activity of the analyte within the thin layer (i.e., the sensing film). The first and most obvious was the insertion of a diffusional barrier at a distance, L, from the working electrode. This imposes a boundary condition
( ) 14 470 at 450 nm) (transparent at 450 nm)
[∂C(x,t)/∂x]x)L ) 0
(1)
(E° ) 1.05 V vs Ag/AgCl) The general procedure for an experiment was as follows. The spincoated ITO glass, after soaking overnight in supporting electrolyte, was assembled into the sample cell, which was then filled with supporting electrolyte. The optics were aligned to maximize the throughput of light and the potential cycled to obtain the backgrounds for both the electrochemical and optical signals. A given concentration of Ru(bipy)32+ (1 × 10-5 or 5 × 10-6 M) was injected into the sample cell and allowed to partition into the film until equilibrium was reached, after which the given experiment was performed. Absorbance was calculated as the logarithm of the ratio of initial signal to the attenuated signal; therefore, variations in the optical properties between different pieces of ITO glass (which can be significant) canceled out.
in which C is the concentration at distance x from the electrode and time t after the start of the simulation. The second was to ensure that the film simulated was represented by a reasonable number of diffusional elements (boxes). In simulations of this sort, distance and time are related by
∆X ) x6∆tDmax
(2)
where Dmax is the diffusion coefficient of the fastest moving species. For a film whose thickness is L cm, the number of diffusional boxes, Nbox, is given by
Nbox ) L/x6∆tDmax
(3)
SIMULATION Simulations were performed with an explicit finite difference program based on the work of Feldberg.11 Originally this program was compiled in Fortran but has been modified over the years, and the version used here was compiled in Power Basic. Historically, use of this particular program has been exclusively for uncoated electrodes; one is concerned with semi-infinite diffusion of the analyte to the electrode surface.12-14 In these experiments, however, the only Ru(bipy)32+ present was that within the Nafion-
One can either fix the number of boxes to a preestablished value, such as 20, and allow the time interval to float or control the time interval and allow the number of boxes to float. Since the temporal response of the sensor was one of the parameters of interest, the latter approach was employed. The desired voltage range and sweep rate (for cyclic voltammetry) was chosen, which established the time interval, ∆t, by the constraint that data would be varied at 1-mV intervals in a cycle. The starting value of ∆t was subdivided by a factor of 10 and the number of boxes calculated.
(10) Slaterbeck, A. F. Ph.D. dissertation, University of Cincinnati, 1998. (11) Goldberg, I. B.; Bard, A. J.; Feldberg, S. W. J. Phys. Chem. 1972, 76, 25502559. (12) Ridgway, T. H.; Van Duyne, R. P.; Reilley, C. N. J. Electroanal. Chem. 1976, 67, 1-10. (13) Van Duyne, R. P.; Ridgway, T. H.; Reilley, C. N. J. Electroanal. Chem. 1976, 69, 165-180.
(14) Hanafey, M. K.; Scott, R. L.; Ridgway, T. H.; Reilley, C. N. Anal. Chem. 1978, 50, 116-37. (15) Kuwana, T.; Winograd, N. Spectroelectrochemistry at Optically Transparent Electrodes I. Electrodes Under Semi-Infinite Diffusion Conditions. In Electroanalytical Chemistry A Series of Advances; Bard, A. J., Ed.; Marcel Dekker: New York, 1974; Vol. 7, pp 1-78. (16) Goldberg, I. B.; Bard, A. J. J. Electroanal. Chem. 1972, 38, 313.
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This procedure was continued until the number of boxes in the film layer was at least 15. For sinusoidal excitations and potential steps, the desired number of samples and the period of the excitation were selected and then the time interval was subdivided as before. The optical penetration of the evanescent field into the solution was modeled as an exponential decay. Both the arc lamp/ monochromator and the LED were treated as monochromatic sources in the simulation. The merits of this assumption are discussed below. RESULTS AND DISCUSSION The three waveforms under investigation (square, triangle, sinusoid) each have their own advantages. Square wave is simple to implement instrumentally and to predict the response for; it also has been the most extensively investigated in spectroelectrochemical systems.12-27 It has the disadvantage of being the least selective (no potential screening), and it also has the highest energy requirements of the three. This latter fact can be seen by considering the Fourier transform of the three waveforms. A square wave of frequency ω can be constructed from a series of odd harmonic sine waves by
f(x) )
4
∑
[
1
π n)1,3,5... n
sin
]
nπx L
(4)
while a triangular wave is given by
f(x) )
1 2
-
4 2
π
∑
n)1,3,5...
