Anal. Chem. 1988, 58,3256-3257
3256
chemists interested in the details of the curing process. The in situ MAS experiment could also find analogous applications such as the study of gelation of silacate solutions, as during zeolite synthesis or sol-gel synthesis of ceramics.
ACKNOWLEDGMENT We thank Mike Meadows of Dow Chemical, Freeport, TX, for suggesting this experiment. Registry No. Poly(bispheno1A diglycidyl ether), 25085-99-8; triethylenetetramine, 112-24-3. LITERATURE CITED (1) Lee, H.; Neville, K. Handbook of Epoxy Resins; McGraw-Hill: New York, 1967. (2) Randall, J. C. ACS Symp. Ser. 1984, No. 247. (3) Garroway, A. N.: Monlz, W. B.; Resing, H. A. Faraday Symp. Chem. SOC. 1978, 13, 67-74. (4) Fyfe, C. A,; Mckinnon, M. S . ; Rudin, A.; Tchir, W. J. Macromolecules 1983, 16, 1216-1219.
(5) Chuang, 1.4.; Maciel, G. E.; Myers, G. E. Macromolecules 1984, 17, 1087- 1090. (6) Yannoni. C. S. Acc. Chem. Res. 1982, 15, 201-208. (7) Maciel, G. E. Science (Washington, D .C.)1984, 226, 282-288. (8) Gerstein, B. C. Anal. Chem. 1983, 55, 781A. (9) Gerstein, B. C. Anal. Chem. 1983, 55, 899A. (IO) Rothwell, W. P.; Waugh, J. S. J. Chem. Phys. 1981, 74, 2721-2732. (11) VanderHart, D. L.; Earl, W. L.; Garroway, A. N. J Magn. Reson. 1981, 44, 361-401. (12) Haw, J. F.; Johnson, N. A., unpublished work, Texas A&M University, Station College, TX, April 1966.
’ Present address:
Dow Chemical, Freeport, TX.
James F. Haw* N. Alan Johnson1 Department of Chemistry Texas A&M University College Station, Texas 77843
RECEIVED for review May 27,1986. Accepted August 1,1986. Support for this work was provided by Dow Chemical Co.
AIDS FOR ANALYTICAL CHEMISTS Use of Cross-Correlation for Ratio Measurements in Mass Spectrometry Ahmet Celikkaya and tjefik Siizer* Department of Chemistry, Middle East Technical University, Ankara, Turkey Use of cross-correlation methods for analysis purposes is an elegant computational technique and is becoming more popular with the widened use of computers (1-15). Unfortunately, the mathematical background needed to comprehend the method is discouraging for beginners. Excellent presentations of the method and its application to spectroscopy are given by Hieftje (2-4) and Horlick (5-8). The basic mathematical principles of cross-correlation methods are well documented in standard textbooks (16). Cross-correlation of two spectra containing 2N + 1 points and taken at equal intervals, Fl(I) and F2(r),where I is an integer between -N and + N representing the spectral steps, is given by N
G(7) = 7
CJ’,(n.J’2(I + 7)
-N
(1)
= integer between -N and + N
and is most conveniently obtained by Fourier transforming F , and Fz into the frequency domain, multiplying the transformed functions, and back transforming into the time domain. However, for some applications one is only interested in the cross-correlation value a t zero displacement, Le., 7 = 0
This is simply obtained by point-by-point multiplication and summing and can be obtained without the use of Fourier transformation. The cross-correlation value a t zero displacement ( 7 = 0) of the spectrum of a mixture with that of the pure component (i.e., multiplying the mixture spectrum with that of the pure component and adding them up) gives a measure of the content of the component in that mixture and can be used for quantitative measurements. Mann et al.
recently reported successful applications of this method for quantitative analysis in IR spectroscopy (10-14). Use of cross-correlation for peak detection (17) and for spectral searches has already been applied in mass spectrometry; however, application to ratio measurements has not been reported. In this work, we investigate the applicability of the cross-correlation method for ratio measurements in the analysis of mixtures using mass spectrometry. Mixture analyses in mass spectrometry using the method of least squares (18)and a set of linear equations (19) have also been reported. Ratio measurements in the mass spectrum of a mixture are usually carried out by ratioing peak heights or areas of two or more representative peaks belonging to each component in the mixture. Use of cross-correlation values a t zero displacement for ratioing instead of peak heights or areas improves the precision of the measurement as will be demonstrated below.
EXPERIMENTAL SECTION A quahpole mass filter,Balzers QMS 311, interfaced to a DEC MINC 11/03 computer is used for recording the mass spectra. Ion currents, produced by a secondary electron multiplier (SEM), are converted to voltages by a Keithley 419 picoammeter. The voltages are fed into the input of a 12-bit analog to digital converter and read by the computer. Stepping of the mass spectrometer is controlled by a 12-bit digital to analog converter, and signal averaging is done to improve the signal to noise ratio. Binary mixtures of gases and liquids are prepared synthetically.
