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(17) Ernest, M. J.; Kim. Ki-Han J . Bkd. Chem. 1974, 2449, 6770. (18) Ogko, T.; Tamura, S.; Kato, Y.; Siglura, M. J. Biochem. (Tokyo) 1974, 7 6 , 147. (19) Shinoda, T.; Tsuzukida, Y. J . Biochem. (Tokyo) 1974, 7 5 , 23. (20) Benjamin, D. M.; McCormack. J. J.; Gump, D. W. Anal. Chem. 1973, 45, 1531. (21) Rltchie, G.; Chen, C. Y. I n Surfece Enhanced Raman Scattering; Chang, R. K., Furlak, T. E., Eds., Plenum: New York. 1982; pp 361-37%. (22) . . IshMa, H.; Fukuda, H.; KataQiri, G.; Ishitani, A. Appl. Spectrosc. 1988. 40, 322. (23) Cotton, T. M.; Schlegei. V. L., University of Nebraska-Lincoln, unpublished results. (24) Anderson, J. S.; 60%A.; Ogden, J. S. J. Chem. SOC.D 1971, 1381. (25) Kumar, K.; Carey, P. R. J . Chem. Phys. 1975. 63, 3697. (26) Soriaga, M. P.; Hubbard, A. T. J. Am. Chem. Soc. 1982, 104, 2742. (27) Soriaga, M. P.; Hubbard, A. T. J. Am. Chem. SOC.1982, 104, 3937.
(28) Efrima, S. I n Modern Aspects of Electrochemistry; Conway, 6. E., White, R. E., Bockris, J. O'M., Eds.; Plenum: New York, 1965; Vol. 16, pp 253-369. (29) Merlin, J. C.; Thomas, E. W. Spectrochim. Acta, PartA 1979, 35A. 1243. (30) Cotton, T. M.; Kim, JaaHo; Uphaus. R. A,; Mobius, D., University of Nebraska-Lincoln, unpublished results. (31) Murray, C. A.; Bodoff, S. Phys. Rev. Lett. 1984, 52, 2272. (32) Metiu, H. Prog. Surf. Sci. 1984, 1 7 , 153.
RECEIVED for review November 30, 1987. Accepted March 22,1988. We are grateful to the National Institutes of Health for support of this work (GM 35108-03). T.M.C. is the recipient of a NIEHS Career Development Award (ES00169).
Comparison of Digital and Optical Processing of Time Varying Pulsed Laser Excited Photothermal Spectroscopy Signals Stephen E. Bialkowski* and Salvador Herrera Department of Chemistry and Biochemistry, Utah State University, Logan, Utah 84322-0300
This research appiles digital and linear incoherent optical signal processing for rapid photothermal signal magnitude analysis. Temporal signals are processed by both digltai and optical matched filtering technlques and compared in terms of their respective signal to ndse ratlos. The optical processlng resuits in rapld repetitive quantitative slgnai estimation. But the optkalry processed data are not found to compare favorably to those obtained by using conventbnai digital processed signals. The greater constant noise found In the optically processed data Is an artifact of the blased signal processlng technlque utiilred In these experiments.