[
1
n
2
cos
]
nπx L
(5)
From these relationships it can be seen that the square wave has the highest frequency content and the sine wave the lowest. Since double-layer charging is typically the dominant current path in trace analysis and current through a capacitor is given by I(ωt) ) Cdl∆E/ω, it is apparent that the square wave requires the most current and the sine wave the least. The triangular wave exhibits intermediate current requirements, allows discrimination among the responses from multiple couples within the potential window, and has a large body of published work relating to its character(17) Winograd, N.; Kuwana, T. J. Am. Chem. Soc. 1970, 92, 224-226. (18) Winograd, N.; Kuwana, T. Anal. Chem. 1971, 43, 252-259. (19) Winograd, N,; Kuwana, T. J. Am. Chem. Soc. 1971, 93, 4343-4350. (20) Heineman, W. R.; Kuwana, T. Anal. Chem. 1972, 44, 1972-1978. (21) Jan, C.; Lavine, B. K.; McCreery, R. L. Anal. Chem. 1985, 57, 752-758. (22) Kolb, D. M. UV-Visible Reflectance Spectroscopy. In Spectroelectrochemistry Theory and Practice; Gale, R. J., Ed.; Plenum Press: New York, 1988; pp 87-188. (23) Foley, J. K.; Korzeniewski, C.; Daschbach, J. L.; Pons, S. Infrared Vibrational Spectroscopy of the Electrode-Solution Interface. In Electroanalytical Chemistry A Series of Advances; Bard, A. J., Ed.; Marcel Dekker: New York, 1986; Vol. 14, pp 309-440. (24) Beden, B.; Lamy, C. Infrared Reflectance Spectroscopy. In Spectroelectrochemistry Theory and Practice; Gale, R. J., Ed.; Plenum Press: New York, 1988; pp 189-261. (25) Goelz, J. F.; Yacynych, A. M.; Mark, H. B.; Heineman, W. R. J. Electroanal. Chem. 1979, 103, 277-280. (26) Hansen, W. N.; Prostak, A. Phys. Rev. 1968, 174, 500-503. (27) Piraud, C.; Mwarania, E., Wylangowski, G.; Wilkinson, J.; O’Dwyer, K.; Schiffrin, D. J. Anal. Chem. 1992, 64, 651-655.
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istics, although not much of this relates to spectroscopic modes of detection, in the sense of quantitative analysis of a sample.15,28 The sine wave is the most energy efficient, but has been rarely considered in its larger amplitude analog to cyclic voltammetry. The application discussed here is distinctly different from that of Kuhr, who has employed a high-frequency sine wave.29 Only one application of a large amplitude sine wave at low frequencies was found in the literature: Weber was interested in its ability to provide a low-noise current response for electrochemical detection in chromatography.30,31 In some respects, it is the most difficult to synthesize via digital instrumentation, although it is not significantly worse than the approximation of a ramp by a staircase as in most computer-controlled cyclic voltammetry. Aspects of the digital synthesis of sinusoidal waveforms for use in ac voltammetry have been discussed.32,33 The main consequence is a slightly higher true energy requirement due to the small amount of higher frequency components arising from the approximation. When the electrochemical response for a reversible system is plotted as signal vs potential, the results are qualitatively similar to those obtained from the triangular waveform. In addition to the issue of power consumption, selection of the excitation waveform should also be based on time efficiency. Under the conditions of a continuously repeating excitation potential waveform, a steady-state condition is approached, allowing the use of signal-averaging techniques to reduce random noise contributions to the monitored optical response. The three waveforms under investigation have been shown to approach steady state at different rates; square was the most rapid, followed by sinusoidal, and then triangular.7 Considering both factors that contribute to the desirability of an excitation potential waveform, the large-amplitude sinusoidal waveform appears to be a good candidate for use in spectroelectrochemical sensing. Given the limited theoretical background for its use in electrochemistry, there are fundamental questions that arise concerning its use. Explicit finite difference simulation is a tool that has long been used to investigate electrochemical phenomena.11-13,16,34-38 While one can often write the exact equations describing the diffusion of analytes and their electrochemistry at the electrode surface, solving these equations in closed form can range from difficult to impossible. Instead, a mathematical model of the electrochemical system can be constructed whose behavior follows