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Anal. Chem. 1989, 61, 2416-2422
throughput analyses in GC/MS and GC/MS/MS. Measurement of the column resistance was shown to be a simple yet accurate method of directly sensing the temperature of low thermal mass Al-clad columns. It was demonstrated that linear voltage programming of the Al-clad columns can be used to approximate linear temperature programming. Future application of proportional-integral-differential (PID) feedback control of the column temperature and elimination of the column insulation is expected to further improve the thermal response characteristics of direct resistive heating of these columns.
ACKNOWLEDGMENT The authors thank the staff of the UF Department of Chemistry electronics and machine shops for their invaluable assistance in this work. Registry No. Si02, 60676-86-0; Al, 7429-90-5. LITERATURE CITED Gaspar, G.; Annino, R.; Viil-Madiar. C.; Guiochon, G. Anal. Chem. 1976, 5 0 , 1512-1518. TiJssen, R.; van den Hoed, N.; van Kreveld, M. E. Anal. Chem. 1987, 59. - - , 1994-1996 . - - . .- - -. van Es, A.; Janssen, J.; Bally, R.; Cramers, C.; Rijks, J. HRC CC, J. fflgh Resolut Chromatogr Chromatogr Commun . 1987, 1 0 , 273-279. Schutjes, C. P. M.;Vermeer, J. A.; Rijks, J.; Cramers, C. J. Chromatogr. 1982, 253, 1. Ewels, B. A.; Sacks, R. D. Anal. Chem. 1985, 5 7 , 2774-2779. Laming, L. A.; Sacks. R. D.; Mouradlan, R. F.; Levine, S.P.; Foulke, J. A. Anal. Chsm. 1988, 60, 1994-1996. Yost, R. A.; Fetteroif. D. D.; Hass, J. R.; Harvan, D. J.; Weston, A. F.; Skotnicki, P. A.; Simon, N. M. Anal. Chem. 1984, 5 6 , 2223-2228. Trehy, M. L.; Yost, R. A.; Dorsey, J. G. Anal. Chem. 1988, 58, 14-19. Trehy, M. L.; Yost, R. A.; McCreary, J. J. Anal. Chem. 1984, 5 6 , 1281-1285. McClennen, W. H.; Richards, J. M.; Meuzelaar, H. L. C. Roc. ASMS Conf. Mass Spectrom. Allled Top ., 36th 1988, 403-404.
.
.
.
(1 1) Richards, J. M.; McClennen, W. H.; Bunger, J. A.; Meureiaar. H. L. C. R o c . ASMS Conf. Mass Spectrom. Allled Top ., 361h 1988.547-548. (12) Hail, M. E.; Yost, R. A. Roc. ASMS Conf. Mass Spectrom. Aliled Top., 36th 1988, 803-804. (13) Hail, M. E.; Yost, R. A. Anal. Chem., preceding paper in this issue. (14) Zlatkis, A.; Fenimore, D.C.; Ettre, L. S.; Purceil, J. E. J. Gas Chromatogr. 1985, 3 , 75-81. Walsh, J. T.; Merritt, C. J . Gas Chromatogr. 1967, 5 , 420-423. Nygren, S.;Anderson, S. Anal. Chem. 1985, 5 7 , 2748-2751. Nygren, S.; Mansson, P. E. J. Chromatogr. 1976, 123, 101-108. Nygren, S. J. Chromatogr. 1977, 142, 109-116. Costa Neto, C.; Koffer, J. T.; De Alencar, J. W. J . Chromatogr. 1964, 15, 301-313. Kelley, J. D.; Walker, J. Q. Anal. Chem. 1989, 4 1 , 1340-1342. Lee, M. L.; Yang, F. J.; Bartle, K. D. Open Tubular Gas Chromatcgraphy: T h e w and Practice; John Wiiey & Sons: New York, 1984; Chapter 4. Hall, M. E.; Berberich, D. W.; Yost, R. A. Anal. Chem. 1989, 67, 1874- 1879. Rudat, M. A. R o c . ASMS Conf. Mass Spectrom. Allied Top., 30th 1982. 868. (24) Sears. F. W.; Zemansky. M. W.; Young, H. D. University Physics, 5th ed.; Addison-Wesley: Reading, MA, 1978; Chapter 16. (25) Sears, F. W.; Zemansky, M. W.; Young, H. D. Universlty Physks, 5th ed.; Addlson-Wesley: Reading, MA, 1978; Chapter 26. (26) Davies, N. W. Anal. Chem. 1984, 5 6 , 2618-2620. (27) Davies, N. W. J. Chromatogr. 1985, 325, 23-35. (28) Cramers, C. A.; Scherpenzeel, G. J.; Leciercq, P. A. J. Chromatogr. 1981, 203, 207-216. (29) Varian Model 330013400 Operator‘s Manual; Varian Associates, Inc.: Walnut Creek, CA. (30) 8 o b , K. On-Column Injection in Caplllary Gas Chromatography; Huethii: Heidelberg, 1987; Chapter B. (31) Bretell, T. A,; Grob, R. L. Am. Lab. 1985, 77(11), 50-68.
RECEIVED for review January 27,1989. Accepted August 4, 1989. This research was sponsored in part by the US.Air Force Engineering and Services Center, Environics Division (HQ-AFESC/RDVS) at Tyndall Air Force Base and by the US. Army Chemical Research Development and Engineering Center (CRDEC) at Aberdeen Proving Grounds. Patent application no. 071372, 272 filed June 27, 1989.
