466
Anal. Chem. 1904, 56, 466-470
gating whether the use of peak height rather than peak area significantly improves the quantitation capability of GC/FTIR techniques. Without the examination of the indexes of variation as shown in Tables I11 and IV, it is doubtful that a consideration of the sources of error would have occurred. It is in this manner that the use of the indexes of variation, as presented here, becomes most beneficial to the analytical chemist.
CONCLUSIONS The analytical chemist working on the development of a new industrial hygiene method must already go through a number of calculations to verify that the variance or dispersion in his data is not “too large”. We have demonstrated here that by expanding slightly on those calculations and calculating in a similar manner the coefficient of root variation, the standard deviation, and one or both of the “inverse” coefficients, the chemist can, after pooling and analyzing these coefficients, better make use of his data to shed light on the nature of trends in the variance of the data. Furthermore, one of the indexes described here, namely, the CRV, has been shown to encompass the OSHA sliding scale requirement. We believe that it expands on concepts originally developed as the motivation for OSHA’s implementation of the sliding scale requirement. Finally, an identification of the functional form of the dispersion or variance in a set of data can be used to properlv develop a weighted regression model of the data. In our laboratory, we have found that the use of these indexes significantly helps the chemist identify possible sources of error in a potential method and also aids in his or her selection when the choice of several similarly functioning
analytical methods is available. In this study an analysis of the indexes of variation led us to the conclusion that there may be a sampling problem for the higher boiling anilines in the method using “flash loading” and thermionic detection and also that the quantitation procedure for the GC/FTIR method may need improvement. Had only the coefficient of variation been calculated, as is usually done, it is doubtful that these potential problems would have been considered. Registry No. NIPA, 768-52-5; EMA, 24549-06-2; DEA, 57966-8; DCA, 626-43-7; aniline, 62-53-3.
LITERATURE CITED (1) Taylor, D. G.; Kupel, R. E.; Bryant, J. M. “Documentation of the NIOSH Validation Tests”; DHEW (NIOSH) Publicatlon No. 77-185, Clnclnnatl, OH, 1977. (2) Code of Federal Regulatlons; Title 29, Part 1910.17: Vinyl Chloride. (3) Bartlett, M. S. Biometrics 1947, 3 , 39. (4) Kurtz, D. A. And. Chim. Acta 1983, 150, 105. (5) Draper, Norman; Smith, Harry ”Applied Regresslon Analysls”; Wiley: New York, 1966; pp 77-81. (6) Crable, J. V.; Taylor, D. G. “NIOSH Manual of Analytical Methods”; DHEW (NIOSH) Publication No. 75-126, Cincinnatl, OH, 1974. (7) Becher, G. J . Chromtogr. 1981, 21 1 , 103. (8) Grubbs, F. E. Technometrics 1972, 14, 847. (9) Grubbs, F. E. TeChi7Of?7etf~CS1969, 1 1 , 1. (IO) Bethea, R.; Duran, B.; Bouillion, T. “Statistical Methods for Engineers and Scientists”; Marcel Dekker: New York, 1975; pp 247-251. (11) Hall, R. C. CRC C f k . Rev. And. Chem. 1978, 7 , 323. (12) Worley, J. W.; Rueppel, M. L.; Rupel, F. L. Anal. Chem. 1980, 52, 1845. (13) Erickson, M. D. Appl. Specfrosc. Rev. 1979, 15, 261.
RECEIVED for review October 22, 1981. Resubmitted October 20, 1983. Accepted November 18, 1983. Presented in part at the American Industrial Hygiene Conference, Portland, OR, May 25-29, 1981.
Reiterative Least-Squares Spectral Resolution of Organic Acid/Base Mixtures S. D. Frans and J. M. Harris* Department of Chemistry, University of Utah, Salt Lake City, Utah 84112
A method of data anaiysls for acid/base equllibria employing multiwavelength detectlon Is shown to recover both the dissociation constants and absorption spectra of organic acid/ base pairs in complex mixtures. The resolvlng power of the method is studied by using synthetic data and demonstrated experlmentaiiy on multicomponent mixtures. The multiple wavelength tltratlon curves are used to form a matrix, D, which Is then factored Into matrices A, containing the absorption spectra of the components, and C, contalnlng their pH-dependent concentrations. The correct pK,’s and absorption spectra are arrlved at by a leastgquares minimization in which the only parameters varied are the pK,’s.
