ANALYTICAL CHEMISTRY, VOL. 50,
during the 0.6-ps retrace time of the OMA detector. Otherwise the conditions were identical to those employed for the repetitive-pulse spectrum. The S / N of the single shot spectrum, 3.5 for peaks C and H, is the expected factor of 36 poorer than for the repetitive-pulse spectrum, and approximately a factor of 8 poorer than the CW-scanned spectrum. Nevertheless, the main features, peaks C, E, H, and perhaps F, are visible in the single-shot spectrum. The acquisition time for the single-shot spectrum is a flat factor of 7 X 10" shorter than that for the CW-scanned spectrum in Figure 1. Considering the S/Ndeficit suffered by the single-shot spectrum, allowing the CW spectrum to be acquired 64 times faster than that in Figure 1 to give S / N equal to the single-shot spectrum, this represents a real improvement of ten orders of magnitude over the conventional Cary 82 spectrometer in the temporal acquisition of comparable spectra. We feel that the S / N of the single-shot spectrum can be improved by a factor of three to ten by improving the present scattering geometry, without changing other experimental parameters. Compared to the previous TR3 studies ( 4 , 5 ) ,the present report represents a conspicuous improvement in S/N for repetitive-pulse TR3 for comparable time resolution, and an improvement of two orders of magnitude in time resolution over the only previously reported single-shot TR3 spectra ( 5 ) . We are presently pursuing in these laboratories applications of TR3 and related techniques to the dynamics of heme protein ligation and electron transfer reactions.
LITERATURE CITED (1) T. G. Spiro and T. M. Loehr in "Advances in Infrared and Raman Spectroscopy", Vol. 1, R. J H. Chrk and R. E. Hester, Ed., Heyden, London,
NO. 9, AUGUST 1978
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1975,Chapter 3. (2) Wiilim H. Woodruff and George H. Atkinson, Anal. Chem., 48,186 (1976). (3) William H. Woodruff and S.Farquharson in "New Applications of Lasers in Chemistry", G. M. Hieftje, Ed., American Chemical Society, Washington, 1978. in preparation. (4) A. Campion, J. Terner, and M. A. El-Sayed. Nature (London), 265,659 \1.1- ,~. 1 , .7 7 )
(5) R. Wilbrandt, P. Pagsberg, K . B. Hansen, and C.V. Weisberg, Chem. Phys. Len., 39, 538 (1976). (8) M. Bridoux, A. Deffontaine, and C. Reiss, C. R . Hebd. Seances Acad. Sci.. Ser. C . 282. 771 (19761. (7) M. Delhaye in "Proceedings of the 5fh InternationalConference on Raman Spectroscopy", E. E. Schmid et al., Schuiz, Freiburg, 1976, p 747. (8) W. L. Peticolas, ref. 7,p 163. (9) K. B. Lyons, H. L. Carter, and P. A. Fleury in "Light Scattering in Solids", M. Balkanski. R. C. C. Leite. and S.P. Porto. Ed.. Flammarion Sciences. Paris, 1976,' 0 244 (IO) D. L. Jeanmarie, M. R. Suchanski, and R. P. Van Duyne, J . Am. Chem. Soc., 97, 1699 (1975). (1 1) D. L. Jeanmarie and R. P. Van Duyne, J . Am. Chem. SOC.,98,4029 (1976).
William H. Woodruff* Stuart Farquharson Department of Chemistry, The University of Texas a t Austin, Austin, Texas 78712 RECEIVED for review February 27, 1978. Accepted May 19, 1978. The authors are grateful for support of this work by NSF Grant CHE77-15220, by Research Corporation Cottrell Grant 7557, and by an instrumental setup grant from The University of Texas a t Austin. This work was presented a t the Symposium on New Applications of Lasers in Chemistry, 175th National Meeting, American Chemical Society, Anaheim, California, March 14, 1978.
