Recently introduced digital signal processing (DSP) can be used, instead of two ... of the ac optical signal at the electrochemical modulation frequency must be ...
Digital Signal Processing for Step-Scan Phase and Electrochemical Potential Double-Modulation Fourier Transform Infrared Spectrometry DM ITRI A. BREVNOV, ELIZA HUTTER, and JANOS H. FENDLER* Center for Micro-Engineered M aterials, University of New Mexico, Albuquerque, New M exico 87131 (D.A.B.); and Center for Advanced Materials Processing, Clarkson University, Potsdam, New York 13699-5814 (E.H., J.H.F.)
Step-scan double-modulation (phase and electrochemical potential) Fourier transform infrared (FT-IR) spectro metry provides both spectroscopic and dynamic information about faradaic reactions. Recen tly introduced digital signal processing (DSP) can be used, instead of two lock-in ampli ers, for the optical signal demodulation at two modulation frequencies. In order to establish the m erits of double-modulation FT-IR spectrom etry with DSP, spectro-electro chem ical experiments are performed in the attenuated total re ection con guration and with the commonly used ferri/ferr ocyanide redox couple. Because of a large potential drop associated with the uncompensated resistance, a satisfactory signal-to-noise ratio for the alternating curren t (ac) optical measurem ents is obtained only with the employment of positive feedback compensation. In this arrangement, the amplitude of electrochem ical m odulation is suf ciently large to convert a signi cant fraction of the reduced form to the oxidized form and back to the reduced form. Large amplitude ac voltamm etry demonstrates that the phase of faradaic admittance at the form al potential is approximately 458 at 2.00 Hz. In addition, these experiments allow for calculation of the interfacial ac potential. This variable is needed for the normalization of the in-phase and the quadrature spectra in order to overcome the problem associated with the iR u drop. Because of the integral relationship between the faradaic current and the electrom odulation re ectance coef cient, the phases of electrom odulation re ectance coef cient with respect to the interfacial ac potential are expected to be 2458 and 1358 for the reduced and oxidized forms, respectiv ely. H owever, dynamic information from double-modulation FT-IR spectrometry is available only if demodulation at the electrochem ical potential modulation frequency is performed with respect to a de ned phase. Because of an unde ned demodulation phase implemented in the current version of DSP software, step-scan double-modulation FTIR spectrom etry with DSP is suitable only to provide spectroscopic information. In order to overcome this limitation, the demodulation of the ac optical signal at the electrochem ical modulation frequency must be synchronized in phase with the ac potential modulation applied to the electroch emical cell. Index Headings: Fourier transform infrared spectro scopy; FT-IR spectroscopy; Digital signal processing; DSP; Step scan; Electrochem ical potential; Double modulation.
INT RODUCTIO N Fourier transform infrared (FT-IR ) spectroelectrochemistry is a powerful method for the in situ investigation of the electrode/electrolyte interface since it permits the identi cation of the electrochemically active species. 1– 6 The m ain issue in adopting FT-IR spectrometry for electrochemical problems is the strong solvent absorption. The majority of spectroelectrochemical FT-IR experiReceived 30 June 2003; accepted 7 October 2003. * Author to whom correspondence should be sent. E-mail: fendler@ clarkson.edu.
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ments have been perform ed in the external re ection con guration, which minimizes the solvent absorption with the employment of a thin-layer cell.7,8 However, FT-IR spectrometry methods can also be applied for the electrochemical interface by using the internal attenuated total re ection (ATR) con guration.9 The total internal re ection element is usually an IR-transparent prism m ade from a high-refractive-index material (m ost often silicon or germanium), which can be coated with a thin layer of metal (such as gold, platinum, or copper) to function as the working electrode. In this case, the solvent absorption is suppressed because the IR beam propagates through the prism to the electrolyte solution by evanescence and only to a distance determined by the penetration depth (for the silicon prism , used here, the penetration depth is 394 nm at 2000 cm 2 1 ). The IR beam must have suf cient energy to penetrate through the thin metallic layer. Therefore, internal ATR spectroelectrochemistry is, of necessity, limited to metallic electrodes, which are suf ciently thin to permit the penetration of the IR beam. The electrode/electrolyte interface has been conventionally characterized with rapid-scan FT-IR spectrometry. This is accomplished by coadding scans at each of two direct current (dc) potentials and calculating the difference spectrum. This m ethod is called subtractively no rm alized in terfacial F T-IR spectrom etr y (S N IF TIRS). 10,11 The sensitivity of FT-IR m easurements can be improved through the application of external modulation of the spectroscopic signals. One way to achieve better sensitivity is to employ polarization modulation. 