for free-lying bands, i.e., the number of inflection points must be twice the number of bands. If the base line is to be calculated in the curve-fitting routine, a sufficient number of base line points must be included in the sampled area. If the base line is determined independently, this requirement can be relaxed to the extreme bands of the system being free from overlap.
ACKNOWLEDGMENT The authors express their gratitude to J. H. Kelderman for helpful discussions about the computer programs and for his permission to exploit his peak-find procedure before publication.
LITERATURE CITED (1) R. D. B. Fraser and E. Suzuki. Anal. Chem., 41,37 (1969). (2) K. S. Seshadri and R. N. Jones, Spectrochlm. Acta, Part A, 19, 1013 (1963). (3) R. P. Young and R. N. Jones, Chem. Rev., 71,219 (1971). (4) A. M. Kabieland C. H. Boutros, Appl. Spectrosc., 22, 121 (1968). (5) F. C. Strong Ill, Appl. Spectrosc., 23, 593 (1969). (6) J. Pltha and R. N. Jones, Can. Spectrosc., 11, 14 (1966). (7) J. Pitha and R. N. Jones, Can. J. Chem., 44, 3031 (1966). (8) R. N. Jones etal., Nat. Res. Counc. Can., Bull. No 11 (1968). (9) R. N. Jones et a/., Nat. Res. Counc. Can., Bull. No 12 (1968). (10) R. N. Jones et ab, Nat. Res. Counc. Can., Bull. No 13 (1969). (11) A. H. Anderson, T. C. Gibb, and A. B. Littlewood, J. Chromtogr. Scl., 6, 640 (1970).
(33) (34) (35) (36)
A. H. Anderson, T. C. Gibb. and A. B. Littlewood, Anal. Chem., 42, 434 (1970). A. H. Anderson, T. C. Gibb, and A. B. Littiewood, Chromatographla, 2, 466 (1969). D. Audo, Y. Armand, and D. Arnaud, J. Mol. Struct., 2, 287 (1968). D. Audo, Y. Armand, and D. Arnaud, J. Mol. Struct., 2, 409 (1968). J. W. Perrarn, J. Chem. Phys., 49, 4245 (1968). A. R. Davis etal., Appl. Spectrosc., 26, 384 (1972). J. R. Beachamand K. L. Andrew, J. Opt. Soc. Am.. 61, 231 (1971). J. Pitha and R. N. Jones, Can. J. Chem., 45, 2347 (1967). L. M. Schwartz, Anal. Chem., 43, 1336 (1971). R. N. Jones, Pure Appl. Chem., 18, 303 (1969). H. V. Drushel e t a / . ,Anal. Chem., 40, 370 (1968). D. Papousek and J. Pliva, Collect. Czech. Chem. Commun., 30, 3007 (1965). H. Stone, J. Opt. Soc. Am., 52, 998 (1962). P. C.Jurs, Anal. Chem., 42, 747 (1970). J. Meiron, J. Opt. SOC.Am., 55, 1105 (1965). J. R. Morrey, Anal. Chem., 40, 905 (1968). E. Grushka and G. C. Monacelli, Anal. Chem.. 44, 464 (1972). A. W. Westerberg, Anal. Chem., 41, 1770 (1969). A. Savitzky and M. J. E. Golay, Anal. Chem., 36, 1627 (1964). A. Ralston and H. S.Wilf. Ed., “Mathematical Methods for Digital Cornputers II”, Wiiey & Son, New York, N.Y., 1967, p 192. iUPAC (International Union of Pure and Applied Chemistry), Butterworths, London, 1961. R. N. Jones and A. Nadeau, Spectrochlm. Acta, 20, 1175 (1964). J. T. Bulrner and H. F. Shurvell, J. Phys. Chem., 77, 256 (1973). J. T. Bulrner and H. F. Shurvell, J. Phys. Chem., 77, 2085 (1973). W. Zenker, Anal. Chem., 44, 1235 (1972).
RECEIVED for review March 18, 1975. Accepted July 1, 1975.
Analytical Lines for Long-Path Infrared Absorption Spectrometry of Air Pollutants Bruce M. Golden and Edward S. Yeung Ames Laboratory-ERDA
and Department of Chemistry, Iowa State University, Ames, Iowa 500 10
A scheme for selecting resonant frequencies for the analysis of gaseous air pollutants using long-path absorption of narrow-band infrared sources Is presented. A computer search is conducted using existing spectrometric data to determine lines with minimum interference and maximum sensitivity. Results are given for the pollutants 0 3 , N20, CO, CH4, and the nonpolluting species, H 2 0 and COP.
