E. Sawicki, S. P. McPherson, T. W. Stanley, J. Meeker, and W. C. Elbert, lnt. J. Air Water Pollut., 9, 515 (1965). T. W. Stanley, J. E. Meeker, and M. J. Morgan, Environ. Sci. Techno/., I, 927 (1967). > , RTC. Lao, R. S. Thomas, H. Oja, and L. Dubois, Anal. Chem., 45, 908 (1973). "Air Quality Data for Organics 1969 and 1970 from the National Air Surveillance Networks" Report APTD-1465, Environmental Protection Agency, Research Triangle Park, NC, June 1973. lntersociety Committee: Methods of Air Sampling and Analysis, American Public Health Association, Washington, DC, 1972, p 173. A. Liberti, G. P. Cartoni, and V. Cantuti, J. Chromatogr., 15, 141 (1964). M. C. Goldberg. L. DeLong, and M. Sinclair, Anal. Chem., 45, 89 (1973). K. Grob and G. Grob, J. Chromatogr., 62, 1 (1971). D. Grosjean and S. K. Friedlander, 67th Air Pollution Control Association Annual Meeting, Paper No. 74-154, Denver, CO, June 9-13, 1974. R. K. Patterson, Anal. Chem., 45, 605 (1973). D. Grosjean and S. K. Friedlander, in preparation. D. Schueltze, A. L Crittenden, and R. J. Charlson. J. Air Pollut. Control Assoc., 23, 704 (1973). D. Schueltze, D. R. Cronn, A. L. Crittenden, and R. J. Charlson. 172nd National Meeting, ACS, Chicago, IL, August 27, 1973. M. Gruenfeld, Environ. Sci. Techno/., 7, 636 (1973). R. J. Gordon, Atmos. Environ., 8, 189 (1974). A. L. McClellan, "Tables of Experimental Dipole Moments", Freeman, San Francisco, CA, 1963. A. A. Maryott and E. R. Smith, National Bureau of Standards Circular No. 54, Washington, DC, August 10, 1951. J. H. Hildebrandt and R. L. Scott, "The Solubility of Non-Electrolytes". 3rd ed., Dover Publications, New York, NY, 1964. L. R. Snyder, "Principles of Adsorption Chromatography", Marcel Dekker, New York, NY, 1968, Chap. 8. C. Reichardt and K. Dimroth, Fortschr. Chem. Forsch., 11, 1 (1968). L. R. Snyder, J. Chromatogr., 92, 223 (1974). L. Rohrschneider. J. Chromatogr., 22, 6 (1966). L. Rohrschneider, Anal. Chem., 45, 1241 (1973). ~~
(33) (34) (35) (36) (37) (38)
(39) (40) (41) (42) (43) (44) (45) (46)
W. 0. McReynolds, J. Chromatogr. Sci., 8, 685 (1970). K. L. Hoy, J, Paint Techno/., 42, 76 (1970). C. Hansen. lnd. Eng. Chem., Prod. Res. Dev., 8, 2 (1969). R. A. Keller, E. L. Karger, and L. R. Snyder, "Gas Chromotography 1970", R. Stock and S. G. Perry, Ed., Institute of Petroleum, London, England, 1971, p 125. A. Hartkopk, J. Chromatogr. Sci., 12, 113 (1974). J. Cholak, L. J. Schaefer, D. W. Yaeger, and R. A. Kehoe, "The Nature of the Suspended Matter", Section Vlll in "An Aerometric Survey of the Los Angeles Basin, August-November 1954", Air Polution Foundation, Los Angeles, CA, 1955. A. Anusiem and P. A. Hersch, Anal. Chem., 45, 592 (1973). C. McAuliffe, J. Phys. Chem., 70, 1267 (1966). E. J. Gallegos. Anal. Chem., 45, 1399 (1973). J. Timmermans, "The Physico-Chemical Constants of Binary Systems in Concentrated Solutions". Vol. 1 and 2, Interscience, New York, NY, 1959. H. M. N. H. Irving, "Ion Exchange and Solvent Extraction", Vol. 6, J. A. Marinsky and Y. Marcus, Ed., Marcel Dekker. New York, NY, 1974, Chap. 3. p 139. W. F. Linke, "Solubilities, inorganic and Metal-Organic Compounds". American Chemical Society Pub., Washington, DC, 1965, Vol. 2, 4th ed., pp 709-727. H. Stephen and T. Stephen, "Solubilities of Inorganic and Organic Compounds", Macmillan, New York, NY, 1963, Vol. 1, Part 1, p 745. lntersociety Committee on Methods for Ambient Air Sampling and Analysis No. 3, E. E. Saltzman, Chairman, Health Lab. Sci., 7, 267 (1970).
RECEIVEDfor review November 8, 1974. Accepted January 15, 1975. This work was supported by Environmental Protection Agency Grant No. R802160. The contents do not necessarily reflect the views and policy of the Environmental Protection Agency.