12 In this case, the polarization of the incident light is modulated with a photo-elastic modulator at approximately 37 kHz. By measuring the external re ection at the grazing angle from a mirror’s surface, re ection/absorption spectra of thin lms on metal surfaces are obtained due to the different absorption of s- and p-polarized light. An alternative method to attain better sensitivity for the electrode/electrolyte interface is to m odulate the amounts of IR-absorbing and electrochemically active species. This is achieved by applying electrochemical potential modulation at approximately 5–50 Hz. Dispersive IR experiments with potential modulation (EMRIS) were pioneered by Bewick and co-workers 12 and developed further by others. 13 However, the adaptation of this m odulation for a conventional, rapid-scan FT-IR spectrometer is not feasible because the low m odulation frequency overlaps with the Fourier frequencies generated by the moving mirror in the interferom eter. This problem has been overcome by the development of step-scan FT-IR
0003-7028 / 04 / 5802-0184$2.00 / 0 q 2004 Society for Applied Spectroscop y
APPLIED SPECTROSCOPY
spectrometers. 8 In the step-scan mode, the moving mirror is translated from one position to another. In addition, it is possible to dither the piezo-mounted xed mirror at each step point while data is being collected. This oscillatory m ovement is called ‘‘phase modulation’’. Demodulation of the optical signal at a phase modulation frequency results in a reference (background) interferogram. Demodulation of the optical signal at an electrochemical potential m odulation frequency results in two interferograms (in-phase and quadrature) that re ect changes in IR absorbance caused by potential modulation. Simultaneous acquisition of these interferograms improves signal-to-noise ratio and reduces the m easurement time. Inphase and quadrature difference spectra are determined after perform ing the Fourier transformation of interferograms and calculating a ratio of resulting responses. Because the step-scan double-modulation (electrochemical potential and phase modulation) FT-IR provides spectroscopic information unobtainable from electrochemical methods, it is a useful approach for investigating electrochemical interfaces. In the past, demodulation of the spectroscopic signal at two m odulation frequencies was realized with two lock-in ampli ers. However, the recent introduction of digital signal processing (DSP) by Digilab and other manufacturers of FT-IR spectrometers allowed researchers to substitute external hardware (lock-in ampli ers) with comm ercial software. It has been shown that DSP simpli es experimental setups and data analysis.14 Stepscan double m odulation (phase and m echanical stretching) combined with DSP was applied to investigate the stress-induced, rheological properties of polymers.14 Subsequent to demodulation, the interferograms carried both spectroscopic and dynamic inform ation about the elasticity of polymers. In a very similar fashion, step-scan double-modulation (phase and electrochemical potential) FTIR spectrometry can provide both spectroscopic (to identify the electrochemically active species) and dynamic information (to estimate the rate of faradaic reactions on the electrode/electrolyte interface). The rst objective of the present work was to demonstrate the feasibility of employing DSP to process the step-scan double-modulation (phase and electrochemical potential) ATR FT-IR data. The second objective was to develop and apply a reliable and simple procedure to account for the iR u drop in the electrochemical cell, which decreases the magnitude of the alternating current (ac) potential modulation and distorts dynamic information accessible from step-scan double-modulation FT-IR experiments. The electrochemical and ATR FT-IR measurements, both based upon electrochemical potential m odulation, independently result in two complex variables: the faradaic admittance and electromodulation re ectance coef cient. A correlation between these variables allows us to determine if the kinetic status of faradaic reactions can be assessed from step-scan double-modulation ATR FT-IR experiments combined with DSP. TH EORY In the following paragraphs, a brief theoretical description will be given to demonstrate how to extract dynamic inform ation about the rates of faradaic reactions from ac
optical measurements. It has been shown that the most accurate representation of the ac optical signal, originating from electrochemical potential modulation, is the electromodulation re ectance coef cient. 15 In the time domain, the electromodulation re ectance coef cient is de ned by Eq. 1: x(l, E dc ) 5 1/R 3 dR /dE inter
(1)
where R is the background optical signal, dR is the ac optical signal at the m odulation frequency, and dE inter is the interfacial ac potential de ned by Eq. 2: dE inter 5 dE measured 2 iR u
(2)
The interfacial ac potential is the total cell ac potential from the potentiostat electrometer, dE measured , corrected for the iR u drop, where R u is the electrochemical cell uncompensated resistance. Normalization to the interfacial ac potential is important for obtaining accurate dynamic information. The ac optical measurements are norm ally performed with respect to the phase of the total cell ac potential, whereas the driving force for the ac optical signal is the interfacial ac potential. Electrochemical potential modulation may result in two independent phenomena at the electrode/electrolyte interface. M odulation of the absorption coef cients with the electric eld (electrochromism) constitutes the rst phenomenon. The second is the m odulation of the amount of electrochemically active species (ured , for example) due to faradaic reactions. In the latter case, the ac optical signal arises only if the difference between the absorption coef cients of the reduced and oxidized forms (Dk 5 k red 2 k oxi ) is not zero. Both of these phenomena are combined in Eq. 3: x(l, E dc ) ; (dk /dE ) u 1 Dk(E dc ) 3 (dured /dE )