algebraic laws derived from the equations that describe diffusion and mass (28) Kuwana, T.; Strojek, J. W. Discuss. Faraday Soc. 1968, 45, 134-144. (29) Singhal, P.; Kawagoe, K. T.; Christian, C. N.; Kuhr, W. G. Anal. Chem. 1997, 69, 1662-1668. (30) Long, J. T.; Weber, S. G. Anal. Chem. 1988, 60, 2309-2311. (31) Long, J. T.; Weber, S. G. Anal. Chem. 1990, 62, 2643-2645. (32) Anderson, J. E.; Bond, A. M. Anal. Chem. 1981, 53, 1394-1398. (33) Anderson, J. E.; Bond, A. M. Anal. Chem. 1982, 54, 1575-1578. (34) Feldberg, S. W. Electroanal. Chem. 1969, 3, 199. (35) Feldberg, S. W. In Computers in Chemistry and Instrumentation; Mattson, J. S., Mark, H. B., MacDonald, H. C., Eds.; Marcel Dekker: New York, 1972; Vol. 2, Chapter 2. (36) Prater, K. B. In Computers in Chemistry and Instrumentation; Mattson, J. S., Mark, H. B., MacDonald, H. C., Eds.; Marcel Dekker: New York, 1972; Vol. 2, Chapter 8. (37) Maloy, J. T. In Computers in Chemistry and Instrumentation; Mattson, J. S., Mark, H. B., MacDonald, H. C., Eds.; Marcel Dekker: New York, 1972; Vol. 2, Chapter 9. (38) Maloy, J. T. In Laboratory Techniques in Electroanalytical Chemistry, 2nd ed.; Kissinger, P. T., Heineman, W. R., Eds.; Marcel Dekker: New York, 1996; Chapter 20.
Table 1. Concentration of Ru(bipy)32+ in Film film concentration (M) initial solution concn (M)
difference
normal incidence
Faraday’s law
average
1 × 10-5 5 × 10-6
0.169 0.087
0.158 0.108
0.170 0.087
0.166 0.094
transport within the electrochemical cell. By use of this model, the behavior of the experimental system is simulated, allowing for more fundamental investigations of the electrochemistry than would otherwise be possible. Calculation of Electrochemical Parameters for Simulation. The first step in modeling the spectroelectrochemical response of the sensor was to define the parameters that characterize the electrochemical behavior of the analyte. Table 1 lists the concentrations determined for Ru(bipy)32+ within the film. Table 2 lists the relevant film parameters and the values assigned to model the electrochemical and optical response of Ru(bipy)32+. Concentration of Ru(bipy)32+ within the Sensing Film. The first value determined was the concentration of Ru(bipy)32+ within the sensing film. Three different experiments were employed to obtain this concentration. The given concentration of Ru(bipy)32+ was injected into the sample cell and allowed to soak overnight to ensure complete equilibration with the sensing film (∼12-h soak time). After equilibrium was reached, a sample of the Ru(bipy)32+ solution was removed from the cell and its absorbance spectrum obtained. This spectrum was compared to that of the initial solution. The concentrations of each solution were calculated using Beer’s law. The difference in the two concentrations was assumed to be the quantity of Ru(bipy)32+ that had partitioned into the film. Relating this concentration to the volume of solution in the sample cell (8.0 mL) gave the number of moles within the film. The concentration of Ru(bipy)32+ within the film was then obtained by dividing this number of moles by the volume of the film, determined by multiplying the geometric surface area of the electrode exposed to solution (8.4 cm2) by the thickness of the film (400 nm). The resulting concentrations are given in Table 1 under the column heading “difference”. For both concentrations, an increase by a factor of ∼104 over the initial solution concentration was observed. Ru(bipy)32+ has been shown both in the literature39 and by experiments in this laboratory to partition tenaciously into Nafion films; after hours in supporting electrolyte, negligible amounts of Ru(bipy)32+ will leach out of the film. This attribute allowed the next two methods of determining the concentration of Ru(bipy)32+ within the sensing film. After removing the Ru(bipy)32+ solution from the sample cell for the previous experiment, the cell was filled with supporting electrolyte and chronoamperometry performed. The potential was stepped from 0.9 V, Ru(bipy)32+ present in the film, to 1.3 V, generating Ru(bipy)33+. Then 1.3 V was applied until the current response decayed to ∼0 mA. Since the sample cell was filled with supporting electrolyte, there was no contribution from solution species to the current measured. The potential was then stepped back to 0.9 V and the current response monitored until it again decayed to ∼0 mA. The current plots (39) Shi, M.; Anson, F. C. Anal. Chem. 1997, 69, 2653-2660.
