2228
Anal. Chem. 1981, 53, 2228-2231
resulting metal chelate complexes.
ACKNOWLEDGMENT The authors gratefully acknowledge William Artis and his staff, School of Dermatology, Emory University, Atlanta, GA, for their collaboration in studying Fe in human skin and the Center for Disease Control, Nutritional Biochemistry Division, Atlanta, GA, for supplying the serum samples.
LITERATURE CITED (1) (2) (3) (4) (5) (6) (7) (8) (9)
Boumans, P. W. J. M. Opt. Pura Apl. 1978, 1 1 , 143. Barnes, R. M. Anal. Chem. Fundam. Rev. 1976, 48, 106R. Fassel, V. A.; Kniseley, R. N. Anal. Chem. 1974, 46, I I I O A , 1155A. Dahlquist, R. L.; Knoll, J. W. Appl. Spectrosc. 1978, 32, 1. Barnes, R. M., Ed. "Applications of Inductlveiy Coupled Plasmas to Emission Spectroscopy"; Franklln Instltute Press: Philidelphia, PA, 1978. Abe;crombie. F. N.; Silvester, M. D.; Cruz, R. B. Adv. Chem. Ser. 1979, No. 772, 10. Fassel, V, A.; Peterson, C. A,; Abercromble, F. N.; Knlseley, R. N. Anal. Chem. 1976. 48, 516. Merryfield, R. N.; Loyd, R. C. Anal. Chem. 1979, 51, 1965. Kniseley, R. N.; Fassei, V. A,; Butler, C. c., Clin. Chem. ( Winston-Sa/em, N.C.) 1973, 19, 807.
Motooka, J. M.; Mosier, E. L.; Sutley, S.J.; Viets, J. G. Appl. Spectrosc. 1979, 33, 456. Cresser, M. S. "Solvent Extraction in Flame Spectroscopic Analysis"; Butterworths Press: London, 1978. Moshier, R. W.; Sievers, R. E. "Gas Chromatography of Metal Chelates"; Pergamon Press: New York, 1965. Gulchon, (3.; Pommier, C. "Gas Chromatography in Inorganics and Organometallics"; Ann Arbor Science Publisher: Ann Arbor, MI, 1973. Rodriquez-Vazquez, J. A. Anal. Chim. Acta 1974, 73, 1. Burgett, C. A. Sep. Purif. Methods 1976, 5 , 1. Black, M. S.; Browner, R. F. Anal. Chem. 1981, 53, 249. Hansen, L. C.; Scribner, W. G.; Gilbert, T. W.; Sievers. R. E. Anal. Chem. 1971, 43, 349. Wolf, W. R.; Taylor, M. L.; Hughes, B. M.; Tiernan, T. 0.; Sievers, R. E . Anal 14'12 44 616 . Chem _ Black, M. S.; Sievirs, E.Anal. Chem. 1976, 48, 1872. Wolf, W. R. J. Chromatogr. 1977, 134, 159. Fay, R. C.; Piper, T. S. J. Am. Chem. SOC. 1963, 85, 500. Carter, R. J. "Summary Report: Trace Metals Survey I"; U.S Department of Health, Education and Welfare. Center for Disease Control: Manta, GA, 1977.
d.
.
RECENEDfor review July 7, 1981. Accepted August 24,1981. M.B.T. acknowledges his support by the National Science Foundation Undergraduate Reasearch Program, 1980. This work was supported by the National Science Foundation under Grant No. CHE-8019947.
Wavelength Modulation in Photoacoustic Spectroscopy S. L. Castleden,' G.
F. Kirkbright," and D. E. M. Spillane
Department of Instrumentation and Analytical Science, The University of Manchester Institute of Science and Technology, P.0. Box 88, Manchester M60 100, United Kingdom
A simple modification of a photoacoustic spectrometer to allow for the direct generation of first- and second-order differential spectra is described. Uncorrected spectra are presented for a number of samples; the apparent enhancement in the resolution of the system and the ability to locate with increased preclsion the position of absorptlon band edges and maxima and minima are demonstrated.