Optical signal processing (OSP) is currently being applied to a variety problems involving parallel processing and rapid pattern recognition (1). Vector and matrix mathematics can be performed in time frames that are orders of magnitude shorter than conventional electronic computations. In fact, the speed of OSP is limited only by the path length of the optical signal divided by the speed of light. Many promising applications of OSP await for data processing in chemical analysis. This is especially true in the case of spectroscopic signals since they are inherently in a form that lend themselves to OSP (2). Compared to electronic processing using transducers, OSP has less inherent noise due to the absence of the optical equivalent of Johnson noise in the visible spectrum. Image processing, in either optical or electronic forms, is an inherent facet of photothermal lens spectroscopy (TLS) and in certain implementations of photothermal deflection spectroscopy (PDS) (3). Probe laser beam image processing using a photodiode array and a microprocessor has been used in TLS experiments (4). But although the results were better than the pinhole aperture method (3),the method was not viable for rapid analysis due to the long times required for laser beam profile analysis. More recently optical image processing, in the form of an optical transfer function, has been applied to TLS (5). The latter study demonstrated that the signal obtained by using a rapidly variant transmission mask placed in the laser beam was also superior to that obtained by using the usual pinhole aperture. The mask used for image 0003-2700/88/0360-1586$01 SO/O
processing was an integral part of the TLS apparatus, taking the place of the pinhole aperture. In effect, this aperture or mask performed rapid OSP of the laser beam in much the same fashion as the electronic image processor using the photodiode array, although the algorithm was quite different in these two cases. Nonetheless, with the mask, signals were processed in real time. This cannot be accomplished with the photodiode array image processor. The experiments described herein utilize both digital and linear incoherent optical signal processing (LIOSP) (6,7)for rapid magnitude estimation of time-dependent, pulsed laser excited PDS signals (8). LIOSP is limited to applications involving linear mathematical processing wherein the result is a s u m of individual products. In incoherentlight processing, the light intensity is monitored. By measurement of the intensity, processing steps are limited to sums and products since there is no negative intensity. This apparent limitation is overcome either by processing positive and negative components of the signal independently or by the biased estimate technique wherein some finite light intensity is assigned to be zero (6). The present study is similar to the optical image processor mentioned above in that a transmission mask is utilized. But the differences are important. The major difference is that time varying signals, not images, are processed. Further, the mask is not an integral part of the spectroscopic apparatus. Rather, LIOSP is used in place of electronic processing, normally performed after signal detection. More specifically, this paper explores the application of LIOSP for matched filter processing of optically encoded impulse-response signals resulting from pulsed laser excited PDS (3, 8). Pulsed laser excited PDS is utilized because of the large intensity modulation relative to the constant background intensity of the probe laser. The analytical signal is a modulation in the probe laser beam intensity past an aperture used to discriminate the angle of this beam beyond the sample cell. Subsequently, these optical signals constitute a nearly ideal test case for the application of LIOSP to time-dependent signal analysis.
THEORY Pulsed laser excited photothermal spectroscopy is an absorbance measurement technique. The signal is derived from 0 1988 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 60, NO. 15, AUGUST 1, 1988
a continuous probe laser beam as it passes through a sample with a refractive index perturbed by absorption of a portion of the pulsed pump laser energy (3,8). The intensity of the probe laser past an aperture is modulated by either a blooming effect, as in TLS, or a deflection, as in PDS, induced by the absorption of pump laser energy by the sample. Absorption of energy results in sample heating, which perturbs the refractive index of the sample. In turn, this refractive index perturbation affects the propagation characteristics of the probe laser beam. The probe beam intensity past an aperture is comprised of three major components: the impulse response, the signal magnitude, and a constant background term I&) = Io(Sf(t) + C) (1) where I&) is the time-dependent intensity, Iois the probe laser beam intensity before the sample cell, S is the signal magnitude, and f ( t ) is the impulse response. The constant, C, is included to account for background light intensity. For short pulse excitation the signal magnitude is independent of the form of the temporal impulse-response function for a given matrix. In this case f ( t ) is a function of the thermal characteristics of the matrix and the geometry of the pump and probe laser beams
M
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Figure 1. Illustration of the processor used in these experiments. The signal beam Is synchronously scanned across the transmission mask (M) with a galvanometer (G). A cylindrical lens (Ll) is used to focus the signal only in the dimension scanned. Past the mask, the beam is focused (L2)onto a photodetector (D).
(2) In this equation r is the radial offset of the parallel pump and probe laser beams, w is the pump laser Gaussian electric field beam waist radius, and t, is the characteristic thermal time constant, t , = w 2 / 4 K , where K is the thermal diffusion coefficient. The magnitude of the impulse response is proportional to the pump laser energy absorbed by the sample
plished by summing over the time-dependent spatial elements. The dot product is accumulated over the signal duration time and is subsequentlyprocessed with an integration device. The result is the signal magnitude estimate. The signal estimate obtained in this fashion is biased. That is, when there is no impulse-response signal, the LIOSP system will result in a finite value. This is due to the loC product in eq 1. The biased signal estimate does not present a problem in signal interpretation if indeed the background intensity is constant. That value corresponding to only the constant background being present is assigned to zero signal.