The analysis of complex multicomponent samples has been greatly facilitated by the use of “hyphenated” analytical methods (1-3), which can facilitate the identification and resolution of individual components of a mixture (4-10). The informing power of a two-dimensional measurement lies in the large number of information channels which increase by the product of the number of channels in each dimension, 0003-2700/84/0356-0486$0 1.50/0
provided that the measurement dimensions are uncorrelated. When one measurement dimension, which has few degrees of freedom and can be modeled, is combined with a second measurement dimension of higher informing power (more independent information channels),one can utilize the benefits of each dimension for the resolution of mixtures (11,12). By fitting the data along the lower informing power dimension using a physical model to provide a functional form, one can extract the richer analytical information from the other dimension. Because of the independent nature of the two dimensions, considerably more overlap can be tolerated than with one-dimensional curve fitting (13). Example applications of this reiterative least-squares method have included timeresolved fluorescence spectrometry (11) and GC/MS (12). The reiterative least-squares technique could naturally be applied to data involving chemical equilibria vs. some higher informing power dimension. For the purposes of this study, a pH-dependent, acid/base equilibrium is chosen where the second dimension is based on UV/Vis spectrophotometry. The use of pH as a variable in spectrophotometric studies, especially for biochemical systems, appears to be universal (14). Numerous other techniques have been used to determine 0 1984 American Chemical Soclety
ANALYTICAL CHEMISTRY, VOL. 56, NO. 3, MARCH 1984
the ionization constants of polyfunctional acids and bases and the absorption spectra of intermediate ionic forms of a compound (25-21). Generally in these studies, either more information was known in advance, the pK,’s or isolated absorption spectra, or a large number of parameters had to be individually optimized. The reiterative least-squares approach has the unique advantage of requiring no prior information about the data to be fit. Furthermore, for a mixture of n acid/base pairs, only n parameters, the pK,’s, need to be optimized in order to resolve the absorption spectra of the components. The reiterative least-squares method is evaluated in this work by using synthetic data and demonstrated experimentally on multicomponent mixtures.
THEORY The pH dependence of the absorption spectrum of a mixture of acid/base pairs can be expressed as a matrix, D, where the wavelength of the measurement is the index, i, for the rows and the pH of the solution is the index, j, for the columns. If the spectroscopic conditions are met for the Beer-Lambert relationship to hold (narrow slit width, low stray light), then the absorbance at any wavelength and pH, dij, will be the s u m of the contributions from the n components of the sample n
The first n columns of A corresponding to the first n rows of C are difference spectra given as the product of the molar absorptivity difference between base and acid forms of component k, the path length, and the total concentration aik
=
(EA-
- ~ H A ) ~ ~ ~ (-I[H [A-l)k AI
D = AC
(2)
where A contains the absorption spectra of the n components in its columns and C contains the pH-dependent distribution curves for these components in its rows. Given a measurement of D, the data analysis task is to decompose the matrix into its factors A and C which can be used for subsequent identification and quantitation of the sample components. In order to carry out this task, the rows of C must be linearly independent so that a unique, best fit solution exists. One of the peculiarities of the pH-dependent data set is an interdependence of the distribution curve of an acid with that of its conjugate base, where the fraction of acid a t a given pH is given by akj
= [HA]/([HA]
+ [A-1) = [l + 10(pH-pK~)]-l(3)
and the fraction of base is given by
To develop a set of linearly independent vectors for the C matrix from a mixture of acid/base pairs, one must choose a smaller “basis set” of functions which span the same measurement “space”. Practically, this may be accomplished by taking as the kth row in the C matrix the difference distribution curve ckj
= @kj - ffkj = 1 - 2 a k j
The redundant vectors arising from the sum of the distribution curves, ffk + /?k = 1, can be combined into a single constant row in the C matrix. For a mixture of n acid/base pairs, the elements of this constant row which preserve the area of the original distribution relationships are c , + ~ = ~ n.