Fast Fourier Transform Based Interpolation of Sampled Electrochemical Data Sir: The expanding use of on-line, computerized digital data acquisition in scientific measurements has many demonstrated benefits. However, one apparent disadvantage of this measurement approach is the fact that the acquired data are sampled, rather than continuous. If sampling rates cannot be made sufficiently large, resolution problems can arise which are not encountered with continuous analog data. For example, precise identification of magnitude and position of peak-type responses, as well as recognition of peak-shoulder combinations, in chromatography, spectroscopy, and electrochemistry may be hindered by inadequate resolution of sampled data. These difficulties can be overcome somewhat by drawing a smooth curve through the sampled data. However, this form of manual interpolation is too subjective to provide a n adequate solution. A more objective interpolation approach, based on a firm mathematical foundation, is needed. One of the most appealing of these is Fourier domain (FD) interpolation, which has been successfully implemented in processing spectroscopic data by Griffiths (I), and Horlick and Yuen (2). F D interpolation is a convenient, simple, and mathematically rigorous technique whereby the F D spectrum of the data array to be interpolated is computed, extended by a factor of 2" (n = positive integer) by "zero filling" ( I ) , and inverse Fourier transformed. The resulting interpolated array contains 2" times the number of points in the original array. The procedure validity rests upon the assumption that the original data array, while possibly providing insufficient resolution to satisfactorily serve its intended purpose, is adequate to define its F D spectrum. 0003-2700/78/0350-1391$01,00/0
Assuming that an on-line minicomputer is the element which controlled the original data sampling, it is convenient to implement the F D interpolation approach using the FFT algorithm as the basis for data domain-Fourier domain transforms. Electrochemical measurements represent a field where sampled data interpolation can be quite useful in assisting evaluation of parameters such as peak magnitude and position, peak full-width a t half-height, half-wave potentials, peak separations, and the like, yet we are unaware of published work in this area. Because FFT software or hardware already is required in FFT faradaic admittance measurements ( 3 , 4 ) the , F D interpolation concept is particularly convenient and appealing in this context, especially when the ac cyclic voltammetric ( 5 ) and rapid dropping mercury electrode (6) modes are invoked with rapid dc potential scan rates. If F D interpolation can be shown to be precise and accurate in an electrochemical context, the concept of reducing total measurement time and computer memory requirements by acquiring fewer-than-normal points along the dc potential, time, or frequency axes can be entertained. Rather than increasing data density by special sampling techniques ( 7 ) ,which put significant demands on measurement repeatability, the data density may be enhanced by FD interpolation. Because of the foregoing considerations, we have evaluated the F D interpolation procedure in the context of faradaic admittance voltammograms, polarograms, and frequency spectra, as well as dc cyclic voltammetry. We believe these data types to be reasonably representative of the response types encountered 'C 1978 American Chemical
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ANALYTICAL CHEMISTRY, VOL. 50, NO. 9, AUGUST 1978
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Figure 1. Fourier domain interpolation of FFT ac cyclic voltammogram. System: 8.0 X l o 4 M TMPD' at Pt-0.1M tetrabutylammonium perchlorate, CH,CN interface, 25 'C. Applied: Pseudo-random, oddharmonic ac waveform (3) with 1.5 mV/frequency component, 40 components, superimposed on a staircase dc scan with triangular envelope whose scan rate = 150 mV/s. Dc potentials are in volts vs. Ag/0.010 M AgCIO,, CH,CN. Measured: faradaic admittance magnitude at 488 Hz, obtained with a single measurement pass without FFT digital filtering (39 other frequency components also measured, but not shown); (A) original data only, (E) original and interpolated (Xp3) data, (C) interpolated data only, and (D) continuous curve constructed by drawing straight lines between interpolateddata points (Figure IC). Notation: 0, = original sampled data, forward and reverse scans, respectively: 0 ,x = interpolated data, forward and reverse scans, respectively
*
Figure 2. Effects of reducing original admittance polarogram aata density on accuracy of FD interpolation. System: Hg-aqueous 1.O M Na2S0,, 1.0 X M Cd(I1) interface, 25 OC. Applied: Same as Figure 1, except 34 frequency components, staircase dc scan synchronized to rapidly dropping mercury electrode of 0.25-s drop life, and dc potentials are vs. Ag/AgCI (sat'd NaCI). Measured: 10 replicate average of in-phase faradaic admittance magnitude at 5 8 5 . 9 Hz., without FFT digital filtering; (A) original 30 sampled data points, and interpolated ( X 2 3 ) result, (8)15 points from original data set and interpolated (Xp4) result, (C) 10 points from original sampled data and interpolated ( X 2 7 result, (D) 8 points from original sampled data and interpolated ( X z 5 ) result. Notation: 0 = original data, o = interpolated data
in electrochemical relaxation measurements. Some typical results are presented here. T h e software routine we have written to invoke FD interpolation utilizes the F F T algorithm. I t also allows one to invoke FFT digital filtering (8) to smooth the data sets prior t o (or after) interpolation. Whether or not digital filtering is invoked, the software fits a polynomial to several points on each extremity of the original data array and subtracts this