(3)
In the absence of electrochromism, Eq. 3 can be written in the following manner, taking advantage of the fact that the amount of the reduced (or oxidized) form is proportional to the integral of the faradaic current: x(l, E dc ) ; Dk (E dc ) 3 (du red /dE ) 5 Dk (E dc ) 3
E
(dI faradaic /dE ) dt /(n 3 F )
(4)
The electromodulation re ectance coef cient is de ned in the frequency domain as X (l, E dc ) and connected with x(l, E dc ) via the Fourier transformation as shown in Eq. 5: X (l, E dc ) ; Dk(E dc ) 3 Y faradaic /(n 3 F 3 jv)
(5)
Therefore, in the frequency dom ain the phase angle between X (l, E dc ) and faradaic admittance, Y faradaic , is 908. The correlation between X (l, E dc ) and Y faradaic is important and can be established under two conditions. First, the ac optical signal must be measured with respect to the phase of the total cell ac potential and subsequently numerically normalized to the interfacial ac potential. Second, corrections for non-faradaic elements (e.g., R u and double-layer capacitance) m ust be performed in order to extract Y faradaic from the measured total cell admittance data. These corrections can be easily performed in the frequency domain assum ing that the generic equivalent circuit includes three elements: R u, double-layer capacitance (or constant phase APPLIED SPECTROSCOPY
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element (CPE), which is frequently used instead of the do uble-layer capacitan ce), an d farad aic im p ed ance. Therefore, independent electrochemical measurem ents of Y faradaic and spectrophotometric measurem ents of X (l, E dc ) provide a fram ework to establish the validity of optical measurem ents based upon ac potential modulation. The procedure for data acquisition and analysis advocated here was reported for UV-VIS electrore ectance experiments performed with a redox species covalently attached to the electrode surface. The expected 908 phase relationship between the faradaic admittance and electromodulation re ectance coef cient was con rm ed experimentally.15 Given the same effect of electrochemical potential modulation on the ac optical signal in both UV-V IS and IR regions, the 908 phase relationship (in the absence of electrochromism) is expected to hold in the IR region as well. An alternative approach to analysis of the ac optical signals resulting from ac potential m odulation has been developed by Sagara and Niki16 for UV-V IS electrore ectance and applied by Osawa 17 for potential m odulation step-scan FT-IR spectroscopy. In this method, dR /R data (not normalized for the interfacial ac potential) are plotted in the complex plane (quadrature vs. in-phase) at a single dc potential and compared with the re ectomittance. This quantity is claimed to correspond to the faradaic admittance, regardless of the fact that the equations used to describe re ectomittance include non-faradaic elements such as R u and the double-layer capacitance. It has been shown that the customary procedure in the frequency domain analysis of electrochemical data, which includes the separation of faradaic impedance from nonfaradaic elements and the analysis of faradaic impedance alone, is also applicable for analysis of ac optical measurements.15,18 In contrast to the method adopted by Osawa, normalization of dR /R to the interfacial ac potential and the elucidation of X (l, E dc ) to represent infrared frequency domain signals allows for the direct comparison of the X (l, E dc ) phase with the faradaic admittance phase. As a result, data analysis of ac optical measurements based upon the ac potential modulation is signi cantly simpli ed. In addition, the approach developed by Sagara and Niki requires explicit assumptions about the faradaic impedance. For example, for surface attached redox species, the faradaic impedance is modeled as a series com bination of a resistor and a capacitor. However, simple m odels are known to describe inadequately the faradaic reactions. For example, in the presence of kinetic heterogeneity, the faradaic impedance cannot be accurately modeled with a single resistor and a single capacitor.19 M oreover, their method assumes that the interfacial dielectric property is modeled as a capacitor, but not as CPE. In contrast, the procedure reported here does not make any assumptions about either the faradaic impedance or dielectric interface. Thus, this procedure is more universal and can be applied for analysis of ac optical measurem ents for any electrochemical system. In conclusion, the simplicity of iR u drop correction for analysis of the ac optical signals and the absence of any assumption about the faradaic impedance m ake the approach applied here advantageous. 186
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F IG . 1. Schematics of the spectroelectrochemical cell used. Details are provided in the Experimental section.
