ANALYTICAL CHEMISTRY, VOL. 50, NO. 9, AUGUST 1978
were identified by both sets of features.
CONCLUSIONS While the analysis of peak potentials yielded the most accurate classification results for the data set used here, these are not generally reliable, and other features must be considered. Curve shape features were very useful for classification of' the voltammograms obtained here. Both the voltammetric features and the Fourier coefficients appeared to contain similar class information and were reasonably good features. Classification based on scan rate dependence of Fourier coefficients was also significant. The fact that the best class clusters were obtained for the curves taken at 695 mV/s indicates that a scan rate in this range may provide the most reliable information. At this scan rate, and the a' values used, data were obtained with negligible charging current contributions. Since some of the curves taken at a' = 0.7 for the fastest scan rate had different shapes from those taken a t a' = 0.3, charging current may have been a contributing factor. Problems with extraneous shoulders on the main peaks obtained a t slow scan rates for some compounds were mentioned earlier. These deviations observed a t the fastest and slowest scan rates were partially the cause for errors in classification based on scan rate dependence. The results indicate that benzophenone (No. 25) probably belongs to a different class of compounds than the four that were represented in the data set. The peak for the reduction of the carbonyl group in m-nitrobenzaldehyde (No. 27) was obviously distorted by the tail of the first reduction peak. The reasons for the other outliers are not obvious. They are probably different because of a change in the reduction mechanism, a change in the value of an, or complications such as adsorption. Considering the limited data set used, the results obtained here were very encouraging. I t does appear t h a t functional
1371
group and some structural information can be identified in voltammetric waveforms by the application of empirical pattern recognition methods. Thus, further studies are warranted, utilizing a more extensive data base. This study has provided a basis for further work by identifying useful data acquisition conditions, analysis approaches, and features.
ACKNOWLEDGMENT The authors thank Lars Kryger for his contributions in the early stages of this project. LITERATURE CITED (1) P. Zuman, "Topics in Organic Polarography", Plenum Press, New York, N.Y., 1970. (2) 8. Kastening in "Progress in Polarography", Vol. 3, P. Zuman, I . Kolthoff, and L. Meites, Ed., Wiley-Interscience, New York, N.Y., 1972. (3) P. Zuman, "Substituent Effects in Organic Polarography", Plenum Press, New York, N.Y., 1967. (4) J. J. Zipper and S. P. Perone, Anal. Chem., 45, 452 (1973). (5) D. R. Ferrier and R. R. Schroeder, J . €lectroanal. Chem., Interfacial Electrochem.. 45, 343 (1973). (6) R. S.Nicholson and I.Shain, Anal. Chem., 36, 704 (1964). (7) H. Clark, "Determination of Hydrogen Ions", Williams and Wilkins Co., Baltimore, Md., 1928. (8) Q. V. Thomas, Lars Kryger, and S. P. Perone, Anal. Chem., 46, 761 ( 1976). (9) D. R. Burgard, S. P. Perone, and J. L Wiebers, Biochemistry, 16, 1051 ( 1977). (10) L. Meites, Anal. Cbim. Acta, 18, 364 ('1958). (11) L. B. Sybrandt and S. P. Perone. Anal. Chem.. 44, 2331 (1972). (12) Q . V. Thomas and S . P. Perone, Anal. Chem., 49, 1369 (1977). (13) Q. V. Thomas, R. A. DePalma, and S. P. Perone, Anal. Cbem.,49, 1376 (1977). (14) J. W. Hayes, D. E. Clover, and D. E. Smith. Anal. Chem.. 45, 277 (1973). (15) M. A. Pichler and S. P. Perone, Anal. Chem., 46, 1790 (1974). (16) K. Fukunaga, "Introduction to Statistical Pattern Recognition", Academic Press, New York, N.Y., 1972, Chapter 10. (17) R. W. Rozett and E. M. Petersen, Anal. Chem., 47, 1301 (1975). (18) D. R. Burgard. P h D Thesis, Purdue University, 1977.
RECEIVED for review February 21, 1978. Accepted May 22, 1978. Work supported by the Office of Naval Research.
Optoacoustic Spectrometry in the Near-Infrared Region M. J. Adams," B. C. Beadle, and G. F. Kirkbright Chemistry Department, Imperial College of Science and Technology, London S. W. 7., U.K.
