Anal. Chem. 1082, 5 4 , 671-674
871
Mathematical Treatment of Mass Spectrometric Data for Analysis of Gas Mixtures Wolfgang K. Schorr, Helnz Duschner,’ and Kurt Starke Fachbereich Physlkailschs Chemle, Kernchemle, Phllipps-Wnlversltat, Hans-Meerweln-Strasse, D-3550 Marburg, West Germany
A mass spectrometrlc technique for gas analyds is described.
To interprete the often complex spectra, we propose a mathematlcai treatment. I n a serles of matrlx calculations, deviations between evaluated and measured Ion currents are reduced to a minimum. The necessary computer program was developed. The procedure was tested with synthetlcally generated mass spectra as well as wlth calibrated gas mixtures. It could be demonstrated that ail gases in a preselected mass range, here between 1 and 60, can be determined. For individual components, the limits of detection are correlated to the degree of peak overiapplng. Thus they are typical for each problem. The full range of mass spectrometric sensitivity, between 100% and about 10 ppm (vol), Is accessible, when base or major peaks, which do not overlap, can be used for calculations. Otherwise, the significance of determlnatlon can be derived from the standard deviations, whlch are Calculated with the gas fractlons slmuitaneousiy.
For final stor,age, low and medium level radioactive waste from nuclear power plants is solidified in matrices such as concrete, bitumen, or polyethylene. One aspect to be considered for safety evaluations is the emission of gases induced by radiolytic degradation of the waste products (1,2).Due to a large variety of gases and very different rates of generation, a multicomponent analytical technique with a wide dynamic range of sensitivity is required. Present methods of gas analysis do not necessarily fulfill these requirements. Classical techniques with volumetric or chemical detection techniques (3) are suited only for specific gas mixtures. IR spectroscopic methods are limited to constituents with appropriate vibrational frequencies. Disturbances arise by overlapping absorption bands. Gas chromatographic techniques require a tedious search for optimum conditions for each gas mixture. In addition, the simultaneous determination of minor and major fractions is difficult if not impossible. Principally, mass spectrometry would provide the required standards. It is sensitive to all elements of the periodic system, allows the identification of chemical compounds, and has excellent relative sensitivities down to the part per million range. Problems arise when complex spectra are generated by multicomponent analytes. With high-resolution systems (4) most inorganic gas mixtures can be analyzed readily, though NO/N02 and CO/CO2 are not to be determined simultaneously. Mixtures containing gaseous hydrocarbons cause spectra with line intensities summing up at some characteristic fragment masses. Interpreting these spectra requires the mathematical and statistical treatment of data. The large number of peaks generated by high resolution and the difficult mass calibration complicate data processing. Therefore low-resolution mass spectra are used as input for evaluation programs. Until now these are available only for gas mixtures of definite composition. Simple mass spectra from qualitatively known gas mixtures can be evaluated by “selected ion monitoring” or similar procedures (5-8). Herewith only ion currents from characteristic fragments not 0003-2700/82/0354-0871$01.25/0
overlapped by thorie of other constituents are taken for evaluation. Thus for n components an equal number of equations is derived, which can be solved by matrix calculations (9). Misinterpretations, however, can result from unexpected components. Alternatively, mass spectra can be treated by least-squares methods. These were applied mainly in residual gas analysis (10, 11). Due to the limited number of constituents to be determined and the imatisfactory relative sensitivity of about 0.2, this method is not suited for the present analytical problem. By another least-squares approach (12) selected reference spectra are fitted to those of the analytes. Consequently small differences of large units often lead to misinterpretations. In contrast to these fitting techniques, which are restricted to very specific problems, an analytical procedure was developed for any given mixture of gases. It is based on unfolding the complex mass spectra by mathematical treatment combined with statistical methods or error reduction. In this laboratory the proposed procedure is applied to the routine analysis of gases induced radiolytically in bitumen, concrete, polyethylene, and poly(viny1chloride) solidification products of nuclear waste.