EXPERIMENTAL A three-electrode cell with a Ag/AgCl reference electrode and a platinum wire counter electrode was used for both electrochemical and ATR FT-IR experiments (Fig. 1). A layer of gold (10 –15 nm) deposited on a silicon prism served as a working electrode. Right-angle silicon prisms were purchased from M acrooptica (M oscow, Russian Federation). Gold was deposited onto the largest face of the prism in a thermal evaporator (Edwards Auto 306 Vacuum Coater) for 1–2 min, at a pressure of 10 2 6 mB and a current of 4.0– 4.4 A. The thickness of the gold lms was m easured with the quartz crystal microbalance incorporated into the evaporator. The deposited gold lm was stable for a period of approximately 6–7 h, which was long enough to complete the whole set of spectroelectrochemical experiments. The gold-coated silicon prism was clamped to the electrochemical cell and placed on a precision rotator in the infrared beam path (Fig. 1). The electrode area, restricted by a rubber O-ring, was 0.785 cm 2 . The position of the electrochemical cell was adjusted by a precision rotator such that the angle of incidence of the infrared beam was 458. The liquid-nitrogen-cooled m ercury cadmium telluride (MCT) detector was positioned in such a way that the angle between the incident and re ected beam was 908. A ll spectroelectro ch em ical ex perim ents w ere p erformed in an aqueous 0.50 M NaF solution containing 25 mM each of K 4Fe(CN) 6 and K 3Fe(CN) 6 . Cyclic voltammetry (CV) experiments were performed with an EG&G 273 potentiostat. The uncompensated resistance was determined with the same potentiostat and an EG& G 5301 lock-in ampli er. These measurements were m ade twice at 10 kHz, with an ac potential amplitude of 20 mV and at two different dc potentials (0 and 500 mV vs. Ag/AgCl). The typical values obtained were 250 –270 Ohms. AC voltammetry (ACV) experiments were performed with the same EG& G potentiostat, lock-in ampli er, and an HP 8116A signal generator. The signal generator was set to apply an ac potential with a frequency of 2.00 Hz and amplitude of 330 mV (peak to peak) to the potentiostat external input. Both the ac potential and the ac current were sequentially measured
with the lock-in ampli er by manually switching a BNC cable between the potential and current outputs on the po tentiostat fro nt pan el. T he m easured adm ittance, Y measured , was calculated as a ratio between the ac current and the ac potential. These m easurements were repeated over a chosen dc potential window between 0 and 700 mV vs. Ag/AgCl in order to collect a suf cient number of points. The iR u drop was partially compensated with positive feedback compensation typically set at 160 Ohms, which corresponded to approximately 60 –65% compensation. Higher values of the positive feedback compensation resulted in potentiostat overload and therefore could not be employed. For analysis of ACV data, the uncompensated part of the resistance (typically 90 – 100 Ohms) was taken into account by further data processing as shown in the Results and Discussion section (Eq. 6). This correction was necessar y because the potential sampled from the front panel of the 273 potentiostat was only corrected for the iR u drop speci ed with the applied positive feedback compensation (60 – 65%). All ATR FT-IR experiments (rapid-scan and step-scan) and data processing were perform ed with a Digilab 7000 spectrometer and Win-IR Pro Version 3.1 software and with s-polarized light. The s-polarized light was chosen because of its higher ability to penetrate through metallic lms in comparison with the p-polarized light.5 The rapid-scan experiments were typically perform ed with the following settings: 20 KHz speed, 5 KHz lter, an undersampling ratio of 2, 4 cm 2 1 resolution, sensitivity of 1, aperture 2 cm 2 1 at 2000 cm 2 1 , and 256 scans to coadd. The step-scan double modulation was performed by using the digital signal processing m ode, DSP(2), incorporated into Win-IR Pro Version 3.1 software.14 The software allowed the user to choose only the sample modulation frequency (which is equivalent to the electrochemical potential modulation frequency), and the two other variables were automatically selected. W hen the sample modulation frequency was chosen to be 2.00 Hz, the step speed was set to 0.1 Hz and the phase modulation frequency to 400 Hz. The phase modulation was provided internally by the spectrometer. Prior to step-scan FT-IR experiments, the centerburst location was determined with the rapid-scan experiments and stored by the software. Static background (phase modulation) and dynamic (in-phase and quadrature) interferogram s were recorded simultaneously as a single, asymmetric scan with a spectral resolution of 8 cm 2 1 . A single step-scan run lasted approximately 3 h. All interferograms were processed with the triangle apodization function. Interferogram s resulting from the electrochemical potential modulation were processed with the ‘‘stored phase’’ method. The inphase phase m odulation interferogram was processed with the automatic phase correction. The phase correction inform ation was recorded to a le. This le was utilized to perform the phase correction for in-phase and quadrature electrochemical potential modulation interferograms. Before the step-scan double-modulation experiments, DSP software calibration was perform ed in order to minimize the electronic delay in acquired interferograms. The DSP calibration was completed correctly because the value of a centerburst in the in-phase background interferogram was two or three orders of magnitude greater than that of a centerburst in the quadrature