With the availability of narrow-band infrared laser sources (1-3), there has been increased interest in using long-path infrared absorption for air pollution monitoring (3-7). Since the emission profile of the laser is very narrow relative to vibrational-rotational absorption lines a t atmospheric pressure, by the proper choice of absorption frequency, determination of a given pollutant should be accomplished with high sensitivity and selectivity. Until now, however, no attempt has been made to determine absorption frequencies which are the most suitable for analysis of gaseous pollutants, i.e., those frequencies where the contributions to the total absorbance of the pollutant of interest are high and all other contributions are low. Consequently, it has been common to rely on accidental coincidences of gaseous absorption lines with fixed frequency lasers (3, 4, 7), or on the assumption that only lines in the “atmospheric windows” are useful (5, 7). To avoid such a hit-and-miss approach, and to establish the best spectral lines for infrared absorption spectrometry for the common air pollutants, we have devised a scheme which allows a systematic search of all reasonably strong absorption lines of a given gas and determines which lines are the most suitable for 2132
use as analytical lines (AL’s). As a test of the method, AL’s for six common atmospheric constituents have been determined and the results are critically evaluated.
COMPUTATIONAL PROCEDURE Our interest will be concentrated on the infrared spectral region from 4 to 20 pm, where all gaseous pollutants have vibrational-rotational resonances and where diode lasers and gas lasers are known to work well. Of special interest in this region are H20 and C02, the nonpolluting atmospheric constituents, whose strong absorptions in certain parts of this region make them a major source of interference in determining pollutant concentrations. In this spectral region, reliable spectral information is available (8, 9) for each of the six molecules HzO, COS, 03,N20, CO, and CH4, and our calculations are based on this. The calculations can readily be extended to include other pollutants, e.g., NO2, NO, SOz, H2S, H2C0, HN03, once the appropriate spectral information becomes available. The entire infrared spectrum of each species is computed from 4 to 20 pm using an IBM 360/65 computer. The details of the computer programs will not be presented here, but will be supplied on request (10). The main reason for computing the entire spectrum of each molecule is that, after the initial calculation of the individual spectra, “backgrounds” for any set of concentrations are easily constructed and are available for all frequencies within the spectral region. Calculation of the degree of interference at an arbitrary frequency is thus facilitated. This is important because the frequencies of the AL’s of a given pollutant are not known in general. Actual computation of a molecule’s spectrum involves
ANALYTICAL CHEMISTRY, VOL. 47, NO. 13, NOVEMBER 1975
knowing the resonant frequency of each transition of that molecule, the line widths, the line strengths, and the energies of the lower states involved. We have obtained such spectral data through a recent compilation by R. A. McClatchey e t al. (8) and revised by K. Fox (9). Instead of the assumption of a Lorentz line shape, we chose to assume a “super-Lorentzian” line shape (11) on the basis that the latter is probably a slightly better approximation, and has a tendency to overestimate rather than underestimate absorbances at far wings. We can thus determine the “worst case” for the interferences. The spectrum is generated over the entire spectral range a t 0.01-cm-l increments, a resolution easily attained with diode lasers and one that will adequately define pressure broadened infrared absorptions. A temperature of 25 “(2 and a pressure of 1 atmosphere are assumed throughout. T o facilitate computation, contributions to the spectrum are neglected if they fall below 2.7 X ppm-l meter-’ in magnitude, or, for line-wing contributions, if they fall below of the absorbance at line center. In the former case, they cannot significantly contribute to any long-path measurements and, in the latter case, the super-Lorentzian assumption cannot be expected to hold. Upon completion of the individual spectra, a “background’’ is constructed for each pollutant. This is simply the sum of spectra of interfering constituents, taking into account all atmospheric species except the species of interest. A different background is generated for each pollutant. The concentrations used for background spectra generation are typical of ambient concentrations (8) and are shown in Table I. For a given pollutant, the values of its absorbance a t all resonant frequencies are then compared to the corresponding background absorbance values. For a ratio of absorbance-of-pollutant to absorbance-of-background of unity, the interfering species accounts for half of the absorbance. This was chosen to be the threshold value. Any resonant absorption having an absorbance-to-background ratio greater than unity is considered to be a preliminary analytical line for that molecule. The concentrations of H2O and CO2 are so high relative to typical pollutant concentrations that contributions to the absorbance a t frequencies which are at considerable distances from band centers are non-negligible. This necessitates a refined calculation of absorptivities of the two molecules a t the preliminary AL frequencies for the other molecules, taking into account such contributions. The absorptivities for all other molecules are retrieved from the original calculated spectra. These values are then used to make a quantitative estimate of the amount of interference from each species for the AL’s, along with a measure of the sensitivities for the AIL’S.
