Anal. Chem. 1984, 56,1409-1411 (6) Myers, S. A.; tracy, D. H. Spectrochlm. Acta, Part 8 1983, 388, 1227-1253. (7) Belchamber, R. M.; Horlick, 0. Spectrochim. Acta, Part 8 1982, 378, 1037- 1046. (8) Lorber, A.; Goldbart, 2. Anal. Chem. 1984, 56, 37-43. (9) Lorber, A.; Goldbart, 2.; Eldan, M. Anal. Chem. 1984, 56, 43-48. (IO) Lawson, C. L.; Hanson, R. J. "Solving Least Squares Problems"; Prentice-Hall: Englewood Cliffs, NJ, 1974. (11) Lorber, A. Anal. Chem. 1984, 56, 1004-1010.
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(12) Bennett, C. A,; Franklin, N. L. "Statlstlcal Analysls in Chemistry and Chemical Industry"; Wlley: New York, 1961. (13) Lorber, A,; Eldan, M.; Goldbart. 2.; Harel, A., unpublished results, Dec 1983.
Received for review December 12, 1983. ~~~~~~d March 14, 1984.
Effect of Particle Size on Photoacoustic Signal Amplitude R. Stephen Davidson* and Doreen King Chemistry Department, The City University, Northampton Square, London EC1 V OHB, United Kingdom
The relationshlp between partlcle size and photoacoustic (PA) signal ampiltude was examlned by the use of potasslum chromate and potassium ferricyanide. For both materials a decrease in partlcle slze resulted In an Increase in the PA signal amplitude. I f reflectance propertles of the materlal are important in determlnlng the PA signal amplitude, a decrease in particle slze should have led to a decrease In the PA signal amplitude. Obviously the Kubeika-Munk theory Is of llmlted use In quanttfylng PA slgnal amplltude measurements, and the results Illustrate the Importance of other factors such as surface area.
The PA theory, as developed by Rosencwaig and Gersho (1) is extremely complicated and, to simplify the theory relating to solid samples, expressions were devised for six special cases. Three of the special cases relate to optically transparent solids, and a further three relate to optically opaque solids (2). The theory has been found to be reasonably sound, when tested experimentally, but modification of the theory was necessary to include light scattering effects (3). A Kubelka-Munk analysis has been applied to correct PA spectra for light scattering effects (4),and the implications of the Kubelka-Munk analysis for the PAS theory have been considered for light scattering thermally thick samples (5). This paper does not deal with a detailed mathematical treatment of the PA effect but with the practical implications of the already developed equations. We have previously examined the relationship between sample concentration and PA signal amplitude for potassium dichromate (6). This compound was found to behave as a typical strong absorber, giving an increase in the apparent absorption with a decrease in particle size (4). The Kubelka-Munk equation
K / S = (1 - R)2/2R where K is the absorption coefficient, S is the scattering coefficient, and R is the reflectance can be used to predict the behavior of weak, as well as strong, absorbers in diffusely scattered light. Consequently, if such a theory is included in an explanation of the PA effect, then the relationship between the Kubelka-Munk theory and the predicted PA effect should be extended to include a study of weak absorbers. This, to date, has not been done for samples which have been ground, as opposed t o samples which have been adsorbed onto substrates (5) and which are relatively weak absorbers. Weak absorbers such as silica and alumina have been used as supports and their optical properties, e.g., reflectance properties, 0003-2700/84/0356-1409$01.50/0
upon the PAS spectra of adsorbed species have been assessed (5). Consequently, we now report a series of simple experiments to determine how the particle size of a light absorbing material affects the magnitude of its PAS signal.