High-Accuracy Gas Analysis via Isotope Dilution Mass Spectrometry: Carbon Dioxide in Air R. Michael Verkouteren* and William D. Dorko
Gas & Particulate Science Division, Center for Analytical Chemistry, National Institute of Standards and Technology, Gaithersburg, Maryland 20899
An absolute method, based on Isotope dllutlon mass spectrometry, Is described for the determination of atmospheric concentratlons of carbon dioxide (CO,) In dry air. I n this study, the relative amounts of sample and splke gases are measured manometrlcally under temperature control before blending. The spike CO, composltlon is approxlmately 0.1 atom % ‘‘C whlle the oxygen lsotoplc composition is “normal”. Exhaustlve assessment of potential error sources leads to accountablllty of observed lmpreclslon and determlnatlon of accuracy confidence intervals (CI).The impreclslon interval (95% C I ) about the mean is smaller than f0.1% (f0.4 pmol/mol) whlle the accuracy Interval (95% CI) Is f0.15% (f0.52 pmol/mol) for alr having a CO, concentratlon of abortt 350 p ” i . Calculated concentratlons of CO, are statistkally Idsthgulshable from those generated by gravknetry, an Independent method of anaiyds. I n this study, the malor contrlbutors to uncertalnty and lmpreclsion are the predetermlnatlon of the gas volume ratio and the measurement of the lsotoplc composnion of the blended CO,, respectively.
INTRODUCTION We report the development of an absolute method, based on isotope dilution mass spectrometry (IDMS), for the determination of the concentration of C02 in air at levels of 300-400 pmol/mol. This technique provides a highly selective, precise, and independent method for verification of our C02-in-air Standard Reference Materials (SRMs), which presently are certified by nondispersive infrared (NDIR) spectrometric comparison with a set of gravimetrically prepared primary standards (I). As an independent reference method, IDMS has advantages of being mass selective and essentially independent of C02chemical yield, while measuring C02 concentrations in delivered air. Isotope dilution mass spectrometry has already found wide application to trace analyses of samples in solid and liquid form. In many of these cases, the precision and accuracy of IDMS have been superior to other techniques (2). Applications of IDMS to atmospheric gas analysis, however, have been limited to noble gases (3-5),nitrogen dioxide (6),and sulfur gases (7-9). The gas isotope ratio mass spectrometer used in
This article not subject to US. Copyright. Published 1989 by the American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 61, NO. 21, NOVEMBER 1, 1989
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Table I. Summary of Isotopic Analyses of Working Standard, C02 from Air, and Spike sources of C 0 2 samples
R6
SW
Ra
working standard air, 375 ppm COB air, 350 ppm C02 air, 305 ppm C02 mike
11.50044 11.85603 11.90643 11.83868 0.87613
0.000 92 0.000 92 0.00092 0.00092 0.00092
4.053 23 4.10399 4.16633 4.097 20 4.12141
mean isotopic ratios and standard deviations ()(lo3) SFM R13 R" R'S P 0.00081 0.00081 0.00081 0.00081 0.00081
10.75126 11.10201 11.14647 11.08531 0.11965
this study was a triple-collector prototype designed for high-precision C02analysis and built a t the NIST (10). On the front end of the mass spectrometer, we report a redesigned gas blending system, needed to improve the accuracy and precision of the gas dilutions as required for our study. In this IDMS method, an aliquot of air is measured precisely and equilibrated physically with a precisely measured amount of isotopically depleted (spike) COP The isotopically altered mixture of COz is isolated from the air and measured, by mass spectrometry, to quantify the extent of isotopic alteration. The concentration (in micromoles per mole) of COP in the original air is then calculated by using the following formula:
0.37459 0.37701 0.37998 0.37669 0.37824
2.022 52 2.047 74 11.66919 2.07886 11.71748 2.044 35 11.65240 2.06059 0.87177
F3
sF45
sF13
0.00092 10.98010 0.00092 11.02359 0.00092 10.96377 0.00092 0.11964
0.00092 0.00092 0.00092 0.00092
sured RG and R* (with appropriate corrections) via standard equations (16). These equations are modified by an empirically derived relationship among naturally occurring oxygen isotopes (17,14) and the exact solutions found by an iterative method. From the atomic ratios, then, molecular ratios for n = 47 to 49 (not directly measurable by the mass spectrometer) may be constructed in accordance with the assumption of random atomic distribution among the molecules (14). Fractional abundances (P), which are closely related to isotopic ratios, are ratios of particular atomic or molecular species of mass n to the sum of all related species, hence F13
= 13C/('2C
+ 13C)
(7)
49
P5= (13C1602+ 12C160170)/[C C 0 2 mass i] i=44
The factors are ratios of absolute pressure (P), volume (V), absolute temperature (T), and thermodynamic compressibility (2)between the pure C02 spike (spk) and air; the bracketed term is the ratio of differences of mass 45 fractional abundances (F6)between the COz of the air, spike, and mixture, and is numerically equal to the molar ratio of COz from the air sample to COzfrom the spike. Explanations of this isotopic notation are found in the following section. Pressures, temperatures, and FSmix are measured for each analysis; the volume ratio, P&, and P , k are predetermined for each set of analyses. Thermodynamic compressibilities of air and C02 are taken from expressions derived from tables compiled for C02 (11)and air (12,131.Because the volumes are calibrated as a ratio, eq 1 solves for concentration directly. The individual quantities of analyte and matrix gas are not determined.
ISOTOPIC NOTATION AND STRATEGY
F45 values, used in eq 1, are calculated from COzmolecular isotope ratios, R46and R*, measured on the mass spectrometer. The notations and expressions that follow are adopted from a prior study (and references therein) on the mass spectrum of carbon dioxide (14). A brief explanation of this isotopic notation and the strategy for converting R6 and R* values into F6values follow. The analyte, C02,consists of two stable isotopes of carbon (12C and 13C) and three stable isotopes of oxygen P O , 170, and Normally assumed is that the distribution of these isotopes within a population of COz molecules is predicated by random probability, which results in a predictable distribution of C02 masses from 44 to 49 amu (15). Isotopic ratios (R") are ratios of particular atomic or molecular species of mass n to the most abundant related species; here we define
R13 = 13C/12C
(2)
R17 = l70/l6O
(3)
R18 = 1so/'60 R45 = (13C1602 + 12C160170)/12C1602 R46 = (12C1702 + 13C160170 + 12C1601S0)/12C1602
(4) (5)
(6) The atomic ratios R13, R17, and R18 are calculated from mea-
The relationships between
(8)
Fn and Rn are
+ R13) p 5= R45/(1 + R45 + R46 + + P 3= R13/(l
(9)
+ R49)
(10)
By this strategy, appropriate fractional abundances for eq 1 are calculated from measured molecular isotopic ratios of COz.