background interferogram. Therefore, only the in-phase background single-beam spectrum was used to normalize the computed dynamic in-phase and quadrature singlebeam spectra. The modulation of electrochemical potential was performed with an HP 8116A signal generator (which was set in the external burst m ode), with a modulation frequency of 2.00 Hz, modulation amplitude (peak to peak) of 330 m V, and 19 bursts. The HP 8116A signal generator was synchronized with the step of the spectrometer. This was accomplished by using the BSTEP output of the analog expansion connector on the rear panel of the spectrometer as an external trigger for the HP 8116A signal generator. Both signals, the BSTEP output and waveform generated by the HP 8116A signal generator, were m onitored with an oscilloscope. The number of bursts was chosen in such a way that the time period during which the electrochemical potential modulation was applied (19 cycles of 2.00 Hz) was less than the time period associated with each step of the spectrometer (10 s). In this case, no trigger input from the spectrometer to the HP 8116A was missed and the waveform (electrochemical potential modulation) had a constant phase from one step of the spectrometer to the next. At each step, the optical signal was sampled and digitized 3750 times with a time resolution of 2400 ms over 9 s. The output of the HP 8116A function generator was set to a sinusoidal waveform used as the external input to the EG& G 273 potentiostat. The potentiostat was set to apply a constant dc potential equal to the formal potential of the K 4Fe(CN) 6 /K 3 Fe(CN) 6 redox couple (260 m V vs. Ag/ AgCl). The positive feedback compensation was employed in exactly the same way as for ACV experiments. RESULTS AND DISCUSSION Penetration of the infrared beam through the layer of gold, deposited onto the silicon prism, was established by verifying the presence of water peaks in an aqueous 0.50 M NaF solution containing 25 mM of K 4 Fe(CN) 6 and 25 mM of K 3Fe(CN) 6 by rapid-scan FT-IR measurements (in the electrochemical cell, shown in Fig. 1). The background data was collected in air, without electrolyte. The presence of two water peaks around 1650 cm 2 1 and 3410 cm 2 1 indicated that the gold layer was thin enough to observe the attenuated total re ection (ATR ) phenomenon. The absence of unambiguous peaks due to the ferri/ ferrocyanide ions resulted in low signal-to-noise ratio. However, peaks at 2037 cm 2 1 for the ferrocyanide and at 2115 cm 2 1 for ferricyanide ions appeared (Fig. 2a) when higher concentrations of the redox couple (100 m M and more) were used. Cyclic voltamm etry (CV) experiments were performed next to establish the continuity and conductivity of the gold layer. The CV curves collected without positive feedback compensation were severely distorted because of the iR u drop. The high iR u drop resulted from both large faradaic currents (a large electrode area and high concentrations of ferro/ferricyanide) and a large uncompensated resistance (thin-layer gold electrode). Norm ally, the uncompensated resistance originates solely from the electrolyte solution. The thin-layer electrodes may also constitute an additional resistance in the electrochemical APPLIED SPECTROSCOPY
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F IG . 3. Cyclic voltammogram of an aqueous 0.5 M NaF air-saturated solution in the presence of 25.0 m M K 4Fe(CN) 6 and 25.0 m M of K 3 Fe(CN) 6 in the electrochemical cell shown in Fig. 1. The experiment was performed with positive feedback compensation of 160 Ohms and at a scan rate of 100 mV/s.
F IG . 2. (a) Rapid scan, (b) step-scan in-phase, and (c) quadrature FTIR spectra collected in an aqueous 0.5 M NaF air-saturated solution in the spectroelectrochem ical cell shown in Fig. 1. Spectrum a was obtained in the presence of 100 mM K 4 Fe(CN) 6 and 100 mM of K 3 Fe(CN) 6 . The spectra shown in b and c were obtained in the presence of 25.0 m M K 4 Fe(CN) 6 and 25.0 m M of K 3 Fe(CN) 6. The peaks at 2037 cm 2 1 and 2115 cm 2 1 correspond to the ferrocyanide and ferricyanide ions, respectively. The in-phase and quadrature spectra were recorded at an electrochem ical modulation frequency of 2 Hz, amplitude of 330 mV, and positive feedback compensation of 160 Ohms.