A single-beam optoacoustic spectrometer is described for operation in the near-infrared spectral region. Correction for varlatlons in source emission intensity with wavelength is achieved sequentially with the aid of a digital scan recorder. The instrument has been employed for the examination of the absorption bands observed from a variety of sample types.
In recent years there has been considerable interest in the optoacoustic effect and its applications for analysis in optoacoustic spectrometry (OAS) for the study of the ultraviolet and visible absorption spectra of solid and solution samples. Several OAS spectrometers have been described in the literature for studies in this spectral region (1-3). OAS monitors the heating effect produced by the absorption of electromagnetic radiation and the corresponding rise in pressure of a filler gas contained with the sample in a sealed cell of constant volume. The periodic pressure variations within the cell, achieved by modulation of the incident radiation, are measured with the aid of a sensitive microphone. Several advantages of the technique over conventional optical 0003-2700/78/0350-1371$01 .OO/O
transmission and reflectance spectrometric methods of analysis have been proposed, including the ability to examine a wide variety of sample types and optically opaque materials. Rosencwaig has reported the use of OAS in studies of inorganic ( 4 ) and biochemical ( 5 ) samples, and Adams et al. (6) have recently employed the technique as a calorimetric method for the determination of absolute fluorescence quantum efficiencies. As a pressure transducer is employed to monitor indirectly the periodic temperature changes occurring within a sample following the absorption of radiation, no photometric detector is required and, provided the incident radiation is of sufficient power to produce a measurable signal, the optoacoustic effect may be employed in any spectral region. To date, the majority of the studies undertaken with condensed phase samples have been concerned with the ultraviolet-visible region. Adams et al. ( I ) , however, have recently described a double-beam optoacoustic spectrometer employing a high-pressure xenon arc continuum source capable of operation within the spectral range, 250 nm to 2.5 pm. Unfortunately, rare-gas continuum sources exhibit intense line emission in the near-infrared, thus making difficult the correction of spectra for the variation in 1978 American Chemical Society
1372
ANALYTICAL CHEMISTRY, VOL. 50, NO. 9, AUGUST 1978
/A\
n
I
i\
Sample
Cell
Body
w
Micropbone
I
10
I
15
I
2 0
I
25
-Al,pl-
Figure 2. The near-infrared optoacoustic spectra of (-)
-
holmium oxide
and (- -) dysprosium oxide
Figure 1. The optoacoustic cell
source emission intensity with wavelength. Absorption bands observed in the near-infrared spectral region, 0.75 to 2.5 pm may usually be attributed to low-energy electronic transitions or the harmonics (overtones) and combinations of fundamental vibrational modes observed in the molecular species examined. T h e overtone bands arise from the anharmonicity of the molecular vibrations and combination bands are observed in polyatomic species due to interactions between functional group vibrations. The overtone vibrational frequencies most commonly examined in the near-infrared region are hydrogenic systems, particularly those of -CH and -OH. This paper reports the use of a single-beam optoacoustic spectrometer in the near-infrared spectral region; a tungsten filament source is employed and sequential correction of spectra for variation in source emission intensity with wavelength is undertaken with the aid of a digital storage scan-recorder. T h e application of this spectrometer t o the study of a variety of sample types is described.