obtained were integrated and the moles of Ru(bipy)32+ present in the film calculated from the charge obtained using Faraday’s law. The amount of Ru(bipy)32+ was then converted to concentration of Ru(bipy)32+ in the film using the film volume. The concentrations are given in Table 1 under the column heading “Faraday’s law”. Finally, once all of the experiments were complete, the ITO glass was removed from the sample cell and normal incidence absorbance spectra were obtained. After subtracting the absorbance of the “empty” sensing film on the ITO glass (obtained prior to the beginning of this study), the concentration was calculated with Beer’s law using the thickness of the film, 400 nm, for the optical path length. The concentrations are listed in Table 1 under column heading “normal incidence”. The correlation among the three methods proved to be quite good; therefore the average of the three values was used for the concentration of Ru(bipy)32+ within the film. Diffusion Coefficient of Ru(bipy)32+ within the Sensing Film. Several mechanisms by which Ru(bipy)32+ diffuses within Nafion films have been proposed in the literature.39-43 Discerning the relative contributions of these mechanisms within the NafionSiO2 blends was not the focus of this study; however, an effective diffusion coefficient was required to simulate the sensor response. Several approaches were used to determine experimentally this effective diffusion coefficient for Ru(bipy)32+ within the film. First, the Randles-Sevcik (R-S) equation was applied to cyclic voltammograms obtained from the same film-coated ITO glass used above. The R-S equation defines the cyclic voltammetry peak current as
ip ) (2.69 × 105)n3/2AD1/2C*ν1/2
(6)
where ip is the peak current, n is the number of electrons in the process, A is the surface area of the electrode, D is the diffusion coefficient of the analyte, C* is the bulk concentration of the analyte, and ν is the scan rate. The area was assumed to be the geometric area of the working electrode exposed to solution (8.4 cm2), the concentration was provided by the previous calculations, and the scan rate for all of these studies was 10 mV/s. The resulting diffusion coefficients for both concentrations are shown in Table 2. These values were cross-checked by applying the Einstein equation to the i vs t curves obtained from the chronoamperometry experiments described in the section above. The Einstein equation defines the diffusion coefficient as
D ) (∆x)2/2∆t
(7)
where, for this study, ∆x was the thickness of the sensing film, 400 nm, and ∆t was the time necessary to oxidize the Ru(bipy)32+ within the film after the potential step was applied. The values calculated here agree with those from the R-S equation (Table 2). (40) Buttry, D. A.; Anson, F. C. J. Electroanal. Chem. 1981, 130, 333-338. (41) Rubinstein, I.; Bard, A. J. J. Am. Chem. Soc. 1981, 103, 5007-5013. (42) White, H. S.; Leddy, J.; Bard, A. J. J. Am. Chem. Soc. 1982, 104, 48114817. (43) Martin, C. R.; Rubinstein, I.; Bard, A. J. J. Am. Chem. Soc. 1982, 104, 48174824.
