337
Anal. Chem. lQ00, 58, 337-344
differed from that of the 87 series by an amount significant at the 0.01 (two-tail) level. They were the FID propane series 93 and 94 and the TCD series 96, 97, 98, and 99. Four 1 means in the FID series differed from the 0.9991 of the 87 series by an amount significant at the 0.01 level. They were the methane series 88 and 89, the propane series 94, and the methane in helium series 101. The 1 mean of the propane series 93 differed by an amount significant at the 0.05 level. For the TCD runs, it was not appropriate to compare the exponent with that of the FID, but significant departures from linearity were obvious at 1.7% nitrogen in helium (98) and 18% methane in helium (100). Exponent 1 Trends. The methane in nitrogen FID results for 1 bear out the expectation that 1 1 as the carbon feed rate diminishes. This was true both for the H P and the PB FID’s. The unpublished P B results are available from the author. The meager TCD data suggest the same conclusion about linearity as sample concentrations in helium carrier gas become lower. For the FID, the 1 values (0.9980 and 0.9975) a t similar methane peak levels, for nitrogen and helium carrier gases (experiments 88 and 101), seem consistent in their degree of departure from linearity. The FID propane in nitrogen experiments types 93 and 94 returned 1 values of 0.9982 and 1.0035, respectively. This latter value seems high compared to the 0.9991 methane value at the same carbon feed rate. It is suggested that a nonlinear adsorption isotherm for propane on the inner walls of the small sample loop could account for this observation, if in fact the detector characteristics do not. It is expected that such adsorption problems would be minimized by using smaller molecules or higher temperatures. Corrected Area Ratios (CARS). The CAR’s are a function of the raw area ratios and the corresponding 1 exponents (eq 3). If an exponent is biased on the high side (as was suggested for propane), the corresponding effect on the CAR will be to bias it to the low side. As the propane 1 means are biased high, if at all, the already high CAR means for FID propane samples lose none of their significance. The TCD CAR’s, except for experimental series 100, a single representative of its type, are all significantly different from that of the 87 series. Also, there is a significant difference within the TCD CAR’s between those for propane in helium and methane in helium (experimental series 99 and 97). The likely reason for these differences is that the profile of a large-loop ambient pressure peak is different to the profile
-
of a small-loop supercharge peak of the same height, and this profile difference would depend on the mutual diffusion coefficient of the analyte and carrier gas. Hence the calculated exponent may not be strictly applicable to the CAR calculation, eq 3. The available equipment was not able to investigate peak shapes in more detail. Another interesting point is the significant difference between the CAR means for similar samples fed to the TCD and FID. The samples were methane in helium, and the result, appended with an “a” in series 101 in Table 111, should be compared to the CAR value for series 97 in this table. It is suggested that this particular difference may be related to the differential peak shape modification arising from the different detector time constants. Repeatability and Accuracy. The CAR results served to monitor potential deterioration of the system during the experimental series. This was possible because of the relative standard deviation (RSD) of about 0.06%. The exponent 1 results had about the same RSD% and therefore trends in 1 means could be compared after sufficient estimations were made. The main uncertainty in the 1 calculation is in the pressure transducer calibration. From the observed calibration spread it is probably safe to estimate 1 results as accurate as fO.OO1 for the nonadsorbed species helium, nitrogen, and methane when evaluated by this loop supercharge method. For other species, a bias may have been introduced by the mechanisms previously suggested.
LITERATURE CITED Krugers, J. Philips Res. Rep. Suppl. 1965, 2 0 , 70-82. McWilliam, I.0.; Dewar, R. A. Nature (London) 1958, 787, 760. Desty, D. H.; Goldup, A.; Geach, C. J. I n “Gas Chromatography 1960”; Scott, R. P. W., Ed.; Proceedings 3rd International Symposium, Butterworths: London, 1960; pp 46-64. Colson, E. R. Anal. Chem., following paper in this issue. . , Shatkay, A.; Flavian, S. Anal. Chem. 1977, 14,2222-2228. (6) Bromly, J. H.; Roga, P. J. Chromatogr. Sci. 1980, 78, 606-613. (7) Deans, D. R. Chromafographia 1968, I , 187-194. (8) Albertyn, D. E.; Bannon, C. D.: Craske, J. D.; Ngo, T. H.; O’Rourke, K. L.; Szonyi, C. J. Chromatogr. 1982, 247,47-61. (9) Brltish Standard 2520:1967.
RECEIVED for review December 13,1984. Resubmitted August 14,1985. Accepted August 14,1985. The author thanks the directors and management of the Gas and Fuel Corporation of Victoria for their support and for permission to publish this work. A summary of this paper was presented at the International Conference on Detectors and Chromatography in Melbourne, Australia, on May 30, 1983.