EXPERIMENTAL Apparatus. The source employed is a 250-W quartz-halogen, tungsten-filament bulb (Type Al/233, Wotan Lamps Ltd., London, U.K.) operated at 25 V/dc. The radiation from the source is focused, using a concave, front-surfaced mirror, through a variable speed rotating sector mounted a t the entrance slit of a f/4 monochromator. The optical system employed has been described previously (2). Studies in the near-infrared region were undertaken with a plane (300 lines mm-', 50 mm X 50 mm) grating, blazed at 2.0 pm and with fixed, 2.5-mm wide, entrance and exit slits. This arrangement provided for a reciprocal linear dispersion at the exit slit of 12 nm (0.012 pm) mm-'. To prevent overlapping spectral orders of diffraction being transmitted to the optoacoustic cell, low-wavelength cut-off filters were positioned at the exit slit of the monochromator. The spectral transmission range of the two filters employed was 0.8-1.5 pm and 1.5-2.7 pm. The radiation from the exit slit of the monochromator was focused into the optoacoustic cell by means of a concave mirror. The optoacoustic cell employed is shown in Figure 1 and is similar to that described by McClelland and Knisely (7). The cell was constructed from aluminum with a 20-mm diameter silica entrance window. A type 4166 capacitor microphone (Bruel and Kjaer Ltd., Hounslow, U.K.) was employed as the pressure transducer. The polarization voltage (240 V) and preamplifier voltage (25 V) for the microphone were supplied from a dry-battery source. Samples were placed in highly polished aluminum cups (16-mm id., 3-5 mm deep) and sealed within the cell by means of four locking-nuts. The optoacoustic signal at the microphone transducer was led directly to a lock-in amplifier (model 186, Princeton Applied
Research Corp., Princeton, N.J.); the reference signal was derived from the rotating sector. The output from the lock-in amplifier was led to a digital scan-recorder system (Model 4101, PAR Corp., Princeton, N.J.). This recorder was employed in the two-channel mode to store the reference (lamp emission) spectrum and a sample spectrum. Spectral correction was achieved with the aid of the internal ratiometer unit. The corrected optoacoustic spectra were displayed on a conventional potentiometric chart recorder. All the optoacoustic spectra reported were obtained with a wavelength scan-rate of 300 nm min-I and an amplifier time constant of 1 s. Reagents. The rare-earth oxides were obtained as high purity, fine powders (Johnson Matthey Ltd., London, U.K.). Type 60 silica gel, TLC grade, was employed for the -OH studies (Merck, Darmstadt, Germany). The n-hexane and benzene mixtures were prepared with laboratory grade reagents and the crude oil samples were supplied by Shell Research Ltd. (Thornton, U.K). Procedure. The source emission spectrum (reference) was obtained by recording the OAS spectrum of a silica plate coated with carbon black; the blackbody absorption characteristics of this sample were confirmed by comparison of the spectrum with the source emission spectrum obtained with a calorimeter detector as described previously for ultraviolet-visible studies (8). Samples were examined by placing the powder (ca. 100 mg) or solution (ca. 100 pL) into the alumimum sample cup and sealing this into the optoacoustic cell.
RESULTS AND DISCUSSION Low Energy Electronic Transitions. Electronic transitions in molecular species characteristically occur in the ultraviolet-visible region of the spectrum. However, many inorganic compounds exhibit low-energy transitions which may be examined by their near-infrared absorption spectra. Figure 2 shows the absorption spectra of two rare-earth oxides in the 1 t o 2.7 pm spectral region. As with the UV-visible spectra of these materials, the electronic transitions are observed as intense, narrow absorption bands due to the shielding of the 4f electrons (9). The rare-earth oxides absorption bands are well defined and may be employed for wavelength calibration of the spectrometer. -OH Absorption Bands. The fundamental oxygen-hydrogen vibrations of a nonbonded hydroxyl group (water) occur at ca. 2.7 to 2.8 pm and the first overtone at ca. 1.4 pm; the combination band is observed a t 1.9 pm. For bonded hydroxyl groups, the first overtone is apparent also at 1.4 pm but the combination band occurs a t 2.2 pm. Thus, nearinfrared absorption studies may be employed to characterize the nature of -OH groups present in a sample. Figure 3 shows several optoacoustic spectra obtained from samples of TLC grade silica gel. The activity of this material for thin-layer chromatography depends on the surface hy-
ANALYTICAL CHEMISTRY, VOL. 50, NO. 9, AUGUST 1978
1373
v '
I
10
I
I
2 0
15
-AI,!-
2 5
Id
Figure 3. The near-Infrared optoacoustic spectra of TLC grade silica gel; (a) untreated, (b) after drying at 1000 OC, and (c) after drying at 1000 OC and exposure to water vapor