S = - g A r l ~ u E ( d n / d T ) ~ / . ~ m w ~ p C , (3) where A is a constant of the particular experimentalapparatus, 1 is the sample path length, a is the exponential absorption coefficient, E is the pulsed laser energy, n is the refractive index, T i s the temperature, P is the pressure, p is the density, and C, is the heat capacity. Normally, the signal magnitude alone is sought in an analytical measurement of sample absorbance. However, it has been shown that a better estimate of the signal magnitude can be obtained by using the entire transient waveform (9, 10). In the latter studies, a linear digital filter was used to accomplish real time filtering of individual signal transients s^ = Ch(t)l,(t) (5) Here, s^ is the signal magnitude estimate and h(t)is the linear smoothing filter function. The smoothing filter can be chosen so as to result in a maximum signal to noise ratio (SNR). Under the assumption that the noise is zero mean and normally distributed, the optimum SNR is obtained when h(t) a constant factor times the expected signal impulse response, f(t). The filter is thus matched to the expected signal, admitting signal measurements proportional to the expected SNR. For digital signal processing, h(t)is made zero mean in order to suppress response to the constant background, C. Extension of this digital filtering procedure to LIOSP is straightforward. The important components to the LIOSP arrangement are illustrated in Figure 1. With the exception of the type of the optical detection, this processor is similar to that described by Bromley in 1973 (11). The input to this processor is I&) defined in eq 1. The input beam is timeto-space multiplexed, using a beam scanning device, and passes through a mask before being detected. The mask has an optical density that varies along the dimension scanned. Thus the mask in combination with the beam scanner make up a time-dependent transmission. This transmission is the filter function, h(t). While scanning, the intensity past the mask represents the term by term product of the signal with the filter impulse response. The vector dot product is accom-
The PDS apparatus used in these experiments has been discussed previously (12). Briefly, a pulsed TEA-C02infrared laser at 9.229 pm was used to excite gas phase samples and a HeNe laser (Melles-Griot Model 05-LHP-121)at 632.8 nm was used to probe the resulting refractive index perturbation. The experimental repetition rate was 3.75 Hz, limited by the rate at which the pulsed laser could be triggered. The energy of the pump laser was variably attenuated using a venician blind infrared attenuator (13). Two r a m blades were used to aperture the probe laser beam. The first was positioned so as to aperture the probe beam before entering the gas cell and the second was placed after the cell. The second razor alone results in an intensity modulation of the probe laser beam when deflection takes place. The razor positioned before the cell limited the total intensity of the probe beam that paased the second razor in the absence of beam deflection,thereby reducing the constant term in eq 1. Positions of both razor blades were adjusted to result in a maximum intensity modulation relative to the constant intensity of the probe laser beam. After the second razor blade aperture, the probe laser beam was focused with a 10 cm focal length lens onto the mirror of a fast galvanometer beam scanner (CEC Model 7-326). The galvanometer was driven by a triggered electronic linear ramp generator. The main components of this circuit consisted of a gated digital clock made from two 74123 dual one-shot circuits and a 74161, eight-bit digital counter. The digital counter was used to drive a DAC-08, eight-bit digital to analog converter. The output of this converter was matched to the galvanometer with a LM741C operational amplifier circuit. The time constant of the latter was chosen such as to smooth out the "staircase" output potential into a linear ramp. The galvanometer scanning circuit triggers synchronously with the trigger for the COz laser. Past the galvanometer, the diverging beam was focused with a 10 cm focal length cylindrical lens in order to produce a line that illuminated the entire width of the mask. This line was scanned over the length of the mask in time upon being triggered. The rest position of line was outside of the aperture of the mask. This served both to limit the light on the subsequent photodetector and to reduce the timing linearity error during mirror acceleration. Photographictransmission masks were produced by first making dot density images on 8.5 in. X 11in. paper using a digital plotter (Hewlett-Packard Model 7225B). These images
f ( t ) = exp[-2r2/w2(1
+ 2 t / t C ) ] / ( 1+ 2t/t,)2
EXPERIMENTAL SECTION
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ANALYTICAL CHEMISTRY, VOL. 60, NO. 15. AUGUST 1, 1988 A
'"1
EXCITATION ENERGY CmJ) Flgure 2. A typical negative mask used for matched finer smoothing of the signal. Time zero is the high dot density portion on the left. Longer times are to th-s This particular mask extends to a relatie time of 5tc
m.