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Table 2. Electrochemical Parameters for Simulation solution concn (M) 1×
10-5
5 × 10-6
film parameter diffusion coeff transfer coeff R heterogeneous rate const, k diffusion coeff transfer coeff R heterogeneous rate const, k
calculated 10-11
4.46 × (Randles-Sevcik) 5.10 × 10-11 cm2/s (Einstein) cm2/s
5.57 × 10-11 cm2/s (Randles-Sevcik) 5.14 × 10-11 cm2/s (Einstein)
simulated 4.6 ×
10-11
cm2/s (best fit)
0.5 (best fit) 2.5 × 10-6 cm/s (best fit) 5.8 × 10-11 cm2/s (best fit) 0.5 (best fit) 2.5 × 10-6 cm/s (best fit)
Figure 2. Comparison of simulated and experimental current responses to triangular excitation waveform. (a) Response for Nafion-SiO2coated ITO electrode exposed to 1 × 10-5 M Ru(bipy)32+. (b) Response for Nafion-SiO2-coated ITO electrode exposed to 5 × 10-6 M Ru(bipy)32+. Parameters for simulation listed in Tables 1 and 2. Potentials measured vs Ag/AgCl reference electrode. Triangular excitation waveform scanned at 10 mV/s.
A significant assumption implicit in the use of eqs 6 and 7 was that experimental conditions exist such that diffusion was semiinfinite; no boundary conditions were placed upon the diffusion of analyte from bulk solution and simple diffusion was the only mechanism by which analyte was transported to the electrode surface (i.e., an uncoated electrode and no migration). The use of these equations was justified by several factors. Even though the Ru(bipy)32+ was confined within the film, under the conditions employed, the shape of the voltammograms was quite similar to that in bulk solution at bare ITO (Figure 1b). Also, while the Ru(bipy)32+ was confined within the Nafion-SiO2 film and at a concentration for which migration cannot be ruled out, the concentration of sulfonate sites within the film (calculated to be ∼5 M) was such that this effect should be minimized.44 As a final means by which to establish the credibility of the diffusion coefficients used in this study, the calculated numbers were compared to published values for Ru(bipy)32+ in pure Nafion film-coated electrodes. A search of the literature provided values for the effective diffusion coefficient within pure Nafion films ranging from 3 × 10-11 to 2.7 × 10-9 cm2/s.39-43 This suggests that the values obtained by the R-S and Einstein calculations are reliable. The remaining parameters required for simulation (the electrontransfer coefficient, R, and the heterogeneous rate constant, k) were obtained by “best fit” of the simulated current-potential curves to experimental data. The final parameters obtained from the calculations and subsequent simulations are shown in Table 2. Figure 2 compares the simulated electrochemical response to
the experimental current response for both concentrations in the film-coated electrodes when using the values listed in Table 2. The optimal values obtained by simulation still did not provide a perfect match to the experimental results. The peak currents are quite similar, but the shapes of the curves are slightly different. The small differences observed are most likely due to complications from iR drop within the cell and also the nonequipotential of the ITO, which has been documented as causing nonlinear deviations in the current response of ITO.45 This conclusion was further supported by the correlation of the simulation data with the electrochemical response of a well-behaved electrode (gold disk), which was quite good (data not shown). While efforts were made to minimize the iR effects during the experiment, the inherent problems with ITO can only be avoided by changing the configuration of the electrochemical cell or the electrode material, neither of which was an option in this case. To obtain a better fit of the simulated response, the program will need to be modified to account for both contributions. Since the peak values were in agreement, this modification was left for future study. Simulation of Optical Response with Arc Lamp. Using the same parameters listed in Table 2, the optical responses to the triangular, sinusoidal, and square waveforms were simulated. These simulated responses were compared to the experimental attenuated total reflection (ATR) response when using the xenon arc lamp/monochromator (450 nm light selected) and a NafionSiO2-coated ITO slide equilibrated with 1 × 10-5 M Ru(bipy)32+, Figure 3. The simulator program requests values for the wavelength of light employed, selected here as 450 nm, and also for
(44) Rubinstein, I. J. Electroanal. Chem. 1985, 188, 227-244.
(45) Strojek, J. W.; Kuwana T. J. Electroanal. Chem. 1968, 16, 471-483.