Response Characterization of the Tritium Ionization CrossSection Detector Ewan R. Colson Scientific Services Department, Gas & Fuel Corporation of Victoria, No. 7 Liardet Street, Port Melbourne, Victoria-3207,
Seven binary gas mixtures were fed to either, or both, of two tritium ionization cross-section detectors in order to find a general characterizing relation. A relation was found between a defined detector response parameter (v) and molar composition ( X ) , of the form
y = -
X
A. - (A - B - l)X - BX2
where A and B were the coefficients of a linear regression. A single regression coefficient relation was also proposed. The root mean square of the percentage difference between observed and calculated detector response, over the 130 more accurately blended mixes of the 291 observation pairs reported, was 0.32 YO.Under favorable conditions, the detector responded to composition changes of 50 to 100 PPm.
The ionization cross-section detector of Lovelock et al. ( I ) , using a tritium ionization source, was inferred to be linear to a t least 50% vapor concentration by volume. These authors, and Shoemake ( 2 ) , presented calibration curves for a micro parallel plate detector plotted on a log/log scale from data collected using an exponential decay cell, as described by Lovelock ( 3 ) . I t has also been stated ( I ) that the ionization cross-section detector of Pompeo and Otvos ( 4 ) is linear to 100% gas or vapor concentration.
Australia
Washbrooke ( 5 ) reported that the responses of both the tritium and strontium 90/yttrium 90 detectors were linear over many orders of magnitude. Published experimental evidence to adequately support these claims seems to be lacking. In fact, Deal, Otvos, Smith, and Zucco (6) presented calibration data with nitrogen-heptane blends, and Boer (7) showed curves for nitrogen-butane blends which indicated a diminishing response per unit of concentration change as the concentration of the heavier component increased. This detector used comparatively higher energy &particle sources of strontium 9O/yttrium 90 in larger volume cells than the detector of ( I ) . The paper of Deisler et al. ( 8 ) , showed nonlinear calibration curves for several binary gas mixtures in a gas analysis cell using, as the main ionizing species, a-particles produced by the decay (in three stages) of radium D. The choice of radiation source for these detectors has in part been based on the consideration that the mean energy of the ionizing species should be nearly uniform within the measuring zone. The cell geometries have been designed to make the possible path lengths of the energetic particles a smal1,proportion of their mean range in the medium (6). Thus, the use of weak @-particlesfrom tritium was practical only with the micro version of the detector ( I ) . This paper describes experimental observations of obviously nonlinear binary mixture responses of two versions of the tritium ionization cross-section detector. A characterizing relation is then developed which seems to adequately conform to the experimental data and so enable the wider practical application of the detector. ANALYTICAL CHEMISTRY, VOL. 47, NO. 6, MAY 1975
805
u I CH.
Flgure l a . Dual source detector (1) FoiVradiation
source. (2) Plain foil. (3) PTFE insulator/spacer. (4) Silicone elastomer O-ring. (5)Electrical lead. (6) PTFE insulator. (7) Gas inlet/outlet
EXPERIMENTAL A chromatograph was assembled for the analysis of permanent gases. This incorporated a home-made parallel plate micro crosssection detector (MXD) with hydrogen as carrier gas. T h e detector had a plate separation of approximately 0.5 m m , and was built generally according to the design of ( I ) (Figure l a ) . T h e carrier gas flow rate was about 43 ml/min and the gas sample size about 0.7 ml. With this system, nonlinearity of peak area calibrations was observed. I t is estimated that the peak maximum concentration from a sample of pure nitrogen reached 20% in the carrier gas. These experiments, numbered 1 to 3, used soap film metered gas blends of nitrogen-hydrogen and carbon dioxide-hydrogen as samples and are not reported in detail here. These observations prompted the investigation of a similar detector, in isolation from a chromatographic separating system, using an exponential decay cell. As non-linearity was still apparent, the interelectrode gap was reduced to a minimum. T h e foils were then within about 0.05 m m of actual contact. (Henceforth, in this paper, the interelectrode gap specification will refer to the estimated closest distance of the two electrodes. However, because of the nonplanar surface of the foils, it was certain t h a t the average gap was about 0.15 mm larger.) T h e deviation from linearity was reduced and, with such nonplanar, low energy tritium sources, it was obvious t h a t a practical “linearity performance” limit had been reached. Ionization C u r r e n t M e a s u r e m e n t s Further work was carried out by digital logging of the voltage analog of the ionization current. This was measured with a Keithley 417 picoammeter whose output was coupled to an Infotronics CRS-100 digital integrator. T h e picoammeter panel meter was switched off to allow the output voltage to go to more than 8 volts and thus improve the dynamic range. T h e picoammeter voltage output was divided by 8 to match the integrator input requirement. The integrator base-line tracking circuits were turned off and the machine operated in the “digitize” mode, after pressing the “manual” and “integrate” buttons, by opening a normally closed external reed switch for precise fivesecond intervals every ten seconds. The reed switch was connected between pins K and E on the integrator “remote” socket, and its timing was controlled by an external (to the integrator) crystal oscillator, dividing network, and flip-flop circuit. T h e standard deviations of counts obtained from a test setup including a stable voltage supply, l/8 divider system, and integrator 806