Flame Ionization Detectors and High-End Linearity Ewan R. Colson Gas and Fuel Corporation of Victoria, Scientific Services Department, P.O. Box 83, Highett, 3190, Victoria, Australia
Thls work reports sensltivity varlatlons of two commercial flame lonlzatlon detectors in the slgnal range 5 X 10-7-10-10 A, foliowlng exponential dilution of a contlnuousiy fed sample species. Helium, nitrogen, argon, and two carrler gas mixtures and a total of 11 sample types were used in the study. The samples were Cl-CB hydrocarbons and one oxygenate. Twenty-seven llnearlty devlatlon plots were prepared, and the paper discusses the origlns of the many interesting features of the plots and advises operating strategies to minlmlre thelr Influence on quantltative analysis.
One of the appealing features of the flame ionization detector (FID) of McWilliam and Dewar (1) is its wide linear range (2). The linearity parameter has been measured (3)by the exponent in the relation
S = A(dm/dt)”
(1)
where S is the detector signal, dmldt is the sample mass flow rate, and A is a sensitivity constant. The detector dynamic range is sometimes specified by the range over which this exponent does not deviate more than a chosen amount from
0003-2700/86/0358-0337$01.50/00 1986 American Chemical Society
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ANALYTICAL CHEMISTRY, VOL. 58, NO. 2, FEBRUARY 1986
unity, the n value for a linear detector. Another specification of dynamic range is that range above the lowest detectable limit that encompasses a sensitivity deviation of less than a chosen percentage about the mean sensitivity over the range ( 4 ) . The sensitivity is defined (5) by the quotient of the signal and the mass flow rate of the detected species. Many workers (6-11) have reported FID sensitivity variations that could not be adequately characterized by eq 1,and two basic methods have been applied. One involves feeding a sufficient number of calibrated mixtures to ensure that real inflections in the response curve will not be dismissed as experimental error (3,6,8,10, 12,13). The other method uses the exponential dilution flask (EDF)of Lovelock (4). Detailed evaluations of this technique have been published by King and Dupr6 (8)and Ritter and Adams (14). It has been applied to the assessment of FID linearity in ref 14-16. The aim of this project was to investigate FID linearity at the high end of the response range, for a range of light hydrocarbons, using a simple EDF in a novel way. Peak area/sample size plots are normally used to identify and overcome linearity aberrations, and the literature has many accounts of FID errors disclosed by this method ( 7 , 9 , 11,17-21). For a definable (or developing) peak profile, detector linearity corrections gathered without chromatographic separation can be converted to peak area corrections. Petitclerc and Guiochon (22) made this transformation for a particular case where separate Gaussian and parabolic functions described the peak profile and error, respectively. In the work now to be reported, it will be demonstrated how correction factors calculated from EDF data could be used to predict area corrections applicable to peaks of known heights. A spot check of this procedure was made with an area correction derived by an independent method, described in ref 23. This reference also provides support for the assumption, requisite for the calculations t o follow, that FID response approaches true linearity (n 1)as the sample feed rate becomes low.
-
EXPERIMENTAL SECTION Detectors. The FID (Dl, Figure 1) was a Model 901, as normally installed in the Packard Models 427-439 chromatographs (Packard-Becker B.V., Delft, The Netherlands). It had a quartz jet with a tip inner diameter of 0.3 mm, inside a metal polarizing ring electrode. The hydrogen and air flows were set, nominally, at 24.5 and 300 mL/min, respectively. The FID D2 was the 9/80 upgraded version of that installed in a Hewlett-Packard 5880A chromatograph (Hewlett-Packard, Avondale, PA). The inner diameter of the grounded metal jet was 0.28 mm, but one experiment was done with the alternative 0.45 mm i.d. jet. The hydrogen and air flows were set, nominally, at 30.8 and 420 mL/min, respectively. EDF and Gas Flow System. The EDF would be classified as type II by Ritter and Adams (14). Initially a PTFE rotor vane was used, but this was replaced with a nickel foil vane to minimize obvious adsorption errors. The plumbing connections are shown in Figure 1. The injector IN and D1 were in a heated block at the