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Anal. Chem. 1981, 53, 2034-2036
Measurement of Single-Pulse Photoacoustic Signals Michael F. Cox and Geoffrey N. Coleman" Department of Chemistry, University of Georgia, Athens, Georgia 30602
Studles of the photoacoustlc signal generated by a slngle pulse of llght demonstrate that the slgnal devlates from the predlcted sawtooth wave form when the pulse duratlon exceeds approximately 15 ms. The response of the condenser mlcrophone employed is the primary limitation. The processes Involved in the generation and decay of the photoacoustlc slgnal are examlned, as well as the appllcebllity of condenser mlcrophones as detectors In photoacoustic spectroscopy.
The magnitude of a photoacoustic signal depends on a variety of factors, including the thermal and absorptive properties of the sample involved and the characteristics of the spectrometer itself. It is primarily a function of the thermal diffusivity of the sample (the ratio of thermal conductivity to specific heat and density), the absorptivity of the sample at the wavelength of the incident radiation and the incident radiant light flux (1).The predicted signal is inversely related to modulation frequency. Experimentally, signal increases linearly with decreasing frequency to about 30 Hz. Below that only a slight increase is typically observed. It should be recognized that the detected signal is also a function of the response characteristics of the microphone, the geometry of the photoacoustic cell, and the fidelity of the data acquisition system. Generally, instrumental parameters are optimized to yield the maximum signal-to-noiseratio at a given modulation frequency. They are held constant in succeeding experiments and are justifiably assumed to affect each measurement in an identical fashion. Consequently, the nature of the photoacoustic signal has not been throughly investigated. Theoretical relationships involving the generation of a photoacoustic signal have been described in detail elsewhere (1-5). However, the photoacoustic signal is generally believed to appear as a triangular-shaped or sawtooth wave form which may be explained as follows. When a solid material is irradiated at an appropriate wavelength, absorption occurs in a specific volume of the sample as defined by the dimensions of the incident radiation beam and its depth of penetration. The latter is a function of the optical properties of the sample. Thermal relaxation from the excited state heats a boundary layer of gas, causing an increase in cell pressure. The delay between the initiation of irradiation and the appearance of the PAS signal is a function of the thermal conductivity of the sample and is manifested as a phase difference between the PAS signal and the reference wave form from the optical modulator. The transfer of heat to the gas continues during irradiation, and, as a result of the increasing pressure due to the expanding gas, the signal is expected to increase until the radiation is terminated. At this point the signal will briefly continue to increase while heat transfer continues between solid and gas, and then it will decrease, forming the downward slope of the wave form. The rate of decrease is generally a function of the rate a t which the gas cools, which is related to the thermal conductivity and volume of the cell gas as well as to the surface area and conductivity of the photoacoustic cell walls.
The prediction of a triangular or saw-toothed photoacoustic signal is based on the assumption that the increasing signal is not greatly affected by the rate of thermal transfer between the gas and the cell walls and that the propagation of the pressure wave is much faster than the propagation of heat. Shaw (6) has demonstrated that the photoacoustic wave form produced by a 1 ps pulse of laser radiation follows the predicted wave form, but the nature of the photoacoustic signal has not been investigated at low modulation frequencies where maximum sensitivity should be attained. We describe the characterization of the photoacoustic signals resulting from single pulses in the range of approximately 14-70 ms, which correspond to modulation frequencies ranging from about 70 to 14 Hz, respectively. EXPERIMENTAL SECTION The experimental apparatus shown in Figure 1is a modification of our double beam-in-time photoacoustic spectrometer (7). The output of a 300-W Xenon arc (Varian) is directed through a single fused silica lens onto the aperture of a variable-speed shutter. When the shutter is opened, a pulse of radiation is briefly focused on the entrance aperture of a 1/4-mmonochromator (Jarrel-Ash). The monochromatic radiation, set arbitrarily at 450 nm, is then directed through a second fused silica lens (L2)to a stationary mirror which reflects the light through another fused silica lens (L3) to the sample contained in the photoacoustic cell. The resultant photoacoustic signal is detected by a condenser microphone (Realistic EM16) and amplified by use of a capacitively coupled preamplifier circuit similar to that described by Eaton and Stuart (8). The output of the preamplifier is fed to a digital oscilloscope (Nicolet) for storage. The oscilloscope is triggered by a phototransistor (Realistic FPT-100) placed at the edge of the source beam where it does not interfere with the radiation focused on the entrance aperture of the monochromator yet provides both a trigger signal and a measure of the optical pulse length. The digital oscilloscope has direct XY outpub which are fed to an XY recorder (Hewlett-PackardModel 7004B) for hard COPY. Reagents. Carbon lampblack (Fisher) was diluted with magnesium oxide (Baker) to obtain the l o % , 2570,and 50% carbon black samples. Holmium oxide (Alfa, Ventron Corp.) was also employed. All studies used approximately5 mg samples of reagent material. RESULTS AND DISCUSSION The photoacoustic signals obtained for ten repetitions of a 14.3-ms pulse are shown in Figure 2 along with ten blank scans which differ only in that the cell was covered to prevent light from entering. It is clear that the PAS signal is reproducible and follows the predicted behavior. Figure 3 contains the response curves obtained for carbon black with different periods of illumination. The rise time of all photoacoustic responses is nearly identical. However, once the maximum amplitude is reached at approximately 14 ms, the signal magnitude levels off. After about 30 ms, the amplitude of the photoacoustic response begins to decay. The rate of signal decay that occurs after irradiation is terminated is relatively constant, as expected, since it is a function of the geometry, physical makeup, and thermal conductivity of the photoacoustic cell as well as the volume and thermal conductivity of the fill gas, all of which are held constant. However, the signal actually decays below the base line noise level, the extent of which is related to the duration of illu-
0003-2700/81/0353-2034$01.25/00 1981 American Chemical Soclety
ANALYTICAL CHEMISTRY, VOL. 53, NO. 13, NOVEMBER 1981
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Flgure 1. Schematic diagram of instrumentation empioysd for measurement of single-pulse photoacoustic signals.
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Figure 2. Photoacoustic signals obtained for carbon black with ten repetitive 14.3-msradiation pulses (A), and ten scans of base line noise levels (6).
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Flgure 3. Photoacoustic response curves obtained for carbon black with varying periods of illumination.
mination, before it returns to base line. This effect appears to be a result of the transient response of the microphone itself. A replacement microphone showed identical results. In addition, opening the cell through an integral fill gas valve (7) to allow response only to transients also showed the same effect. The electret (or condenser) microphone consists of a metallic diaphragm which physically moves with a change in cell pressure and a parallel plate which forms the other half of a capacitor. The charge on a capacitor is given by (9) Kda
q = eo%
where €0 is the permittivity of free space, Kd is the dielectric constant, a is area of the plates, V is the polarization voltage, and s is the spacing between the plates. Since current is the rate of flow of charge per unit time, taking the derivative yields dS c. = - dq = -0- Kda dt Vs2 dt
Figure 4. Photoacoustic response curves obtained for varying concentrations of carbon black diluted with magnesium oxide with a radiation pulse width of 14.3 ms.
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Figure 5. Photoacoustic response curves obtained for varying coiicentrations of carbon black diluted with magneslum oxide with a radiation pulse width of 42.8 ms. Thus, the microphone current is a result of the movement of the diaphragm, not the distance between the condenser plates. As the diaphragm is displaced by a pressure pulse, the spacing between the plates decreases and the microphone output is positive in response to the rate of displacement: as the diaphragm returns to its equilibrium position, the plates are separating and the output is negative. Therefore, the shapes of the response curves shown in Figure 3 are convoluted with the response characteristics of the microphone. When the sample is initially illuminated, the change in cell pressure is rapid, as is the movement of the diaphragm, which correspondingly yields an increase in signal. After approximately 14 ms, competition between a reduction in cell pressure due to thermal transfer from the gas to the cell walls and an increase in pressure due to the PAS signal becomes significang thus, the overall rate of increase in the cell pressure decreases, which causes a reduction in the microphone output. When illumination is terminated the cell pressure decreases and the microphone diaphragm returns to equilibium causing a negative signal response. The extent of the negative response, or “flyback, depends upon the magnitude of the diaphragm displacement. Therefore, as shown in Figure 3, a longer period of irradiation produces a larger negative response. Since the “flyback” effect is a function of the physical makeup of the detector, it will be observed for all condenser or electret microphones. Figures 4 and 5 confirm that pulse response is related to concentration. Although saturation, which limits the amplitude of a PAS signal, is evident for pure carbon black, subsequent dilutions show a linear relationship between signal amplitude and concentration regardless of pulse length. The fact that the duration of decay to the base line noise level is constant confirms that the characteristics of the decay are independent of concentration or signal magnitude but are a function of the properties of the sample material, fill gasl
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ANALYTICAL CHEMISTRY, VOL. 53, NO. 13, NOVEMBER 1981
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Flgure 6. Photoacoustic response curves obtained for holmium oxide with varying periods of illumination.