EXPERIMENTAL SECTION A range of potassium chromate (BDH) and potassium ferricyanide (Koch-Light) particle sizes were obtained by first grinding the powders and then passing the powders through a set of sieves, to give a particle size range of 45 pm to >250 pm diameter. Powders of diameter 45 pm to 53 pm were also diluted by adding magnesium oxide (Fisons, average particle diameter 40 rm). PAS measurements were obtained as outlined previously (6). The magnitude of the PAS signal was not significantly affected by small variations in the weight of the sample contained in the sample tray. However, for all measurements, the sample tray waa filled to a constant volume without attempting to compact the powders. Reflectance measurements were carried out with a PerkinElmer Lambda 5 UV/visible spectrometer. This is a double-beam ratio recording instrument with a filter-grating monochromator in a Littrow configuration. It has a holographic grating of 1440 lines/mm and the light sources are deuterium and tungstenhalogen lamps. The extinction coefficients for the compounds used were measured in aqueous solution with a Perkin-Elmer 402 UV/visible spectrometer and are given below h
Cr,O,ZCrO,*Fe(CN),3-
362 370 420
E
x 103 3.5 2.5 0.8
RESULTS Figure 1 shows the effect of particle size on the PA signal amplitude for the powder samples of potassium chromate and potassium ferricyanide. For both materials there is a decrease in signal amplitude with an increase in particle size. In the case of potassium chromate there is a slight visual increase in the strength of the yellow color as the particle size increases. For potassium ferricyanide, however, there is a very marked visual change in the color of the powder as the particle size increases. For small particle sizes the powder has an orange/yellow color, whereas for large particle sizes the color is orange/red. Reflectance measurements showed that for both potassium chromate and potassium ferricyanide powders an increase in particle size led to an increase in the amount of light absorbed (Figure 2). Figure 3 shows the PA spectra of the powders diluted with magnesium oxide. A Kubelka-Munk treatment of these PAS resulta does not result in a linear relationship between the K/S 0 1984 American Chemical Society
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300
ANALYTICAL CHEMISTRY, VOL. 56, NO. 8, JULY 1984
500
300 Wavelength ( n m )
500
500
300
500
300
500
Wavelength ( n m )
Flgure 1. PA spectra of (left)potassium chromate particles and (right) potassium ferricyanide particles.
300
300
500
Waveiength I n m )
Figure 2. Reflectancespectra of (left)potassium chromate particles and (right) potasslum ferricyanide partlcles.
values and the percentage (by weight) of magnesium oxide. It is noteworthy that the shape of the PA spectra are not altered by the addition of magnesium oxide (compare Figure 1 (left) with Figure 3 (left) and Figure 1 (right) with Figure 3 (right)). The PA absorption shoulders of both potassium chromate and potassium ferricyanide are much broader than those recorded from solutions used in the UV/visible spectrometer. The observed increase in PA signal intensity as the loading is increased demonstrates that even at the high levels of loadings utilized, signal saturation is not occurring. Similarly, reflectance measurements of these two compounds showed very broad absorption bands. In general, the light scattered from solid surfaces is dependent upon the ratio of diffuse (isotropic) to regular (anisotropic or specular) reflectance. Regularly reflected light is akin to light reflected from a mirror surface. The presence of this regular surface reflection always causes the curves obtained from the reflectance of powders to be greatly flattened compared with the spectra obtained in the transmission mode. The fact that PAS measurements often show rather featureless spectra led to the suggestion that light scattering may, despite earlier claims (2),be important in PAS as well as reflectance spectrometry. Consequently, attempts have been made to apply the Kubelka-Munk equation to PAS (4, 5).