top of an air oven. Depending on the FID under test, the jumper J was a short link within the oven to D1, or a 1200-mm unheated nickel line across to D2 in the 5880A. Hydrogen and other detector gases, except air, were passed through molecular sieve filters. Instrument grade air was supplied for combustion directly from a cylinder. Dilution gas flowed via 11,FC, R2, and valve V. V operated between two modes-inject (solid lines, Figure 1)and backflush (dashed lines). Typical flows (mL/min) in each path for the inject mode are annotated in Figure 1,with those for the backflush mode in parentheses. The capillary R1 was connected to a vacuum system that was regulated by VC to allow an approximate 1 mL/min flow out of the system. In the inject mode, about 15 mL/min of gas carried the samples out of the injector IN and this flow was joined by a 1 mL/min purge
Flgure 1. Exponential dilution gas flow system: (A) air turbine inlet, (Dl,D2) alternative detectors, (F) ED flask, (FC) flow controllers, (H) air preheater, (11) carrier gas Inlet, (12) makeup gas inlet, (IN) injection point, (J) jumper link, (M) insulating mat, (-P) vacuum gauge, (PU) outlet to vacuum pump, (RI-R4) capillaries, (S)air turbine magnetic stirrer, (V) six-port valve, (VC) vacuum controller. Items F, H, M, S, and V
were in the same air oven. flow from capillary R3 via the valve. Thus the total 16 mL/min (plus an injection surge) swept the EDF and was joined by the makeup flow from 12, prior to transfer to the detector. In the alternative backflush mode, the injection plumbing was purged back into the vacuum system at about 1mL/min and 16 out of 17 mL/min continued to sweep the EDF. This ensured against sample adsorption errors from the septum and inlet tubing. Pressure, Temperature, and Flow Measurement. The EDF outlet pressure was added to the corrected barometric reading for the estimation of cell pressure. The oven temperature was controlled to a range within kO.1 "C and was measured by a digita? thermocouple indicator that was corrected to agree within 1 "C of a standard mercury thermometer. The EDF dilution flow was calculated on a dry basis at the cell pressure and temperature after water saturation and soap-film metering at ambient temperature and pressure. Detector gas flows were recorded after correction to a water-saturated basis at 20 "C and 101.3 kPa. EDF System Control and Data Acquisition. A time program (Run Table) in the 5880A system memory invoked the valve V backflush mode and organized the storage of the decay profile as area slices. The report was then stored on magnetic tape in a cartridge. The jet ring of detector D1 was grounded and its collector connected to a tapping on the D2 collector. The D1 detector polarization was provided at the collector by the floating -240-V power supply built into the 5880A FID amplifier. EDF Computations. The general exponential decay curve can be represented by the expression c = coe-nt
(2)
where c,, is the concentration at t = 0 and (Y is the decay constant, which should equal r / V, for an ideal EDF, r being the sweep gas flow rate measured at the flask temperature and pressure and V , being the free volume of the flask. If eq 1 is rewritten by incorporating the carrier gas flow rate with the constant A , it becomes
s = IC"
(3)
where c is the concentration and I is a new constant. The combination of eq 2 and 3 gives S = ICone-nat
Thus, the signal from a nonlinear detector, whose response characteristics are defined by eq 3 and which is monitoring the
ANALYTICAL CHEMISTRY, VOL. 58, NO. 2, FEBRUARY 1986
n SO
I \r-'-,
% DEVIATION ZONE DECAY CONST. T OF CURRENT VERSUS FROM MODEL MODEL
CURRENT A T MID 4 MIN. PERIOD
GRAMS/SEC
SPECIFIC RESPONSE A/G/S C FOR ZONE
2.014E-07 1. W E - 0 7 1.097E-07 8.035E-08 5.8293-08 4.195E-08 3.002E-08 2.14OE-08 1.522E-08 1.081E-08 7,6658-09 5.432E-09 3.853E-09 2.727E-09 1.9323-09 1.3683-09
1,0561-05 7.469E-06 5.2823-06 3.735E-06 2.642E-06 1.868E-06 1.321E-06 9.342E-07 6.606E-07 4.672E-07 3.304E-07 2.336E-07 1.652E-07 1.1683-07 8.262E-08 5.843E-08
1.9063-02 1.9891-02 2.0773-02 2.151E-02 2.207E-02 2.246E-02 2.273E-02 2,2903-02 2.304E-02 2.313E-02 2,3203-02 2.325E-02 2.332E-02 2,3343-02 2.338E-02 2.341E-02
CARBON
~~
I /P
339
-27.10 -36.22 -31.58 -24.21 -17.02
-18.75 -15.22 -11.49 -8.32 -5.96 -4.29 -3.14 -2.39 -1.80 -1.42 -1.12 -.90 -.61 -.52 35 -.25
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-4 IO7 -2 I 4 1 -2.61 -1.68 -.53
-. 38
-.
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MODEL BASED ON DATA T O STARS BELOW.