’
RESULTS A N D CONCLUSIONS Table I1 is a listing of the absorptivities for all of the molecules of this investigation at the selected AL frequencies. This is the most valuable information of this study in that it gives the frequencies that are most suitable for analytical determination of the four molecules 0 3 , N20, CO, and CH4 and permits calculation of the amount of interference expected from any arbitrary set of concentrations for the major air constituents. Calculations can also be made to determine the sensitivities of the various AL’s. Note that Table I1 is only a partial listing of the analytical lines obtained from this study. The ones listed are the best in terms of the amount of interference predicted when all species are assumed to have the ambient concentrations listed in Table I. A complete listing for all the acceptable AL’s can be obtained upon request (IO).
~~
Table I. Ambient Concentrations of Atmospheric Constituents Molecule
HZO CO2
Concentration, ppm
10,000~ 330
0 3
0.48b
NZO
0.28
co c H4
0.075 1.6 Corresponds to about 30% relative humidity at 25 “C. Typical maximum concentration is used here to determine effects in the worst case. Ambient ozone levels can be as low as 0.02 ppm.
Table I11 shows the amount of interference predicted for each of the AL’s in Table I1 on the basis of percent contribution to the total absorbance by each molecule. Ideally, 100% of the absorbance should be due to the molecule to be determined, indicating no contributions from other species. At the ozone AL frequencies, a nearly ideal situation exists. This is also true for over 100 other resonant frequencies in the frequency region from 1010 to 1050 cm-’. In this case selection of practically any ozone resonant frequency will give satisfactory results. For the remaining three pollutants, the case is far from ideal. Nitrous oxide and methane are seen to have AL’s in the region centered around 1300 cm-l, N2O having AL’s generally below this frequency and CH4 having AL’s generally above. For both of these species, there are non-negligible contributions t o the total absorbance a t their AL frequencies from water vapor. The average amount of interference is about 34% for N20 and approximately 2096 for CH4. An important point to note is that the calculation of interference is based on the background concentrations listed in Table I. For H20, the concentration listed is lo4 ppm, a figure representing a relative humidity of about 30%. Thus, the contribution to the total absorbance a t AL frequencies from water vapor, as shown in Table 111, will be higher for higher ambient H2O concentrations. Table I11 also shows that N20 and CH4 also interfere with each other but, in this case the amount of interference is relatively small and would be of little consequence in an experimental situation. Another point worthy of mention is the proximity of NzO and CH4 AL’s. Diode lasers generally have limited output frequency ranges. By choosing AL’s whose frequencies are closely spaced, analysis of more than one pollutant may be accomplished using one diode laser, as may be the case with the N20 line at 1278.11 cm-’ and the CH4 line at 1283.45 cm-l. Of the four pollutants studied, carbon monoxide had the most severe interferences. In this case, COS is the major source of interference, amounting to over 60% for the best CO AL’s. Minor interferences can also be expected from water and ozone. However, as the concentration of any one pollutant increases from its typical ambient concentration, the amount of relative interference for that pollutant decreases. This point is shown graphically in Figure 1 for increasing methane concentrations. For the AL a t 1303.71 cm-l, the background interference amounts to approximately 20% when all species are at ambient concentrations. As the methane concentration is doubled, the relative interference drops to 11%and drops further to 7% a t 6.4 ppm. Thus, as the concentration of the pollutant of interest increases, interference naturally becomes less of a problem. Such is the case with tolerance limits set by, e.g., the Occupational Safety and Health Administration, which are typically much higher than the ambient concentrations given in Table I.