DISCUSSION Some important facts arise from a consideration of the Kubelka-Munk equation. The scattering coefficient S increases with decreasing particle size. K also increases the decreasing particle size, but regular reflection decreases with decreasing particle size, and regular reflection decreases the apparent absorbance (7). If R increases, then K/Sdecreases. Although the scattering coefficient increases with decreasing particle size, the depth of penetration of the radiation decreases with decreasing particle size, and the net effect is a visual decrease in the color of weak absorbers as the particle
Flgure 3. PA spectra of (left)potassium chromate powder diluted with
magnesium oxide (expressed as weight ratio potassium chromate: magnesium oxide) and (right) potassium ferricyanide powder diluted with magnesium oxide (expressed as weight ratio potassium ferricyanide:magnesium oxide). size is reduced. Both powdered potassium chromate and powdered potassium ferricyanide are considered to be weaker absorbers than potassium dichromate (7). In the case of very strong absorbers the fraction of regular reflectance is very important. The regular reflectance diminishes with decreasing particle size, and as the regular reflection diminishes the apparent absorbance, so the apparent absorbance increases with decreasing particle size. Unlike the weak absorbers, for which the S term dominates the function, for strong absorbers the K term dominates the function, and the apparent absorbance increases with decreasing particle size. For potassium dichromate it was found that both diffuse reflectance spectra and PA spectra showed a trend of increasing absorption with decreasing particle size ( 4 ) . The results shown in Figure 2 (left) demonstrate that there was no increase (but in fact a decrease) in absorbance (measured by reflectance) as the particle size of potassium chromate was reduced. Similar results were obtained for potassium ferricyanide (Figure 2 (right)). The observed decrease in absorption with decrease in particle size is consistent with the view that these compounds are behaving as weak absorbers. However, by way of contrast, both potassium chromate and potassium ferricyanide gave an increase in the PA signal amplitude with a decrease in particle size which clearly indicates that light scattering is not the factor which dominates the magnitude of the PA signal. , Obviously the Kubelka-Munk theory is applicable to the reflectance measurements of potassium chromate and potassium ferricyanide. The theory also appears to be applicable to PA measurements of strong absorbers, e.g., potassium dichromate, but, this is not the case for the weak absorbers. In the cases presented, the weak absorbers are in the form of pure particulate samples. Thus the variation in particle size will have little effect on the amount of light absorbed but it will have an enormous effect upon the efficiency of transfer of heat from the solid to the gas since the smaller the particle size the greater the surface area. As a consequence, in such systems, particle size plays a major role in determining the PA signal amplitude. As long ago as 1881Bell noted that the most intense signals were produced from substancesin a loose, porous, spongy condition (8). Since the PA signal amplitude is determined by the efficiency of heat (generated by light absorption) transfer from the sample to the surrounding gas, it would appear that the surface/volume ratio must be a very important parameter in determining the PA signal amplitude. Consequently, it seems likely that the relationship between light scattering/surface area/signal intensity, for PAS of neat samples (as opposed to materials mixed or adsorbed on inert substrates), is a great deal more complex than was originally
Anal. Chem. 1984, 56, 1411-1416
supposed and that in certain circumstances the surface area may be the dominant factor in determining the PA signal amplitude for powdered neat samples. For a sample adsorbed onto inert support, the signal intensity will be determined by such factors as the extinction coefficient of the adsorbate, the size of the adsorbate particle, the thermal properties of the adsorbate particle, and the particle size of the adsorbent. Registry No. Potassium chromate, 7789-00-6; potassium ferricyanide, 13746-66-2.
LITERATURE CITED (1) Rosencwaig, A. “Photoacoustics and Photoacoustic Spectroscopy”; Wiley: New York, 1980.
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(2) Rosencwaig, A.; Gersho, A. Sclence 1975, 190, 556-557. (3) Helander, P.; Lunstrom, I.; McQueen, D. J. Appl. Phys. 1980, 51 (7), 384 I -3847. (4) Freeman, J. J.; Friedman, R. M.; Reichard, H. S. J. Phys. Chem. 1980, 8 4 , 315-319. (5) Burggraf, L. W.; Leyden, D. E. Anal. Chem. 1981, 53, 759-764. (6) King, D.; Davidson, R. S . ; Phillips, M. Anal. Chem. 1982, 5 4 , 2191-2194. (7) Kortum, G. “Reflectance Spectroscopy”; Springer-Verlag: West Berlin, 1969. (8) Bell, A. G. Philos. Mag. 1881, 7 1 (5), 515.
RECEIVEDfor review September 12,1983. Accepted February by the SERC and the This work was 13, Foundation.