TFigure 2. Signal vs. time curve from a typical FID experlment (solid Ilne); exponentlal decay curve (dashed Ilne).
outlet of an ideal EDF system, will also decay exponentially, but with a decay constant of -na. This result has been discussed in ref 8, 14, and 16, but the implication for this work was that the definition of a zone of true FID linearity (Le., where n = 1) made possible the determination of the decay constant, a, of a nonideal EDF, without knowledge of exact sample concentrations. This enabled subsequent quantitation of linearity errors. To further conform to the terminology of Ritter and Adams, na will be henceforth designated k . Thus S = Soe-kt
(4) In the log transformation of this expression, k becomes the slope of the derived In S vs. t linear relationship. An exponential decay curve is plotted in Figure 2 as a dashed line merging with a solid line representing experimental reality. Two equal time intervals are bounded by tl, tz, and t3. The area 1 between the exponential curve and abscissa, bounded by the ordinates at tl and t2, can be calculated by integration as area 1 = (-So/k)[e-kt]t,tz This relation can be rearranged to solve for So So = +area l)/(e-kt2 - e-ktl)
(5)
Because areas 1 and 2 in Figure 2 are of equal width, the area 2/area 1 ratio can be reduced to area ratio = e - k ( W d thus k = In (area ratio)/(tl
- tz)
Four-minute overlapping segments of the solid curve were each regarded as approximations of independent exponential curves, hence 48 slope k estimates were made from the succession of 2-min area slices acquired during each sample dilution run. For each 4-min zone, an So value was estimated by substituting the corresponding k estimate and the area between tl and t z into eq 5. Each matching So and k estimate pair was then substituted into eq 4 along with the appropriate t2,and thus an estimate was made of the actual current signal (Sa)at each area bounding time (ABT). The pattern of k estimates during each run was examined, firstby the t statistics. These enabled a zone of concordant slopes (CSZ) to be located at the low current end of each data set. The mean slope within the CSZ and the total zone area were used to determine a mean So value via eq 5. The mean slope and Sovalue were substituted into eq 4,and at each ABT a signal estimate S, was made. The fractional difference (Sa- S,)/S, at each ABT within the CSZ was squared and s u m m e d across the zone. This slope averaging and subsequent calculations were repeated after reducing the number of slopes included in the CSZ until the sum of squares of fractional signal deviation was minimized so that further elimination of data pointij produced an insignificant improvement in an F-ratio statistic.
4.1323-08
9.6863-10 6.858E-10 4.850E-10 3.431E-10 2.427E-10 1.716E-10 1.214E-10 8.5673-11
*********
2,9223-08 2.066E-08 1.461E-08 1,0333-08 7.308E-09 5.168E-09 3.654E-09
-.lo
2.3413-02 - . 2.3173-02 2.1473-02 2.348E-02 2.3493-02 2.3481-02 2.348E-02 2.344E-02 ~
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T D ' S OF FREEDOM (FULL DATA S E T ) = 14
*
MODEL-FIT ZONE
DECAY CONST. 8.662E-OZ/MIN FLOW RATE ESTIMATED FLOW RATE SET DIFF..
SO ESTIMATE
********
*
REL. S.D.. 17.90 ML/MIN 18.40 ML/MIN -2.7 %
0.360 %
MEAN DEV.. S.D.,DEV.-
0.042 % 0.068 \
3.4731-07 AMPERE
FIRST ROW POSN. OF FIT ENTER NO. OF ROWS U P ( + ) OR DOWN(-)
'0
LAST ROW POSN OF FIT ENTER NO. OF ROWS UP[+, OR DOWN[-I
'0
Flgure 3. Reformatted printout of FILIN program; only every second observation is shown. This fie, H/P 65X, is also plotted as Figure 28.
This final mean slope was assumed to characterize the decay from time zero so that an estimate of c, from knowledge of sample gas and EDF volumes, or better, a determination of c at a known time, could be used to calculate c's at any ABT and hence the FID sensitivity by each S,/c quotient. Figure 3 is a reformatted output of a typical experiment, showing some fit-adjustment dialog. Selected output data were stored as computer-readable strings (58806 Run Table format) for transfer by serial interfaces to a memory disc of a HewlettPackard model 86 computer. This system was used to prepare 49 plots of detector linearity percent deviation vs. FID signal current. Apart from the detector origin, the chief variables in the test conditions were the flow and nature of the dilution gas, makeup gas (if any), and sample type.