ANALYTICAL CHEMISTRY, VOL. 47, NO. 6, MAY 1975
Figure 1b. Single source detector (1) FoiVradiation source. (2) Plain foil. (3) PTFE insulator/spacer. (4) Silicone elastomer O-ring. (5) Electrical lead. (6) PTFE insulator. (7) Gas inlet/outlet
as digitizer were measured a t near the maximum count rate (1 mHz) and a t a low count rate (125 kHz) for 140 and 113 separate five-second intervals, respectively. The relative standard deviations were 4zO.0012 and f0.0035%, respectively. The linearity of the picoammeter/digitizer system was checked by measuring output count increments corresponding to constant input current increments applied over eight parts of the measuring range. T h e upper half of this range was from 0.52 to 0.76% more sensitive than the lower half, increasing with ambient temperature over the range 22 t o 31 “C. Experiments Nos. 4 to 9 were not corrected for this integrator nonlinearity. The experiments Nos. 10 to 27 were corrected in the data processing program. In later experiments the nonlinearity, expressed in the same way, was reduced to from -0.03 to 0.13% over the range 21 to 30 “C, by replacement of the voltage-to-frequency converter circuit board in the integrator. After this change, linearity corrections were not applied to the digitized data. Experiments 4-9. In these first experiments with the measuring equipment described above, two gases were mixed after separate flow measurement with a single soap film meter, and fed to the isolated detector, held at a temperature in the range 65-68 “C. T h e blends were of hydrogen with each of nitrogen, carbon dioxide, and a commercial butane. The detector was operated with the nominal 0.05-mm (+0.15 mm) gap using a 45-volt battery power supply and with a nominal 0.20-mm (+O.l5 mm) gap using a 240volt battery power supply. E x p e r i m e n t s 10-12. A new series of experiments was then commenced, incorporating a more convenient gas flow control system, and the hydrogen and nitrogen gases were dried via a molecular sieve column. In order to easily make blends a t extremes of the measuring range, 50-ml and 5-ml capacity soap film burets were first calibrated relative to each other by running nitrogen through both in series connection, a t several flow rates. In these experiments the same 50-ml buret was used for each component of binary blends over the approximate percentage range 10:90 to 9O:lO. Both burets were used with an interchange of the metered species to cover the lower and upper 10% blends. The three mixtures contemplated for these runs were hydrogennitrogen, hydrogen-carbon dioxide and hydrogen-propane. However, during observations with propane being fed to a detector, displacing the dried hydrogen, it was noticed t h a t the ionization current was falling unusually rapidly with time. Subsequent inspection of the cell interior revealed t h a t the tritium sources, and also the exposed stainless steel faces opposite
the sources, were showing optical interference fringes, indicating the formation of a thin film over t h e surfaces. As this rapid ionization current decay with propane had not been observed prior t o the drying of the hydrogen gas, it was tentatively assumed that perhaps traces of water vapor had inhibited a radiation induced polymerization of the propane. T o guard against this fouling of the detector, t h e gas fed to the detector was dosed with a constant partial pressure of water vapor. T h e apparatus used to blend t h e test gases and maintain this constant humidification is shown in Figure 2. Hydrogen and t h e other mix component were fed a t approximately 400 k P a (58 lbf/in2) t o points 1 and 2, respectively, in the figure. Both components were reduced in pressure to about 70 k P a by regulators 3 and 4 (Model 113, Mason-Neilan division of Worthington Corp., Norwood, MA). T h e hydrogen stream was split through two parallel driers 5, and t h e other stream was passed through a drier in the case of nitrogen, b u t not otherwise. T h e driers were 1 m X 0.5-cm i.d. columns of 50/60 mesh Molecular Sieve 5A (Analabs, Inc., North Haven, CT). T h e streams now passed through three flow regulating needle valves 6 (Type 2SA, Nupro Co., Cleveland, OH). T h e two hydrogen streams were directed to opposite ports of a four-way switching valve 7 (Part No. A 330-2D22, Teledyne Republic Manufacturing Co., Cleveland, OH), and t h e other gas stream flowed to a n identical valve 8. One of the hydrogen streams was dosed with water by t h e diffusion dilution method (9) from glass reservoir 10 and regulating needle valve 9 (Nupro SS-2MA) which were enclosed in the temperature controlled oven 17 (Cat. Nos. 12104 and 12264/1, Pye Unicam Ltd., Cambridge, England), operating a t 65 'C. Valve 7 directed either wet or dry hydrogen to either valve 8 or, via a tee piece, to temperature controlled tube 11, measuring 6 cm X 0.6-cm i d . , and packed with Porapak T , 50/80 mesh (Waters Associates, Milford, MA). Valve 8 directed the alternative outlet of valve 7 or t h e other gas to either a temperature controlled needle valve 16 (Nupro SS2MA) or to a point D which could be vented or