were subsequentlyreduced in size on standard 35-mm film as the negative image, resulting in a clear on black format. High-contrast film processing was used in order to obtain a small minimum transmission. The dot density image plots were based on the expected signal impulse response, eq 2, for the maximum signal that OCCUIS when r is equal to 1/2w. For each time element of the mask, the number of dots per length element was determined from the expected signal and then the dots were plotted in a random fashion. A typical negative image is show in Figure 2. Since all light passing through the mask is detected, diffraction due to the periodic dot spacing is inconsequential. Since the impulse response of the PDS signals varies only in the time scale, relative to a particular t,, only one mask was required for processing signals with different t,. Adjusting the matched filter scan time to the experimental impulse-response time was accomplished hy changing the clock rate of the triggered ramp generator and by translating the mask in the dimension of beam propagation. The zero time offset was adjusted hy moving the mask in the direction of the scanned heam. Directly after the transmission mask the beam was focused onto the photocanode of a 1P28 photomultiplier with a 6 cm diameter, 6.2 cm focal length lens. The average intensity was low and a relatively high, 600-V bias was used for the photomultiplier. Signals were recorded with an eight-hit transient waveform recorder (Data Precision Model 522-A) interfaced to a computer (Digital Equipment Corp., Model PDP 11/23) in order to allow direct comparison between optical and digital processing. ac coupling was used at the waveform recorder providing a 2-Hz low-frequency cutoff. Digital matched filter processing was performed for the data obtained without optical processing. The linear smoothing filter function matched to experimental data by ensemble averaging several transients (9, lo). The averaged transient was then made zero mean. Optical processed signals were subsequently processed with digital gated integration. The same optical and digital apparatus was used in both cases hut the heam was not scanned when digital matched filtering was performed. The pump laser energy was monitored by splitting the beam with germanium flat and using a Laser Precision Model RjP735 detector. This signal was subsequently digitized with an analog to digital converter so that upon each pulse of the pump laser, both signal and pump laser energy were recorded. The data processing programs were written in FORTRAN-77 and the procedures have been described in previous publications (12-24). The gas samples were a mixture of chlorodifluoromethane (PCR/SCM Specialty Chemicals) in argon (Liquid Air Corp.) made up to 100 kPa total pressure. Analyte concentrations were typically 1-10 ppm (v/v). RESULTS AND DISCUSSION Figure 3 illustrates typical results obtained hy utilizing both digital processing and LIOSP. Each point in these scatter
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.wa
.is
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.+s
EXCITATION ENERGY
1.88
1.25
(mJ)
Figure 3. Data obtained for #@%ai (A) and optical (E) pocessed signais. Chlorodifiuoromethane concentration was 1.7 ppm (vlv) in argon at 101 kPa total pressure. The data in pari B have been scaled to match those of A.
