375
Anal. Chem. 1988, 58,375-379
Supercritical Fluid for Sample Introduction in Supersonic Jet Spectrometry Hiromi Fukuoka, Totaro Imasaka, and Nobuhiko Ishibashi* Faculty of Engineering, Kyushu University, Hakozaki, Fukuoka 812, Japan
The rotational temperature of NO, In the supersonlc jet was estimated from the profile of the hlgh-resolutlon excltatlon spectrum of NO,. When only Ar was used as an expansion gas, the observed temperature was 5 K. It gradually increased with increasing partial pressure of CO, contalned In the expansion gas (10 K at 100% CO,). The observed values were consistent wlth the translational temperatures calculated from the theory. The fluorescence and excltatlon spectra of perylene were measured by using varlous supercritical fluids as a carrler. The cooilng effect increased In the order of nhexane N n-pentane < benzene methanol < COP< Ar. These results show that the coollng effect is strongly affected by rotational and vibratlonai modes of freedom of the carrier molecule.
Supersonic jet spectrometry is a powerful technique for preparing an ultracold molecule, and it provides greater selectivity in chemical analysis due to its capability to give a simplified spectrum (1,2). This spectroscopic technique has recently been used for determination of several hydrocarbon molecules (3-12). In this method the sample is vaporized in a nozzle and then expanded into a vacuum; therefore only a gaseous or volatile samples have currently been studied. Many nonvolatile samples, such as drugs and vitamins, have not been investigated. The ability to apply supersonic jet spectrometry to these nonvolatile samples might have an impact on not only analytical applications but also more fundamental studies, such as physical chemistry and biophysics. For analysis of nonvolatile samples, many analytical chemists currently use high-performance liquid chromatography (HPLC), where water or organic solvents such as methanol are used as carrier solvents. A mass spectrometric detedor is already combined with HPLC, in which the sample solution is first nebulized at atmospheric pressure, and solvent molecules are then removed from sample droplets by raising the temperature (13-19). It may also be possible to apply this interface for sample introduction in supersonic jet spectrometry. However, the solvated molecule is rather stable at room temperature, and it is quite difficult to remove solvent molecules from the cluster. In our preliminary study, this clustering prevented sample cooling by the supersonic jet, so this approach was not successful at the present stage. Supercritical fluid has recently been used as a carrier for chromatography because of its capability for fast separations and high resolution. The determination of polycyclic aromatic hydrocarbons and biochemical substances has already been reported (18,191. The most common detectors are based on ultraviolet absorption (20,211. The other methods using a thermal lens effect (22) and a flame ionization technique (23) are useful for more sensitive detection of the sample species. It is already combined with mass spectrometry and is used for determinations of many thermally labile substances (24-26). When the supercritical fluid is expanded to atmospheric pressure, the sample molecule may readily release solvated molecules since the cluster is unstable in this con0003-2700~86~0358-0375$0 i.50/0
dition. This method might be more preferable for sample introduction in supersonic jet spectrometry. In this study we used several supercritical fluids, such as COz, as carrier media for supersonic jet spectrometry. First, we investigate the cooling effect using NO2 as a sample and COz as a carrier gas. Second, we demonstrate the measurement of the fluorescence and excitation spectra for perylene by using various organic solvents and COz,which are currently used as carriers for supercritical fluid chromatography. We compare the cooling effect for these media, and the involvement of rotational and vibrational modes of freedom of the carrier molecules is discussed.