RESULTS AND DISCUSSION Table I gives some details of the 27 experiments reported in this work. The flow difference '70 column records the difference between the observed diluent flow and that calculated from the decay constant k in the CSZ. k and its % relative standard deviation (typically 4 1 estimates) are also shown. The last column references the figure number of the corresponding plot. In these plot figures, the upper and lower limits of current defining the CSZ are marked with vertical dashed lines across the plot trace. The current corresponding to an estimated carbon feed rate of 1p g / s is marked close to the curve with one arrow and sometimes also with an axial pointer. The location of these arrows is, of course, related to the specific sensitivity, and occasionally there arose sample injection problems because of syringe needle blockages. Because the primary aim was to study linearity vs. current, rather than vs. feed rate, the experiment was continued. Therefore, the specific sensitivity figure in each caption is likely to be inaccurate, and a 10% negative error is quite feasible in the presented data. Where a curve departs from the plot limits, an arrow and number show for one such position per curve
340
ANALYTICAL CHEMISTRY, VOL. 58, NO. 2, FEBRUARY 1986
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Figure 8. n-Hexane, N, 30, 18.8, P/B 178KD.
Figure 4. Sample species (methane), carrier gas (nitrogen), flow (30 mL/min), sensitivity In CSZ (20.2 mC/g carbon), and file (P/B 1490). Henceforth this is abbreviated as follows: methane, N, 30, 20.2, P/B 1490.
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Figure 6. Propane, N, 29, 18.7, P/B 167P. 2 t . , .
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Figure 11. Methyl isobutyl ketone, N, 30, 15.3, P/B 176KY.
Figure 7. Isobutane, N, 29, 18.4, P/B 151N.
the location and magnitude of the excursion. Features of Plots-Packard-Becker Detector. Figures 4-7 show results for the first four saturated hydrocarbons with the P/B detector and a nitrogen flow rate of about 30 mL/ min. The general trend is for negative deviations a t high sample feed rates, becoming less negative as molecular weight increases. Figures 8-11 show examples of response plots, including an oxygenate, carried out at higher cell and detector temperatures to minimize expected adsorption difficulties with
4 2
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Figure 12. Acetylene, N, 29, 24.5, P/B 1520.
,
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ANALYTICAL .CHEMISTRY, VOL. 58, NO. 2, FEBRUARY 1986
-8
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the injected liquids. An "alternating effect" (6) or a "superlinear" zone (7) is apparent in the benzene plot. This feature will be called here a "high-end rise" (HER). The two figure groups 12,13,5 and 14,6 show transitions from unsaturation to saturation at carbon numbers 2 and 3. The obvious HER characteristic of acetylene and ethylene shows below the base line for propylene and also as a slope reversal for ethane and an inflection for propane. Two groups, Figures 15,13 and 16,6,17,show for ethylene and propane, under otherwise similar conditions, the effect of increasing nitrogen flow rates. The HER'S are enhanced as the flow diminishes. Figure group 18,4,19 and 20,13,21 and 2 2 , 6 , 2 3 and 24, 7, 25 show for four light hydrocarbons the changes in FID linearity corresponding to the transition from helium to nitrogen to argon as carrier gas at approximately the same flow rate, 30 mL/min. With the exception of methane, the trend toward H E R S at high sample feed rates is greater for helium,
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Flgure 21. Ethylene, Ar, 30, 21.2, P/B 143N.
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342
ANALYTICAL CHEMISTRY, VOL. 58, NO. 2, FEBRUARY 1986
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Figure 22. Propane, He, 30, 12.6, P/B 163s.
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Figure 25. Isobutane, Ar, 29, 21.8, P/B 1530E. 2 t . 3 .
then argon, and lastly nitrogen. (The second curve in Figure 25 will be explained below.) The use of helium as carrier gas prior to an FID is common in capillary column practice. Therefore it is interesting to compare Figures 22, 26, and 27 where the effect of adding nitrogen or argon to a 16 mL/min flow of helium carrier gas on propane linearity and sensitivity is shown. Some earlier work (P/B 40,43 not plotted) showed that for ethane (and hence probably propane) the HER effect was much greater with a helium flow of 16 mL/min rather than 54 mL/min. Considering the other flow effects already noted here, it seems that capillary column helium flows are likely to produce severe HER effects, which can be ameliorated by limiting sample size or by the addition of nitrogen or argon as a makeup gas. Hewlett-Packard Detector. Figures 28 and 29, for methane and propane, respectively, should be compared with Figures 4 and 6 for the P/B detector. There may be a difference, or a drift has affected the Figure 28 results, but the propane results match fairly well.
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Figure 30. Propane, N, 30, 16.6, H/P 66V; flame
jet 0.46 m m i.d.