EXPERIMENTAL SECTION Apparatus. The inlet system of the magnetic deflection mass spectrometer (Vacuum Generators MM12B: electron impact source, 0-5 kV accelerating voltage, secondary electron multiplier) was optimized for gas volumes of about 20 cm3. The mass spectrometer was connected to an analog-to-digital converter housed in a laboratory peripheral accelerator (Digital Equipment LPA11) on the unibus of a PDP 11/34 computer (124k words memory). The LPA11, basically a microprocessor, has direct memory access and thus allows digitization of spectral data. Simultaneously a peak search routine evaluates peak positions and heights from the digitized spectrum. With the LPAll the necessary routines could be written in Fortran and run in a multiuser mode. Thle mass spectrometer is started from the computer via a separate line. A Fortran IV program system was developed to acquire, store, and evaluate the spectra. It converts the measured peak positions into mass units by a parabolic function. The relevant parameters are derived from spectra of mixtures containing equal fractions of hydrogen, methane, nitrogen, argon, and carbon dioxide. Mass units are transformed into integer ones. The input ion currents for the evaluation were obtained from the mean values of the manifold (17)measured peak heights. For conversion, the characteristic spectrometer parameters were considered. Spectrometer sensitivities for individual gases are expressed by their base peak ion currents relative to their pressures in the inlet system. These could be varied in a wide range (4 to 1*E44 mbar) by the injection of variable gas volumes (Toepler pump) into inlet systems of different size. Reference spectra are obtained from those of individd gases, normalized with respect to the base peak. Both, reference spectra and sensitivity values are input data for the proposed program and are stored on disk. Procedure. For qualitative and quantitative analyses of gas mixtures, the more or less complex mass spectra are unfolded into those of individual components by a computer-supported mathematical treatment. The characteristic of the procedure is that the constituents of the analyte may be any gases in a given mass 0 1982 American Chemical Society
672
ANALYTICAL CHEMISTRY, VOL. 54, NO. 4, APRIL 1982
range, presently between 12 and 60. Thus the most frequently occurring gases are included: nitrogen, oxygen, the oxides of nitrogen and carbon, low hydrocarbons, amines, neon, and argon. For gases below mass 12, hydrogen and helium, no mathematical treatment is necessary due to the simple spectra. In a first step of the evaluation process presumable components of the analyte can be preselected by the operator. Such a limitation is not necessary but sometimes very helpful in eliminating sources of error. Then, the calculated peak positions are compared to those of the base peaks of the references. Reference spectra, the base peaks of which are not identified in the analyte spectrum, are rejected. Thus further calculations are limited to "high probability" components. Their ion currents relative to the base peak ( a i , , where i = 1, m, mass range, and j = 1, n, number of components) in the form of the matrix A (eq 1) are input data
I: ami.
I I:I I:I ............amn
for the evaluation program. Matrix A is multiplied by a vector X,representing the unknown ion currents of the components base peaks. Generally, the resulting system of linear equations is overdetermined (rn > n). Due to the statistical character of spectral data, left and right sides of the "equation" are not balanced exactly and, consequently, cannot be solved by usual techniques. A statistical treatment is necessary. The present approach is based on the Gauss algorithm. The deviations between the experimental ion currents and those calculated by a leastsquares method are reduced stepwise. Details of the following mathematical treatment of the data are given in mathematical handbooks (e.g., ref 13). Thus only the main steps of the procedure are outlined here. The Gauss normal equations are formed with the different statistical weight of the ion currents taken into account by a factor (u). It is derived from their standard deviations plus a threshold value to reject electronic noise. The normal equations can be comprehended to a new square matrix (dimension n): Bx = J
(2)
From this matrix the base peak ion currents x can be derived. Several methods were described, here matrix inversion is used. Thus, x values are obtained in a first approach. They are inserted into the matrix A to evaluate the weighted standard deviation (dev) of the calculated spectrum from the measured spectrum
f = m - n degree of freedom
The standard deviations (s) of the individual base peak ion currents can then be calculated sj = dev&
(4)
b'is the respective diagonal element of the inverse of matrix B. The mean value of the x , according to t distribution is in the interval f j
- tf*Sj 5
"j
5
f j
+ tf*Sj
(5)
where tf is the Student factor for given probability and degree of freedom f. After the first run a preliminary list of constituents with the respective ion currents is obtained. In many cases data from gases not present in the analyte are listed too. These are characterized by relative standard deviations above 100% or by calculated ion currents below the mass spectrometric limit of detection. Thus, they can be readily rejected. After each elimination the math-
Table I. Evaluated Gas Fractions from One of the Test Runs with Synthetically Generated Spectra gas fraction for components (each 14.29%) CH4
'ZH2
C2H4
C2H6
C3H6
C3H8
evaluated 14.16 14.32 14.91 13.89 14.31 14.40 14.00 fraction (%)
std dev
k0.20 k0.41 i0.67 k0.36 k0.18 kO.19 i0.26
ematical procedure is repeated until standard deviations and minimum peak heights are within preselected limits. Then the final list of the individual components and their fractions is printed together with the standard deviations.