connected to the mixing tee a t the inlet of tube 11. T h e single component or mixture after leaving tube 11 passed through filter 1 2 (Nupro B-2F7) and out of the oven to point E which was usually connected to F, the detector inlet line. This line ran from F t o vent G through t h e oven via a particle trap 13 and one (or two) cross-section detectors, 14 and 15. Between mixtures, the detector was left in equilibrium with hydrogen containing about 0.1% molar of water vapor introduced via components 5, 6, 10, 9, 7, 11, 12, and 13. T h e column 11 also adsorbed water vapor to equilibrium and maintained a steady water vapor concentration for a t least the first 250 ml of dry gas passing through after the changeover of valve 7. This retention volume was determined by observing the time for a detector signal decrease following a valve 7 switch, substituting dry hydrogen for the hydrogen flowing past t h e diffusion tube lO/needle valve 9 tee junction. Another effect of column 11 was to delay t h e concentration buildup of the heavier component of a mixture in proportion t o t h e retention volume of t h a t component on the column (typically 120 ml for propylene). During the equilibration period, the flows of hydrogen and t h e other component were measured using a n appropriate soap film buret at point D, the measured species being selected by valve 8 and regulated by one of t h e needle valves 6. T h e regulator 3 and 4 outlet pressures were matched (at about 70 kPa) so that the comparatively small extra back pressure of the detector system would have an insignificant effect on the flow ratio of t h e two mixture components. T o send a mixture to the detector, valve 7 was switched first to divert t h e dry hydrogen to the column (and detector) inlet. Then point D was connected to the tee a t C, thus blending with hydrogen t h e gas ex regulator 4. After column 11 break-through of t h e blend, the detector signals for a t least three five-second samples of t h e same number of consecutive ten-second intervals were used for response data. Throughout this d a t a acquisition period, the diffusion tube hydrogen flow was channelled via valves 7 and 8 t o valve 16 which was used as a pressure drop simulator, preset t o match the pressure drop of the series connected items 11, 12, 13, 14, and 15 when hydrogen was flowing at t h e 30 ml/min rate used past the diffusion tube tee. After each set of mixture data was recorded, the detector system was changed back to humidified hydrogen and a t least ten minutes allowed for the system to re-equilibrate. Meanwhile, the mixture component flows were re-measured. T h e averages of the after-test
2
I
dl4
17
- - - - ..- .- ..- . . .....- - .- - .
.......
Figure 2. Gas blender arrangement, experiments 10-27
flow rates with the before-test flow rates were used in subsequent calculations. Between mixture observations, the detector signals for hydrogen and the other component were frequently recorded, together with t h e atmospheric pressure. Approximately 30 observation pairs taken over three days were gathered in this way for each of the component pairs, hydrogennitrogen, hydrogen-carbon dioxide and hydrogen-propylene. T h e use of propane as a component still resulted in the formation of a polymer film, even with the small water vapor pressure in the detector blends. T h e gases used to make these, and later blends were: HydrogenN55 (>99.9995%, Liquid Air Australia Ltd., Braybrook, Vic., Australia (L.A.A.)) or -High Purity (>99.98%, Commonwealth Industrial Gases Ltd., Preston, Vic., Australia (C.I.G.)). Nitrogen-High Purity (>99.995%, C.I.G.). Oxygen-High Purity (>99.8%, L.A.A.). Carbon Dioxide-Analytical Grade (>99.995%, Carba Australia Ltd., Abbotsford, Vic., Australia). Propane-Research Grade (>99.99%, Phillips Petroleum Company, Borger, T X (P.P.C.)). Propylene-Research Grade (>99.99%, P.P.C.). Helium-U.S.B.M. Grade A (>99.995%, C.I.G.). Methane-N 35 (>99.95%, L.A.A.). Butane-Commercial (i-CdH10 = 33.5%, n-C4Hlo = 66.5Oh). E x p e r i m e n t s 13-27. Experiments 13-16 used the same experimental arrangements as Nos. 10-12, but observations were made on the gas pairs, hydrogen-carbon monoxide, hydrogen-methane, hydrogen-oxygen, and hydrogen-argon. In experiments 17-27, three binary mixtures of hydrogen with propylene were prepared and analyzed by gas chromatography. T h e blends were fed to two cross-section detectors-the one previously used, and a commercially available (in 1970) single-source tritium detector (Model PV-4113, Philips Industries Ltd., South Melbourne, Australia). T h e interelectrode spacing in t h e commercial detector, shown in Figure l b , was varied by using different spacing washers and it was installed in the oven in series with the home-made unit. T h e blends were fed to the detectors via point F (Figure 2). Although the results of all these fifteen experiments showed clearly the nonlinear nature of the detector response, an insufficient number of observation pairs were taken for statistically acceptable support or rejection of the main characterization hypotheses under study and the results are not reported. They showed t h e need for more observation pairs per experiment, or more accurate blending (or analysis), or improvements in both areas. E x p e r i m e n t s 28-46. T h e previous experiments were then supplemented with a new series, using mixtures blended by a gas mixing pump (Type 18/3, H. Wosthoff O.H.G., Bochum, West Germany). ANALYTICAL CHEMISTRY, VOL. 47, NO. 6, MAY 1975
807
A. b
II
: . :: * . 1 ..9 ..-. I ...