microphone, and cell geometry. The response curves for holmium oxide with varying optical pulse widths are shown in Figure 6. While the decay characteristics of the data closely resemble those observed for carbon black, the shape of the rising acoustic signals is slightly different due to a change in the penetration depth and thermal conductivity of the solid sample. Moreover, the period between initiation of the radiation and onset of the photoacoustic signal is noticeably greater for holmium oxide than for carbon black. A long optical pulse should yield a steady-state condition. The rate of heat production at the sample should equal the rate of heat loss to the walls; the pressure should reach a maximum and remain there as long as the sample is irradiated, provided that a competing process such as photodecomposition is insignificant. On the basis of the foregoing discussion, the microphone signal should asymptotically approach zero since the pressure is constant. Extrapolation of the signal curves in Figures 3 and 6 supports that conclusion. In addition, experimental studies have shown that the signal does indeed decay to zero after approximately 500 ms.
CONCLUSIONS For analytical applications, achieving the maximum signal-to-noise ratio (SNR) is imperative. Theory predicts that the lowest possible modulation frequency provides the greatest signal until l/fnoise becomes overwhelming. We have shown that distortion of the signal by an inexpensive microphone detector of the condenser type prevents the maximum SNR from being achieved. Two remedies are possible. One is to
bias the condenser with an ac voltage rather than dc. The resulting signal would be related directly to capacitance (and therefore plate spacing) rather than the change in capacitance. The difficulty here is that one must measure a small change in a large signal. Nor is this feasible with electret microphones which differ from condenser types only by the introduction of a charged plastic layer, usually on the diaphragm, to provide internal polarization. A second approach is to use piezoelectric crystals which provide a potential proportional to applied pressure. Unfortunately, these are much more expensive and much less sensitive than condenser microphones. The theory of photoacoustic signals is based on the assumption that the boundary layer of hot gas at the sample surface has a small volume. For short pulses, the theory and experiment agree quite well. However, the present study of long pulses has been limited by detector response. Several workers using electret or condenser microphones of widely varying quality have alluded to slow leakage around the diaphram ( 2 , 6 , 1 0 )which may either contribute to the distortion or be an alternative explanation to the one presented here. Experimental details are not sufficient to permit comparison. In an earlier publication we described a double beam-intime photoacoustic spectrometer (7). In that system both sample and reference are contained in one cell having one detector; but sample and reference are alternately illuminated. The pulse response we have observed is the primary reason for the system performance being less than expected. The below base line response for the reference is in phase with the signal from the sample. The net effect would be a reduced apparent photoacoustic signal. We have shown here that this is a limitation of the microphone, not the double beam-in-time system.
LITERATURE CITED (1) (2) (3) (4) (5) (6) (7)
(8) (9)
(10)
Adams, M. J.; Kirkbright, G. F. Ana/yst(London) 1977, 702, 281. Kerr, E. L. Appl. Opt. 1973, 72, 2520. Bennet, H. S.; Forman, R. A. Appl. Opt. 1976, 15, 347. Rosencwaig, A. ”Advances in Electronlcs and Electron Physics”; Academic Press: New York, 1978; Vol. 46, pp 208-311. Chow, H. C.; Powell, R. C. Phys. Rev. 1980, 21, 3785. Shaw, R. W. Appl. Phys. Lett. 1979, 35, 253. Cox, M. F.; Coleman, G. N.; McCreary, T. W. Anal. Chem. 1980, 52, 1420. Eaton, H. E.; Stuart, J. D. Anal. Chem. 1918, 5 0 , 587. Malmstadt, H. V.; Enke, C. G.; Crouch, S. R.; Horlick, G. ”Electronic Measurements for Scientists”; W. A. Benjamin: Menio Park, CA, 1974; p 169. Aamont, L. C.; Murphy, J. C. J . Appl. Phys. 1978, 49, 3036.
RECEIVED for review June 4,1981. Accepted August 6,1981.