(see text). This detector was fitted with the alternative 0.46 mm i.d. jet and a propane run was made with nitrogen as carrier gas. The results in Figure 30 seem inferior in sensitivity and linearity to those of the standard 0.28 mm jet (Figure 29). Twenty-two other data plots are available on application to
ANALYTICAL CHEMISTRY, VOL. 58, NO. 2, FEBRUARY 1986
343
Table I. Selected Experiments and Results flow difference,
a
file name
sample species
P / B 1490 P / B 1470 P / B 167P P / B 151N P / B 178KD P / B 177ED P / B 179JF P / B 176KY P / B 1520 P / B 145N P / B 1460 P / B 165s P / B 1645 P / B 171W P / B 158U P / B 155P P / B 161R P / B 143N P / B 163s P / B 142M P / B 1620E P / B 1530E P / B 184U P / B 183P H / P 65X H / P 64R H / P 66V
methane ethane propane isobutane n-hexane benzene cyclohexane MIBK" acety 1ene
ethylene propylene ethylene propane propane
methane methane ethylene ethylene propane propane
isobutane isobutane propane
propane methane propane propane
%
63 64 63 63 122 122 122 130 63 64 64 63 63 65 63 63 63 64 63 64 63 63 64 63 64 64 64
134 133 134 134 151 156 150 158 134 133 133 133 133 134 135 133 132 133 136 133 136 133 134 132 120 120 120
0.35 -1.26 1.28 0.47 -3.01 -1.51 -2.37 -2.10 0.41 -1.25 -1.03 0.97 2.51 -0.60 1.98 2.28 2.70 -0.46 1.50 -0.02 0.81 1.80 0.20 0.21 -2.72 -0.89 -0.47
decay const, min-l 8.31 X 8.35 X 8.39 X 8.22 X 8.97 X 8.86 X 8.93 X 9.03 X 8.29 X 8.38 X 8.37 X 8.55 X 8.50 X 8.90 X 8.66 X 8.03 X 8.65 X 8.32 X 8.49 X 8.38 X 8.43 X 8.19 X 8.42 X 8.24 X 8.66 X 8.63 X 8.99 X
k, % std dev
figure no.
0.22 0.58 0.34 0.39 0.59 0.45 0.27 0.32 0.35 0.52 0.53 0.26 0.23 0.43 0.27 0.35 0.29 0.23 0.37 0.19 0.94 0.44 0.34 0.46 0.36 0.19 0.39
4
lo-' lo-'
lo-' loT2 lo-' lo-' lo-'
lo-' lo-'
5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Methvl isobutvl ketone.
the author. Among the six other H / P results were reasonable pattern matches to the P / B Figures 16 and 23 for propane/ nitrogen and propane/argon, under similar flow regimes. Area Corrections. Figures 25 and 28 each show a second, dotted curve whose ordinate is the % area error incurred by a peak originally of Gaussian profile, which has been distorted to the abscissa height (in amperes, of the dotted curve) by a detector whose linearity is defined by the solid curve. The new curve was calculated after a Simpson's rule summation of Gaussian ordinates, individually corrected by reference to the detector linearity curve. Peak area correction curves can be compared with appropriate results obtained by the loop supercharge technique (23). For example, the experimental series 87,88, and 89 reported in Table I11 of that reference used the same detector, analyte (methane), and operating conditions as those of Figure 28. Firstly, the series 88 and 89 peak area/sample size exponents are adjusted to accommodate the assumptioq that the series 87 exponent is 1.000 (i.e., the detector is linear up to A). Then it can be calculated that area mea3.8 X surement of a peak of height 9.8 X lo+' A should incur an error of -0.8%. The comparable value in Figure 28 is -1.0%. Errors in Exponential Decay. The a values set in these experiments were in the range 0.078-0.104/min. The k(na) values determined in the CSZ's of the 49 experiments had % relative standard deviations in the range 0.18-0.94. Excluding 11 high-temperature runs, the mean % relative standard deviation (RSD) of k for 38 runs was 0.36 with standard deviation of f0.15. For the same 38 runs, the mean difference % between the k values found in the CSZ's and the corresponding values predicted from each r / V, was 0.2 with standard deviation of f1.3. It can be shown by taking partial derivatives of eq 4 that % RSD of S = 1OOd-
where S is the detector signal and ah and or are the standard errors of the .& and t estimates, respectively.