RESULTS Evaluation of Synthetic Spectra. Double track testing is necessary for computer programs when statistically distributed spectral data are to be processed. Before spectra of calibrated gases are evaluated, the theoretical limits of the proposed procedure have to be demonstrated. This necessitates the exclusion of experimental errors which usually cannot be identified. Therefore, in a first run synthetically generated m a s spectra, simulating those of gas mixtures, were fed into the computer. The synthetic spectra are obtained from reference spectra by appropriate summation of peak intensities. The resulting sum peaks are varied by a random number generator in the range of maximum *5%, to simulate characteristic statistical variations of mass spectrometric measurements. Thus any series of realistic mass spectra corresponding to those of gas mixtures can be generated. There are no limitations for the simulation of either qualitative or quantitative combinations. Thus the capability of the program can be tested readily by each applier for any analytical problem. The variety of gas mixtures simulated cannot be realized by experimental preparation. Due to complex cracking patterns, mixtures of low hydrocarbons yield spectra with multiple overlapping lines. Generally, these cause most difficulties in evaluation, especially in combination with widely differing concentrations of individual components. Therefore simulated spectra of mixtures of the seven lowest hydrocarbons (Table I) were chosen for the test. For each identical composition seven different spectra were generated by the random method. Thus results from a large series of different spectra could be compared. First, spectra simulating a gas mixture of equal fractions (14.29% vol) of all components were subjected to evaluation. The calculated fractions (Table I) agree well with the given ones. The range given by the calculated mean values and their standard deviations covers the given percent fractions of all gases ( x - s Ix 5 x + s). Standard deviations are low and in the relative scale between 1 and 5%. Obviously the agreement is correlated to the degree of peak overlapping. In a subsequent test run the simulated concentrations of CzH4were decreased stepwise from 14.29 to 0.80%. C2H4 was chosen, because in the previous experiment it had the largest standard deviation and the highest degree of peak overlapping. Thus it is well suited to test the reliability of the evaluation procedure. The relative deviations of evaluated concentrations are given in Figure 1. Deviations close to zero, indicating good agreement, are observed when the fractions are above 3-4%. Below, the deviations increase nearly exponentially. They are about 100% when the simulated fractions are as low as 0.80%. Evaluation of Spectra from Calibrated Gas Mixtures. In addition to the experiments with synthetic spectra the mass spectrometric system was tested with commercially available gas mixtures. These were chosen to produce spectra with gradually increasing peak overlapping. The components were mainly gases with base peaks (from C2H4,N2, C2HC) or major
ANALYTICAL CHEMISTRY, VOL. 54, NO. 4, APRIL 1982
673
Table 11. Comparison of Given and Evaluated Gas Fractions Calculated from Spectra of Calibrated Gas Mixtures composition, % -standard gas 1 standard gas 2 standard gas 3 gas given determ given determ given determ H* CH4 CZ% C*H, c 2 El,
NZ C3H6
Ar
c 3
H,
CO, C4HlO
25.2 f 0.5
26.9
1.9
22.0 f 0.4
23.7 f 1.9 0.5 i 0.3
1.1 f 0.1 25.3 f 0.5
0.2 f 0.1 0.9 f 0.2 25.3 f 1.6
22.0 f 0.4 10.1 f 0.2
24.9 f 1 . 8 5.1 f 2.3
23.7
i
0.5
23.0
f
1.2
24.1 f 0.5
24.2 f 2.1
24.7
f
0.5
23.8
f
1.0
21.8 f 0.4
22.1 f 2.5
f
-.
100
0
-100
5
1.6 f 0.4 11.6 f 1.0
1.0 f 0.1 86.0 f 1.4
1.2 f 0.2 83.8 f 4.7 0.1 f 0.1
1.0 f 0.1
0.9 f 0.1
1.0 f 0.1
0.9 f 0.1
analytical problem, an appropriate extension of the program has not been introduced so far. When the nitrogen fraction, however, is superior to that of the hydrocarbons (e.g., standard gas 1)no interferences are to be expected. The hydrogen fraction, calculated from the molecular peak only, is somewhat too high for standard gas 3 but still acceptable. The deviation originates from interferences of the low hydrocarbons, especially from methane. In the absence of the hydrocarbons, hydrogen can be determined correctly.