polynomial from the original array before interpolation and/or filtering. This data domain modification ensures that the data domain array will begin and terminate a t zero magnitude, with a negligible first derivative, effectively suppressing truncation error (8-10) which can arise in either the filtering or interpolation step. A suitably interpolated version of the polynomial is added to the interpolated data domain array as the final step, producing the enhanced version of the original data
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Table I, Parameters Obtained from Interpolated Data of Figure 2 no. of sampled data points in initial array
interpolation factor
peak dc potential, V
peak admittance, mho x lo4
peak full-width at half-height,
3 Oa 30 15
x 20 x 23 x 24
-0.544 -0.5442 - 0.5444 -0.5444 -0.5437
8.80 8.827 8.828 8.753 8.284
47 47.4 48.7 48.8 53.9
10 a
x 25
x 25 Best estimates from original data. 8
mV
t
600
Figure 3. Effect of FFT digital filtering and interpolation on a noisy in-phase faradaic admittance polarogram. System, applied, and measured as in Figure 2, except frequency is 195.3 Hz., 0 = original sam led data, * = original data after digital fikering, and + = interpohted ( X 2 ), filtered data
P
array. When a data domain set does not contain 2n ( n = integer) points, as required by the F F T algorithm, the data set is zero-filled to the nearest 2"-point value, following the polynomial subtraction routine. As long as preceded by polynomial subtraction, zero-filling causes no errors. The program is interactive, allowing the operator to enter appropriate parameters for the data domain polynomial modification, the optional F F T filtering, and the F F T interpolation. We call attention to a recently presented interpolation algorithm ( 2 2 ) which is equivalent to the F F T approach described here, but uses significantly fewer calculations. However, significant time savings are not realized with the small transforms used in this work. Figure 1 shows interpolation results with some ac cyclic faradaic admittance voltammograms on the TMPD+/TMPD couple (TMPD = tetramethylphenylenediamine) a t a Pt electrode in a nonaqueous electrolyte. An essentially perfect match between the interpolated and original data trend results (Figure l B ) , and identification of the forward and reverse scan "crossover point" (22),peak potentials, and peak magnitudes is significantly assisted by the FD interpolation (Figure IC). Points are sufficiently close-spaced in the interpolated voltammogram that the ultimate interpolation, a continuous curve, can confidently be generated by the expedient of a straight line fit between adjacent data points (Figure 1D). An important question when considering use of FD interpolation is how many sampled data points are required to accurately define the data array FD spectrum. This question is addressed in Figure 2, where a relatively narrow two-electron reduction faradaic admittance polarogram is considered. The original polarogram, composed of 30 sampled data points, is interpolated to 232 points in Figure 2A. Figure 2, B-D show results of deleting data points from the original data set, followed by interpolation to approximately 232 points. Casual examination of the results clearly indicates that beginning with only 8 data points (Figure 2D) leads to qualitative distortion of the polarogram. However, such distortion is not evident for the 15 and 10 sampled data point cases (Figure 2, B and C). Indeed, careful inspection of admittance magnitude printouts indicates that, although systematic error in the
+--+ 0 1
- 0 62
-0 60
-0.56
-0.56
- 0 5q
-0.52
POTENTIAL/VOLT
Figure .4. Effect of FFT digital filtering and interpolation on a typical cot I$ polarogram. System and applied as in Figure 2. Measured: cot I$ vs. dc potential at 585.9 Hz., where (A) uses same notation as Figure 3, and (B) is continuous curve obtained as in Figure 1D
.
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/
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FD interpolation applied to a d c cyclic voltammogram. System, applied, and measured as in Figure 1, except dc component measured, (A) shows original (0)and interpolated (0)data, and (B) is a continuous curve obtained as in Figure I D Figure 5.
admittance magnitude becomes detectable with 10 points, the FD interpolation results with this sparse data set still yield satisfactory peak parameters (Table I). Figures 1 and 2 eschew F F T digital filtering because the raw data are relatively noise-free. This is not the case in Figure 3, which shows results of combining digital filtering and
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ANALYTICAL CHEMISTRY, VOL. 50, NO. 9, AUGUST 1978
0
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The results shown in Figures 1-6 demonstrate that FD interpolation of electrochemical data can be performed with precision, and to the point of allowing generation of a continuous analog readout, the ultimate interpolation. Ease of identification of peak potentials, widths, and magnitudes are greatly assisted. When F F T digital filtering and FD interpolation are combined, rather substantial data enhancement can be realized, allowing one to recover from a relatively noisy and/or sparse data array quite satisfactory electrochemical response parameter values. The concept of reducing sampled data density to conserve computer memory and/or measurement time, and recovering the lost resolution via FD interpolation is supported by the above results.