EXPERIMENTAL SECTION Apparatus. The experimental apparatus of supersonic jet spectrometry is shown in Figure 1. The sample of perylene is placed in a 1/4-in.stainless-steel tube. A cylinder (70 atm) with a siphon supplies liquid COz to the stainless-steel tube. After the stop valve was closed, the sample in the tube was heated to 100 "C. This raised the pressure to 150 atm. A HPLC pump (Shimadzu,LCdA) was used for supercritical fluids that are liquid at room temperature. The nozzle was wrapped with a tape heater and was maintained at -100-300 O C . The structure of the nozzle is shown in Figure 2 and is identical to a continuous-flow, hightemperature nozzle developed in the previous study (9). However, a narrow stainless-steel tube (0.30 mm i.d., 0.55 mm 0.d.) is introduced inside the 1/16-in.stainless-steel tube (0.8 mm id.). The narrower tube used for sample introduction is simply pinched at the top of the nozzle to maintain the high pressure (-70-150 atm). The glass capillary nozzle, whose top is narrowed by use of a gas flame, may give more reproducible results. This approach was also tested, but it was sensitive to the mechanical shock and was not used in this study. The supercritical fluid of COz dissolving the sample is mixed with Ar and is subsequently expanded into a vacuum from a pinhole (0.3 mm i.d.) made of a sheet of stainless steel. The spacing between the pinched restrictor and the pinhole orifice was adjusted to 1mm. The vacuum chamber is a 4-in. cylinder with four windows located perpendicular to each other. It was evacuated with a 6-in. diffusion pump (Ulvac, ULK-06, 1400 L/s) equipped with a cold trap (Daia, L-type), which was followed by a mechanical booster pump (Shimadzu, MB-30 H, 520 L/min) and a ratary pump (Ulvac, PVD-l80K, 186 L/min). An excimer laser (Lambda Physik, EMGlOBE, 170 mJ) , pumped dye laser (Lambda Physik, FL2002,0.007 nm line width) excites the sample molecule in the supersonicjet 5 mm away from the nozzle. Fluorescence is collected by a lens with a focal length of 10 cm and is introduced onto the entrance slit of a 40-cm double monochromator (Jasco, CTdOD) equipped with a photomultiplier (Hamamatsu Photonics, R928 or R212). A photoelectron current is measured by a boxcar integrator (NF Circuit Design Block, BX530A). Timings of the signals are controlled by a homemade pulse generator through a data-link system (Mitsubishi Rayon, Eskalink, EDO101). Reagents. The C 0 2 and AI were obtained from Etoh Oxygen CO.,and organic solvents of n-hexane, n-pentane, benzene, and methanol were from Kishida Chemical Co. The sample of perylene was purchased from Aldrich Chemical Co. and used without further purification. The gas cylinder of NO2was obtained from Takachiho Chemical Co. The laser dyes of 7-(diethylamino)-4methylcoumarin (7D4MC) and 1,4-bis[2-(5-phenyloxazolyl)]benzene (POPOP) were supplied from Eastman Kodak Co. and Kishida Chemical Co., respectively.
I
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1986 American Chemlcal Society
378
ANALYTICAL CHEMISTRY, VOL. 58, NO. 2, FEBRUARY 1986
1 PulseGeneratorH-1 Figure 1. Supersonic jet spectrometer using supercritical fluid for sample introduction.
(A) Ceramic insulator 200 400 600 7 0
w, n 1 . '
~
'
Partial pressure
(A)
co2 (torr)
(B)
Effect of partial pressure of C02 on (A) rotational temperature and (B) fluorescence intensity of P(2) line of NO, emission,
Heater
pressure was adjusted to -400-500 torr, at which point a maximum signal intensity was obtained.
lwate
1 Pinhole
Supersonic Jet
[+ Supercritical Fluid
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Partial pressure of
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Copper Ring Stainless Foil
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Supersonic jet nozzle structure (A) and top of nozzle (B).