droxyl groups bound to the silica. It is evident from the spectrum of the untreated sample (Figure 3a) that both bound hydroxyl groups (1.4 and 2.2 pm) are present as well as surface water (1.4 and 1.9 pm). After drying this sample a t ca. 1000 "C, the activity of the silica gel is destroyed and, as shown in Figure 3b, this is accompanied by a loss in -OH absorption bands. Figure 3c demonstrates how, upon exposure to water vapor, the preheated silica gel may adsorb water (1.4 and 1.9 pm) but does not regain the bonded hydroxyl groups necessary for TLC activity. -CH Absorption Bands. The fundamental carbonhydrogen stretching vibration absorption band is observed normally a t ca. 3.3-3.5 pm, and the first overtone a t ca. 1.7 pm. In practice, however, numerous absorption bands are observed in the near-infrared due to C-H bending overtones and the many combination bands possible. As the separation of C-H overtones is greater than that between the fundamentals from which they arise, the near-infrared region may be employed for their identification and characterization. T h e optoacoustic spectra of a series of aromatic samples are shown in Figure 4 and compared with an aliphatic system, n-hexane. The similarities in the aromatic hydrocarbons are evident and the differences may be attributed to physical nature of the sample, Le., its solid or liquid nature. The aromatic C-H absorption band at 2.2 pm was observed not to occur in aliphatic systems and was employed as a means of quantitive analysis for aromaticity in organic mixtures. The absorption band intensities have been shown to be additive, according to the number of absorption centers in a molecule ( I O ) . Mixtures of benzene in n-hexane were prepared and 100-pL aliquots of these examined by OAS. A linear relationship was observed between peak-height, a t 2.2 pm, and benzene concentration between zero and 100% benzene in the samples. Figure 5 shows the OAS spectra of undiluted Iranian crude oil samples to which standard additions of benzene have been made; linear plots were obtained for peak-height, at 2.2 pm vs. concentration of benzene present.
CONCLUSION T h e single-beam optoacoustic spectrometer described enables the study of absorption spectra in the near-infrared region. Unlike the majority of spectrometers described in the literature, the system discussed employs a relatively low power tungsten filament continuum source. While rare-gas filled arc-lamps have a greater radiant flux and are suitable for use
i I
1
l10
2Io
115
-hIy
2'5
I-*
Figure 4. The near-infrared optoacoustic spectra of (b) anthracene, (c) benzene, and (d) n-hexane
h
I
1 1
+II I
// /
I
(a)benzanthracene,
I
IO
I 2c
1 '5
-Alp1
-
I
25
Figure 5. The near-infrared optoacoustic spectra of Iranian crude oil with standard additions of (a) 10% benzene, (b) 30% benzene
in the ultraviolet regions, their use is limited in the nearinfrared because of the intense narrow line emission superimposed on the continuum background, thus making double-beam operation difficult to achieve. The tungsten filament source described above provides a near blackbody emission spectrum with an emission wavelength maximum, with the above spectrometer, a t ca. 1.4 pm. The use of the spectrometer to examine a variety of sample types has been described and clear spectra have been obtained from solid powder, solution, and thixatropic oil samples. The near-infrared spectral region may be employed for the examination and characterization of inorganic and organic materials by the absorption bands in this region because of low energy electronic transitions, overtone bands, and combination bands. With the advantages already proposed for OAS, the extension of the working spectral range to include the near-infrared, as described above, should provide for many further applications of the technique in the examination of materials which are normally difficult to study. Quantitative analysis is possible in the near-infrared and, as described, may b e employed for the determination of aromaticity in organic mixtures.
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ANALYTICAL CHEMISTRY, VOL. 50, NO. 9, AUGUST 1978
ACKNOWLEDGMENT We are grateful to the Department of Industry for the provision of a studentship to one of us (B.C.B.). LITERATURE CITED
(5) A. Rosencwaig. A. P. Grisberg, and J. W. Koepke, Inorg. Cbem., 15, 2540 (1976). (6) . , M. J. Adams. J. G. Hiahfield. and G. F. Kirkbriaht. A n d . Cbem... 49.. 1850 (1977). (7) J. F. McClelland and R. N. Knisely, Appl. Opt., 15, 2967 (1976). (8) M. J. Adams, A. A. King, and G. F. Kirkbright, Analyst (London), 101, 73 (19761 \
(1) M. J. Adams, B. C. Beadle, and G. F. Kirkbright, Ana/yst(London),102, 569 - - - (19771 (2) D. M. Munroe and H. Reichard, Am. Lab., 9, 119 (1977). (3) A. Rosencwaig, Rev. Sci. Instrum., 48, 1133 (1977). (4) A. Rosencwaig and E. Pines, Biocbim. Biophys. Acta, 493, 10 (1977). \ . - . . I .
- I
(9) W.B. White, Appl. Spectrosc., 21, 167 (1967). (10) , , 0 H. Wheeler. Chem. Rev.. . 59.. 629 (1959). . ,
RECEIVED for review March 13, 1978. Accepted May 24, 1978.