plots represents one pulse of the infrared pump laser. The pump laser energy was varied over to obtain the 1024 samples in each case. The digital processed signal magnitude estimate is relative to the matched filter used to process the raw data. A magnitude of one would represent that point where the signal magnitude was equal to that of the matched filter. The optically processed signal magnitude estimates have been scaled to result in the same relative excursion. Moreover, a constant term has been subtracted from the optically processed data. This constant term is discussed in more detail below. The apparent nonlinear signal versus excitation energy behavior seen in both plots is not due to the experimental apparatus but rather is due to multiphoton excitation and optical saturation of the analyte (12). These particular data were chosen for illustration because they allow a direct comparison between the digital and optical processed signal magnitude estimates. The error in signal magnitude estimation can he surmised by analysis of the data scatter along the vertical signal axis. It is apparent that the signal estimation error increases with the signal magnitude in both cases. At the highest signal magnitudes illustrated in these data, the SNR of the two processing methods is about the same. At an excitation energy of 1 mJ/pulse, the digital processed estimate had a SNR (defined as the ratio of the average signal magnitude to the standard deviation) of 24 while that of the optically processed signal estimate was 25. These two SNR are not significantly different, as would have been expected since both digital or optical matched filter processing results in the optimum signal estimate. But it is clear that the SNR is dominated by proportional noise or, more appropriately, proportional error. In the past, we have
ANALYTICAL CHEMISTRY, VOL. 60, NO. 15, AUGUST 1, 1988
found the errors to be due to pump laser beam shape variations and pointing noise, and to pointing and intensity noise in probe laser beam (14).Since neither processing method accounts for these errors, it is not surprising that both are limited by these effects for large signal magnitudes. Although the large signal SNRs are about the same, the limiting minimum SNRs in these two data sets are different. The error in the digital processed data decreases with decreasing signal to a SNR that is about half of that observed in the LIOSP estimate. The relative magnitudes of these limiting small signal standard deviations were reproducible. All attempts to reduce the small signal limiting noise in the LIOSP case were unsuccessful and we therefore assume that this noise is intrinsic in the respective techniques. The limiting small signal noise is apparently constant in both instances and the standard deviation of the data is a more appropriate measure of the signal estimate quality. For the digitally processed estimates, the standard deviation in the small signal limit is 0.002 unit. Relative to the digital method, LIOSP appears to be rather "noisy" for the low signal magnitudes, with a standard deviation of 0.005 unit. The difference between these two noise levels is of interest. In theory, both processing schemes should have yielded nearly equivalent noise characteristics since both cases were shot noise limited. But the biased LIOSP technique used here results in a large constant term in the signal estimate that is in fact proportional to the probe laser intensity. The larger standard deviation observed in the small signal limit for the LIOSP case is probably due to the probe laser beam intensity fluctuation. The noise of both digital processing and LIOSP can be put on a quantitative basis. From eq 1 and 4,the total variance in the signal estimate is :a
+
= Io2[Ch(t)2]2us2 I02[Ch(t)]%C2
+
+ CCh(t)l%I2 (5)
where us2 and uc2 are the signal magnitude and background variances, u: is the probe laser intensity variance, and h ( t ) has been substituted for f ( t )in eq 4 for the matched filter. For the digital matched filter, h(t)is modified to be zero mean and vector length normalized. In this case, eq 5 reduces to the simple expression
The finite noise at zero signal found experimentally is due to random fluctuations in the probe laser intensity and the electronic signals over the time that the signal is recorded. This random fluctuation must resemble the expected signal to result in a finite filter response. It must therefore have the same frequency components as that of the expected signal. We have previously measured the noise over the frequency band of the PDS signal and have found it to be dominated by the low-frequency flicker noise component of the probe laser intensity (14). Much of the flicker noise was effectively eliminated in the case of digital processing simply by using the 2 Hz cut off, ac signal coupling. Noise due to intensity fluctuations between 2 Hz and about 250 kHz was reduced by using a zero mean linear filter smoothing function. Nonetheless, this noise source predominates at low signal levels and is assigned to the signal variance in the first term of eq 6. Both the first and second terms in eq 6 are responsible for the proportional noise. Accordingly, the proportional noise from the second term is directly dependent on the probe laser intensity variations and the signal magnitude. The unaccounted sources of proportional noise, including laser pointing errors and excitation beam profile variations, will result in an increase of us which is proportional to S. Certain simplifications can be made in the LIOSP case as well. First, the bias term in eq 1 will not have a significant
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variance and the term proportional to this variance can therefore be neglected in eq 5. Second, the ratio of sums over h(t)versus h(t)2corresponding to the mask in Figure 2 (i.e. up to 5tJ is about 4.3:l. With these numbers, the simplified signal estimate variance is = Io2us2
+ ( S + 4.3C)2U?