: :: _
.
i
0
4
5
uu Figure 3. Gas mixing pump arrangement, experiments 28-45 (1) ‘A’ gas source. (2) ‘6’ gas source. (3) Pressure regulators. (4) Needle
valves. (5) Excess pressure bubblers. (6) Differential Pressure Gauge (Magnehelic, 6 to 0 to 6 c m H20, Dwyer Instruments Inc., Michigan City, IN). (7) Pump assembly. (8)Mixing vessel. (9) Outlet back pressure control bubbler. (10) Mixed gas flow control needle valve. (1 1) To point F, Figure 2
This pump assembly comprised two identical reciprocating pumps immersed in an oil bath. One was driven at a constant speed and the other at a geared equal or lesser speed so that, by changing-over feed gas connections, mixtures of two components could be made in the ratio range 9:l t o 1:9. The pump mixtures were fed to the symmetrical two-source detector and to the single-source detector by splitting off a small side stream from the pump outlet and connecting t o point F (Figure 2). The blends studied in these runs were not humidified, so the diffusion tube 9 and column 11 were not used. The pump connections are shown in Figure 3. The mixtures chosen were of hydrogen with each of nitrogen, oxygen, and carbon dioxide, and of nitrogen with carbon dioxide, and a blend of (helium + 3.5% methane) with nitrogen. The standard interelectrode gap on the commercial detector was about 0.50 mm. In this series of tests, observations of this detector response were taken with gaps of 0.05,0.5, and 1.0 mm and at a detector temperature of 65 OC. Seven to ten pump blends were used in each experiment to cover the molar fraction range 0.15 to 0.85. Between mixes, the pure components were fed to the detector to establish response reference points. After completing the observations comprising experiments 28 to 41, it was observed by comparison to the MXD hydrogen response that the hydrogen feeding the pump inlet via 2 m of 6-mm i.d. PVC tubing was slightly contaminated. This problem was assumed to arise from diffusion of atmospheric water vapor through the tubing wall. The diffusion rate observed was sufficient to increase an apparent nitrogen molar fraction by 0.0002 at the lowest hydrogen flow rate of 130 ml/min when the nitrogen molar fraction was 0.85. The final experiments, numbered 42 to 45, were carried out with the plastic feed lines replaced with aluminium tube lengths, butted closely together, and joined with PVC tubing sleeves.
RESULTS AND DISCUSSION The characterizing relation which was sought had to be generally applicable to binary mixtures and t o detectors with different geometry and sources. Therefore, it was necessary to convert the data corresponding to the analog of the ionization current, and t o the composition, into forms which would enable all experiments t o be analyzed in the same way. The detector response was reduced in each case to a “span fraction” ( Y )which was defined as the difference between the specific mixture signal and the base gas signal, divided by the difference between the heavier gas signal and the base gas signal. The span fraction was therefore independent of the units of current measurement. 808
ANALYTICAL CHEMISTRY, VOL. 47, NO. 6, MAY 1975
The molar fraction (X)was the molar fraction of the heavier blend component. Corrections, Y Data Stream. The raw count means were linearized, if required, and corrected t o the basis of equal ideal gas volumes a t a standard 1 atmosphere (101.325 kPa) pressure and a t the detector temperature. The pressure coefficient of the detector response was determined for each detector configuration by observing the increase in detector signal caused by applying moderate back pressures (about 2% of atmospheric pressure) with pure species whose detector responses were included in the span of interest. A quadratic expression was then fitted to calculate unknown pressure coefficients at other detector signal levels. The interaction second virial coefficient for each component pair a t the detector temperature was calculated by the method described by Mason and Spurling (IO),and values for the pure components were abstracted from the book of Dymond and Smith ( 1 1 ) . T h e second virial coefficient for each specific mixture composition and, hence, the mixture compressibility factor was determined. In conjunction with the calculated pressure coefficient, the compressibility factor was then used to correct detector signals t o the basis of equal ideal gas volumes. The weakness in these corrections was that the pressure coefficient was composition dependent, and it was impractical t o determine this value on every mixture composition under test. Hence, this compressibility factor correction was only partially effective. This may have slightly influenced the results of experiments involving mixtures containing butane, propylene, and carbon dioxide, in descending order of importance of the influence. The other test mixtures were close enough to ideality so that the maximum gas law deviation encountered was insignificant in comparison to experimental error. From these corrected raw count means, the Y values were calculated according to the previous definition of span fraction. Corrections, X Data Stream. The methods of calculating molar fraction (X) in the experiments reported here relied ultimately on the metering of gas on a volume basis. Hence, the compressibility factors calculated as before, but a t the metering temperature, were used t o correct volume fractions to molar fractions. Gas Mixing Pump X Data. The gas mixing pumps were claimed by the maker (12) to be “calibrated a t the 5:5 mixing ratio with oxygen and nitrogen t o a degree of accuracy of 50.00 f 0.06%”. The maker also presented in the manual, a family of correction curves t o be used when gases of different molecular weights were blended a t different ratios. It was assumed that the corrected blend proportions thus obtained were on a volume, rather than a molar basis, and further corrections were applied to estimate the molar blend fractions. The sensitivity and stability of the MXD was quite adequate t o check the equality of the gas mixing pumps by running with a 1:1 gear ratio and changing-over gas feed inlets so that the components being pumped in the cylinders were also interchanged. An estimating procedure was devised for the magnitude of the pump unbalance. This was expressed as a % difference in the apparent pump displacements and varied during experiments 28 t o 45 from 0.034 t o 0.608% with a mean of 0.252% and a standard deviation (not relative) of 0.168% (see Tables Ib and IC).This mean value is very different from the maker’s specification, and it is regretted that no similar pump was available for comparison. The pump unbalance estimate was used to recalculate
Table Ia.Summary of Results. Experiments 4 to 12, Soap Film Buret Blends Experiment No.