ANALYTICAL CHEMISTRY, VOL. 47, NO. 13, NOVEMBER 1975
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Table 11. Analytical Lines and Interferences Absorptivitiesa at AL Frequencies Frequency, cm-1
0 3
NZO
co
CH4
0
1025.08 1026.52 1031.OO 1034.84 1038.53 1047.61 1278.11 1292.29 1293.89 1295.48 1297.05 2111.55 21 15-63 2119.68 2123.70 2127.69 21 54.60 1283.45 1303.71 1306.11 1327.06 1332.71
H20
6.3 x 6.7 X lo-'' 8.1 x lom1' 6.9 X 7.2 x lo-'' 7.7 x 10-12
1.3 X 1.5 X 1.6 x 1.7
X
1.7 6.3 6.3 6.2 8.0 5.9 4.6 1.8 1.8 2.6 2.5 3.1
X X X
10"' lo-''
x x lo-'' x 10-10 X X
lomio lo-*
x x X X
1V8 1V8
c02 4.6 X lo-'' 4.6 X 10'" 4.5 x 10-1' 4.5 x 10-1' 4.6 x 5.3 x 10-11 2.8 x 10-14 2.5 x 1 0 - l ~ 2.5 x 10-14 2.5 x lom1' 2.4 x 10-14 1.0 x 10-6 1.1 x 10-6 1.1 x 10-6 1.1 x 10-6 1.2 x 10-6 1.4 x 2.4 x 10-14 2.1 x 10-14 2.1 x 10-14 1.8 x 10-14 1.8 x 10-14
03
3.1 3.4 4.7 4.3 3.9 4.8 4.8 4.1 3.9 3.8 3.6 5.7 2.7 4.3 3.7 1.8 1.0 4.6 2.9 2.6 4;o
10-4 10-4 10-4 10-4 x 10-4
3.3 x 3.3 x 5.8 x 8.0 x 1.2 x 2.2 x 9.0 x 1.0 x 1.1 x 1.1 x 1.1 x 8.0 x 8.6 x 9.2 x 9.9 x 1.1 x 3.8 x 7.7 x 9.6 x 1.6 x 9.9 x 7.3 x
x 10'4 X
10" lo-*
x
10'8
X
lo-*
X
x
x 10-6 x 10-5 x 10-5 x 10-5 x 10-5 x 10" X lo-* x x lo+
x 10-9 1.2 x 10-9
Units: ppm-1 meter-1; absorptivities are set to zero when less than 2
co
N20
x x x x
10-9
CH4
0 .o
0.0 0.0 0 .o
10'9
10-9 10-9 10-8 10'8
0.0
0.o 0 .o
0 .o 0 .o 0.0
10-4
0 .o 0 .a
6.1 x lom6 3.6 X 9.0 x 1 0 ' 6 9.1 x 10-6 6.6 X 0.0 0.0
0.0 0.0 0 .o 0 .o
10-3 10-3 10-3 10-3 10-7 lom7 10'7
0.0 2.0 2.3 2.5 2.5 2.3 2.2
10'7
10-6 lom6
x
x 10-3 x
10'3
x x
10'3
0 .o 0.0 0.0 0 .o
10'3
x 10-3
0 .o 0 .o 0.0 0.0 0.0
10'5
10-5 10-4
10-7 10'7
3.8 5.5 7.1 7.0 6.8
x 10-4 x 10'4 x 10-4 x 10-4 X
X
Table 111. Percent Contribution to Total Absorbance a t AL Frequencies
- 4.0
AL
N
P
5 3.2 W
v
O3
2 24 m
a
I6
m a 0.8
NZO
0D 1302
1303
1304
I305
1306
FREQUENCY I N CM-'
Flgure 1. Computer-generated absorption spectrum of methane in air at various concentrations, 10-m path, calculated at 0.01 cm-' resolution
Because of the relatively large amounts of interference expected in monitoring certain pollutants, it may be necessary to do a multicomponent analysis to determine the concentrations of pollutants whose AL's have major interferences, especially at concentration levels close to ambient. For this reason, AL's for H2O and COP are also needed. Listed in Table IV are a number of AL's and their associated absorptivities for water and carbon dioxide. These AL's are determined a t line centers, as are all AL's, and have essentially no interferences. Thus, absorptivities of other molecules are not listed. The concentrations of HzO and C02 determined from these lines could then be used to correct for interferences present in AL's for the pollutants. The AL's for H20 and C02 were chosen not only on the basis of minimal interference, but also on the basis of absorptivity. Lines were chosen that had a range of absorptivities (thus sensitivities) because the strongest line is not always the most desirable for analysis. An AL which is less sensitive may be needed if the transmittance from the strong line is too low to measure accurately in the same path as for the determination of the pollutants. 2134
CO
CH,
cm-1
H20
1025.08 1026.52 1031.00 1034.84 1038.53 1047.61 1278.11 1292.29 1293.89 1295.48 1297.05 2111.55 2115.63 2119.68 2123.70 2127.69 2154.60 1283.45 1303.71 1306.11 1327.06 1332.71
0.0 0.0 0.0 0.0 0.0 0.0 33.6 33.2 32.9 34.4 35.3 1.3 1.2 1.1 1.4 1.0 0.7 22.2 16.9 18.3 18.6 22.1
C02
0.0 0.0 0.0 0.0 0.0 0.0 0.0
0.0 0.0 0.0 0.0 68.9 65.2 63.4 63.7 67.2 74.1 0.0 0.0 0.0 0.0 0.0