In recent years photoacoustic spectroscopy (PAS) has become established as a useful technique for the qualitative (1, 2) and quantitative (3, 4) examination of condensed phase samples. At present the conventional photoacoustic spectrometer employing a continuum source cannot be regarded as a high-resolution instrument owing to the requirements for a high-energy throughput which necessitates the use of a relatively large monochromator band-pass. Although it is clear that taking the differential of a spectrum does not result in an increase in the actual informing power of the system, the observation of an apparent enhancement in spectral resolution will be expected as a result of the change in the presentation of the information obtained. A number of experimental methods exist in spectroscopic practice whereby differentiation of signal amplitude with respect to wavelength may be obtained ( 5 , 6 ) . These may be classified into three broad categories, namely, digital storage of the zero-order spectrum followed by computation of the nth order derivative, analogue differentiation of the spectrum, and techniques which employ some form of wavelength modulation to produce differential spectra directly. Digital signal processing is ultimately the most satisfactory and flexible method for the generation of a differential signal; Present address: D e p a r t m e n t of Chemistry, I m p e r i a l College, L o n d o n SW7. U.K.
it is relatively straightforward to obtain higher order differentials with provision for the careful control of smoothing functions. However, digital signal processing normally requires a considerable investment in hardward and software as well as a relatively long development time. Analogue differentiation, although simple and inexpensive, can result in differentiation of artifacts caused by temporal variations in source intensity and in the degradation of signal-to-noise ratios caused by the differentiation of detector noise. The latter problem is particularly relevant to photoacoustic spectroscopy in which the system is detector-noise limited. The production of differential spectra using wavelength modulation may be achieved by performing a relatively minor modification to a conventional photoacoustic spectrometer without the degradation in signal-to-noise ratio experienced with analogue differentiation systems. Conventional PAS relies on the periodic interruption of the incident radiation for the production of a signal. This may be achieved by using electronic modulation of the source or by mechanical chopping using a rotating sector. However, wavelength modulation will provide an alternative method of producing a periodic signal. If the absorption coefficient of the sample is not constant with wavelength, the periodic variation of the wavelength of the incident radiation will result in the production of a periodic photoacoustic signal. Thus large changes in absorption coefficient will result in large photoacoustic signals and small changes lead to small amplitude variations. It is evident that obtaining the P.A. signal by wavelength modulation is directly analogous to taking the first-order differential of the conventional photoacoustic spectrum. Therefore, wavelength modulation is expected to provide a simple means for the generation of differential photoacoustic spectra while simultaneously removing the requirement for a periodic interruption of the incident radiation.
0003-2700/81/0353-2228$01.25/00 1981 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 53, NO. 14, DECEMBER 1981 30:
w
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2229
PHOTOACOUSTIC SPECTRA OF
MDhOC “ Q M A T 3 R
HOLMIUM OXIDE
\
uncorrected
~
I
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I
I
I T
DIFFERENTIAL PHOTOACOUSTIC SPEC;ROMETER
I
t Figure 1. Schematic of a differential photoacoustic spectrometer.
EXPERIMENTAL SECTION Apparatus. The photoacoustic spectrometer used in the following investigations has been described elsewhere (7). The spectrometer was modified to produce the arrangement shown schematically in Figure I. Continuum radiation from a 300-W xenon arc (Type VlX300 W, Varian Associates) was focused onto the entrance slit of an f/4 monochromator fitted with a plane diffraction grating blazed at 300 nm (Diffraction Gratings and Optics Limited, Chobham, Surrey, UK). The radiation was reflected through the exit slit of the monochromator by a plane mirror (25 mm X 19 mm) mounted on a penmotor (ModelR4077, MFE Corp., Salem, NH). A concave folding mirror was used to focus the radiation from the monochromator into the photoacoustic cell (EDT Research Limited, London NW10, UK). A signal generator (Model 3300A, Hewlett-Packard) was used to provide a periodic triangular wave form which was amplified to drive the ;penmotor. A square wave output synchronous with the triangular wave form was used as the reference input to a lock-in amplifier (Ortholoc Moclel9502, Brookdeal Electronics Limited, Bracknell, UK). The signal from the photoacoustic cell was detected synchronously by the lock-in amplifier and the output taken to a scan recorder (Model 4101, Princeton Applied Research Corp., Princeton, NJ). The output from the scan recorder was displayed on an X-Y plotter (Model 25000, Bryans Southern Instruments Limited, Mitcham, UK). Procedure. Ilifferent ial spectra were recorded in the single beam m d e and thus the output was uncorrected for the variation of source intensity with wavelength. Conventional photoacoustic spectra were easily obtained by switching off the drive to the oscillating mirror and placing a mechanical chopper in the light path. Spectra corrected for variation in the source emission characteristics were obtained by recording a spectrum of carbon black (powdered animal charcoal, particle size range 36-63 pm) in the second channel of the scan recorder and outputting a point-by-point ratio of the signal from the sample to the signal from carbon black at each wavelength. Mixtures of anatase and rutile (spectroscopically pure) were prepared by grinding together preweighed quantities of each using an agate pestle and mortar. No sample pretreatment was found to be necessary for any of the other samples examined. All spectra were recorded by using the lock-in amplifier as a vector voltmeter except for those shown in Figure 6 which were recorded by use of the lock-in amplifier to measure the signals in-phase and at pc rad out of phase. Second-order differential spectra were obtained by setting the lock-in amplifier to detect the second harmonic of the reference signal (5). The second differential spectra presented are inverted to give peaks rather than troughs at the maxima of the absorption spectrum. The system was found to give an optimal signal-to-noiseratio at ca. 15 112, the signal-to-noise ratio degrading rapidly with increasing chopping frequency. The optimal value for the amplitude of modulation was determined individually for each compound by varying the amplitude of the wave form output by the signal generator. The optimal value was found to be a compromise between improved signal-to-noise ratio at greater amplitudes of modulation and improved resolution at smaller amplitudes. The practical range of wavelength modulation was ca. 2-4 nm.