(7) The striking difference between the digital processing and LIOSP signal estimate variances is the predominance of the constant noise term in eq 7. Since all else is equal, the latter term must be responsible for the factor of 2.5 increase in the noise observed in the small signal limit of the LIOSP data. The greatest signal magnitude was 1% of the constant background for the signals in Figure 3. For optically processed signals approaching zero, the error is a constant independent of signal magnitude, and the constant bias term of eq 7 predominates. Clearly, this small signal limiting noise can be reduced by using an intensity stabilized probe laser. However, by use of the results of Figure 3, the relative probe laser noise over the measurement bandwidth is found to be only 0.001% . Thus probe laser beam intensity variations cannot alone account for the -*2% proportional noise at higher signal strengths for either the LIOSP or the digital processing case. Although there are problems with the current implementation of LIOSP, there are also advantages, both potential or real, that inspire us to continue exploring this processing scheme. The first advantage is in implementation. The LIOSP matched filter is simple in concept and in implementation. T o construct the digital equivalent, in particular the transient waveform recorder, would have taken a considerable time. Another advantage is that optical processing is much faster than the digital counterpart. By use of the PDP 11/23 computer with KEF11-AA floating point, 512-point transients can be filtered at a maximum rate of only 10 Hz. This rate is limited by both the time required to perform the calculations and the transfer of the data from the waveform recorder to the computer. With the LIOSP apparatus the repetition rate is limited only by the time required to scan the input signal beam over the mask. The limiting processing rate for the present apparatus is calculated to be about 1 kHz due to the 3-kHz resonance frequency of the galvanometer used here and allowing for "fly-back" of the beam. This rate could be increased by utilizing faster beam scanning devices. Ultimately, this rate too will be limited by digital conversion for storage on the computer. It is unfortunate that the pulsed laser repetition rate was the limiting factor in our experiments. A more philosophical point is that Johnson noise and electrical interferences will be absent from the LIOSP signal estimate. Coherent electrical interference is a particularly difficult problem encountered when using pulsed lasers. The current apparatus is not free of such problems since time integration is performed electronically. This problem may be overcome. Our future work in this area will involve methods to perform the integration optically prior to electronic conversion. Besides the inherent noise reduction, the precision of the optical filter is higher than the digital one. This mask negative illustrated in Figure 2 has a maximum of 480 points plotted along the vertical axis. This corresponds to a transient waveform recorder of approximately nine-bit accuracy. The accuracy was not limited by the resolution of our plotter, which has an ultimate resolution of 1part in 6800 or 13 bits, but rather by the pen size. Use of the appropriate pen would result in -13 bit magnitude accuracy and also the effective number of points in time could be increased to 8800 for a 17-fold increase in the effective measurement high-frequency roll off over that of the 512-point digital recording. In summary we must concede that there are problems with the current implementation of LIOSP, in particular the bias related noise, that apparently favor digital processing for this a62
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experiment. However, this noise problem may be unique to our implementation of LIOSP or to our particular application. Currently, one must weigh the benefits of rapid, cost-effective processing against that of noise dependence on light intensity. But this problem is of a “hardware” nature and would not be present if better equipment was in hand. One might expect that the limitations, e.g. speed and background bias related noise, will be overcome with advances in experimental LIOSP apparatuses and with advances in electrooptics. We note in closing that advances are being made in the design of optical systems which have properties that are analogous to ac coupling in electronic circuitry (15, 16). Registry No. CC1F2H,75-45-6; Ar, 7440-37-1.
(4) Muyalshi, K.; Imasaka, T.; Ishlbashi, N. Anal. Chem. 1082, 5 4 , 2039-2044. ( 5 ) Jansen, K. L.; Harris, J. M. Anal. Chem. 1088, 57, 1698-1703. (8) Rhodes. W. T.; Sawchuk, A. A. Optical Signal Procesdng Fundementab; Lee, S. H., Ed.; Springer-Verlag: New York, 1981; Chapter 3. (7) Casesent, D. P. Optical Signal Processing Fundamentals; Lee, S. H., Ed.; Springer-Verlag: New York, 1981; Chapter 5. (8) Biaikowski, S. E. Spectroscopy (SprlngfkM, Oreg.) 1088, 7 , 26-48. (9) Nickolaisen, S. L.; Blalkowski, S. E., J . Chem. Inf. Comput. Sci. 1086, 2 6 , 57-59. (10) Blalkowski, S. E. Rev. Sci. Instrum. 1087, 58. 887-695. (11) Bromley. K. Opt. Acta 1073, 2 1 , 35-41. (12) Blalkowski, S. E.; Long, G. R. Anal. Chem. 1987, 59, 873-879. (13) Blalkowski, S. E. Rev. Scl. Instrum. 1087, 58. 2338-2339. (14) Long, G. R.; Blalkowski, S. E. Anal. Chem. 1086, 58, 80-86. (15) %to, T.; Kojima, H.; Ikeda. 0.; Odai, Y. Appl. Opt. 1987, 26, 2016-20 19. (16) Anderson, D. 2.; Lininger, D. M.; Feinberg, J. Opt. Lett. 1087, 72, 123- 125.