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Table 3. Comparison of Simulated and Experimental Data
waveform simulation experiment
Figure 3. Comparison of simulated and experimental ATR responses to three excitation waveforms. All data from Nafion-SiO2coated ITO electrode exposed 1 × 10-5 M Ru(bipy)32+: (a) square, τ ) 40 s; (b) triangle, ν ) 10 mV/s; (c) sine, 10mV/s equivalent. Arc lamp source, 450 nm selected. Simulated wavelength, 450 nm. Simulated film thickness, 400 nm. Potentials measured vs Ag/AgCl reference electrode.
the thickness of the sensing film, selected here as 400 nm. For each figure, the initial potential was 0.9 V vs Ag/AgCl. For the square waveform (Figure 3a), one period was 80 s; the potential was stepped out from 0.9 to 1.3 V for 40 s, oxidizing the Ru(bipy)32+. Then the potential stepped back to 0.9 V for the remaining 40 s, converting the Ru(bipy)33+ formed in the forward step into Ru(bipy)32+. For the triangular (Figure 3b) and sinusoidal (Figure 3c), waveforms the potential was scanned at 10 mV/s to 1.3 V vs Ag/AgCl where the Ru(bipy)32+ was oxidized to Ru(bipy)33+. The potential was then scanned back to 0.9 V, reducing
square triangle sinusoid square triangle sinusoid
∆A arc lamp 0.497 0.406 0.413 0.497 0.403 0.421
LED
cycles to steady state
0.278 0.244 0.248 0.278 0.244 0.265
2 3 5 5 15 10
the Ru(bipy)33+ formed in the forward scan back to Ru(bipy)32+. The simulated responses matched reasonably well with the experimental data when the arc lamp/monochromator was employed. The best fit was obtained with the square wave excitation (Figure 3a). The deviations observed may be a consequence of the same factors discussed regarding the electrochemical current responses. In addition to concerns addressed for the electrochemical simulation, the optical simulation must also account for the penetration depth of the evanescent wave. The evanescent wave was simulated as an exponentially decaying field, penetrating 450 nm (400 nm through the sensing film and 50 nm of supporting electrolyte solution). This should be equivalent to the experimental conditions. If the profile of the experimental evanescent field does not conform to the ideal exponential decay, then there will be deviations in the simulated optical responses. Given the known electrochemical deviations between simulation and experimentation, no qualitative remarks can be made regarding the differences observed in the shapes of the experimental and simulated optical responses. Even with these differences, the magnitude of the simulated response correlates quite well with the experimental values for all three waveforms (Table 3). Steady-State Response. A crucial aspect of the simulation involves its ability to predict the response of the sensor approaching steady state. One significant advantage of spectroelectrochemical sensing is the ability to ensemble average the optical responses from multiple cycles, thereby reducing noise and allowing a lower limit of detection.7 To implement ensembleaveraging techniques, the sensor response must approach steady state. As repeated cycles of each excitation potential waveform are applied, the simulated system should approach steady state in the same number of cycles as the experimental system. For the experimental system, this approach to steady state was dependent upon the type of excitation waveform employed and the scan rate of the waveform.7 Figure 4 compares the simulated optical responses to those of the experimental system for 20 cycles of the triangular, sinusoidal, and square excitation potential waveforms. Cycles 1, 5, 10, 15, and 20 are shown. The square waveform was the first to arrive at steady state (Figure 4a,b). In both the experimental and the simulated systems, nearly imperceptible changes occur between cycles 1 and 5. After cycle 5, the response was the same for each successive cycle. Experimentally the sinusoidal waveform was the second most rapid to approach steady state (Figure 4e,f). For the experimental system, only slight differences were observed between cycles 1 and 5. After cycle 5, further changes were not readily discerned from the plots. The triangular waveform was the slowest to Analytical Chemistry, Vol. 72, No. 22, November 15, 2000
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Figure 4. Comparison of experimental (a, c, e) and simulated (b, d, f) ATR responses to square, triangular, and sinusoidal excitation waveforms approaching steady state. Waveforms were continuously cycled for 20 periods. Cycles 1, 5, 10, 15, and 20 are shown. All data from NafionSiO2-coated ITO electrode exposed to 1 × 10-5 M Ru(bipy)32+. Scan rates: square, τ ) 40 s; triangle, ν ) 10 mV/s; sinusoid, 10 mV/s equivalent. Arc lamp source, 450 nm selected. Simulated wavelength, 450 nm. Simulated film thickness, 400 nm. Potentials measured vs Ag/AgCl reference electrode.