Poly(ethy1ene maleate)-Cyclopentadiene: A Model Reactive Polymer-Vapor System for Evaluation of a SAW Microsensor Arthur Snow and Hank Wohltjen*
Naval Research Laboratory, Chemistry Division, Code 61 70, Washington, D.C. 20375
A model reactlve polymer-vapor system based on the DlelsAlder reaction has been used to verlfy the behavlor of a surface acoustlc wave (SAW) devlce chemlcal microsensor. Poly(ethy1ene maleate) (PEM) was syntheslzed and characterlzed both spectroscoplcally and thermally for use as a selectlve receptor of cyclopentadlene vapor. The formatlon of a nonreverslble Dlels-Alder adduct between the PEM fllm coatlng a SAW delay line osclllator and the cyclopentadlene resutts In a fllm mass change which Is easlly measured by the SAW device. Physlcal absorption of nonreactlng solvent vapors can be dlstlngulshed from the cyclopentadlene Interactlon. The resultlng cyclopentadlenedosimeter Is capable of detectlng 200 ppm of vapor In 1 mln. Slgnlflcantly lower detactlon llmtts are possible If longer vapor Integration perlods are allowed.
Surface acoustic wave devices are attractive for chemical microsensor applications because of their small size, low cost, and sensitivity. First reported in 1979 ( I ) , SAW devices have subsequently been used by several groups to construct sensors for various chemical vapors (e.g., ref 4-6). Vapor sensors based on SAW technology require a coating film which is sensitive and selective for the vapor to be detected. SAW microsensors consist of a small slab of polished piezoelectric material on which two sets of interdigital microelectrodes have been microfabricated. Typical devices range in size from less than a square millimeter to several square centimeters. When a set of interdigital electrodes is excited with a radio frequency (rf) voltage, a mechanical Rayleigh surface wave is generated. This wave is then free to propagate across the surface until it is “received” by the other set of electrodes and is converted back into an rf voltage. Connection of these two sets of electrodes together through an rf amplifier (Figure 1) permits the device to oscillate at a resonant frequency determined by the interdigital electrode spacing and the Rayleigh wave velocity. Coating of the device with a thin (e.g., 1pm thick) organic film results in a substantial reduction of the Rayleigh wave velocity and a corresponding decrease in the resonant frequency of the device. Vapors which can adsorb or absorb into the coating will alter the mass and
mechanical properties of the coating thereby producing easily measured frequency shifts. It has been shown ( 2 , 3 )that the resonant frequency shift produced by a thin coating film can be described by the following relationship:
where Af is the change in SAW resonant frequency due to perturbation of the Rayleigh wave velocity by the thin overlay f i i . Parameters kl and kz are material constants for the SAW substrate, f o is the unperturbed resonant frequency, h is the thickness of the film, p’ is the film density, V , is the unperturbed Rayleigh wave velocity, A’ is the Lam6 constant, and p’ is the modulus of the overlay film. It should be noted that the product of hp’ is simply the mass per unit area. Thus, theory predicts that the SAW frequency shift depends primarily on two factors; the mass per unit area and the mechanical properties (i.e., Lame constant and modulus) of the film. For typical organic films (e.g., polymers) the modulus is small enough to permit the mechanical property terms to be neglected thereby allowing 1 to be simplified to
Af
E
(k, + kz)f&p’
(2)
In the case of a typical 1pm thick (h = 1X lo4 m) polymer film (p’ = 1000 kg/m3) coated onto a YX quartz (k, = -9.33 X kz = -4.16 X lo4 m2 (s/kg)) SAW delay line oscillator resonating at 31 MHz, equation 2 predicts a frequency shift of -129.6 kHz. Frequency shifts of this magnitude are observed experimentally for various polymeric films (3). Application of films which are too thick result in excessive attenuation of the Rayleigh wave energy and a subsequent quenching of oscillation. It has been found that coating thicknesses approximating 1% of the acoustic wavelength are desired so that the mass absorbtion capacity for vapors will be high enough for good sensitivity but not so thick that quenching of the oscillation occurs. At 31 MHz (SAW wavelength = 100 pm on ST-Quartz) film thicknesses of about 1 pm meet this criterion. The objective of this study is to observe the behavior of a SAW vapor sensor coated with a film having a high degree of selectivity for a particular vapor. Information regarding
Thls article not subject to U.S. Copyright. Publlshed 1984 by the American Chemical Society