5
4
Light comp. H? Heavy comp. N? Radiation source 0.05 Gap, m m (see text) 45 Detector voltage 7 No. obsn pairs 130** F statistic (10)' 47** F statistic (11)" A coefficient (10) 0.7880 B coefficient (10) -0.0714 1.284 E r r o r M . Sqb x 1 0 '
7
6
9
3
10
12
llg
co2
H2 C4HIO
H2 H2 H? H2 H2 CAO co2 CJHiO N? N? Parallel plate MXD with tu70 tritium sources (dual)
H2
0 -05 45 7 4.3 6.1 0.6849 -0.0432 18.38
0.05 45 7 2.1 1.o 0.4778 0.0563 36.44
0.05 45 14 8.0' 3.9 0.4913 0.1140 174.5
0.05 45 29 78** 95** 0.6974 -0.0350 4.496
0.05 45 37 45** 106** 0.6378 -0.0290 5.992
1.18 2.10 0.22
2.22 6.12 0.08
0.52 1.16 0.03
0.94 3 -26 0.05
H?
0.20 240 12 1437** 182** 0.3003 -0.1712 1.738
0.20 240 15 502** 197** 0.5756 -0.0706 1.330
0.05 45 33 46** 53** 0.7677 -0.0439 14.03
C3H6
Col. /row 32'
Sqr . Mean Sq,% Max.abs, 5 at 2y =
0.11 0.18 0.73
0.72 -1.33 0.58
0.22 0.57 0.07
0.67 1.83 0.09
0.81 -1.85 0.21
Responses
4.74 ... ... ... ... ... 4.76 4.74 ... L . comp. Ae x 10" 8.43 Heavy /Light c0mp.f 4.02 5.81 10.60 6.44 3.34 4 .OO 5.80 10.23 F test statistic for numbered relation, from output of program C2. (see also Figure 7). **, * after F value imply significance, at 170, 5% levels, respectively. * Error mean square (Relation lo), ex analysis of variance table (C2 O/P). Next three rows summarize Col. or Row 32 (Relation 10) ex C2 O / P . Lowest X value (molar fraction) of occurrence of Max, abs. %. e Detector current (unit, 10 Ampere), light component, corrected to pressure, 101.32 kPa. Current response ratios, pure components. 8 Second run of Experiment 11 data, with two outlying observation pairs extracted.
'
Table Ib. Summary of Results. Experiments 28 to 36, Gas Mixing Pump Blends Experiment No. 28
Light comp. Heavy comp. Radiation source Gap, mm (see text) Detector voltage Pump unbalance, No. obsn pairsh F statistic F statistic (11)' A coefficient (10) B coefficient (10) E r r o r M . Sq.b x IO5
31
30
29
33
32
34
36
35
H? N2
H?
H?
N?
N?
H?
0 2
Single
H? N2
0 2
Single
Dual
Single
COZ Du a1
Single
0.05 45
0.05 45
7 17.7** 17.6** 0.6677 -0.0230 1.222
7 4.5 5.8 0.6514 -0.0117 1.261
0.05 45 0.279 7 18** 9* 0.7316 -0.03 84 3.395
0.05 45 0.334 7 46* * 17** 0.7457 -0.0746 5.037
0.05 45 0.468 7 108** 44** 0.7544 -0.0216 3.1795
Du a1 0.05 45 0.487 7 189** 41** 0.7721 -0.0413 0.3738
CO? Single 0.05 45 0.608 7 101** 851** 0.6959 0.1411 8.237
0.05 45 0.398 7 123** 567** 0.6456 0.2045 14.10
0.50 240 0.274 7 279** 105** 0.4745 -0.0529 0.4149
S q r . Mean Sq, %
0.16
Max. abs, atX=
0.21 0.25
0.18 0.26 0.25
0.30 -0.52 0.15
0.38 -0.68 0.15
0.10 0.16 0.25
0.14 -0.24 0.15
0.79 -1.54 0.15
1.21 -2.3 1 0.15
0.09 0.13 0.25
4.45
2.62
2.67
4.45
2.66
4.45
10.2
16.7
4.92
H2
H2
COP Dual
...
co2
...
co2
Col. Jrow 32C
a
Responses
L . comp. Ae x 10''
Heavy/Light c0mp.f. 5.45 5.51 3.76 3.85 4.69 1.429 4.61 1.451 4.21 a-f See also notes, Table Ia. a , b ~ r , dRegression analyses referred-to, apply, where possible, to pump balance-corrected Y, X data. No. of observation pairs used in analysis reduced by one, when pump unbalance YO has been estimated.
t h e X values, on the assumption t h a t it applied t o all pump mixture ratios. This will be discussed later. It would be unfair to say t h a t these unbalance estimates were typical of this type of mixing pump after a few hundred hours of operation, but it is suggested t h a t other pump users a t least consider these results. Development of Regressions. Figures 4 and 5 show t h e results of six experiments plotted on linear Y , X axes. The same experimental results of Figure 5 are replotted in Fig-
ure 6 with logarithmic axes. The curves of Figure 6 may also be compared with the log/log plots of reference ( I ) . T h e data of the earlier experiments was examined by means of the General Electric (G.E.) Mark I time sharing library programs SIXCR$ and MULRGg. T h e relation
Y =
X A
+
CX
(1)
was found t o provide a fit superior t o a simple linear relaANALYTICAL CHEMISTRY, VOL. 47, NO. 6, MAY 1975
809
Table IC. Summary of Results. Experiments 37 to 45, Gas Mixing Pump Blends (Continued) Experiment S o .