D e w I t i o n / perccint
0
1.0 f 0.1 10.0 f 1.0
15
10
C,H,
/ percent
Figure 1. Relative deviations of evaluated ethene percentages, calculated from synth~stlcallygenerated spectra.
peaks (from CBH8,COz, C4H10) at mass 28 (Table 11). Thus, for interpretation, complications were to be expected. Additional components were Ar and CHI. Ar has no peaks common with the other gases. Methane peaks overlap with minor peaks of nitrogen and carbon dioxide. In Table I1 the certified values of the gas fractions (supplier; Messer Griesheim) are compared with those obtained by the proposed procedure. The components were identified correctly; though, in each analysis BL small fraction (0.145%) of a noncertified hydrocarbon is determined by the program. However, the high standard deviations are of the order of magnitude of the respective percent fractions. This should be sufficient evidence to reject these gases from the list. The agreement of the quantitative results naturally depends on the degree of peak overlapping. Therefore CHI, CZH&Ar, CSHg,COz, and C4H10 could be determined correctly with relative standard deviations lower than 10%. When their fractions are as low as 1.0%, the standard deviations are between 10 and 20%. Difficulties are to be expectgd for base peak overlapping8 of components with no other major peaks. This applies especially for nitrogen, the 10.1% fraction of which could not be determined correctly in the presence of 22.0% CZH& The respective sum peak is broadened due to the unresolved small mass differences. Thus the measured peak height is no longer proportional to the sum of the ion currents. The calculated nitrogen fraction therefore substantially differs from the given one. This interference immediately becomes obvious by the high standard deviation which is about 50%. For correct interpretation, the peak areas instead of the peak heights should be the basis for the evaluations. Because of minor importance to the present
CONCLUSIONS The proposed evaluation procedure, tested with synthetic spectra as well as with those of gas mixtures, leads to the following conclusions: (1)Optimal sensitivity is obtained when at least one major peak of a component is not overlapped. Then the limit of quantitative determination is a function of the sensitivity of the mass spectrometer only. In the present experiment this was in the 10 ppm (vol) range. For components with interfering lines a t least the sum of their concentrations can be given at this level. These are the nitrogen oxides, the carbon oxides, and the low hydrocarbons. (2) Fractions above 10% of the low hydrocarbons are the main source of misinterpretations. Then incorrect results are to be expected for the determination of CO, COz, NO, and to a somewhat smaller degree of Nz.Below 10% the hydrocarbons do not influence the determination of the above mentioned gases in fractions greater than 1% . The separation of the hydrocarbons is possible for fractions above 1% of the individual constituents. Otherwise, either the total concentration can be given or gas chromatographic separation prior to mass spectrometry is necessary. (3) Generally valild and fixed limits of qualitative and quantitative determination of the individual gases cannot be given. They are a function of peak overlapping and thus characteristic for each analyte. In the present evaluation procedure the significance of a determined ion current can be derived directly frlom the standard deviations. At a given level of confidence aind degree of freedom (e.g., S = 99%, f 30) the interval of confidence can be calculated (tr 2.8). This is equivalent to confidence limits which are &loo% of the determined mean value, when the relative standard deviations are above 35%. In these cases the components are probably not present in the analyte, so that the determinations should be classified “not significant”. Thus erroneous or not significant determinations are evident immediately from the computer output.
-
-
LITERATURE CITED (1) Duschner, H.; Schasr, W.; Starke, K. Radlochlm. Acta 1977, 2 4 , 133-137. (2) Schorr, W.; Duschner, H.; Starke, K. AtomkernenerglelKerntech. 1878, 33, 265-269. (3) Lelchnltz, K. Chem. Labor Betr. 1978, 29, 127-131.
674
Anal. Chem. 1802, 54, 674-677
(4) Flte, W. L.; Irvlng, P. J. Vac. Sc/. Techno/. 1074, 11, 351-356. (5) Sweely, C. C.; Elliot, W. H.; Fries, I.; Ryhage, R. Ana/. Chem. 1066, 38, 1549-1553. (6) Jeltsch, E.; Graf, W. KFA Julich Report No. 1007-RX, 1973. (7) Nlshl, I.; Sugal, S.; Tanaka, K.; Tomizawa, G. Mass Specfrosc. 1076, 24, 07-105. (6) Flucklnger, R.; Schalcher, M. 7th International Mass Spectrometer Conference, Florence, Italy. 1076. (9) Klenltz, K. Z.Anal. Chem: 1058, 164, 60-00. (IO) Dobrozemskl, R.; Farber, W. Vak.-Tech. 1071, 6,231-239. (11) Raimondi, D. L.; Winters, H. F.; &ant. P. M.; Clarke, D. c. IBM J . Res. Dev. 1071, 15, 307-312.
(12) Tunnlcliff, D. D.; Wadsworth, P. A. Anal. Chem. 1065, 37, 1082-1065. (13) Margenau, H.; Murphy, 0. M. “The Mathematics of Physics and Chemlstry”, 2nd ed.; D. van Nostrand Co.: Princeton, NJ, 1956.