(6)
The last, n + 1, column of A, corresponding to the constant row of C,is the sum of all absorbing species in the solution including the contributions of any non-pH varying components. Given a linearly independent model for the distribution matrix, C, all that is required to specify the elements in this matrix are the n pK,’s of the acids in the system. The minimum number of pH point! required to solve for the corresponding spectral matrix, A, would be n 1, in which case C is square and can be inverted to obtain
+
A = DC-1
(7)
To reduce the impact of noise in the data matrix on the spectral result, one can overdetermine the solution by measuring many more pH points Jhan components. The corresponding best spectral matrix A is found by multiplying the data matrix by the pseudoinverse or least-squares inverse (22-24) of C
A = DCT(CCT)-I where aik,in absorbance units, is the product of path length, molar absorptivity, and formal or total concentration of the kth component at the ith wavelength and ckj, dimensionless, is the relative fraction of a particular conjugate form of the kth component a t the j t h pH. The relationship of eq 1 is conveniently expressed as a matrix product
467
(8)
which minimizes the squared error between the actual data and the model
where r is the number of rows or wavelengths in the data matrix and c is the number of columns or pH measurements and where
D =Ac
(10)
Overdetermining the C matrix provides another important advantage in that the pK,’s of the acids in the system need not be known in advance. The value of x2 obtained by the above procedure will depend on the choice of pK,’s used to construct C. The closer the choice of pK,’s to the actual values for the components in the system, the smaller will be the residual error in the fit indicated by x2. As a result, the optimum set of pK,’s to fit a given data matrix can be found by minimizing x2 with, for example, a SIMPLEX algorithm (25-28). This reiterative approach can be further expanded to determine the number components in the system. By examination of the minimum value of x2 as a function of the number of components in the fit, n, an indication of the proper value of n can be realized. The IND function, developed by Malinowski (29,30)for identifying the correct dimensionality of a factor space
IND = (x2)l12/(c- n)2
=[-
r(c -1T I ) ~ i
J
(diJ -
iiLJ)2
Ill2
(11)
includes a penalty for increasing the number of components in the model which is stronger than just the number of degrees of freedom, r(c - n). Empirically, this results in a minimum value of the IND function when n has been defined correctly.
EXPERIMENTAL SECTION Aqueous stock solutions of acid/ base indicators were prepared as follows (31). Bromcresol green, 0.1 g, was dissolved in 14.3 mL of 0.01 M NaOH and diluted to 250 mL with deionized water. Chlorophenol red, 0.1 g, was dissolved in 23.6 mL of 0.01 M NaOH
ANALYTICAL CHEMISTRY, VOL. 56, NO. 3, MARCH 1984
468 0,lP
,
I
II
Flgure 1.
Synthetic data for a binary acid mixture. A large spectral separation has been selected for illustration, R , = 0.75; resolution along with the pH dimension is also large, ApK, = 2.0. Acid spectra dominate on the left at lower pH; base spectra grow in on the right at higher pH.
and diluted to 250 mL with distilled water. Similarly, 0.1 g of phenol red was dissolved in 28.2 mL of 0.01 M NaOH and diluted to 250 mL with deionized water. Methyl orange was prepared by dissolving 0.1 g of the dye in 1L of deionized water. The above stock solutions were diluted by a factor 50 with a buffer solution which was 2 mM in phosphoric, acetic, and boric acids. T h e buffer was chosen to provide spectroscopic transparency and linear buffering (20) over the spectral and pH ranges studied. The spectra of the individual components and mixtures were measured with a Cary 17D spectrophotometer which was interfaced to a DEC LSI 11/23 through an Intel 8031 microcontroller. The samples were introduced into a l-cm quartz flow cell by using a closed loop flow system powered by a Gilson peristaltic pump. This procedure allowed pH changes and measurements to be made external to the spectrophotometer without removing the cell, thereby minimizing cell repositioning error. The pH was measured with a Beckman Research pH meter calibrated against standard buffer solutions. Titration was performed with 12 M KOH and 11.6 M HCl thus incurring negligible volume change in the sample. The digitized spectra were collected at 5-nm intervals, stored on floppy disks, and subsequently transferred to a DEC 20160 for analysis. RESULTS AND DISCUSSION Synthetic D a t a Studies. In order to characterize the performance of the reiterative least-squares method, an evaluation was first carried out with synthetic data, which allows the systematic variation of the spectral, equilibrium, and noise characteristics. Binary mixtures of monoprotic acids were modeled as 50 wavelength row by 21 pH column data matrices to which random, Gaussian weighted noise of fixed relative standard deviation was added. An example of such a data matrix is shown in Figure 1. The pH dimension has a sampling interval of 0.1 pH units. The spectra are modeled as Gaussian peaks where the acid peaks and base peaks are well separated while the acidlbase pairs are overlapped. The resolution of the overlapped peaks is the same for both acid and base, defined by a resolution factor (12) Rs = (111 - 112)/4g where M~ and F~ are the mean positions of the bands and u is the standard deviation, where R, = 1.0 indicates base line resolution. For any set of conditions, 10 data matrices were generated with different random noise ensembles and evaluated. The primary study which was carried out was to determine the effect of spectral resolution on the reproducibility of the fit in both pH and spectral dimensions. The results are shown in Figure 2a,b and Figure 2c,d for 2% and 10% relative noise, respectively. In both cases, the pK,'s of the acids differ by 0.4 pH units, As one might expect, the quality of the fit in both dimensions improves as the spectra are separated. For
Parameter estimation vs. spectral resolution. ApK, = 0.4: (a) pK, precision, 2% noise; (b) spectral precision, 2% noise; (c) pK, precision, 10 % noise; (d) spectral precision, 10 % noise.