cell. Although the thin m etallic lm m ay produce a distribution of ohmic resistances along the electrode surface, this effect is averaged out because the whole electrode surface is sampled in the electrochemical measurements. 20 Thus, the distributed m etallic resistances can be effectively represented as a lumped resistive element. Because the electrolyte and electrode resistances are connected in series, their combination is m odeled as a single uncompensated resistance in both electrochemical and FT-IR experiments. The CV experiments perform ed with positive feedback compensation (60 – 65% compensation) resulted in better-de ned CV peaks, with the peak separation being approximately 450 –500 m V as shown in Fig. 3. This large peak separation indicates that even with positive feedback compensation the uncompensated resistance still dominates the current response and signi cantly increases the peak separation. The peak separation of approximately 60 mV is expected for a reversible redox couple. Regardless of the fact that the high electrode resistance results in the large peak separation, the thin lm gold electrodes still demonstrate metallic characteristics. This statement is validated by the occurrence of the reversible faradaic reaction: both cathodic and anodic faradaic currents appear in Fig. 3. During preparation of this m anuscript, it was brought to our attention that thick (200 nm) and, consequently, less resistive gold lms on silicon were used as electrodes in ATR FT-IR experi188
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ments. 21 However, our FT-IR experiments with thick gold lms demonstrated little penetration of the IR radiation to the electrolyte solution. This decrease might result from the presence of a layer of silica on the prism’s surface. The objective of this project was to employ doublemodulation ATR FT-IR with DSP for a freely diffusing redox couple in the diffusion layer. Thus, the surfaceenhanced IR absorption effect, which is usually restricted to the species adsorbed on thin m etallic surfaces, was not investigated. Although CV is a fast and widely used m ethod, ACV provides more quantitative inform ation on kinetics of faradaic reactions.15 Being complementary to electrochemical impedance spectroscopy, ACV combines a dc potential scan and a single-frequency ac potential perturbation. A generic equivalent circuit that is frequently used to model a three-electrode electrochemical cell consists of three elements: the faradaic impedance, Z f, the constant phase element (CPE), which is used instead of the double-layer capacitance, and the uncompensated resistance, R u.15 For freely diffusing electrochemically active species, the faradaic impedance can be decomposed further as a series combination of the Warburg (diffusion) element and the charge transfer resistance. The analysis of ACV data was based upon the equivalent circuit described above. Figure 4a demonstrates the measured admittance, Y measured . The interfacial admittance, Y inter , a parallel combination of CPE and Z f, was determined by Eq. 6, where R u represents the uncompensated part of the uncompensated resistance: Y inter 5 [(Y measured ) 2 1 2 R u] 2 1
(6)
The faradaic admittance, Y , was found after subtraction of the CPE admittance from Y inter . The CPE admittance was found by linear interpolation from 2100 mV to 700 mV. Y inter and Y faradaic are shown respectively in Figs. 4b and 4c. The phase of faradaic admittance (a ratio of the real and imaginary components) carries accurate information on the standard heterogeneous rate faradaic
F IG . 5. Interfacial ac potential calculated according to Eq. 2 from ac voltammetr y performed in an aqueous 0.5 M NaF solution in the presence of 25.0 mM K 4Fe(CN) 6 and 25.0 m M of K 3 Fe(CN) 6 with a modulation frequency of 2 Hz, am plitude of 330 mV, and positive feedback compensation of 160 Ohms. The uncompensated part of uncompensated resistance was 90 Ohms.
F IG . 4. AC voltammograms of an aqueous 0.5 M NaF solution in the presence of 25.0 mM K 4 Fe(CN) 6 and 25.0 mM of K 3 Fe(CN) 6 : (a) measured total cell admittance, (b) interfacial admittance, and (c) faradaic admittance. ACV was performed with a m odulation frequency of 2 Hz, amplitude of 330 m V, and positive feedback compensation of 160 Ohms.
constant only if the linear relationship between the ac current and ac potential is satis ed. This requirement means that ACV experiments are to be performed with a small-amplitude ac potential perturbation (e.g., 5–10 mV RM S). For consistency with following step-scan doublemodulation ATR FT-IR experiments, ACV experiments were performed with a large-amplitude ac potential (233 mV RM S). Therefore, under our experimental conditions, the linear relationship did not hold and the faradaic admittance data could not be used to accurately estimate the rate of faradaic reactions. Nevertheless, dynamic information (faradaic admittance and, as will be shown be-
low, the interfacial ac potential) available from ACV experiments was valuable and, in fact, necessary to validate that correct dynamic inform ation m ight be extracted from step-scan double-modulation ATR FT-IR m easurements. Figures 2b and 2c demonstrate the in-phase and quadrature spectra resulting from the electrochemical potential modulation. Although the two peaks at 2037 cm 2 1 and 2115 cm 2 1 are easily distinguished from the background in the spectra reported here, the initial step-scan doublemodulation ATR FT-IR experiments suffered from a low signal-to-noise ratio. These experiments demonstrated that a large amplitude ac potential modulation (330 m V) alone was not suf cient enough to produce a satisfactory optical response to electrochemical potential modulation. Careful data examination revealed that the interfacial ac potential (the driving force for the ac optical signal) was appreciably sm aller than the ac potential applied to the electrochemical cell because of a high iR u drop. Therefore, all subsequent experiments were perform ed with positive feedback compensation. Only in this arrangement was the interfacial ac potential suf ciently large to convert a signi cant fraction of ferricyanide to ferrocyanide and back to ferricyanide during the electrochemical potential m odulation cycle. It is important to stress that the ac optical signal and, therefore, signal-to-noise ratio, are proportional to the extent of this conversion. It is instructive to determine the interfacial ac potential as a function of dc potential during ac voltamm etry experiments perform ed with positive feedback compensation. Figure 5 demonstrates the interfacial ac potential calculated according to Eq. 2, where R u represents the uncompensated part of the resistance. Because of a large faradaic current, the interfacial ac potential is signi cantly depressed around the formal potential even with the highest achievable value of positive feedback compensation. Figure 5 emphasizes three points. First, the interfacial ac potential can be easily calculated from electrochemical data. Second, ac voltamm etry experiments APPLIED SPECTROSCOPY
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F IG . 7. Vector diagram that demonstrates the phase delays among the faradic admittance and electromodulation re ection coef cients (theoretical and experimental).
