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ANALYTICAL CHEMISTRY, VOL. 51, NO. 1, JANUARY 1979
Double-Beam Photoacoustic Spectrometer for Use in the Ultraviolet, Visible, and Near-Infrared Spectral Regions Richard E. Blank" and Theodore Wakefield I1 Research and Development, Gilford Instrument Laboratories. Inc., Oberlin, Ohio 44074
A double-beam photoacoustic spectrometer has been designed and constructed to permit acquisition of optical, thermal, and dimensional data from a variety of substances including opaque materials. Powders, gels, solids, and liquids may be analyzed directly with a minimum of sample preparation. Some spectra such as that of holmium oxide powder are included to illustrate instrumental operation and the simplified theoretical description.
Photoacoustic spectrometry (PAS) has generated considerable interest as a technique for the study of solid and liquid samples, especially when the samples are difficult to analyze by other methods (1-11). Most work to date has been done on instruments specially designed and constructed by instrumentally oriented researchers, but our work has been directed toward making instrumentation available to a broader group of scientists. In a photoacoustic spectrometer, a powerful source emits radiation which is modulated either electromechanically or electronically. T h e source may be an arc, a laser, an incandescent lamp, or other device depending on the spectral region of interest. T h e radiation used may or may not be monochromatic depending on the properties of the sample to be studied. The radiation illuminates a sample in a sealed chamber and, from the resulting temperature variation, an acoustic signal is generated. The acoustic signal is detected by a sensitive microphone, preamplified, and fed to a lock-in amplifier. The signal from the lock-in amplifier can then be processed and displayed in a number of modes.
THEORY T o understand photoacoustic spectrometry, it is desirable to have an understanding of the mechanism by which the photoacoustic signal is generated. T h e mathematical theory has been presented by Rosencwaig and Gersho (12)who have derived expressions for the magnitude and phase of the acoustic signal resulting from a sample of known optical and thermal properties in a sealed cell. Fortunately, the mechanism can be qualitatively understood without t,he complete expressions. When a modulated optical source illuminates a sample. the radiation penetrates to a depth dependent on the optical absorption coefficient, /3. The intensity a t position x in the sample obeys the relationship:
I = I,e-3XM (1) where x = 0 is the surface of the sample as shown in Figure 1 and I , is the incident optical flux. M is a modulation function and in the case of sinusoidal modulation may be given by: M = X ( l + COS u t ) (2) where w is the angular frequency of modulation (rad/s). The power supplied per unit volume (W/cm7)known as the heat density can be written: Hd = PIM (3) or 0003-2700/79/0351-0050$01.OO/O
Often the optical absorption length p P = I/@is used instead of p. Hd is plotted for three values of /3 in Figure 1. Large values of 2p result in rapid absorption of the incident energy near the sample surface as in carbon black. Small values of @ as in the case of transparent materials result in energy being liberated more uniformly deep within the sample. The optical penetration depth is not affected by modulation frequency but is dependent on wavelength for most materials. As heat is generated in each volume element, the temperature begins to rise but this is partially offset by the flow of heat out of the volume. A simplified way of viewing this is that the temperature profile as measured with distance from the source has an approximately exponential decrease. As an illustration, consider a thin absorbing plane in an otherwise transparent sample. A possible temperature profile about the plane is shown in Figure 2. I t is possible to define a characteristic thermal diffusion length, ps,which is analogous to pB, Thus p, represents a characteristic thermal length in the exponential solutions to the thermal equation. Figure 2 schematically shows the effect of changes in the thermal diffusion length, p,. In a homogeneous medium, the heat will flow both toward and away from the illuminated sample plane a t x = 3 as illustrated. The sample surface temperature depends on how far within the sample the heat is liberated (optical absorption length) and how effective the sample is in transferring the heat t o the surface (thermal diffusion length). Rosencwaig and Gersho (12) have classified solutions according to the cases: (1) p o large, p small, optically transparent sample; (2) go small, @ large, optically opaque sample; and (3) p, large, a, small, thermally thin sample; (4) p, small, a, large, thermally thick sample, where a, is the thermal diffusion coefficient defined by a, = l / p s . The magnitudes of p g and p, should be compared to the sample length. T o date, PAS has been applied principally t o opaque materials because transparent ones can be analyzed by transmission spectrometry. T h e most important case for opaque materials ( p o