38
37
Light comp. Heavy comp. Radiation source Gap, mm ( s e e text) Detector voltage Pump unbalance, % N o . obsn pairsh F statistic F statistic (11)' A coefficient (10) B coefficient (10) E r r o r M. S q . b x 10'
39
41
40
42
H?
H?
H?
H?
H?
He:CHii
N?
O?
N?
02
CO?
N?
0.50
240 0.405 7 428** 70** 0.5859 -0.0333 0.1075
45
44
43
He:CHJi H, N? CO?
H? CO?
Parallel plate MXD with one tritium source (single) 1.oo 1.oo 1.00 0.50 0.50 0.50 0.50 240 240 240 90 90 90 90 0.144 0.163 0.367 0.039 0.192 0.136 0.034 7 7 7 8i 8' 8' 8i 547** 1855** 915** 6.6* 1548** 2.9 2681** 156** 56** 95** 203** 3.4 108** 1.1 115** 0.5962 0.4991 0.5006 0.3688 0.5753 0.4776 0.5721 0.4796 -0.0417 -0.0861 -0.0851 -0.0905 -0.0089 -0.0611 -0.0070 -0 .0680 0.0555 0.5584 0.1610 0.3707 0.4915 0.0993 0.7105 0.0708
0.50 240 0.311 7 1296**
Col. /raw 32'
Sqr. Mean Sq, % M a x . abs. % atX=
0.03 0.05 0.15
0.06 0.11 0.50
0.30 -0.57 0.15
0.14 -0.23 0.15
0.14 0.21 0.15
0.21 -0.42 0.15
0.08 -0.13 0.15
0.30 -0.66 0.15
0.09 -0.13 0.15
Rl?Spcmsl?S
L . comp. Ae x 10" Heavy/Light comp.' a - f
4.94 3.26
4.92 6.47 6.46 6.45 5.82 4.76 5.81 2.902 3 -39 3.86 3.54 1.724 3.34 1.718 ~See ~ notes, Tables Ia, I b . 1 No. of observation pairs used in analysis reduced by two, after estimate of pump unbalance %.
4.75 3.33
Figure 4. Typical response plots dual source detector
Figure 5. Typical response plots, single source detector
Experiment 0, hydrogen:commercial butane, source gap 0.20 mm. Experiment 31, hydrogenmitrogen, source gap 0.05 mm, Experiment 35, nitrogen: carbon dioxide, source gap 0.05 mm
Experiment 29, hydrogen:carbon dioxide, source gap 0.05 mm. Experiment 30, hydrogenmitrogen, source gap 0.05 mm. Experiment 41, hydrogemcarbon dioxide, source gap 1.0 mm
tion as judged by the comparative ' F ' test (or variance ratio) statistics and from the tabulated residuals. Consideration of the residuals tables suggested that the relations X Y = A + C X + BX'
and for Equation 3
and -r
Y =
n
A + CX + BXlD might provide a better fit than Equation 1, and re-examination of the data after processing by means of the G.E. Mark I library program MULFT$ showed that both Equations 2 and 3 provided significant improvements in f i t compared to Equation 1. T o use the program MULFTg for this purpose, it was necessary first to convert Equations 2 and 3 to linear forms and use transformed variables. The linearized forms which were used were: f o r Equation 2 1/Y = C + A / X + B X (4) 810
ANALYTICAL CHEMISTRY, VOL. 47, NO. 6, MAY 1975
1/Y = C
+
A/X
+
B/X'I2 (5)
For the practical purpose of this work, there is a serious objection to the forms 1, 2, and 3. This is because, by definition of Y and X, a suitable characterizing relation must be satisfied by (0,O) and (1,l). However, all of these forms, when fitted to data through transformations like Equations 4 and 5 will allow a substantial misfit as the point (1,l)is approached. This is particularly unacceptable when the molar fraction (1 - X )of the lighter component is to be estimated. Relations of the forms 1, 2, and 3 can be satisfied by (1,l) only if the sums of the coefficients in the RHS denominators are equal to 1. Thus, Equations 1, 2, and 3, respectively, become Y =
Y =A
A
+
X
(1 - A)X A
-
(A - B - l)X - B X 2
EXPERIMENT NO. 30 DqTE 130917 FILE FGlNH SINGLE SOURCEIGAP(SE*E TEXT) o05MM 45VOLT MIX PUMP BLENDS-NO BALANCE CORRECTION Y I X TRANSFORMATION (l-Y)/Y/((l-X)/X) =A tB *X A MEAN 01132 COEF*A.BI F TEST STATISTIC I 29 REG. ACTUAL ACTUAL ACTUAL