F IG . 6. (a) In-phase and (b) quadrature components of the electromodulation re ection coef cient calculated according to Eq. 1.
even with a large amplitude (330 mV) and large uncompensated resistance produce reliable data because the magnitude of the interfacial ac potential decreases to 20 mV around the formal potential. As a result, the halfwidths of the faradaic waves (Fig. 4c) are only about 130 mV, signi cantly narrower than those in the case of a severe disturbance of the electrochemical system by large ac potential modulation. 22 For a one-electron electrochemically reversible reaction, a half-width of 90 mV is expected when ac voltammetry experiments are performed with less than 10 m V ac potential modulation. 23 Third, Fig. 5 shows that the phase of the ac interfacial potential (the driving force for the ac optical signal) is signi cantly different from the phase of the ac potential measured from the potentiostat front panel, which was always set to zero at all dc potentials. This phase difference m eans that ac optical signals m easured with respect to the phase of total cell ac potential do not produce reliable phase information because of a severe problem with iR u drop. As discussed in the Theory section, this problem is overcome by normalization of in-phase and quadrature spectra, dR /R, (Figs. 2b and 2c) to the inphase and quadrature interfacial ac potential determined at the formal potential. Figure 5 shows that at the formal 190
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potential the interfacial ac potential is approximately equal to (17 2 i 3 12) mV. The calculated in-phase and quadrature electromodulation re ectance coef cients are shown in Figs. 6a and 6b. Comparison of Figs. 2b and 2c and Figs. 6a and 6b shows that the in-phase and quadrature dR /R and in-phase and quadrature X (l, E dc ) carry different phase information. W hile the in-phase component is signi cantly larger than the quadrature component in Figs. 2b and 2c, both components are almost equal in Figs. 6a and 6b. As argued in the Theory section, this phase difference results from the fact that the determination of X (l, E dc ) allows for elimination of the iR drop effect from the ac optical measurem ents. Therefore, a direct comparison of the X (l, E dc ) phase with the faradaic admittance phase is possible. In the absence of electrochromic effects, the integral relationship between faradaic admittance and the electromodulation re ectance coef cient provides a framework to compare the phase difference between these two complex variables. This integral relationship escaped attention in the majority of previously reported double-modulation FT-IR experiments. At the form al potential, the phase of faradaic admittance was approximately 458. Therefore, according to Eq. 5 the phases of the electromodulation re ectance coef cient were expected to be 2458 and 1358 for the reduced and oxidized forms, respectively. However, the phases of electromodulation re ectance coef cients experimentally determined from analysis of Figs. 6a and 6b were approximately 428 and 21288 for the reduced and oxidized forms, respectively. The vector diagram (Fig. 7) represents ve complex variables: faradaic admittance and theoretically expected and experimentally determined electromodulation re ectance coef cients for the reduced and oxidized forms. Figure 7 shows that the phase delay between experimental electromodulation coef cients of reduced and oxidized form s is 1708, close to the one (1808) expected for the electrochemically active species undergoing a reversible faradaic reaction.6 At the same time, the phases of theoretically expected and experimentally determined electromodulation re ectance coef cients do not coincide. In order to understand this discrepancy, it is necessary to explain the implementation of digital demodulation in ‘‘Win-IR-Pro, Version 3.1’’ software. Step-scan double-
modulation ATR FT-IR experiments result in dynamic inphase and quadrature spectra, which obviously carry information about a delay of faradaic admittance with respect to the interfacial ac potential. However, these dynam ic m easu rem en ts are on ly m eaningfu l if the demodulation of ac optical signal is performed with respect to a known phase of ac potential m odulation, which is usually the phase of ac potential applied to the electrochemical cell. In the current version of the software, digital demodulation is performed at the frequency as speci ed in the step-scan DSP(2) menu and with respect to a constant (the HP 8116A signal generator is synchronized with each step of the spectrometer) but unde ned and arbitrarily chosen phase. Originally, the DSP(2) option of ‘‘Win-IR-Pro, Version 3.1’’ software was designed and im p lem ented fo r d ou ble-m od ulation m ech an ical stretching experiments. In this con guration, a reference material, which is assumed to have an instantaneous response to m echanical stretching, is rst employed to calibrate the FT-IR system with the DSP(2) calibrate option. The phase delay of the reference m aterial is measured and all sequential dynamic m easurements with other materials are referenced to that phase delay. Unfortunately, this approach, which is well adopted for m echanical stretching, is not applicable for spectroelectrochemical experiments. In order to overcome this limitation of current DSP implementation, the demodulation