RESULTS AND DISCUSSION Figure 1 shows portions of the spectra of (a) pure 02, (b) pure N20, and (c) a gaseous mixture of Oz and N20, using 70-eV electron impact ionization and a sample pressure of mbar. Three different calibration lines are obtained when calculated ratios vs. prepared mole ratios of four different mixtures of O2 and N20 are plotted. In the first plot, calculated ratios
0003-2700/86/0358-3256$01.50/00 1986 American Chemical Society
Anal. Chem. 1986, 58, 3257-3261
:o;
:0 '
to 0.9844 for ratios of 02+ and N+ peaks, and finally to 0.9959 when cross-correlation ratios are used. The increase from 0.9726 to 0.9844 is due to the fact N+ is more intense than NO+; hence, more precise values are obtained. Further improvement to 0.9959 by using cross-correlation values for ratioing is due to the fact that in this method all the available data (i.e., all the peaks in the spectrum) are utilized in computing ratios as opposed to a part of the data being used in sample ratios. Application to eight different liquid mixtures of CCll and cyclohexane has given more dramatic improvements in precisiion due to the increase in the number of peaks in their spectra. In this case, the correlation coefficient increases from 0.9482 for ratios of C+ (12) and CH3+(15) peaks to 0.9819 for ratios of C1+ (35) and CzH3+(27) peaks and finally to 0.9957 when cross-correlation ratios are used. This method is expected to be applicable to any kind of spectroscopic measurements of mixtures for improving precision. However, the cross-correlation of the spectra of a mixture and a pure component may have a finite value even if the mixture does not contain the component; hence, caution must be used as has already been pointed out by Mann et a1
(a)
;I
3257
:k
3
N,O+
(9).
LITERATURE CITED ;ai
2 i' 15
20
25
-
30
35
;1 L5
LO
Mass(or m l z )
(C)
(1) Black, W. W. Nucl. Instrum. Methods 1979, 71, 317-327. (2) Hieftje, G. M. Anal. Chem. 1972,4 4 , 81A-88A. (3) Hleftje, 0. M.; Bystroff, I . R.; Lim, R. Anal. Chem. 1973, 4 5 , 253-258. (4) Powell, L. A.; Hieftje, G. M. Anal. Chim. Acta 1978, 100, 313-327. (5) Horlick, G. Anal. Chem. 1973,45, 319-324. (6) Kelly, P. C. and Horlick, G. Anal. Chem. 1973,45, 518-527. (7) Ng, R. C. L.; Horlick, G. Spectrochim. Acta, Part B 1981, 366, 529-547. (8) Ng, R. C. L.; Horllck, G. Spectrochim. Acta. Part B 1981, 368, 543-551 . .. (9) Mann. C. K.; Golenlevskl, J. R.; Slsmanidls, C. A. Appl. Spectrosc. 1982,36, 223-227. (10) Tyson, L. L.; Vickers, T. J.; Mann, C. K. Appi. Spectrosc. 1984,38, 663-668. (11) Tyson, L. L.; Ling, Y. C.; Mann, C. K. Appl. Spectrosc. 1984,38, 697-700. (12) Bingham, 0.;Burton, C. H. Appl. Spectrosc. 1984,38, 705-709. (13) Vickers. T. J.; Mann. C. K.; Moriev, N. A,; Kina, T. H. I n t . Lab. 1984 (Nov.-Dec.) 12-26. (14) Ng, R. C. L.; Horlick, G. Appl. Spectrosc. 1985,39, 834-840. (15) Ng, R. C. L.; Horlick, G. Appl. Spectrosc. 1985,39, 841-846. (16) Brigham, 0. The Fast Fourier Transform; Prentice-Hall: Englwood Cliffs-, NJ. 1974 (17) Bryant, Wm. F.; Trlvedi. M.; Hinchman, B.; Sofranka, S.; Mitacek, P., Jr. Anal. Chem. 1980, 5 2 , 38-43. (18) Schorr, W. K.; Duschner, H.; Starke, K. Anal. Chem. 1982, 5 4 , 671-674. (19) Brown, C . W.; Lynch, P. F.; Obremski, R. J.: Lavery, D. S. Anal. Chem. lS82,5 4 , 1472-1479.
- - --
L
. : .. , *
. ..
::
15
:s
,uUi
W
20
25
.
35
30
I
40
45 Mass(or m l z )
Flgure 1. Mass spectra of (a) pure 02,(b) pure N,O, and (c) a mixture of N20 and 02.
are obtained by using peak areas of 02+ (32) and NO+ (30), for the second, areas of 02+ (32) and N+ (14) are used, and for the last, cross-correlation values at zero displacement are used. The same set of data is used for computing ratios in all three graphs. The correlation coefficient (R) of the calibration lines is one measure of the precision of the method and increases from 0.9726 for ratios of 02+ and NO+ peaks
-.
RECEIVED for review February 28, 1986. Accepted July 16, 1986. We wish to acknowledge the Volkswagen Foundation of the Federal Republic of Germany for the generous grant which supplied the mass spectrometer and the vacuum system.
Selectivity and Sensitivity Improvements at Perfluorinated Ionomer/Celiulose Acetate Bilayer Electrodes Joseph Wang* and Peng Tuzhi Department of Chemistry, New Mexico State University, Las Cruces, New Mexico 88003 Polymer-modified electrodes are of considerable recent interest. In addition to electrocatalytic applications, such electrodes show great promise for electroanalysis. Analysis with polymer-coated electrodes can benefit from their catalytic (1) and discriminative (transport) (2,3)properties, as well as from their use as preconcentrating surfaces (4,5). As a result,
substantial improvements in the selectivity, sensitivity, versatility, and reproducibility of voltammetric measurements can be achieved. One useful strategy involves electrostatic binding of ionic analytes at electrodes coated with polymeric ion exchangers. In particular, the use of Du Pont's Nafion perfluorinated films
0003-2700/86/0358-3257$01.50/00 1986 Amerlcan Chemlcal Soclety