EXPERIMENTAL SECTION Air Samples. To study the effectiveness of our IDMS technique for determining COz concentrations in air, the system was evaluated over a concentration range bracketing the current seasonally corrected mean global atmospheric concentration of 351 pmol/mol(18). Samples of air were chosen from our inventory containing COz nominally at 375, 350, and 305 pmol/mol. All air samples were contained in pretreated (Aculife, Scott Specialty Gases) high-pressure 30-L(internal volume) aluminum cylinders (Luxfer). The 375 and 305 pmol/mol air samples were blended at Scott Specialty Gases: for the 375 pmol/mol air, pure COz and NzO were added to real dry air, for the 305 pmol/mol air, synthetic air (78% NP,21% 02,1% Ar)was blended into real dry air. The 350 pmol/mol air was collected in Colorado at Niwot Ridge in December of 1986. This air was dried during collection by using a cold trap in series with a P205 (Aquasorb) filter. The HzO contents of all samples of air were less than 20 pmol/mol. Concentrations of N20 in each air cylinder were determined by gas chromatography (GC) using an electron capture detector. The isotopic compositions of the COz in each air cylinder (Table I) were determined by methods described in the isotope dilution and mass spectrometry sections below, with the following exceptions: (1) the air is expanded into both V , and V,, containers (Figure 1) to approximately double the amount of air-C02 cryocollected, and (2) no spike COPis added. Spike Material. In IDMS analysis, the isotopic composition of the spike material is usually made as different as possible from the isotopic composition of the analyte. A large difference between spike and analyte compositions minimizes the imprecision of the molar ratio term (the bracketed term in eq 1) in the IDMS equation. Accuracy, however, is forfeited when standards required for calibration of such spike materials are unavailable, which is currently the case with isotopically altered COP Additionally, memory effects become more acute when materials of vastly different compositions are analyzed in the same instrument. Given the constraints of the analyticalprecision necessary for this study and precision capabilities of the maSS spectrometer, the minimum difference necessary between the isotopic compositions of analyte
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ANALYTICAL CHEMISTRY, VOL. 61, NO. 21, NOVEMBER 1, 1989 15
w k
~
@
3
Mass Spectrometer
Table 11. Sources and Nominal Magnitudes of Corrected Systematic Biases factor p8pk
pur V , k/
V,,,
rPr
P5m,l
/x5
n
20
Flgure 1. Gas handling system: (1) V,, container, modified from two Nupro SS-4CS-TW-10 miniature sample cylinders, stainless-316: (2) Vat container, 6-L spherical container, stainless-304, Scientific Instrumentation Specialists, inlet/outlet ports at 90°, no internal tubing; (3) V,,, container, 6-L borosilicate glass vessel used for doubling amount of air when cryocollecting air-CO,; (4-7) valve configuration: solid triangle designates port which faces the valve seat; (4) manual diaphragm valve, Nupro, SS-DLBW4-ST; (5) manual shut-off valve, bellows or diaphragm type; (6) pneumatically driven bellows valve, Nupro, SS-HBM 1-0; (7) pneumatically driven bellows valve, Nupro, SS-HBV5 1 4 ; (8) flexible tubing, Cajon, stainless-321;(9) fused silica zigzag single-U cold trap with fritted filter (Horibe-type); (10) mass flow meter with digital output, Hastings, ST-1K; (1 1) metal bellows pump, Metal Bellows Corp., MB-21; (12) dual vacuum system (see text); (13) turbomolecular pump, Bakers, TPU 050; (14) rotary vane pump; (15) thermocouple gauge with digital output,RCA 83-04; (16) thermocouple gauge with analog output, Hastings, DVdM; (17) presswe transducer, Ruska DDR-6000, with 5'1, dlgit display, Hewlett-F'ackard, DVM3456A, and chart recorder fitted with 12 V maximum variable offset; (18) air cylinder; (19) spike CO, storage vessel, borosilicate glass: (20) delineation of temperature-controlledglovebox.