The second term under the square root sign is insignificant at these k values, so the following typical substitutions can be made into the above relation where 2l1I2 represents the a6
= 0.0036
X
0.09/*
divisor needed to obtain the standard error of a mean of the typical 21 estimates of slope standard deviation and f = 69, being a typical time lapse, in minutes, from the'start of an experiment to the median of the CSZ. At this assumed .& value of 0.09, uh as % RSD = f0.079. The foregoing ab translates to the value of h0.5% for the RSD of an S estimate based on a known (or more realistically, notional) Sovalue. This RSD is an order of magnitude better than those implied by Table I of ref 14, but this difference can be explained by the fact that the slope has been averaged only during a single run and not over runs spread over several days. The positioning of area and detector correction curves has been determined by the perception of a CSZ of ( k ) estimates, and this perception has been clouded by the scatter (standard deviation) of these estimates. The pattern of entries in the % deviation column in the CSZ of computer outputs (e.g., Figure 3), reinforced by the loop supercharge results, leads to the expectation that the CSZ's should be located below about 4 x A, more than a decade lower than their current general position. The implication of this is that a positive bias of perhaps 0.5-1% may exist in the positioning of the solid curves at about 4 x A, and this value can be assumed as a likely correction to the position of curves above 4 x A. It should also be noted that, after an initial injection surge, the total flow emerging from an EDF comprises sample and dilution gas at the same rate as the inlet flow of dilution gas. In gas chromatography, the carrier flow underlying peak elution will also be disturbed from its quiescent level, and the instantaneous sample/carrier gas proportions a t a defined sample feed rate need not match those obtained by exponential dilution. In this work, initial sample molar concentrations in the EDF were about 10% for C1, 8% for C2, 5%
344
ANALYTICAL CHEMISTRY, VOL. 56, NO. 2, FEBRUARY 1986
for Cs, and 3.8% for C4, and these were further diluted by the makeup gas. From this and other work it can be expected that the sensitivity in the CSZ will fall by about 11% when an Nz carrier flow changes from 30 to 18 mL/min. Linear interpolations of this sensitivity fall by individual sampleproduced reductions in carrier gas flow result in time-zero sensitivity errors of -1.5% for C1, -1.2% for Cz,-0.8% for C3, and -0.6% for Ck These errors would be enhanced about 1.6 times for a flow of 18mL/min and reduced about 4 times after dilution to a carbon feed rate of 1pg/s. This is a minor error source compared to the magnitudes and forms of the high-end features of most of the plots. High-End Features. It should be pointed out that, while the experimental techniques and theory of ref 14 have been appropriate for discussion so far, Ritter and Adams were assessing, at low propane concentrations, an FID in which the analyte was introduced with the air "carrier gas". The obvious A clearly complexities of these plots above about 1 X demonstrate that eq 1is unsuitable for FID characterization outside a determined CSZ (where n = 1.000). The downstream positive charge carriers in FID's of the present configuration were shown by a mass spectrometric study (24)to be hydrated oxonium ions, H30+(HzO),, which freely migrate from the outer flame edge to the negatively polarized collector. The high-end features observed here can be explained partly by the assumption that these sensitivity modifications correlate inversely with the mean distance that the upstream charge carriers must travel between the jet (or jet-region) electrode and the flame front. The uncertainties in this assumption might be resolved by plotting the linearity deviations of an oppositely polarized FID. Many factors influencing the flame shape were suggested and discussed by Sternberg et al. (25) who also presented linearity data for an FID with 60 mL/min He as carrier and a propane sample. These results are not comparable to the present work because of a 2-decade gap in high-end sample concentrations. One of these flame-shaping factors was the mixture flame speed, and after reference to the plots it can be argued that the commonly observed fall in specific sensitivity as currents exceed the upper limit of the CSZ is due to the flame speed of mixtures of hydrogen with most hydrocarbons being less than that of hydrogen alone. This factor, together with the increased oxygen requirement of the additional fuel, would tend to expand the flame front so that the upstream charge carriers were required to traverse a more difficult path. The obvious exception to this generality is acetylene (Figure 12). However, acetylene-hydrogen mixtures burn faster (26) than hydrogen alone. The relatively high response per carbon atom of acetylene has been discussed by Blades (27). The other prominent features among the plots are the HER'S. In the case of helium carrier gas, these could be explained by the momentum increases a t the jet, due to the heavier sample molecules causing more rapid air inspiration and bringing the flame front (and a zone of higher energy density) closer to the burner and electrode, and thus providing a easier path for the upstream charge carriers. More generally, the position (or occurrence) of an HER might be determined by a dynamic equilibrium between the competing, flame-locating influences of jet momentum and the flame speed of a particular fuel mixture. Greater HER'S are noticed with argon as compared to nitrogen carrier gases at the same flow rate-for example,
compare Figures 23 and 6 for propane and Figures 25 and 7 for isobutane. These differences may be explained by ionforming reactions involving nitrogen (28). The H E R S in many of these examples peak and then fall at the highest sample loadings. This feature is surely due to lack of air access to the fuels and subsequent incomplete combustion. Suggested Revisions in Technique. Major contributions to the scatter of slope estimates in the CSZ were gas purity variations due to changing ambient temperatures, adsorption effects (particularly for the heavier molecules), and erratic rotor speeds. For further work in this field, gas purities equivalent to an FID hydrocarbon background of less than about A and control of the ambient temperature of gas lines and filters are recommended, as well as cell design and rotor speed control improvements. Registry No. Methane, 74-82-8; ethane, 74-84-0; propane, 74-98-6;isobutane, 75-28-5; n-hexane, 110-54-3;benzene, 71-43-2; cyclohexane, 110-82-7;methyl isobutyl ketone, 108-10-1;acetylene, 74-86-2; ethylene, 74-85-1; propylene, 115-07-1.