Procedure. The typical flow rate of the supercritical fluid was 300 pL/min. The flow rate of Ar was not measured but was
carefully adjusted to not exceed the maximum exhaust rate of the pumping system. When the excessive sample gas was introduced into the chamber, the path of the laser beam was visible due to light scattering by gas remaining in the chamber. In this case the flow rate was reduced to maintain the free expansion condition. Calculation of Temperature. The rotational temperature of the supersonic jet was measured by recording a high-resolution excitation spectrum of NOz at around 450 nm, according to the procedures previously reported (27, 28). In this experiment a pulsed nozzle (pinhole diameter, 0.8 mm) was used. The exciting source was a homemade nitrogen laser pumped dye laser, which had a spectral resolution of -0.01 nm. The carrier gas was prepared by mixing COzand Ar in a vacuum line. The stagnation
RESULTS AND DISCUSSION Temperature i n Supersonic Jet. The rotational temperature of NOz was measured a t various partial pressures of COP The result is shown in Figure 3A. When only Ar was used as an expansion gas, the observed rotational temperature was 5 K. When the partial pressure of COz, is increased the temperature linearly increases to 10 K. It is noted that the observed temperature is less accurate at a higher temperature since the poor spectral resolution of the dye laser cannot completely resolve the congested rotational structure. The distance from the nozzle and laser beam was X = 8 mm, and the diameter of the nozzle was D = 0.8 mm; the ratio of X / D = 10. In this condition the achieved Mach numbers are 15 for Ar and 7 for COz (29),and the translational temperatures in the jet are calculated to be 3.9 and 38 K, respectively. These values are consistent with the observed rotational temperatures. The increase of temperature with an increase in the partial pressure of C02 may be due to the freedom of rotation for COP. The fluorescence intensity of the P(2) rotational line is greatly decreased with an increase in the partial pressure of COz, as shown in Figure 3B. Addition of Ar to a carrier gas cancels the dilution effect. The signal decrease of the P(2) line may be attributed to the smaller population in the low rotational level with an increase in temperature. It may be possible that collisonal quenching of fluorescence occurs even in the supersonic jet, because of its large cross section for NO2 and a short expansion distance of X = 8 mm. Supersonic Jet Spectrum of Perylene i n Ar. The fluorescence spectrum of perylene is shown in Figure 4,where Ar (-500 torr) is used as a carrier gas and the sample is heated to 300 O C . Sharp vibrational lines are observed, and congestion of the rotational structure is almost completely absent. The line width of the peak is limited by the spectral resolution of the monochromator (0.25 nm). The excitation spectrum of perylene was also measured, and the vibrational lines were clearly resolved (9). The observed line width (0.06 nm) was limited by a rotational envelope determined by the jet tem-
ANALYTICAL CHEMISTRY, VOL. 58, NO. 2, FEBRUARY
1986
377
Wavelength(nm) Flgure 4. Fluorescence spectrum of perylene: spectral resolution, 0.25 nm; diluent gas, Ar. "420
do
4iO 4;O 460 Wavelength(nm)
"420
4jO 440 450 Wavelengthh)
(B)
(A)
Figure 8. Fluorescence spectra of perylene; supercritical fluid, benzene: diluent gas, (A) none, (B) Ar; spectral resolution, (A) 0.25 nm, (B) 0.5 nm; nozzle temperature, 300 OC; pressure, (A) 200 atm, (B) 90 atm.
hz415.41nm
I
I
420
430 440 450 Wavelengthhm)
(A)
4
0 420
430 440 450 Wavelength(nm)
480
4 I
(B)
-
Flgure 5. Fluorescence spectra of perylene: supercritical fluid, n hexane; diluent gas, (A) none, (B) Ar; spectral resolution, 1 nm; nozzle temperature, 250 OC; pressure, 5 0 atm. The broken line represents the spectrum measured at 290 OC In the gas phase using a statlc cell.