and spike was calculated to be about 1% (absolute) in carbon-13. C02made from nearly isotopicallypure carbon-12, which is readily available, fulfilled the spike requirements. Spike C02was prepared by combusting, at 900 "C, 99.9 atom % carbon-12 amorphous carbon (Isotec, Inc.) in a flow of ultrahigh-purity oxygen gas, passing the flow over beds of Pt/CuO (800 "C) and Ag wool (515 "C), and cryotrapping the C02 in a series of liquid nitrogen cold traps. The C02was then distilled several times at -78 "C to remove water. Mass spectrometric analysis showed no traces of impurities above one part in low4. Tunable diode laser absorption spectrometry (TDLAS) indicated that the spike COz contained 0.98 f 0.01 bmol/mol of N20, a concentration that does not significantly affect C02 isotopic analysis. The results of isotopic analysis of the spike COP,by methods described in the Mass Spectrometry section below, are given in Table I. Gas Handling System. The components of the gas handling system are identified in Figure 1. The critical components of the system are contained in a temperature-controlled glovebox. Spatial and temporal variations in temperature within this box are minimized by the circulation of air via a small fan, by the use of a glove port for valve manipulations, and by the semiadiabatic nature of the box itself (wooden with metal interior). Both stainless steel containers of V,, and V,, are internally electro-
source of bias barometric head barometric head temperature dependency N 2 0 content N,O content
magnitude,
%
-0.0040 -0.0039 +0.281/1"C (Td,) +0.021
-0.0076
polished and chemically passivated (Summa process, Molectrics, Inc.); the volume ratio of these containers was determined by a series of two-stage gas expansions (19). This method of calibration has the advantage of determining the volume ratio (and its temperature dependence) under conditions for which the system is actually used. Individually, the air and spike volumes are 6.38 L and 7.77 mL, respectively. Interconnecting tubing is 4 mm (i.d.1 premium grade stainless steel (Supelco, Inc.); system components are welded or fitted with all-metal couplings (Cajon, VCR couplings). A dual vacuum system allows rough evacuation of the system through a rotary vane pump. When the pressure drops to 100-200 Pa, the valves are switched and evacuation proceeds through the turbomolecular pump. The dual vacuum system can be accessed at three separate locations in the gas handling system (see Figure 1). Isotope Dilution. Air to be analyzed is expanded into the V, container to a pressure of about 110 kFa. After a 15-min interval for equilibration, the air in the container is isolated by slowly closing the valve; the pressure and temperature are then recorded. The pressure is read by a force-balance transducer, the temperature measured by a thermistor (ThermoMetrics, Inc., CSP Standard) in thermal contact with the container body. The system is then evacuated (except for V), and allowed to outgas until the vacuum falls below 0.5 Pa. Spike C02is then expanded into the v w k container to a pressure of about 25 kPa and the procedure repeated for measuring pressure and temperature. Excess spike COz is cryotransferred back to its storage vessel. The system is evacuated (except for V, and v,,k) and outgassed at 50 "c to aid in removal of adsorbed spike C02. After the vacuum falls below 0.5 Pa, the system is isolated and the two gases mixed by recirculation through a metal bellows pump. Subsequently, the C 0 2 mixture is frozen out of the air in a liquid argon cold trap. Because COz-depleted air recirculates to dilute the air in V, recirculation for 3-4 h at a flow rate of 400-500 mL/min is required to collect the C02 nearly quantitatively. After noncondensable gases are slowly pumped off, the COzmixture is purified by distillation at -78 "C and cryotransferred to a calibrated volume for yield determination. Mass Spectrometry. The gas isotope ratio mass spectrometer has a 30 cm radius, 90° deflection magnetic sector, extended flight path geometry, and a triple, deep Faraday cup collector (10). Samples of C02are ionized with 50-eV electrons at a current of 130.0 FA, the process controlled by a NIST emission regulator with an instability of 1part in 10s (20). Signals from the Faraday cups are amplified and fed through separate electrometers (Cary, Model 401M for masses 45 and 46, NIST Parametric Electrometer for mass 44) and to three digital voltmeters (HP Model 3456A). There, the mass 44 signal is divided arithmetically into the other two signals to generate real-time ion current ratios. Mass discrimination effects are negated by differential measurement (21). The working standard, 99.995% C02(Matheson Gas Products), is calibrated with a pair of Isotopic Reference Materials [NBS-16 and NBS-17 (22)]to correct for "proportional errors" (23, 24). No corrections for "-44 tailing or valve mixing are necessary. The isotopic correction for nitrous oxide (N20)impurities in C02 derived from air is done according to Mook and van der Hoek (25);the ionization efficiency ratio for N20/C02in our ion source is 0.715. The measured ion current ratios, corrected for the effects above, are taken as molecular isotope ratios (Re and R&). Data acquisition is assisted by a small computer (Hewlett-Packard, Model 86B) which also controls the dual leak C02inlet system. Corrections to Factors. Sources of reproducible systematic bias for each factor of eq 1are listed in Table I1 along with nominal magnitudes; results in Table I11 are corrected for these effects. Below we briefly discuss the corrections.
ANALYTICAL CHEMISTRY, VOL. 61, NO. 21, NOVEMBER 1, 1989
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Table 111. Summary of IDMS Results air set (nominal C 0 2 concn),
concn of N20,
pmol/mol
nmol/mol
375
333
sample
measd C02 concn, pmol/mol
I
mean COz concn, cryoyield, %
pmol/mol
95% CI, rmollmol imprecision accuracy
COOconcn via
g r a v p ~ ~ ~ , pmol/mol
99.2 99.5 99.2 99.3
375.06
+0.36
+0.67
375.30
3 4
374.81 375.30 374.93 375.19
n
I
350
302
5 6 7 8
347.40 347.48 341.43 347.39
100.0 99.9 99.4 99.5
347.43
f0.06
f0.52
347.62
305
272
18 19 20 21 22
ao3.81 303.78 303.59 303.78 303.55
99.6 99.6 98.4 99.2 99.4
303.70
f0.15
f0.48
303.82