approach steady state (Figure 4c,d). For the experimental system, noticeable differences in the optical response were evident between cycles 1 and 5. Between cycles 5 and 10, there were still some very small changes, after which the responses were identical. The simulated system approached steady state more rapidly; after cycle 5, subsequent cycles provided the same response. The simulator underestimated the number of cycles required to approach steady state. The simulator also predicted that the triangular waveform would approach steady state more rapidly 5574 Analytical Chemistry, Vol. 72, No. 22, November 15, 2000
than the sinusoidal, which was not the case experimentally. The results are listed in Table 3. These differences are difficult to resolve in the figures as shown; some of the differences between successive cycles with the arc lamp/monochromator source were only observed when the data plots in Excel were magnified much greater than shown here. The discrepancies between simulated and experimental results are likely due to the model used for the evanescent wave penetration into the film. Simulation of Optical Response with LED. As shown in Figure 1, the LED was not an ideal light source for Ru(bipy)32+
used. This difference arises from the nonideal interaction of the Ru(bipy)32+ with the LED emission. Despite this, a calibration curve of Ru(bipy)32+ obtained with the LED was shown to be linear,7 but the effective molar absorptivity was ∼44% smaller than would be expected. The optical data from the simulation were therefore scaled down 44% when compared to the LED. The agreement between the simulated response and the experimental response obtained with the arc lamp/monochromator was much better than that with the LED for the same concentration of Ru(bipy)32+; compare Figure 3 with Figure 5. This was almost certainly due to the nature of the light employed in the experiments. The arc lamp after passing through the monochromator provided a narrow bandwidth of light whereas the LED emitted a range of ∼150 nm. As discussed above, the experimental absorbance behavior when using the LED was significantly different than when the arc lamp/monochromator was employed. This resulted in differences in the simulations as well; the intensity profile of the evanescent wave resulting from such a range of wavelengths was certainly more complex than that simulated. After simple scaling of the simulated data to account for the smaller effective molar absorptivity of Ru(bipy)32+ with the LED wavelengths, the amplitude of the absorbance changes in the simulated response for the square (Figure 5a) and triangular (Figure 5b) waveforms agreed quite well with the experimental values (Table 3). The simulated response to sinusoidal excitation (Figure 5c) was different both in shape and magnitude. As yet no clear explanation exists for this discrepancy.
Figure 5. Comparison of experimental and simulated ATR responses to square, triangular, and sinusoidal excitation waveforms. All data from Nafion-SiO2-coated ITO electrode exposed to 1 × 10-5 M Ru(bipy)32+. Scan rates: square, τ ) 40 s; triangle, ν ) 10 mV/s; sinusoid, 10mV/s equivalent. LED source. Simulated wavelength, 450 nm. Simulated film thickness, 400 nm. Potentials measured vs Ag/ AgCl reference electrode
detection; the peak emission from the LED did not coincide with the maximum absorbance of the Ru(bipy)32+. Since this type of light source is a realistic option for sensing applications that require a small, portable unit and, consequently, the simulator program needs to account for its behavior, it was included in this study. For a given Ru(bipy)32+ concentration within the sensing film, the experimental absorbance values obtained with the LED are significantly less than when the arc lamp/monochromator was
CONCLUSIONS The spectroelectrochemical sensor under investigation can be successfully modeled by use of an explicit finite difference simulation. The simulation program provides a reasonably good match to the experimental results. As discussed in a previous publication,7 the sinusoidal waveform is the most desirable for this type of sensor due to its time and energy efficiency. The simulation of this waveform, however, raised several issues which warrant further investigation. The discrepancies in the shape of the electrochemical current response need to be addressed. The addition of iR compensation to the simulation may resolve these differences. Also, if a light source such as the LED is to be used in the sensor, modification of the optical parameters within the simulation will need to be made to account for the rather wide emission profile. With these issues resolved, this simulation program should provide a reliable way to investigate the response of the sensor to more complicated systems such as those containing electrochemical and optical interferences or those in which there are chemical kinetics with which to contend. ACKNOWLEDGMENT This work was funded by the Environmental Management Science Program of the Department of Energy, Office of Science under Grant DE-FG07-96ER62311.
Received for review December 21, 1999. Accepted August 15, 2000. AC991460H
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