414
415
416
Wavelength(nrn)
perature. The noble gas has no freedom of rotation and is more preferable as an expansion gas compared to the other media used as supercritical fluids. But, the sample of perylene should be heated to a rather high temperature to maintain a sufficient vapor pressure. n -Hexane. The supersonic jet fluorescence spectrum was measured for perylene dissolved in a supercritical fluid of n-hexane (critical temperature, T, = 234.2 "C; critical pressure, P, = 29.3 atm). The results are shown in Figure 5, where part is recorded with n-hexane as the expansion gas and Part B is obtained by mixing with Ar before expansion into the vacuum. Even when n-hexane is used as a carrier, the jet spectrum is more well-resolved in comparison with that measured in the vapor phase at 290 0C. However, resolution of the rotational structure is poor, and the jet temperature is implied to be considerably high. On the other hand, the temperature can be sufficiently reduced by mixing with Ar. It is noted that the signal-to-noise ratio (S/N) is better for the spectrum measured by diluting the carrier gas with Ar. Rather, it indicates that mixing with Ar enhances the signal intensity and is useful for sensitive detection of the sample species. The investigation was also performed by using npentane (T,= 196.5 "C, P, = 33.3 atm) as a supercritical fluid, and a similar result was obtained. These n-alkanes are currently used as solvents for normal-phase HPLC, and therefore the present instrument may be useful as a detector for HPLC. However, the high critical temperature may not, unfortunately, allow its application to the thermally labile molecules such as vitamins. Benzene. Figure 6 shows supersonic jet fluorescence spectra for perylene, which is introduced after it has been dissolved in benzene (T, = 289.0 "C, P, = 48.4 atm). The spectrum consists of sharp vibrational lines, even when it is measured without using Ar as a diluent gas. The cooling effect
Figure 7. Excitation spectrum of perylene: supercritical fluid, benzene; diluent gas, Ar; nozzle temperature, 300 OC; pressure, 90 atm.
.-
-
-'5$
-
n
fd F3
z
z
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.5
5
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-'i
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;
G O 420 430 440 450 460 Wavelength(nrn) (A)
820 430 440 450 460 Wavelengthhm) (5)
Figure 8. Fluorescence spectra of perylene: supercritical fluid, CO,; diluent gas, (A) none, (B) Ar; spectral resolution, 1.5 nm; nozzle temperature, 100 OC; pressure, (A) 130 atm, (B) 90 atm.
is larger than that of n-hexane. In Figure 7 the excitation spectrum of perylene is shown. The vibrational band of the 0-0 transition consists of a single line, but it is still broad (0.3 nm) because of its small cooling effect. We also investigated for methanol, and the resulb were similar to those for benzene. Methanol is frequently used as an eluent for reverse-phase HPLC, but it has a rather high critical temperature and pressure (T, = 239.4 "C, P, = 79.9 atm). Carbon Dioxide. Figure 8 shows the fluorescence spectra for perylene, which was recorded using C02 as a supercritical fluid (T,= 31.0 OC, P, = 72.8 atm). The flat base line of the spectrum shows that perylene is more rotationally cooled than benzene. The observed line width is determined by the resolution of the monochromator. Similarly, the sharp line
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ANALYTICAL CHEMISTRY, VOL. 58, NO. 2, FEBRUARY 1986
h
6 0
6
0 414
415
416
Wavelength(nm)
(A)
417
414
415
416
417
Wavelength(nm)
(5)
Flgure 9. Excltation spectra of perylene: supercritical fluid, C02; diluent gas, (A) none, (8)Ar; nozzle temperature, 100 O C ; pressure, 100 atm.