ACKNOWLEDGMENT We are indebted to Richard Schwall for developing the polynomial modification software. LITERATURE CITED
Figure 6. Application of FD interpolation on admittance spectral data. System and applied as in Figure 2. Measured: peak admittance vs. u1/2 . Notation: as in Figure 4
interpolation when a distressingly noisy admittance polarogram is presented. The peak potential (-0.545 V) and full-width at half-height (49 mV) obtained from the filtered, interpolated data are in excellent agreement with the values obtained from the more reliable raw data of Figure 2 and Table I. Figures 4 and 5 illustrate typical interpolation results for a cot 4 polarogram and a dc cyclic voltammogram, respectively. Figure 6 depicts an attempt to apply the FD interpolation procedure to admittance spectra data, where the sampled data array is not equally spaced along the abscissa, as the F F T algorithm assumes. Because of this, interpolated data point separations along the abscissa are nonuniform. Nevertheless, this not-strictly-valid procedure yields satisfactory results, including an only slightly flawed continuous spectral response (Figure 6B).
P. R. Griffiths, Appl. Spectrosc., 29, 11 (1975). G. Horlick and W.K. Yuen, Anal. Chem., 48. 1643 (1976). D. E. Smith, Anal. Chem., 48, 221A (1976). R. J. Schwall, A. M. Bond, R. J. Loyd, J. G. Larsen, and D. E. Smith, Anal. Chem., 49, 1797 (1977). A. M. Bond, R. J. Schwall, and D. E. Smith, J Electroanal. Chem., 8 5 , 231 (1977). R. J. O’Halloran, J. C. Schaar, and D. E. Smith, Anal. Chem., 50, 1073 (1978). S. C. Creason, R. J. Loyd. and D. E. Smith, Ana/. Chem., 44, 1159 (1972). J. W.Hayes, D. E. Glover, D. E. Smith, and M. W.Overton. Anal. Chem., 45, 277(1973). G. Horlick, Anal. Chem., 44, 943 (1972). R. de Levie, S. Sarangapani, P. Czekaj, and G. Benke, Anal. Chem., 50. 110 (1978). M L Forman, Appl O p t , 16, 2801 (1977) A M Bond, R J O’Halloran I R u m , and D E Smith, Anal Chem , 48, 872 (1976)
Roger J. O‘Halloran Donald E. Smith* Department of Chemistry Northwestern University Evanston, Illinois 60201 RECEIVED for review March 20, 1978. Accepted May 9, 1978. Work supported by the National Science Foundation (Grant NO. CHE7S-15462).
Fluorescence Line Narrowing Spectrometry in Organic Glasses Containing Parts-per-Billion Levels of Polycyclic Aromatic Hydrocarbons Sir: The fact that carcinogenic and mutagenic properties of polynuclear aromatic hydrocarbons (PAHs) can be strongly dependent on isomeric structure ( I ) has prompted us to develop new laser based methodologies characterized by resolution sufficient to distinguish between structural isomers. In addition to very high selectivity, the requirements that our techniques be quantitative, sensitive (51ppb), nondestructive, and rapid have limited the scope of our investigations. Given the critical dependence of the electronic structure of polyatomic molecules on nuclear geometry and the sub. stantial fluorescence quantum efficiencies of PAHs ( 2 ) , fluorescence based methods for PAH measurements seem very attractive. However, the aforementioned selectivity requirement presents real difficulties and precludes, for example, liquid solution or conventional gas phase fluorescence spectrometry as viable starting points. In the latter case, overlapping rotational structure produceq broad rovibronic 0003-2700/78/0350-1394$01 OO/O
bands while in the former case, solute-solvent interactions also afford broad bandwidths (FWHM -200 cm-’). (All bandwidths stated below are “full-width half maximum” or FWHM.) Although it appears that the problem of overlapping rotational structure can be eliminated (3),we wish to report here on a solid state fluorescence based technique which we believe satisfies all the requirements delineated above. Before describing it, we note that it has been known for over 20 years that the low temperature electronic absorption and luminescence spectra of PAHs imbedded in crystalline matrices can be sharp (55 cm-’) ( 4 ) . This degree of sharpness satisfies the selectivity requirement. For any matrix, selectivity can also be enhanced temporally ( 5 ) since PAH fluorescence lifetimes are known to vary by several orders of magnitude (2). Possible matrices include host PAH crystals, Shpol’skii (n-paraffin) solvents, and, to a lesser extent, “inert” gases like 1978 American Chemical Society