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Flgure 2. Photoacoustic spectra of holmium oxide as obtained and corrected for variations in the spectral output of the source. First- and
second-order differential photoacoustic spectra obtained for holmium oxide powder.
RESULTS AND DISCUSSION The undifferentiated and first- and second-order differential spectra of holmium oxide (99.9% purity) are shown in Figure 2. It may be observed that wavelength modulation results in the expected first and second derivative spectra of the uncorrected holmium oxide spectrum. Clearly, these cannot be taken to be wholly accurate representations of the true derivative spectra as the holmium oxide spectrum is convolved with the emission spectrum of the radiation source employed. The effect of this may be simply understood by considering the relationship between: the corrected photoacoustic spectrum defined by some function {(A) (where f ( X ) represents the photoacoustic signal observed a t wavelength A), the uncorrected photoacoustic spectrum g(X), defined similarly, and the power spectrum of the lamp l(X) which represents the variation in output power of the lamp with wavelength and is often represented by the photoacoustic spectrum of carbon black. For the sample (holmium oxide, in this case)
Hence the uncorrected spectrum can be defined as g = fl
and differentiating with respect to X
dg/dX = l(df/dX) + f(dl/dX)
(2)
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450
ANALYTICAL CHEMISTRY, VOL. 53, NO. 14, DECEMBER 1981
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Flgure 3. Photoacoustic spectra of gallium phosphide as obtained and
corrected and the first-order differential photoacoustic spectra as obtained. provided f and 1 are independent and that g, f, and 1 are continuously differentiable functions over the wavelength range of interest. Rearranging 2 we obtain
5CC
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Flgure 4. Photoacoustic spectra of zinc selenide as obtained and corrected and the first-order differential photoacoustic spectrum as obtained.
1
F I R S T DIF'ERENTIAL
SPECTRA OF TiO,
POLYMORPHS
Substituting for f from eq 1 and rearranging we obtain
-[ -41
af = 1 1%dg dh
12
(3)
From eq 3 there is only one useful case in which a linear relationship between the observed first differential spectrum (dg/dX) and the true first differential (dfldh) can be obtained, Le., when dlldh = 0. This will occur only when the power spectrum is flat with respect to wavelength. This case is obviously relevant only over very limited spectral ranges for the source employed and hence a true representation of the first differential can only be obtained by using eq 3 and with a knowledge of the experimental values for the conventional and first order differential spectra of the sample and those of carbon black (g, 1, dg/dh, dlldh). Further, in the case of the second order differential spectrum, from eq 2 d2g - 1-d2f + 2-a i _
ap
dh
af -
dh d h
+ f-d2i ah2
(4)
and rearranging
Equation 5 is also soluble with experimental knowledge of g, 1, dg/dX, dlldh, d2g/dX2,and d21/dX2,since f and dfldh may be substituted using eq 1 and 3. Bearing in mind that the features in the spectra may be caused by either the sample spectrum or variations in the source emission, it is possible to consider the results obtained for the remaining samples. Differential spectroscopy is a particularly useful technique for locating absorption band edges. The center of the band edge can be regarded as the point of maximum negative slope, i.e., the minimum of a differential representation of the edge. The zero- and first-order differential spectra obtained for samples of gallium phosphide and zinc selenide are shown in Figures 3 and 4,respectively. The absorption coefficient of gallium phosphide changes relatively slowly with wavelength but the observation of the
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Figure 5. First-xder differentlal photoacoustic spectra of some t i n i u m
dioxide polymorphs as obtained. first differential spectrum enables a more precise determination of the absorption band edge. This is demonstrated more clearly for zinc selenide in Figure 4 in which the differential spectrum shows a more marked change at the band edge and a sharp, clear minimum. Other minima reveal the presence of structure in the band edge which is not readily apparent in the zero-order spectrum. The zero-order photoacoustic spectra of the titanium dioxide polymorphs rutile and anatase exhibit band edges at 350-440 and 320-420 nm, respectively. The spectra of mixtures of these polymorphs exhibit a broadening of the spectral region over which the band edge occurs. It may be observed from Figure 5 that these band edges are again clearly defined by the presence of minima and it can also be observed that the presence of anatase in the 10% mixture can clearly be noted, whereas the 50% mixture appears to contain only rutile. The latter observation is in concordance with the known characteristic of rutile to form a coating over anatase in mixtures of titanium dioxide (8). Differential spectroscopy may be used to obtain the wavelength of absorption maxima in a spectrum more precisely than by using measurements from a conventional spectrum. Maxima may be located by considering the intersection of two spectra recorded with a phase difference of a rad. Figure 6 shows the first differential spectra of holmium oxide recorded at relative phases n/2 and 3a/2 rad. The wavelengths a t which the two spectra intersect correspond to maxima and minima in the zero-order spectrum, since the intersections of the curves mark points of equivalence which can only occur
ANALYTICAL CHEMISTRY, VOL. 53, NO. 14, DECEMBER 1981 1
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HOLMIUM OXIDEFIRST DIFFERENTIAL
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Flgure 6. The first-order differential photoacoustic spectrum of holmium oxlde as obtained both In phase and T radians out of phase.