Flgure 2.
the lower noise data particularly, most of the improvement in fit occurs long before the spectral bands are resolved. For a small amount of spectral separation, R, = 0.15, one achieves 90% of the precision improvement for determining the pK,'s that one would observe with totally resolved bands. The precision in determining the spectra of the components improves slower with separation of the bands, requiring R, = 0.25 to achieve 90% of the available enhancement. As shown in Figure 2c,d increasing the noise in the data not only decreases the reproducibility of the results but also increases the degree of spectal separation required to improve the precision of the fit. A second study was undertaken with synthetic data to determine the effect of varying the separation of the equilibrium constants, ApK,, on the reproducibility of the results. The spectral resolution was fixed at R, = 0.2, and 2% relative noise was added to the data matrix. The standard deviation in the pK,'s remained essentially constant at a value of 0.05 pH units for 0.45 1 ApK, 1 0.2; the spectral precision behavior was similar, the relative standard deviation averaging between 5 and 10% over the range above. When the separation of the equilibrium constants was reduced to the pH sampling interval, ApK, = 0.1, the errors in both dimensions became excessive, upK, = 0.3 and the average spectral RSD > 100%. The two equilibrium distribution curves apparently become indistinguishable given the precision in the absorbance measurement and a sampling interval equivalent to the pH offset of the two curves. Studies with Laboratory Data. To assess the capabilities of the reiterative least-squares method on laboratory data, mixtures of acid/base indicators were prepared. Their absorbance was measured as a function of wavelength, at 5-nm intervals over a 350-700 nm range, and pH, a t 0.2 unit intervals over a pH range of 3.C-8.4. The difference spectra and pK,'s determined from reiterative least-squares fitting of the mixture data were compared with results from the chemically isolated, individual components. An example data matrix for a four-component mixture containing methyl orange, bromcresol green, chlorophenol red, and phenol red is shown in Figure 3. It is clear from the figure that the data are severely overlapped. Application of the reiterative least-squares procedure while incrementing the value of n,was successful in identifying the correct number of components, using the IND function as shown in Table I. The results from a two-component mixture, methyl orange and bromcresol green, are also tabulated for comparison, where the IND function again minimizes properly. While the minimum value of the IND function correctly identifies the number of components, the function does not bottom out with a large second derivative. Unfortunately a less than persuasive
.
ANALYTICAL CHEMISTRY, VOL. 56, NO. 3, MARCH 1984
0.6 L!
0.4
1
-0.4 L 350 400
Figure 3. Data matrlx consisting of a four acld/base component mixture. Detailed description is given in the text.
Table I. Determination of the Number of Acid/Base Components four-component two-component mixture mixture IND IND n ( X 105) n (X 105) 1 2 3 4 5 6
9.9 3.12 1.54 0.53 0.56 0.78
1 2 3 4
450
500 550 Vnm)
600
650
1
700
Figure 4. Difference spectra of acid/base pairs. Base minus acid absorbance Is plotted. PR is a phenol red; CR Is chlorophenol red; BG is bromcresol green, and MO is methyl orange. The dashed lines are the spectra of chemically isolated components. The solid lines are numerically resolved from the four-component data matrix. Both are plotted.