Pressure. Barometric head, i.e., the difference in gas pressure between the pressure transducer and gas volume, arises from differences in elevation. This effect is compensated for by the barometric equation (26). Volume. A temperature dependency in VSpk/V,, was quantified by determining this ratio at two temperatures (302 and 306 K). The dependency is assumed linear between these temperatures. Fractional Abundance. Routine corrections applied to measured molecular ratios have been briefly described and referenced in the mass spectrometry section. To correct for N20, we assume that (1) the NZO/CO2sample ratio remains constant during the cryocollection, transferences, and mass analysis of the sample and (2) the isotopic composition of N20 is “normal” (comprised of nitrogen and oxygen isotopes in their naturally occurring ratios). RESULTS AND DISCUSSION Replicate samples from the three air cylinders described above were analyzed; the results are summarized in Table 111. Samples 9 through 17 were compromised by the presence of an internal valve leak in V,,, that caused a bias and increase in imprecision; those results are not listed. Remaining data are listed in order of their analysis. Cryogenic COz collection yields are determined-after calculation of air C 0 2 concentration-by dividing the recovered amount of mixture C02 (in a calibrated volume) by the initial amount of C02from the air and spike. Analytical precision (AP), or reproducibility, within each set is expressed by the 95% confidence interval about a mean (a) of n observations under assumptions of statistical normality, where t is the t table value a t the stated confidence level and s is the standard deviation (eq 11). An account of
95% CI (AP) = f f ts/n1/2 contributors to the observed imprecision is contained in the error analysis section below. Bias bounds (AM),or uncertainties in the mean, are also expressed by a 95% CI about f (eq 12), and are determined by summing (in quadrature) observed imprecision and measured (or estimated) uncertainties in all factor ratios (A,,,), where FacR = P, V, T, Z, and F ratios) of eq 1. Uncertainties are expressed as relative standard errors (RSES)as defiied in the error analysis section. 95% CI (AM) = f f f ( [ t ~ / ( f n ~ / ~ )[2CRSE(AF,,,)]2)1/2 ]~ (12)
+
Lastly, data generated by gravimetry/NDIR on the same samples of air are included for comparison purposes. The uncertainty of the gravimetry/NDIR values is f0.4 pmol/mol a t the 95% confidence level (I). To determine whether the results of the two methods are significantly different, com-
parison was made by the two-sided normal test (27). This test concludes that, at the 95% level of confidence, the biases between the methods are 0.24 f 0.77, 0.19 f 0.64, and 0.12 f 0.61 Fmol/mol, respectively, for the 375, 350, and 305 pmol/mol air samples. Because the bias uncertainty intervals significantly overlap, results generated by these two independent methods are statistically indistinguishable from each other. E r r o r Analysis. Because the technique described is absolute, an exhaustive assessment of all potential error components is necessary to determine error bounds. These error components, with their measured (or estimated) magnitudes, are listed in Table IV. By inspection, the error components may be divided into two types: those leading to random analytical imprecision observed within any particular set of air analyses (left columns), and those leading to uncorrected systematic biases in measurement (right columns). Segregation of random and systematic errors is necessary so that accuracy bounds may be rationally calculated with regard to all systematic errors considered, and secondly, so that an order of influence may be established among random and systematic error sources. Precision and/or accuracy of the technique may then be improved, when necessary, by minimizing the effects of the most influential error sources. In Table IV, each source of error (random and systematic) within each factor is assigned a relative standard error (RSE) which is defined by either eq 13 or 14. Equation 13 is used
RSE = RSE = f
f
measured s fn1/2
estimated error 4
(14)
when replicate analysis enables determination of the factor mean ( f )and standard deviation; eq 14 is used when the error component of the measured factor value (a) must be estimated. Errors are propagated through eq 1 to calculate RSES in factor ratios (28). The estimated level of imprecision (ELI) for the entire measurement system is then calculated by summing each imprecision RSE(FacR) in quadrature RSE(EL1) = f { C [ R S E ( F ~ C R ) ] ~ J ’ / ~ (15) This value can be compared to the analytical imprecision observed within any particular air set. Observed imprecision greater than that predicted signifies an analytical problem (e.g. samples 9-17, previous section) that can subsequently be identified and corrected. The following discussions of error will be limited to each error component having a RSE greater than 0.01%.
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ANALYTICAL CHEMISTRY, VOL. 61, NO. 21, NOVEMBER 1, 1989
Table IV. Sources a n d Magnitudes of Imprecisions a n d Uncertainties
sources of random error (imprecision) valve seat deformation valve seat deformation
factor imprecision % RSE”
factor ratio imprecision % RSE (FacR)
0.024 (3) 0.0001 (3)
0.024
N/A memory-mass
discrimination
0.015 (2)
0.034 (eq 17)
NIA C02 sorption on V, reproducibility of gauge gas sorption on V,, reproducibility of gauge temperature variation of v,pk reproducibility of thermistor temperature variation of V,, reproducibility of thermistor
negligible 0.002 (2) negligible 0.002 (2) 0.001 (3) 0.0005 (1) 0.002 ( 3 ) 0.0005 (1)
0.003
0.002
N/A N/A estimated limits of imprecision %RSE (ELI) = *0.042% (eq 15)
sources of potential systematic error (bias) calibration error (Av)
potential bias (A) 9i RSE“
COZ sorption on V,
0.062 (eq 16) 0.0079 (2) 0.0079 (2) 0.005 (3) 0.73 (2) 0.11 (2) 10.6 (2) 0.012 (3)
gas sorption on V,
0.001 (3)
calibration error
0.003 (1)
calibration error
0.003 (1)
uncertainty of tables uncertainty of tables
0.002 (1) 0.001 (1)
memory-mass discrim calibration error isotopic nonequilibrium calibration error memory-mass discrim calibration error
potential FacR bias % RSE (AF~~R) 0.062
0.040 (eq 18)
0.012
0.004
0.002
total estimated uncertainty %RSE(AM) = 10.075%
“Method of %RSE determination: (1)reported in literature or by manufacturer; (2) eq 13, in text; (3) eq 14, in text.