O3
N20
99.9 99.9 100.0 100.0 100.0 100.0 0.0 0.0 0.0 0.0 0.0 0.6 2.4 3.6 3.0 1.5
0.0 0.0 0.0 0.0 0.0 0.0 63.9 65.6 64.1 62.7 62.4 0.0 0.0 0.0 0.0 0.1
0.0 0.0 0.0 0.0 0.0 0.0
2.7 2.5 3.0 0.0 0.0
0.2
co 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 29.2 31.2 31.9 31.8 30.2 25.1 0.0 0.0 0.0 0.0 0.0
CH4
0.0 0.0 0.0 0.0 0.0 0.0 2.5 1.3 3.0 3.0 2.2 0.0 0.0 0.0 0.0 0.0 0.0 75.1 80.6 78.7 81.4 77.9
As an alternative to a multicomponent analysis, instrumentation may be able to electronically subtract out background interferences. This type of scheme is feasible for AL's which are imposed on a slowly or constantly changing background with respect to frequency. The average background about a given transition is subtracted from the rapidly changing resonant peak. In Figure 1, the methane transition centered at 1303.71 cm-l is imposed on a background which is relatively constant from 1303.50 cm-l to 1303.75 cm-1. A t higher frequencies, the background has an absorbance due to a resonance line centered at 1303.91
ANALYTICAL CHEMISTRY, VOL. 47, NO. 13, NOVEMBER 1975
Table V. Sensitivitiesa of AL's
Table IV. Analytical Lines for HzO a n d COz Frequency, Molecule
H2O
cm-1
1690.13 1714.80 1710.96 1721.56 650.41 690.37 649.54 710.00 2359.39 2375.79 2297.19
Frequency,
Absorptivity, -1 ppm m-'
4.1 1.4 2.6 1.8 4.4 2.1 3.6 1.8 1.6 3.6 2.1
Molecule
x 10-5 x 10-5 X
x 10-4 x 10-4 x 10-5 X
x 10-3 x 10-4 x 10-4
cm-'. If an average background measurement was made that included the interfering resonance lines, an erroneous value of CHI concentration could result. Thus, this CH4 AL is not well suited to this particular type of analysis. A derivative technique, however, such as described by Hinkley et al. ( I ) , might be useful in the determination of CHI by the 1303.71 cm-l AL since the background is constant over most of the line. In addition, Ku et al. (12) have recently shown that a derivative technique can also be used to minimize the effects of atmospheric turbulence on long-path absorption measurements. The information generated by this study can therefore be used to determine whether a given scheme of analysis is feasible using a given AL, by a simple examination of the background in proximity to the AL. The sensitivities of the AL's can be determined from the information compiled in this study. A common measure of sensitivity of a given transition is expressed as the concentration required for an absorbance of 0.01 for a specified path length. Table V shows the sensitivities of the various pollutant AL's for a path length of 1 meter. The actual detection limit for a given line is obviously determined by the detection system used. Assuming a 1%change in the transmittance as the detection limit, a path length of about 25 meters would be needed to detect CO and 0 3 at their ambient concentrations. Methane and nitrous oxide could be detected a t ambient concentrations using a shorter path length because the absorbance per unit path length is more favorable than for carbon monoxide and ozone. Fortunately, the differences in absorbances per unit path length are not great so that all four species can conveniently be measured over the same path length. The scheme described here, however, is not without its limitations. The accuracy of AL frequencies and associated absorptivities is dependent on the spectrometric data used to generate the spectra, and on the validity of the superLorentzian line shape approximation. Interferences from other atmospheric pollutants to AL's have been unaccounted for, but in most cases, the