5.47 0.91 1.06 1.21
minimum typifies the behavior of this empirical function (29, 30,32). A more fundamental basis for deciding the number of components based statistically on the lack of fit (33) requires a priori knowledge of the purely experimental error. If this error is high frequency in nature, then an autocorrelation calculation can be used to estimate ita magnitude (21). This latter approach, which also utilizes an eigenvector decomposition of the data, was tested on these results and also found to be successful in identifying the number of components. If the correct number of components is used to construct the C matrix and the pK,'s are adjusted to minimize x2,the difference spectra of :he individual components should occupy the columns of the A matrix, factored from the data matrix D by the pseudoinverse of C. These column vectors are plotted in Figure 4 for the four-component mixture along with the spectra of the individual components, scaled to equal a r e a to account for differences in concentration. There is little or no systematic error in the numerically resolved spectra, despite the large regions of spectral overlap. This result is further substantiated by the residuals plot, Figure 5, where no pH
Figure 5. Residuals plot for best fit of the four-component mixture, D - D (see eq IO).
or wavelength-dependent bias can be detected. There is some hint of a proportional error source since the residuals, while random, have a larger amplitude in the vicinity of the maximum absorbance of the data matrix (compare with Figure 3). A more quantitative summary of the quality of fit is listed in Table I1 for both the four-component and two-component mixtures. The error in the resolved spectra, expressed as a standard deviation, averages about 4 x absorbance units which is close to the limiting reproducibility of the spectrophotometer. The largest relative errors in both pK, and spectra were observed for methyl orange, which was a weaker absorber in both the four- and two-component mixtures. With the exception of this component, the spectral errors were 1% or less and the pK, error was 0.03 pH units or less, which is
Table 11. Reiterative Least-Squares Resolution of Acid/Base Mixtures PKa isolated
PKa mixture
spectral errora std dev, AU
re1 spectral
x x x x
10-3 10-3 10-3 10-3
2.5 1.0 1 .o 0.9
5.4 x 10-3 3 . 2 x 10-3
2.5 0.9
error, %
Four Component methyl orange
phenol red
3.27 4.77 6.07 7.71
methyl orange bromcresol green
3.27 4.77
bromcresolgreen chlorophenol red
3.39 4.80 6.05 7.71
5.5 3.8 3.4 4.4
Two Component 3.50 4.74
Root mean squared difference between numerically resolved and isolated component spectra, scaled to equal areas. Spectral error divided bv the average. absolute absorbance. a
46Q
470
Anal. Chem. 1984, 56,470-473
a small fraction of the 0.2 pH sampling interval. The reiterative least-squares method appears to be well suited to the spectral resolution of major components in a mixture of organic acids, even where the overlap in both pH and spectral dimensions is severe. Further work will be required to characterize the performance of the method on minor components, where the IND function might be less successful. Application of the method to multiprotic acids would require some adjustment of the model for the C matrix, particularly for ionization steps which are not well separated. Extension of the technique to other equilibrium-based analytical methods, complexation or redox, for example, would be straightforward.
ACKNOWLEDGMENT The authors acknowledge the fine work of D. Heisler who constructed the spectrometer interface. LITERATURE CITED Hlrschfeld, T. Anal. Chem. 1980,5 2 , 297A-312A. Kowalskl, 8. R. Anal. Chem. 1980,5 2 , 112R-122R. Shoenfeld, P. S.;DeVoe, J. R. Anal. Chem. 1976,48, 403R-411R. Sternberg, J. C.; Stlllo, H. S.;Schwendeman, R. H. Anal. Chem 1980.32.84-90. - . Hirschfeld, T. Anal. Chem. 1978,48, 721-723. Brown, C. W.; Lynch, P. F.; Obremski, R. J.; Lavery, D, S. Anal. Chem. 1982,5 4 , 1472-1479. Kralj, Z.; Sirneon, V. Anal. Chlm. Acta 1982, 138, 191-198. Ohta, N. Anal. Chem. 1973,45, 553-557. Connors. K. A.: Eboka. C. J. Anal. Chem. 1979. 51. 1262-1266. Spj~tvoll,E.; Martens,’ H.; Volden, R. rechnomefrics 1982, 2 4 , 173-180. Knorr, F. J.; Thorsheirn, H. R.; Harris, J. M. Anal. Chem. 1 ~ 8 15,3 , 821-825.