structure is observed in the excitation spectrum as shown in Figure 9A, even when the sample is measured without using Ar as a diluent gas. When Ar is mixed with the COz and perylene, the 0-0 band at 415.41 nm is greatly enhanced. The spectral feature and the line width are almost identical to the spectrum obtained when only Ar was used as the carrier gas (9). It indicates that the sample molecule is sufficiently cooled rotationally and vibrationally when the supercritical fluid of COz mixed with Ar is used. In the first stage of our experiment, a narrower stainlesssteel tube (0.15 mm i.d.1 was used to introduce a supercritical fluid. Then, the pressure was decreased at the top of the nozzle. In addition to the nozzle being insufficiently pinched, the measurement was carried out at a rather low sample pressure (-70 atm). Under these conditions no fluorescence signal was observed. It was found that the dissolving power greatly decreased with decreasing sample pressure in the stainless-see1 tube. It is reported that the solubility of naphthalene in COz at 50 "C increases 2 orders of magnitude with an increase in COz pressure from 70 to 150 atm (30). The carrier gas of COz has a large cooling effect in supersonic jet spectrometry, and simultaneously it has the low critical temperature at the moderate pressure. As such, it seems to be a quite attractive medium in supersonic jet spectrometry of thermally labile biochemical molecules. We expect that its application to the detector for supercritical fluid chromatography may be very advantageous for analyzing biological fluids. Cooling Effect. The observed temperature apparently depends on the supercritical fluid used and the mixing ratio with Ar. The cooling effect increases in the order of n-hexane N n-pentane C benzene = methanol C C 0 2 C Ar. This tendency is identical with that of the rotational and vibrational degrees of freedom. It is noted that benzene consists of many atoms, but it is rigid and has high symmetry. Consequently, it has several degrees of freedom of rotation and vibration. In supersonic jet spectrometry, cooling of the sample molecule takes place through the translation-rotation and translation-vibration relaxations after the translationtranslation relaxation between the sample and diluent molecules. When the carrier molecule has many rotational and vibrational modes of freedom, cooling of the sample molecule is very inefficient since the carrier molecule itself is cooled. In this case a large amount of Ar, which has no degrees of freedom, should be mixed with the carrier, though a larger pumping system might be necessary. The use of a pulsed nozzle may be promising to overcome this problem. Sensitivity. The measurements of the fluorescence spectra were carried out at concentrations of M for benzene and M for n-hexane, n-pentane, and methanol. When COz was used as a supercritical fluid, the sample concentration was
unknown. However, the concentration is implied to be -10-5-10-6 M from the S/N ratio of the spectrum in comparison with those of the other spectra. Taking into account pressure reduction from the critical pressure to atmosphere (-100 times), sample dilution with Ar (-3 times), and volume expansion into vacuum ( -IO5 times), the concentration of perylene in the laser irradiation volume is considered to be 10-l' mol/L. The absolute sample molecule is estimated to be mol, which corresponds to 2 X lo4 molecules. This is almost the minimum number of molecules that can be measured by present laser fluorometry with sufficient spectral resolution. This rough estimation informs us that the sensitivity of supersonic jet spectrometry, using a supercritical fluid, is similar to that of conventional absorption spectrometry. Rather poor sensitivity comes mainly from the sample expansion processes; as such, they should be reduced as much as possible for sensitive detection. It is suggested that a pulse nozzle be used to increase the sample density in the molecular jet. Besides, a jet separator that is currently used as an interface between gas chromatography and mass spectrometry may be advantageous, when the molecular weight of the sample is sufficiently larger than that of the solvent. The sample of perylene deposits at the top of the nozzle, since the molecule is unstable at 100 "C in the vapor phase. Then, the spacing between the pinched restrictor and the pinhole orifice should be carefully optimized. If the spacing is too long, the sample deposits at the orifice so that the sensitivity decreases. If the spacing is too short, the mixing with Ar is insufficient so that the cooling effect is small. Therefore, the sensitivity and the cooling effect should be compromised. However, further investigation was not carried out in this study because of irreproducibility of the pinched restrictor. Other