Volume. Nonreproducibility of contact stresses at the valve seat-to-stem interface results in a variation in contact area, with a concurrent change in volume behind the interface. The limit of elastic deformation of these seats is estimated by translating the maximum area of contact (marked by discoloration on a used valve stem) into a volume displacement. The uncertainty of the volume ratio (Av), predetermined by a series of two-stage neon gas expansions (19), is calculated through eq 16. The values of s1 and s2 are the standard RSE(Av)= &([SI/ [ ( v a n , / vair)n11/2112
+
[sZ/ [ ( v s p k / v a n ~ ) n 2 ” ~ ] 1 ~ 1 ” ~
(16) deviations of the two mean volume ratios, V,,/V,, and VSpf/Van,, from nl and n2 observations, respectively. The ancillary volume, V,, is the total volume between V,, and VSpk (see Figure 1) and includes the volume of the pressure transducer. The main error came from estimating the average temperature of the gas in V., This average temperature was estimated as a weighted average dependent upon the estimated relative volumes of the two temperature regimes within V,,. Secondly, V, was less reproducible volumetrically than V., and V, because it included the internal working volumes of the diaphragm valves (designation 4, Figure 1). Fractional Abundance. Values of p,.and F“5,,k, within any particular set of analyses, are constants; therefore, imprecision due to mass spectrometry is limited to the reproducibility of F45mil. This imprecision is estimated by the imprecision of analysis of replicate COz samples used to determine F45air(Table I). The estimated level of imprecision of the fractional abundance difference ratio (ELI-F), then, is calculated through eq 17, where sFais the standard deviation of a mean value of F45ai,. RSE(EL1-F) = f [ s F a / ( p 5 a i r - p 5 m i x ) + s F a / ( p 5 m i x - p 5 8 p k ) l (17) Uncertainty limits of the fractional abundance difference ratios (A,) come from three sources: (1)potential biases in the mean F45ai,and FSspk values of a set (A8); (2) inaccuracies
in the calibration of the working standard (&); and (3) partial or complete oxygen isotopic redistribution between the spike and air C 0 2 (AI). Each is discussed below; RSE(AF) is calculated through eq 18.
RSE(AF) = f:([RSE(A,)]2+ [RSE(Ac)I2+ [RSE(A,)]2)1/2 (18) Memory and mass discrimination effects may bias the mean Uncertainty from these sources is estimated by the imprecision of replicate analyses (Table I). The uncertainty (As) of the fractional abundance difference ratio due to these sources is estimated via eq 19.
P5,,and F45,pkvalues.
RSE(AJ
f2SFa/(~5ai, - ~ 4 5 , ~ ~ )
(19)
Since no isotopic reference materials similar to the spike or mix COPwere available, values of R45,pkand R4- are based upon differential measurement against a working standard calibrated against reference materials of “natural” COZ. The uncertainties of the F46, and p- values, therefore, increase to about lOOA, and 50A,, respectively, where A, = SF^. Calibration biases (&), while potentidy large for p s p k and p-, are largely negated by covariance in the fractional abundance difference ratio. Calibration error of the fractional abundance difference ratio is less than 0.02% when the fractional abundance difference ratio is between 0.98 and 1.02 (eq 20).
RSE(Ac) = f [ l - ([(P5,iX + 50A,) (p5,pk
+ l o O A c ) I / [ ( P 5 a i r + A,) - ( p 5 m i x +
5oAc)11/:((p5mix - p 5 s p k ) / ( p 5 a i r
- p 5 m i x ) 1 1 (20)
In this study, our spike material is isotopically unique in
F 3and F45;hence, using either of these fractional abundances in eq 1 gives highly precise COz concentrations. We chose F46 as the definitive fractional abundance since we expect the COz mixture to be physically equilibrated only, and not isotopically redistributed (via oxygen isotope exchange). In the absence of isotopic equilibrium, assumptions necessary for converting molecular ratios R45and R46 into atomic ratios RI3,R17,and R18 are not valid (14). This not only would invalidate the
ANALYTICAL CHEMISTRY, VOL. 61, NO. 21, NOVEMBER 1, 1989
determination of F3- but also would affect the determination of P&, since it is dependent (to a small extent) upon values of R4’*- calculated upon the same assumptions. Our initial use of a spike material depleted in carbon-13, oxygen-17, and oxygen-18 caused inconsistencies which were due to invalidation of these necessary assumptions. The problem is circumvented by use of a carbon-13 depleted spike C02 having an oxygen isotopic composition similar (within 2%, relative) to the air-C02 samples; in this way the blend is nearly preequilibrated. The error due to the small degree of isotopic nonequilibration (AI) is equal to the difference in calculated C02 concentrations between the use of Pmk and P3mk in eq 1, and is calculated through eq 21.
The extent of COz mass fractionation and isotopic contamination during cryocollection and transference was examined by blending the spike COz into samples of synthetic air (containing no COz),then cryocollecting and transferring this COz for mass ratio analysis. Comparison of this COz with that obtained directly from the spike storage vessel (and not subjected to cryocollection from air) yielded no significant difference between the two samples; hence, no C 0 2 mass fractionation or contamination was evident. This conclusion is supported by the observation that calculated C02 concentrations appear independent of COz cryocollection yields (Table 111). Isotopic contamination of C 0 2 during short periods of storage (C2 days), in 200-cm3quartz vessels sealed with Kel-F seated valves, is significant; the worst case resulted in an observed change to Pmk of 0.05%. This error potential was minimized thereafter by analyzing the collected COz as soon as possible. Storage vessel memory is minimized by dedicating storage vessels to either air, spike, or mixture COP Memory in the stainless steel gas inlet system and ion source is also significant, especially when analyzing spike COz and air COz sequentially within a few hours. The mass spectrometer is dedicated therefore to analyses of only one type of C 0 2 (air, mix, or spike) per day. This minimizes the memory error in the gas inlet and ion source since the mass spectrometer can be evacuated overnight. By measurement of a stable gas standard on different days against the working standard, spectrometer reproducibility in measuring R4 was determined to be 0.005%. Pressure. Our pressure transducer is calibrated against a NIST ultrasonic interferometer (29). Linearity of the transducer across its dynamic range (0-110 kPa) is excellent (r2 = 1.00000000) while reproducibility of response at any particular pressure within this range is better than 0.002%. Adsorption of COz on the walls of the Vspk, V,,, or V,, containment vessels may lead to errors in pressure measurement. Since the rate of exchange for C02(adsorbed) s COz(gaseous)is expected to be rapid in comparison with the allowed time for cryocollection, adsorbed C 0 2 would be equilibrated but not accounted for by gas pressure. A measurement system bias would result if the adsorbed amount of C02was a significant fraction of the total amount of CO,; imprecision would result if this adsorption were not reproducible. Significant adsorption/desorption phenomena of COz in stainless steel systems have been observed (30,31);however, adsorption phenomena are surface specific and no simple trends are apparent in the literature (11,32). Specific effects on Pspk and Psi,are discussed below. For Pspk,adsorption is estimated as uniform monolayer coverage of COz over all surfaces in contact with spike CO,.