interference would probably be small, as with N20 and CH4 interfering with each other. Thus, we hope that in the not-too-distant future, more accurate spectral data on line positions, line strengths, and line widths will become available, so that these calculations can be refined. Such data should become accessible with current laser spectroscopic studies. It must be emphasized that these results are only a first approximation in determining the best frequencies for analysis. Actual analytical lines and their associated absorptivities must be measured experimentally. This will eliminate the need for assumptions such as the super-Lorentzian line shape. The scheme, as it stands, is capable of providing information on the amount of interference that
Sensitivity, ppm
33.0 29 .O 21.0 23 .O 25.0 21.0 11.0 10.0 8.9 9.1 9.4 co 5.1 4.4 4 .O 4 .O 4.3 4.6 27.0 18.0 14 .O 14 .O 15.0 a Concentration t h a t produces 0.01 absorbance for a 1-m path, neglecting t h e effects of interferences.
03
x
cm-1
1025.08 1026.52 1031.00 1034.84 1038.53 1047.61 1278.11 1292.29 1293.89 1295.48 1297.05 2111.55 2115.63 2119.68 2123.70 2127.69 2154.60 1283.45 1303.71 1306.11 1327.06 1332.71
can be expected a t any frequency and the associated sensitivities for any molecule, provided the proper spectrometric data are available. As witnessed from our test case, it is not always possible to find lines where interference effects are negligible. However, one can determine the optimum frequencies, where interference is minimal and sensitivity is the highest, and can obtain a quantitative estimate of both. Our results should be immediately useful since it is not expected that further refinement of spectrometric data would appreciably alter the choice of AL's. Refinements are needed only to define precisely the degree of interference of the other atmospheric constituents on a particular AL. Finally, we note that it is in fact possible to have AL's not in the "atmospheric window" regions (e.g., N20 and CHI), as long as one can determine the magnitudes of the interferences. LITERATURE C I T E D (1) E. D. Hinkiey, K. W. Nill, and F. A. Blum in "Laser Spectroscopy of Atoms and Molecules", H. Walther Ed., Springer-Verlag. Heidelberg (in press), and references therein. (2) H. J. Gerritsen in "Physics of Quantum Electronics". P. L. Kelley et ai., Ed., McGraw-Hill, New York. 1966, p 581. (3) R . T. Menzies, Appl. Opt., 10, 1532 (1971). (4) L. 8 . Kreuzer, N. D. Kenyon, and C. K. N. Patel, Science 177, 347 (1972). (5) E. D. Hinkley. MIT Lincoln Lab. Report (1972), and references therein. (6) B. D. Green and J. I. Steinfeld in "New Concepts in Air Pollution Research", J. Willums, Ed., Birkhauser-Verlag, Basei and Stuttgart. 1974. (7) P. L. Hanst, Appl. Spectrosc., 24, 161 (1970). (8) R. A. McCiatchey, W. S. Benedict, S. A. Clough, D. E. Burch, R. F. Calfee, K. Fox, L. S. Rothman, and J. S. Garing, AFCRL-TR-73-0096, Environmental Research Paper No. 434 (1973). (9) K. Fox, AFCRL-TR-73-0738 (1974), available from National Technical Information Service. (10) B. M. Golden, M. S. Dissertation, Iowa State University, 1975. (11) P. Varanasi, S.K. Saranai, and G. D. T. Teiwani. J. Ouant. Soectrosc. Radiat Transfer, 12, 857 (1972). (12) R. T. Ku, E. D. Hinkley, and J. 0. Sample, Appl. Opt., 14, 854 (1975)
RECEIVEDfor review April 17, 1975. Accepted July 25, 1975. E.S.Y. is an Alfred P. Sloan Research Fellow. Prepared for the U S . Energy Research and Development Administration under Contract Number W-7405-eng-82.
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