Supercritical Fluids. The supercritical fluid COz has a low critical temperature at a moderate critical pressure. Moreover, it has a sufficient cooling effect because of its small modes of freedom of rotation and vibration. In order to decrease the jet temperature further, it may be possible to use a noble gas as a supercritical fluid. Xenon seems to be a very attractive medium, since it has a lower critical temperature (T,= 16.6 "C, P, = 57.6 atm), greater solubility (31), and no modes of freedom of rotation or vibration, although it is rather expensive. Supercritical fluid chromatography combined with Fourier transform infrared spectrometry has already been demonstrated using Xe as a carrier (32). The C 0 2molecule has a small polarity so that it sometimes suffers from poor solubility in polar samples. In this case other inorganic molecules may be used as supercritical fluids. The solubility parameter of the supercritical fluid is given by Giddings et al. (33) 6 = 1.25~,'/~[[p,/p,(liq)]
(1)
where pr and pr(liq) are densities for a supercritical fluid and a liquid, respectively. For example, NH3 (6 13.2; 132.4 "C; 111.3 atm) and NOz (6 12.4; 158 "C; 100 atm) are known to be more polar media (cf. 6 10.6 for C02 and 14.4 for methanol). Smalley et al. have reported a jet temperature of 30 K achieved by expanding pure NOz into a vacuum (34). For modification of the solubility, a small amount of the polar medium may be added to a nonpolar supercritical fluid. Chromatography using the carrier of COz containing -0.16-1.5% methanol is frequently used for analysis of biochemical substances (19). The critical constants of T,and P, for the mixture can be estimated by T , = XATA XBTB (2)
+ P , = XAPA + XBPB
(3)
where X Aand X B are molar ratios for the components, and
379
Anal. Chem. lS88, 58, 379-384
TA and TB and PA and PB are critical temperatures and pressures, respectively, for individual components. By addition of a small amount of methanol, the solubility is greatly increased, but the critical constants me only slighty modified. As such, this approach may be ver$ promising for application to supersonic jet spectrometry of the polar sample. However, it is, at present, unknown whether the expanded sample in the vacuum exists as a bare molecule or is strongly solvated with methanol. Therefore, further investigation may be necessary for complete discussion of this possibility. ACKNOWLEDGMENT The authors thank Taketoshi Sonoda for his cooperation in the construction of the supersonic jet nozzle for nebulization of the liquid sample. LITERATURE CITED
(10) (11) (12) (13)
Hayes, J. M.; Small, G. J. Anal. Chem. 1983, 55, 565A-574A. Johnston, M. V. Trends Anal. Chem. (Pers. Ed.) 1884, 3, 58-81. Warren, J. A.; Hayes, J. M.; Small, G. J. Anal. Chem. 1982, 5 4 , 138-140. Hayes, J. M.; Small, G. J. Anal. Chem. 1982, 5 4 , 1204-1206. Amirav, A.; Even, U.; Jortner, J. Anal. Chem. 1982, 5 4 , 1888-1673. Lubman, D. M.; Kronlck, M. N. Anal. Chem. 1882, 5 4 , 660-865. Sin, C. H.; Tembreull, R.; Lubman, D. M. Anal. Chem. 1984, 5 6 , 2776-2781. Tembreuli, R.; Lubman, D. M. Anal. Chem. 1984, 5 6 , 1982-1967. Imasaka, T.; Fukuoka, H.; Hayashi, T.; Ishibashl, N. Anal. Chlm. Acta 1984. 156. 111-120. Imasaka, T.; Shlgezumi, T.; Ishlbashi, N. Ana/yst(London) 1984, 109 277-279. Imasaka, T.; Hirata. K.; Ishibashi, k. Anal. chem. 1985, 5 7 , 59-62, Yamada, S.; Wlnefordner, J. D. Spectrosc. Left. 1985, 16, 139-151. Yoshlda, H.; Matsumoto, K.; Itoh, K.; Tsuge, s.; Hirata, Y.; Mochizuki, K.; Kokubun, N.; Yoshida, Y. Fresenlus’ 2.Anal. Chem. 1982, 311, 674-680.
(14) Liberato, D. J.; Fenselau, C. C.; Vestal, M. L. Yergey, A. L. Anal. Chem. 1983, 55, 1741-1744. Covey, T.; Henlon, J. Anal. Chem. 1983, 5 5 , 2275-2280. Apffei, J. A.; Brinkman, U. A. Th.; Frei, R. W.; Evers, E. A. I. M. Anal. Chem. 1883, 5 5 , 2280-2284. Wilioughby, R. C.; Browner, R. F. Anal. Chem. 1984. 56, 2826-2631. , Fjeidsted, J. C.; Lee, M. L. Anal. Chem. 1984, 5 6 , 619A-626A. i l 9 l Gere. D. R. Hewlett-Packard Co.: Avondaie. P A ADDlicatlon Note AN .. 600. (20) Takeuchl, T.; Ishli, D.; Saito, M.;Hibi. K. J . Chromatogr. 