LITERATURE CITED (1) Lee, S. H. Opt/cal Signal Processlng Fundamentals; Lee, S . H., Ed.; Springer-Veriag: New Yo&, 1981; Chapter 1. (2) Blalkowski, S. E. Anal. Chem. 1086, 58, 2561-2563. (3) Dovichi, N. J. CRC Crit. Rev. Anal. Chem. 1087, 17, 357-423.
RECEIVED for review October 20, 1987. Accepted March 28, 1988. This research was supported by the National Science Foundation under Grant CHE-8520040.
A Dynamic Model for the Elucidation of a Mechanism of Analyte Transformation in an Inductively Coupled Plasma K. P. Li, M. Dowling, and T. Fogg Department of Chemistry, University of Lowell, Lowell, Massachusetts 01854 T. Yu, K. S. Yeah, J. D. Hwang, and J. D. Winefordner* Department of Chemistry, University of Florida, Gainesville, Florida 3261 1
Axial signal profiles of analyte molecular, atomic, and ionic species contaln information essential for mechanistic studies of analyte transfmatlon. Such proflles are easier to deal with theoretlcaily than radial profiles because the central channel is much less heterogeneous than any other part in the plasma. The large regions often investigated In spatially resolved measwemente render the conventknal local thermal equlilbrium-basedmodels inappropriate for mechanism elucidation. A more general dynamic model Is established, where equilibria and steady states are considered as special cases. Klnetlcs of rate-detemlnlng reactions such as dissociation, atomization, ionization, and recombination are consklered. For mathematical sbnplmcation, we Imagine that the vapor plume results from a single aerosol particle, and the klnetk processes taking place are then closely followed. I n our case, dlfiuslon is approximated as volume expanslon under constant pressure. The resuitant analyte distribution observed should then be a good approximation to the real one, aasumlng an Inductively coupled plasma with reproducible experimental conditions and a uniform solution droplet size distribution. By comparison of the simulated height profiles using different rate constants with experimental height proMes, analyte transformatkn can be more precisely described. On the other hand, measurements of experimental height profiles and evaluation of statistic moments should allow e& tlmation of reaction rate constants.
An analyte introduced into an inductively coupled plasma (ICP) as tiny solution droplets undergoes many physical/ chemical processes such as desolvation, vaporization, atom-
ization, ionization, excitation, recombination, etc., as a function of height (schematically represented in Figure 1). Some of these processes may occur simultaneously and some sequentially; some processes may proceed very rapidly and some relatively slowly. As a result, vertical and radial spatial distribution of atomic, ionic, and molecular species of the analyte is established in the plasma. If the sample introduction is reproducible and if the plasma conditions are constant, the distribution of each species will be time independent and can be conveniently measured with vertical space-resolvedspectrometry. Such a vertical signal profile distribution of the species can be represented by its concentration or number density distribution and is the overall result of the kinetics of processes that generate or remove the species. Hence, the characteristics of the signal profile, e.g., peak area, peak maximum, peak width, etc., are fundamentally related to the kinetics of these processes and therefore to their rate constants. If a correlation between rate constants and spatial profile characteristics can be mathematically formulated,then the kinetics of analyte transformation in the ICP can be revealed through measurement and analysis of these profile features. On the other hand, knowing the rate constant of a system, one should be able to predict or simulate the spatial profile of a given species. Establishment of such a correlation is an essential step toward better understanding of the mechanisms of analyte atomization,ionization, and excitation. Unfortunately,despite many efforta devoted to the elucidation of analyte excitation mechanisms (1-24) and despite the significance of space-resolved spectrometry, such correlations have not yet been developed. This is probably because most people are much more familiar with the conventional local thermal equilibrium (LTE)approach than the more complicated kinetic approach in dealing with phenomena in
0003-2700/88/0360-159O$OlSO/O0 1988 American Chemical Society