when the signal, and hence the derivative, is zero. An interesting aspect of the work described here is the production of a photoacoustic signal without amplitude modulation of the incident radiation. The wavelength modulation used to provide the differential signal in this system also provides the modulation necessary for the production of the photoacoustic signal. Considering the theoretical model of Rosencwaig ,and Gersho (9),the heat density produced at a point x in the sample is given in a fairly simple form by
1/2pIo exp (Ox)(1 + cos ut)
(6)
where fi is the optical absorption coefficient of the sample (cm-I), Io is the incident monochromatic,light flux (W cm-2), w is the chopping frequency (rad s-l), and t is the elapsed time (s). However, for the csituation relating to wavelength modulation expression 6 must be rewritten in a more complex form. If a steady-state system is assumed, with the sample illuminated by monochromatic light, varying periodically in wavelength from h = Ax to X - Ah in a sinusoidal manner and that the spectral output of the source ns invariant over the wavelength range ( A + Ah) to ( A - Ah), then the heat density at a point x in the sample can be represented by exP(PyX) (7) where, fiv is the optical absorption coefficient of the sample a t wavelength 'Yand 'Y= h Ah sin (cot). JOPY
+
2231
Obviously, (7) cannot be used to complete the thermal diffusion equation and provide an exact solution unless the variation of fi with h is known. Similarly, solutions to the thermal diffusion equation would be obtainable if a simple dependence of fi on X was assumed. However, no attempt is made in this paper to derive an exact mathematical equation to describe the differential photoacoustic signal. It is evident from the spectra presented here that it is possible to produce first differential photoacoustic spectra of solid samples using wavelength modulation. Additionally, second differential spectra may be obtained by setting the lock-in amplifier to detect the second harmonic of the modulation frequency. The technique described for obtaining differential spectra may be implemented easily and cheaply without reproducing the problem of signal-to-noise ratio degradation when analogue differentiators are used. The direct generation of differential spectra extends the capabilities of conventional photoacoustic spectroscopy by enhancing the interpretation of information present to aid in the precise location of absorption bands. The spectra presented for the polymorphs of titanium dioxide demonstrate the potential of the differential technique for samples that prove exacting when examined by conventional photoacoustic spectroscopy. It should be stressed that caution should be exercised in drawing conclusions from these uncorrected spectra since the effect of lamp emission must be taken into account; a method for correction is given, however, which should overcome this problem when suitable signal processing equipment is employed.
LITERATURE CITED (1) Rosencwaig, A. Anal. Chem. 1975, 47, 592 A. (2) Adams, M. J.; Beadle, B. C.; King, A. A.; Kirkbright, G. F. Analyst (London) 1976, 101, 555. (3) Castleden, S. L.; Elliott, C. M.;Kirkbright, G. F.; Splllane, D.E. M. A d . Chem. 1979, 51, 2152. (4) Ashworth, C. M.; Castleden, S.L.; Klrkbright, G. F.; Spillane, D. E. M. J. Photoacoust., in press. ( 5 ) O'Haver, T. C. Anal. Chem. 1979, 51, 91 A. (8)Cahlll, J. E. Instrum. Lab. 1980, Jan/Feb, 64. (7) Adams, M. d.; Beadle, B. C.; Kirkbright, G. F. Analyst (London) 1977, 102,589. (8) Klng, A. A. PhD. Thesis, University of London, 1976. (9) Rosencwalg, A,; Gersho, A. J. Appl. Phys. 1976, 47, 64.
RECEIVED for review June 15,1981. Accepted August 12,1981. We wish to thank the Paul Instrument Fund of the Royal Society for the grant which enabled the construction of the photoacoustic spectrometer and EDT Research, London, for the support of an SRC-CASE award to D.E.M.S.