LITERATURE CITED McWllllam, I.G.; Dewar, R. A. Nature (London) 1958, 787, 760. McWilllam, I.G. J. Chromatogr. 1981, 6 , 110-117. Resty, D. H.; Goldup, A.; Geach, C. J. "Gas Chromatography 1960"; Scott, R. P. W., Ed.; Proceedings 3rd Internatlonal Symposium; Butterworths: London, 1960; pp 46-64. Lovelock, J. E. "Gas Chromatography 1960"; Scott, R. P. W., Ed.; Proceedings 3rd Internatlonal Symposium; Butterworths: London, 1960; pp 16-29. Ongklehong, L. "Gas Chromatography 1960"; Scott, R. P. W., Ed.; Proceedings 3rd International Symposium; Butterworths: London, 1960; pp 7-15. Bruderreck, H.; Schneider, W.; Halasz, I.Anal Chem. 1984, 3 6 , 461-473. Bromiy, J. H.; Roga, P. J . Chromatogr. Sci. 1980, 18, 606-613. King, W. H., Jr.; Dupr6, G. D. Anal. Chem. 1989, 4 1 , 1936-1940. Deans, D. R. Chromatographla 1968, 7 , 187-194. Carruth, G. F.; Kobayashi, R. Anal. Chem. 1972, 4 4 , 1047-1050. Marshall, J. L.; Crowe, B. Chromatographla 1884, 18, 393-395. Kaiser, R.; Stoll. W.; Flscher, K. Chromatographla 1969, 2, 20-22. McWllllam, I.G. J. Chromatogr. 1970, 57, 391-406. Ritter, J. J.; Adams, N. K. Anal. Chem. 1976, 4 8 , 612-619. Roske, R. W.; Fuller, D. H. J. Instrum. SOC.Am. 1983, 73-77. Krugers, J. Phlllps Res. Rep. Suppl. 1985, 20, 70-82. Condon, R. D.; Scholly, P. R.; Averill, W. "Gas Chromatography 1960"; Scott, R. P. W., Ed.; Proceedings 3rd International Symposium; Butterworths: London, 1960; pp 30-45. Novlk, J.; Janak, J. J . Chromatogr. 1960, 4 , 249-251. SvCIk, J.; Lips, J. E. Chromatographia 1979, 72, 693-703. Shatkay, A.; Flavian, S. Anal. Chem. 1977, 14, 2222-2228. Albertyn, D. E.; Bannon, C. D.; Craske, J. D.; Ngo, T. H.; O'Rourke, K. L.; Szonyi, C. J. Chromatogr. 1982, 247, 47-61. Petitclerc, T.; Gulochon, C. Chromatographia 1974, 7, 10-13. Colson, E. R., preceding paper. Boiton, H. C.; Grant, J.; McWilliam, I.G.; Nicholson, A. J. C.; Swingler, D. L. Proc. R. SOC.London A 1878, 360, 265. Sternberg, J. C.; Gallaway, W. S.; Jones, D. T. L. "Gas Chromatography", Brenner, N., Callen, J. E., Eds.; Proceedings Instrument Society of America Symposium, June 1961; Academic Press: New York, 1962; pp 231-267. "The Gas Engineers Handbook"; Industrlal Press: New York, 1966; 2/70. Blades, A. T. Can. J. Chem. 1978, 5 4 , 2919-2924. Bolton, H. C. Aust. J. Phys. 1982, 35, 715-725.
RECEIVED for review December 13,1984. Resubmitted August 14,1985. Accepted August 14,1985. The author thanks the Directors and Management of the Gas and Fuel Corporation of Victoria for permission to publish this paper. A summary of this material was presented at the International Conference on Detectors and Chromatography in Melbourne, Australia, on May 31,1983.