RECEIVED for review October 22,1981. Accepted December 21, 1981. Financial support for this work was received from the “Ehdesminister fiir Forschung und Technohie” under Contract No. 02 U 5090.
Characterization of Poly(carb0xypiperazine) by Mass Analyzed Ion Kinetic Energy Spectrometry Salvatore Fotl,’ Angelo Llguorl,* Pletro Maravigna,‘ and Glorglo Montaudo”’ Istltuto Dipartimentale di Chimica e Chimica Industriale, Universita di Catanla, 95 125 Catania, Italy, and Dipartimento di Chimica, Universlta della Calabrla. Arcavacata dl Rende (Cosenza), Italy
Thls work Is concerned wlth a study of poly(carboxyplperazlne) by dlrect pyrolysls-mass spectrometry. The Identity of a key compound In the mlxture of thermal ollgomers orlglnatlng in the polymer pyrolysis was demonstrated by mass analyzed Ion kinetlc energy spectrometry. The mass spectral data allow one to assess that the pyrolytic breakdown of thls polyurea occurs through a slngie-stage decomposltlon mechanlsm that leads to fragments wlth amlno end groups and carbon monoxlde. This appllcatlon of MIKE spectrometry Illustrates the potentlalltles of this technique In the analysis of mlxtures obtalned by direct pyrolysls of polymers in the mass spectrometer.
Although mass spectrometry (MS) is considered an essential technique to elucidate the structure of low molecular weight organic and inorganic compounds, it has been much less used in the case of polymers. This constitutes a relevant difference with respect to other widely applied spectrometric techniques, such as IR and NMR, whose respective importance in the structure elucidation of polymers is similar to that for low molecular weight compounds. It appears evident that, since MS techniques require transfer of the sample in the gas phase, the low volatility of macromolecules has constituted a serious drawback to the application of direct mass spectrometric analysis to polymer systems. In the direct pyrolysis-mass spectrometry technique (1-3), polymers are introduced via the direct insertion probe and the temperature is increased gradually up to a point at which thermal degradation reactions occur; the volatile oligomers formed are then ionized and detected. The mass spectrum of a polymer obtained in these conditions is therefore that of the mixture of oligomers formed by pyrolysis. A general advantage of this technique is that pyrolysis is accomplished under high vacuum, and therefore the thermal oligomers formed are volatilized and removed readily from the hot zone. This, together with the low probability of Universitg di Catania. Universiti della Calabria. 0003-2700/82/0354-0674$01.25/0
molecular collision and fast detection reduces to a great extent the occurrence of secondary reactions, so that almost exclusively primary fragments are detected. Consequently, the information thus obtained is of particular importance in order to assess the primary thermal degradation mechanism of a polymer. Furthermore, since pyrolysis is achieved very close to the ion source and no problem of transport exists, fragments of high mass, which are often essential for the structural characterization of the polymer, can be detected, whereas they are often lost using other techniques. The main problem connected with this technique is, however, the identification of the products in the spectrum of the multicomponent mixture produced by thermal degradation. In fact, in the overall end spectrum of a polymer, the molecular ions of the thermal formed oligomers will appear mixed with the fragment ions formed in the ionization step. In some instances, identification of thermal degradation products can be achieved by using soft ionization methods, by using exact mass measurements, and by matching spectra of authentic samples with those obtained from the polymer (1). A technique which appears attractive for the direct mass spectral analysis of mixtures if that of comparing mass analyzed ion kinetic energy (MIKE) spectra of selected ions in the spectrum of the mixture with MIKE spectra of reference compounds (4). Although it has been pointed out that some care must be exerted in the evaluation of such data (5),the method has proved to be valuable in several cases (4). Applications of the method to the elucidation of mass spectra of mixtures obtained by direct pyrolysis-mass spectrometry of synthetic polymers have not appeared in the literature to date. In the following, we report the utilization of MIKE spectra in the mass spectral characterization of poly(carboxypiperazine).
EXPERIMENTAL SECTION Synthesis. l-4-Bis(piperazinocarbonyl)piperazine was prepared from l-4-bis(chlorocarbonyl)piperazine with an excess of piperazine (1:lO) in benzene at room temperature with stirring. After 30 min the solvent was distilled out at reduced pressure, piperazine and piperazine hydrochloride were extracted with water, and the residue was recrystallized from methylene chloride/hexane, mp 210 O C , according to the literature (6). @ 1982 Amerlcan Chemlcal Society