of ac optical signal at the electrochemical modulation frequency has to be synchronized in phase with the ac potential m odulation applied to the electrochemical cell. Because of the arbitrarily chosen phase for demodulation, extraction of dynamic information from step-scan double-modulation ATR FT-IR experiments is impossible under the experimental conditions reported in this paper. However, the absence of dynamic inform ation from FT-IR spectrometry with DSP is not a severe limitation because dynamic inform ation is readily available from electrochemical experiments based upon the electrochemical potential modulation. Under conditions of a sm all-amplitude ac potential modulation and suf ciently high modulation frequency, the phase of faradaic admittance less than 458 for freely diffusing redox species can be used to determine the standard heterogeneous rate constant. Extraction of kinetic inform ation from both electrochemical and optical measurements requires accurate correction for the iR u drop. In the form er case, R u m ust be subtracted from total cell impedance to determine the interfacial admittance (Eq. 6). In the latter case, iR u must be subtracted from the m easured ac potential to determine the interfacial ac potential (Eq. 2). Therefore, from the theoretical point of view, both frequency domain electrochemical and step-scan double-modulation FT-IR measurements have the same applicability on the short time scale. However, from the practical point of view, a low signal-to-noise ratio and unde ned reference phase in step-scan double-modulation FT-IR experiments with DSP make the frequency domain electrochemical measurements (ac voltammetry) more suitable for determination of the kinetic status of faradaic reactions. The major advantage of FT-IR spectrometry is that this m ethod is capable of identifying species participating in faradaic reactions. In addition, step-scan double-modulation FTIR measurem ents show better sensitivity than rapid scan
measurem ents. Therefore, electrochemical and step-scan do uble-m o du latio n AT R F T-IR m easurem ents, both based upon electrochemical potential modulation, m ay be considered as two methods that are complementary to each other. CONCLUSION We performed step-scan double-modulation (phase and electrochemical potential) ATR FT-IR spectrometry experiments with DSP to investigate faradaic reactions. To our knowledge, this is the rst report on the application of step-scan double-modulation FT-IR m ethods, with digital signal processing, for the analysis of electrochemical reactions. In comparison with previously reported similar step-scan double-modulation FT-IR experiments, with lock-in ampli ers, DSP simpli ed the experimental setup, data acquisition, and analysis. The high iR u drop imposed a signi cant limitation on the extent of inter-conversion of the redox species during the electrochemical potential modulation cycle. Therefore, a satisfactory signal-tonoise ratio in ac optical measurements was obtained only with the employment of positive feedback compensation. Because digital demodulation of the ac optical signal was performed with respect to an arbitrary phase, the dynamic inform ation was not available from DSP FT-IR spectrometry experiments. This problem can be solved by synchronizing the demodulation of the ac optical signal with the phase of ac potential m odulation applied to the electrochemical cell. Regardless of this instrumentation limitation, the electromodulation re ectance coef cient, X (l, E dc ), is suggested to be a more useful quantity than dR /R for representation of the ac optical data in step-scan doublemodulation FT-IR spectrometry. Normalization of dR /R to the interfacial ac potential and elucidation of X (l, E dc ) allow a facile way to correct for iR u drop and direct comparison of the X (l, E dc ) phase with the faradaic admittance phase. Both frequency domain electrochemical and step-scan double-modulation FT-IR measurem ents have the same theoretical applicability on the short time scale because of the limitation imposed by the iR u drop. However, the kinetic status of faradaic processes is more readily available from electrochemical measurem ents based upon electrochemical potential modulation because of a low signal-to-noise ratio and unde ned reference phase in step-scan double-modulation DSP FT-IR experiments. ACK NOW LEDGM ENTS We thank the U.S. Departm ent of Energy for supporting this work. E. Hutter thanks the National Science Foundation for nancial support (Grant No. INT-0206923) for her contribution to this work. We thank David Drapcho (Digilab) for valuable discussions regarding how to implement step-scan double-m odulation FT-IR spectrometry and Prof. Harr y O. Finklea for critical reading of this manuscript. 1. W. N. Hansen, ‘‘Internal Re ection Spectroscopy in Electrochemistry’’, in Optical Techniques in Electrochemistry, R. H. Muller, Ed. (John Wiley and Sons, New York, 1973), vol. 9, pp. 1–60; J. Bauhofer, in Electrochemical Applications of Internal Re ection Spectroscopy, F. M . Mirabella, Ed. (Marcel Dekker, New York, 1993), 1st ed., vol. 15, pp. 233–253; R. J. Gale, Spectroelectrochemistry: Theory and Practice (Plenum Press, New York, 1988); B. Beden and C. Lamy, in Spectroelectrochemistry: Theory and Practice, R. J. Gale, Ed. (Plenum Press, New York, 1988).
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