Evaluation and Optimization of the Standard Addition Method for Absorption Spectrometry and Anodic Stripping Voltammetry J. P. Franke' and R. A. de Zeeuw State University, Laboratory for Pharmaceutical and Analytical Chemistry, D e p a ~ m e n of t Toxicology, Ant. Deusinglaan 2, 97 13 A W Groningen, The Netherlands
R. Hakkert State Unversity, Mathematical Institute, Groningen, The Netherlands
For the determination of the concentration of a substance by standard addition linear regression, which may be applied when the measurements have a common varlance, is compared with other regression techniques based on the assumption of a common coefficient of variation. The latter assumption may be more realistic for atomic absorption spectrometry and anodic strlpping voltammetry. For the optimization of the standard addition method, assuming a common coefficient of variation, formulas are given to calculate, for a desired precision, the amount of standard to be added and the required number of replicate measurements. Optimum precision is obtained by applying a single addltion of the largest possible amount of standard within the linear range of the response concentration curve.
The method of standard addition is often used (1-3) to determine the unknown concentration, io,of a substance in a solution: new solutions are made from the original one by adding successive, known amounts of that substance. Thus, solutions with concentrations &, E, + xl, ..., t o+ x k are obtained, where x1 < x 2 < ... < x k are known positive constants. For each solution several response-readings can be obtained, leading to a set of data (y,,;j = 1, ..., n,; i = 0, ..., k ] , where y I Jrepresents the j t h response-reading on the sample with concentration to(if i = 0) or E, + x, (if i # 0). The statistical analysis will be based on the idea that the response-readings y I Jare the outcome of corresponding random variables Y,], whose joint distribution is such t h a t (1) all Y,, are mutually independent; (2) YI1,..., Y,,, is a random sample from the normal distribution with EY,, = 1,and Var(Y,,) = ;a: (3) after appropriate corrections have been made for any background signal, the concentration-response curve is a straight line passing through the origin, or, more precisely, for some unknown regression coefficient, p, it is assumed that 1,= @(E,
+ 4.
Apart from these basic assumptions, various additional ones can be made with respect to the variances a,' ..., ah2. Most authors, using standard regression methods to estimate ( 4 ,
c0
0003-2700/78/0350-1374$01.00/0
5 ) , implicitly assume homoscedasticity, Le., a', =
al'
=
... =
ah'.
However, theoretical considerations of Mann et al. (6) and our own experimental data contain evidence (Section 4) that this assumption is not always relevant. I t rather looks as if au2< a12< ... < ah'. If sufficient replicate measurements in 0,xl, ..., x k are available, it is possible to estimate a,' ..., separately. If, however, no such replications are available, one has to make some sort of model-assumption. It might be more realistic to assume equality of the coefficients of variation, Le., ao/po= al/,ul = ... = ah/&. Mann et al., dealing with absorption spectrometry (6) and Larsen et al. ( 4 ) , whose data are presented in Section 4, suggested that the latter assumption approximately holds true in the absorption range between 0.2 and 1.0 (6). T h e basic assumptions 1, 2 , and 3 mean in practice that: (1)Each addition of standard should be made to the original sample, without appreciable error, and for each solution the response-readings should be obtained independently. (2) Response-readings, YI1, ..., Y,,, are an independent random sample from a normal distribution. Generally speaking this will be valid for atomic absorption spectrometry and anodic stripping voltammetry (7).Fortunately, small deviations from normal distributions will not have a large effect on the merits of the statistical procedures. (3) The linearity of the concentration-response curve should be checked by experiments over a wide concentration range. By application of standard addition, one should check that the highest concentration is still within the linear part of the curve and the slope of the curve should remain unaffected by the addition of standard. Figure 1 summarizes the necessary terminology. Here, k = 3; no = 3; nl = 3; n2 = 4; n3 = 3 and the individual response-readings yIl are represented by the open circles. The dotted regression line is specified by the unknown parameters toand p, or, alternatively, by the usual regression-parameters, a = F~ and p. Note that 5, = a / @ . In the next section the two existing calculation methods, the graphical method and standard linear regression are evaluated. So far, little or no attention has been paid to the effects of replicating the response-measurements on the C 1978 American Chemical Society