(12) Knorr, F. J.; Harris, J. M. Anal. Chem. 1981,5 3 , 272-276. (13) Bevington, P. R. “Data Reductlon and Error Analysis for the Physical Sciences”; McGraw-Hill: New York, 1969. (14) Scott, J. F. I n “Physical Techniques in Blological Research”; Oster, G., Pollister, A. W., Ed.; Academic Press: New York, 1955; Chapter 3. (15) Leggett, D. J. Anal. Chem. 1977,4 9 , 276-281. (16) Leggett, D. J.; McBryde, W. A. E. Anal. Chem. 1975,47, 1065-1070. (17) Leggett, D. J. Talanta 1977,2 4 , 535-542. (18) Leggett, D. J.; McBryde, W. A. E. Talanta 1974,2 1 , 1005-1011. (19) Leggett, D. J.; McBryde, W.A. E. Talanta 1975,2 2 , 781-789. (20) Gordon, W. E. Anal. Chem. 1982,5 4 , 1595-1601. (21) Shrager, R. I.; Hendler, R. W. Anal. Chem. 1982, 5 4 , 1147-1152. (22) Strang, G. “Applied Linear Algebra”; Academic Press: New York, 1976. (23) Golub, G.; Kahan, W. J. SIAM Numer. Anal., Ser. B 1985, 2 , 205-224. (24) Peters, G.; Wilkinson, J. H. Comput. J. 1970, 13, 309-316. (25) Nelder, J. A.; Mead, R. Comput. J. 1965, 7 , 308-313. (26) O’Neill, R. Appl. Stat. 1971,2 0 , 338-345. (27) Deming, S. N.; Morgan, S. L. Anal. Chem. 1973, 45, 278A-283A. (28) Morgan, S. L.; Deming, S. N. Anal. Chem. 1974, 4 6 , 1170-1181. (29) Malinowski, E. R. Anal. Chem. 1977,4 9 , 606-612. (30) Mallnowski, E. R. Anal. Chem. 1977,4 9 , 612-617. (31) “pH Ranges and Color Changes of Kodak Indicators”; Eastman Kodak Co.: Rochester, NY, 1978; Kodak PublicationJJ-13. (32) McCue, M.; Mallnowski, E. R. Appl. Spectrosc. 1983,3 7 , 463-469. (33) Draper, N. R.; Smith, H. “Applied Regression Analysis”; Wiley: New York, 1981.
- - - - .--.
for September l2, 1983. Accepted DfX€dXr 6, 1983. This research was supported in part with funds provided by the National Institutes of Health through Biomedical Research Support Grant No. RR7092. Additional funding by the donors of-the Petroleum Research Fund, administered by the American Chemical Society, is acknowledged.
Characterization and Determination of Formaldehyde Oligomers by Capillary Column Gas Chromatography David F. Utterback,’ David S. Millington: and Avram Gold* Department of Environmental Sciences and Engineering, School of Public Health, University of North Carolina, Chapel Hill, North Carolina 27514.
A method has been developed for characterization of formaldehyde ollgomers In methanol-water solutions as their trlmethylsllyl derlvatlves, utlllzlng capillary gas chromatography wlth ammonia chemical lonlratlon mass spectrometry. The Me$ ollgomers form stable adducts with the ammonium Ion, (M NH,)’, permtltlng asslgnment of their molecular weights and structures. Quantitative analysis of formalin was accomplished by callbratlng the flame lonlratlon detector for molar response to the oligomers by use of closely related compounds. By thls method, the total formaldehyde content of formalin solutions was accounted for and the dlstrlbutlon of formaldehyde In the lndlvldual ollgomers accurately determined.
+
Despite decades of research, poly(oxymethy1ene) glycols, the oligomers of formaldehyde, and the monomethyl ethers Present address: Department o f H e a l t h Sciences, California State University-Fresno, Fresno, CA. Present address: Division of Genetics and Metabolism, Duke University Medical Center (Box 3028), Durham, NC 27710. 0003-2700/84/0356-0470$01.50/0
of poly(oxymethy1ene) glycols that form upon reaction with methanol, have not been well characterized. The existence of poly(oxymethy1ene) glycols has been established by thermodynamic calculations (1-3) and nuclear magnetic resonance (4) while the silylated oligomers have been partially separated and their relative distribution in formalin solution determined by gas chromatography (4). The analysis of formalin was based on the assumption that the first peak in the series eluting after solvent in the gas chromatogram was the bis(trimethylsilyl) derivative of methylene glycol. Unequivocal evidence for the validity of this assumption and for the structures of the two series of compounds requires additional physicochemical characterization of these compounds once they have been separated. We present here the resolution of the trimethylsilyl derivatives of the poly(oxymethy1ene) glycols and their monomethyl ethers by gas chromatography, their definitive characterization by chemical ionization mass spectrometry, and their quantitation by application of the flame ionization detector (FID) principle of equal per carbon response (5). The genesis of oligomeric oxymethylene glycols and the corresponding series of monomethyl ethers is represented formally in the following equilibria (6, 7): 0 1984 American Chemical Society