2421
This estimation is supported by the observation that a pressure drop, corresponding to monolayer coverage, occurs during the first few minutes of the equilibration period. Adsorption on the vSpkcontainer walls would cause underestimation of P,pk by 0.024% (0.012% RSE); this value is included in our estimate of uncertainty. Adsorption in the ancillary tubing would cause a greater error (0.4%); however, this COz is subject to removal by heat and evacuation. To determine the amount of COz that remains on the ancillary surfaces after the allowed evacuation time, an experiment was done where air and spike COPwere measured into their respective volumes as usual, but the spike coz in the v,,, container was not mixed into the air. Cryocollection of COP proceeded as the air was recirculated through the system; this COz was subsequently analyzed. Comparison of this COz with that obtained without prior introduction of spike C02 into the ancillary tubing showed no significant difference in F5. We therefore make no allowances for spike C 0 2 adsorption on ancillary walls in calculating our uncertainty limits. For P,, homogeneous adsorption of air on the V, container walls is insignificant due to the high ratio of volume to surface area. Selective adsorption of C02, as the worst case, would be significant only if the total amount of COz (adsorbed + gaseous) within the V, container changed significantly during the equilibration period. Since this container comprises about 97% of the total volume and about 82% of the total surface area and since the “sticking” probabilities of COz on the V, and V, container walls are not expected to differ significantly, we expect no significant change in the total amount of C02 in the V , container during the 1Bmin equilibration period; no contributions to uncertainty from this source are included.
ACKNOWLEDGMENT Grateful acknowledgements are made to I. L. Barnes and C. Kendall for discussions and assistance in mass spectrometry, to G. A. Klouda for spike C02 synthesis, to R. C. Myers for NDIR and GC analyses, to R. L. Sams for TDLAS, and to H. L. Rook for his steadfast support. Registry No. COz, 124-38-9.
LITERATURE CITED (1) Myers, R. C.; Dorko, W. D.; Velapoldi, R. A. Report of Analysis (NIST internal report), 553-65-88, Oct 24, 1988; National Institute of Standards and Technology. Gaithersburg. MD. (2) Uriano, G. A.; Gravatt, C. C. CRC Crit. Rev. Anal. Chem. 1977, 6 , 38 ..1-4 . . 10. . .. (3) Bieri, R. H.; Koide. M.; Martell, E. A.; Schoiz, T. G. J . Ge0phy.s. Res. 1970. 75. 6731-6735. (4) Walton, J: R.; Cameron, A. E.; Walker, R. L.; Hebble, T. L. Int. J . Mass Spectrom. Ion fhys. 1973, 112, 439-453. (5) Oliver, 8. M.; Bradley, J. G.; Farrar, H., I V Geochim. Cosmochim. Acta 1984, 4 8 , 1759-1767. (6) Stevens, C. M.; Barat, F.; Nguyen, Nghi, H. Isot. Ratios follut. Source Behav. Indic., Roc. Symp. 1974, 389-401; IAEA: Vienna, 1975. Chem. Abstr. 1976, 8 4 , 110752~. (7) Bandy. A. R.; Tucker, B. J.; Marouiis, P. J. Anal. Chem. 1985, 57, 1310-1 314. (8) Driedger, A. R., 111; Thornton, D. C.; Laievic, M.; Bandy, A. R. Anal. Chem. 1987, 59, 1196-1200. (9) Lewin, E. E.; Taggart, R. L.; Lalevic, M.; Bandy, A. R. Anal. Chem. 1987, 59, 1296-1301. (10) Moraies, P. A.; Barnes, I.L., in preparation; work performed at the National Institute of Standards and Technology, Gaithersburg, MD. (11) Carbon Dioxide, International Thermodynamic Tables of the Nuid State, v . 3 ; compiled and edited by S. Angus, B. Armstrong, K. M. deReuck; IUPAC Project Centre, London, Pergamon Press: New York, 1976. (12) Thermodynamic Properties of Air; complied by V. V. Sychev, A. A. Vasserman. A. D. Koziov, G. A. Spiridonov, V. A. Tsymarny; National Standard Reference Data Service of the USSR; Selover, T. B., Jr., English language ediiion ediior; Hemisphere Publ. Corp.: New York, 1987; originally published by Standards Publishers: Moscow, 1978. (13) Jacobsen, R. T.; McCarty, R. D.;Olien, N. A. Thermophysicalfroperties of Ab, version 2.0 (October 1987); supplement to NASP Technical Memorandum 1005 (March 1987); National Aero-Space Plane Program, Joint Program Office, Wright-Patterson AFB, OH. (14) Santrock, J.; Studley, S. A,; Hayes, J. M. Anal. Chem. 1985, 57, 1444-1448.