1984, 295, 323-331. (21) Greibrokk, T.; Billie. A. L.; Johansen, E. J.; Lundanes, E. Anal. Chem. 1984, 5 6 , 2661-2684. (22) Leach, R. A.; Harris, J. M. Anal. Chem. 1884, 5 6 , 2601-2805. (23) Norris, T. A.; Rawdon, M. G. Anal. Chem. 1984, 56, 1767-1769. (24) Smith, R. D.; Udseth, H. R. Anal. Chem. 1883, 55, 2286-2272. (25) Smith, R. D.; Udseth, H. R.; Kalinoski, H. T. Anal. Chem. 1984, 56. 2971-2973. (26) Smith,k. D.: Kalinoski, H. T.; Udeseth, H. R.; Wright, B. W. Anal. Chem. 1984, 56, 2476-2480. (27) . . Smailev. R. E.: Wharton. L.: Levy, D. H. J . Chem. Phys. 1975, 63, 4977-4989. (28) Havashl, T.; Imasaka. T.; Ishibashi, N., submitted for publication In J . Chem Phys (29) Mikaml, N. Oyo Buturi 1980, 49, 802-812. (30) Arima, M. Kagaku Sochi 1984, 7 , 27-38. (31) Krukonis, V. J.; McHugh, M. A.; Seckner, A. J. J . Phys. Chem. 1984, E E . 2687-2689, -... (32) M. Novotny “Recent Advances in Microcolumn (capillary) Liquid Chromatography: an Overview”; 6th International Symposium on Capliiary Chromatography, Riva del Gerda, Italy, May 14-16, 1984. (33) Giddings, J. C.; Myers, M. N.; McLaren, L.; Keiier, R. A. Science 1988, 162, 67-73. (34) Smalley, R. E.; Ramakrlshna, B. L.; Levy, D. H.; Wharton, L. J . Chem. Phys. 1974, 61, 4363-4384. I
,
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.
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RECEIVED for review June 24,1985. Accepted September 24, 1985. This research is supported by a Grant-in-Aid for Seientific Research from the Ministry of Education of Japan and by a Nissan Science Foundation.
Normalized Distances for Qualitative Near- Infrared Reflectance Analysis Howard Mark Technicon Instrument Corporation, Industrial Systems Division, 51 1 Benedict Avenue, Tarrytown, New York 10591
Near-infrared reflectance spectrometry (NIRA) has been shown to be an accurate and rapid method of qualitative analysis when Mahalanobis distances are used to determine the classification of unknown samples. The use of this concept depends upon the data derived from the calibration samples having certain mathematical properties; in particular, each material in the calibration must occupy a region of multidimensional space that has the same size, shape, and Orientation. I n NIRA, the shape and orientation of these regions are the same, but the sizes can differ. Thls deviation from the assumptions used in the calculations can be compensated for by normalizing the data by the root mean square size of each group. This allows more accurate ciassMcatlons in the face of failure to meet the assumptions on whlch the simpler discrlmlnant calculations are based.
Since the early days of near-infrared reflectance analysis (1-3) there has been considerable development of this technique as a means of quantitative analysis (4-6), but it is only recently that investigations have been made as to the suitability of this technique for qualitative analysis (7-9). One of the bottlenecks to investigations in this field is the requirement 0008-2700/86/0358-0379$0 1.50/0
for the development of suitable mathematical/statistical algorithms to manipulate the data. Our previous investigations have shown that the computation of Mahalanobis distances in multidimensional space is a viable approach to the problem of having a computer match spectra of unknowns to those of various known materials in the face of the extraneous variations superimposed on the spectra (7). When no variations exist to cause problems, as in transmission spectrometry in the mid-IR, a simplified form of the same approach may be used (10). Computation of Mahalanobis distances has several advantages as a method of identification, most of which have been discussed in the previous paper. Another advantage, not previously mentioned, is that this technique may be used as a go-nogo check method. If only a single group representing “good”product to calibrate is included, departures from proper production that change the spectral signature can be detected. This characteristic circumvents the difficulties of the asymmetric case described by Wold et al. ( 1 1 ) )since the distance can be calculated in any direction. Indeed, the use of the HAT matrix by Schenk et al. (9) is an example of such usage; close comparison of the expression for the diagonal elements of the HAT matrix with the expression for Mahalanobis distance (12) reveals them to be identical. Nevertheless, the 0 1986 American Chemical Society