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Anal. Chem. 1989, 61, 2422-2427 Mar rave, J. L.; Polansky, R. E. J. Chem. Educ. 1962, 39,335-337. Moo!, W. G.; Grmtes, P. M. Int. J. Mass Spectrom. Ion Phys. 1973, 12, 273-298. Matsuhisa. Y.; Goldsmith, J. R.; Clayton, R. N. Geochim. Cosmochim. Acta 1978, 42, 173-182. Tans, P., personal communication; NOAAIGMCC, Boulder, CO, March 1989. Elllott, K. W. T.; Clapham, P. E. NPL Report, MOM 28, January 1978; National Physical Laboratory, Teddlngton, Middiesex TW11 OLW, UK. Shldeler, R. W.; Barnes, I.L., in preparation, work performed at the National Institute of Standards and Technology, Gaithersburg, MD. McKinney, C. R.; McCrea, J. M.; Epstein, S.; Allen. H. A,; Urey, H. C. Rev. Sci. Instrum. 1950, 21, 724-730. Coplen, T. E.; Kendall, C. Anal. Chem. 1982, 54, 2611-2612, corrected reprint. Elattner, P.; Hulston, J. R. Geochim. Cosmochim. Acta 1978, 42, 59-62. Coplen, T. B. (2”.Geol. (Isot. Geosci. Sect.) 1988, 72, 293-297. Mook, W. G.; van der Hoek, S. Isot. Geosci. 1983, 1, 237-242. Adamson, A. W. A Textbook of Physical Chemistty; Academic Press: New York, 1973; p 12. Natrella, M. 0.Experimental Statistics, NBS Handb. (US.)1966, no. 91; USDC-NBS (now USDC-NIST) (originally printed in 1963); Chapter 3. QA : Que/& Assurance Handbook; Center For Analytical Chemistry, The National Institute of Standards and Technology: Gaithersburg, MD.; November 20, 1987.
(29) Heydemann, P. L. M.; Tilford, C. R.; Hybnd, R. W. J. Vac. Sci. Techno/. 1977, 14, 597-605. (30) Zumbrunn, R.; Neftel, A.; Oeschger, H. € a m Planet. Sci. Lett. 1982, 60, 318-324. (31) Andree, M.; Moor. E.; Beer, J.; Oeschger, H.; Stauffer, B.; Eonani, G.; Hofmann, H. J.; Morenzoni, E.; Nessi, M.; Suter, M.; Wbifii, W. Nucl. Instrum. Methods Phys. Res, 1984, 233(E5), 385-388. (32) Saxena, S. C.; Joshi, R. K. Thermal Accon#rwdet/on and Adsorption Coefficients of Gases; McGraw-HiWCINDAS Data Series on Material Properties; series editors: Y. S. Touloukhn and C. Y. Ho; McGraw-Hill: New York, 1981; Voi. 11-1.
RECEIVED for review April 20,1989. Accepted August 1,1989. Financial support was provided in part by the U.S. Department of Energy, Offices of Energy Research and Basic Energy Sciences, Carbon Dioxide Research Division. Certain commercial equipment, instruments, or materials are identified in this paper to specify adequately the experimental procedure. Such identification does not imply recommendation or endorsement by the National Institute of Standards and Technology, nor does it imply that the materials or equipment identified are necessarily the best available for the purpose.
Suspended Trapping Pulse Sequence for Simplified Mass Calibration in Fourier Transform Mass Spectrometry David A. Laude, Jr.,* and Steven C. Beu
Department of Chemistry, The University of Texas at Austin, Austin, Texas 78712-1167
A new pulse sequence for Fourier transform m a s spectrometry (FTMS) Is demonstrated to simplify wlde-band mass callbration through a self-regulating procedure that reduces any Initial Ion population In the trapped Ion cell to a level below the space charge Ilmit. The novel feature of the pulse sequence b the addltion of an event folkwlng ioniratlon during whkh the trap plates of the FTMS cetl are grounded to permit the longitudinal efflux of excess Ions from the cell. The actual lon populatlon detected then depends not on the initial neutral population or Ionization conditlons, but rather on the suspending trapplng delay time. At suspended trapping delays of 1-2 ms for both slngle- and duaCsectlon trapped Ion cells, the number of Ions detected Is reduced to a level at whlch the Ion density eiectrlc fleld contrlbutlon to the effective cyclotron frequency Is negligible. Low-part-permllllon error mass callbration tables are generated when suspended trap ping is applled to Initial lon populations whlch extend 2 orders of magnitude beyond the space charge llmit of the cell. This is contrasted with marked deterlorallon in mass callbration performance for identlcai lnitlal Ion populatlons If trapplng voltages are sustained.
It is well documented in Fourier transform mass spectrometry (FTMS) that mass spectra derived from ion populations that exceed the space charge limit of the trapped ion cell are of poor quality. The effects of space charge include Coulombic line broadening ( I ) , complications in mass calibration (2-5), and reduced dynamic range (6-9). If a stable and continuous supply of neutral sample is available and sufficient time exists to tune ionization parameters, ion 0003-2700/89/0361-2422$01.50/0
populations generated with negligible space charge yield high resolution and high mass accuracy spectra characteristic of FTMS. More often, however, the neutral analyte population is transient, poorly controlled, or fluctuating, and preselected ionization conditions often yield the excessive ion populations responsible for space charge distortion. The consequence of a strong dependence of FTMS system performance on the initial ion population in the cell is that for many modes of sample introduction and ionization, FTMS operation is perceived as difficult or unreliable when contrasted with that of other mass analyzers. For example, the dynamic range for FTMS detection of chromatographic effluent is orders of magnitude smaller than for scanning mass spectrometers because ionization parameters established to acquire acceptable spectra at one neutral population will either reduce the detectable signal of smaller neutral populations or exceed the space charge limit for larger populations. FTMS application to desorption/ionization of solids is also unreliable because a transient gas-phase population must be sampled. It is of interest then to develop reliable methods by which more difficult sampling regimes can be examined with FTMS. One approach presented here is the use of suspended trapping pulse sequences as a solution to the problem of generating acceptable ion populations from transient or fluctuating neutral populations. All suspended trapping techniques share the common feature that during at least one event in the FTMS pulse sequence the trapping voltages are altered (typically to ground potentials) to permit the longitudinal movement of ions to and from the analyzer cell. To date the primary function of suspended trapping is to gate externally generated ions into the trapped ion cell. This application has been demonstrated for both quadrupole (10-12) and electrostatic focusing (13,14) external source instruments and for 0 1989 American Chemical Society