1.0
5
‘25
26
I
X
Y
I
01587 e2506 03500 e4983 e4983 e6413 1474 8480
‘01
I
25
Figure 6. Typical response plots, single source detector
1966 03154 e4267 .5789 05811 723 1 6016 8904 e
1
073961 I -e052921 29.9 +* 31 CALCo-29 X DIFF.
7252 7260 a 1235 I224 7 142 7028 07051 6866
32 CALCe-26 % DIFF.
89 05 -e34 -1.28 - e 14 e31 -072 l e 17 e
-e72 -e03 .19 .53 06 - 0 10 14 -e13
Figure 5 replotted with log/log axes.
MIX PUMP BLENDS-INCLUDES BALANCE CORRECTION UNBALANCE XIESTIMATEDI 0279%
x
y = -
A 4- ( 1 - A - B ) X + B X i n Then, by rearranging terms in each case to allow the use of linear regression analysis, Equations 6, 7 , and 8, respectively, can be written (9)
( y ) / ( $ g+) =A
B (1
x “ 2x i , 2 ) +
(11)
I t is interesting to consider the geometrical analog of the new LHS “dependent” variable of Equations 10 and 11. The appropriate scalars are marked for the experiment 8 curve in Figure 4. I t can easily be seen that a diagonal straight line relation is the limiting case of relations 9, 10, and 11 when A 1 snd B 0, and conversely that the degree of departure of the value of A from unity is a measure of nonlinearity of the Y vs. X relation. A computer program C2 was written to fit experimental data to the linearized forms 10 and 11. The transformed dependent variable is a function of both Y and X.The line fitting routine used in this program is according to the matrix method of Draper and Smith (13). This program accessed corrected Y and X data for all the reported experiments from a data file designated C2F. An annotated listing of this data file is available on application to the author. The data transformat ions and the line fitting routine can also be implemented with the computer program MULFT$. The computer program C2 estimated the coefficient A of form 9 on two alternative criteria. The first was on the basis of minimizing the sum of squares of the proportional deviations about the regression line. Thus, if the variable (1 - Y ) / Y is designated P, and the variable (1 - X ) / X is designated Q, then it can be shown that
-
-
.A
=E--/ Qi xQi2 p~2 pi
The second criterion for estimation of the A of expression 9 was on the basis of minimizing the sum of squares of the absolute deviations about the regression line. Thus, A =
CP,Qi/Di2
A MEAN 07124 COEFeAIBI
F TEST STATISTIC
073156 I -0038366 17.9 +*
I
t D’S SUM O F
SOURCE O F VARIATION
I
TO TAL t 1 REGRESSION 8 ERROR S Q R ( ( S S Q 0 ROW 32)/ 5 ) : 26 Y e1966 25 X(1) e1500 32 -e52
03154 -2496 -001
26 Y .tu16 25 X(1) a7485 32 .17
.a904 -8481 -.I4
F
SQUARES
MEAN SQUARE
6 le78E-04 10297E-04 1 6009E-04 6.086E-04 5 1.70E-04 30395E-05 30% 04261 03487 .10
e5803 a4983 0 34
e7231 e6486 .OO
Figure 7. Experiment 30. Part of the output of the computer program C2, showing the fit of the data to Relation 10 before and after application of the balance correction. The column heading numbers 25 to 32 are used as row labels for the same information under the balance-corrected analysis of variance table. Column 3 1 figures represent the percentage difference between the calculated and actual value of the regression. Column or Row 32 figures represent the percentage difference between the calculated and actual value of Y. Row 25 X (1)’s are balance-corrected column 25 X’s
A sample partial print-out produced by the program C2 is shown as Figure 7. This program also, for comparison, fitted a straight line to each untransformed data set by minimizing the sum of squares of the proportional deviations about the regression line Y = AX
(14) In order to assess quantitatively the inferences of reference ( 1 ) about the MXD being linear to a t least 50% vapor concentration, lower-valued parts of each data set could be used to fit model 14 and the fit contrasted with those given by model 9 under both fitting criteria, using the same data. The f i t of these same selected data sets to regressions of form 10 and 11 fixed by the complete data set was also summarized. The printed F test statistic from the program C2 was based on the minimized absolute sum of squares of the error term in the linearized relations of 10 and 11. The F value printed was annotated with a single or double asterisk depending on whether its magnitude exceeded that for ANALYTICAL CHEMISTRY, VOL. 47, NO. 6, MAY 1975
811
E X P E R I M E N T 3 0 - I O N I Z A T I O N X - S E C T I O N DETECTOR. P H I L I P S I G A P 1,TEST R U N 730917 NITROGENIHYDROGEN MIXES EX GAS MIXING PUMP
IN
SPAN
ORDER O F 11 2 MIX TIME NO. C O D E 1
2 3 4 5
6 7 8
1116 1039 1141
1014 I002 1127 1026 I104
24 5.D. COL.26
87 VOL. FRACT.
25 MOLE FRACT.
26 SPAN FRACT.
-000043 -000062 -000057 -000073 .000112 -000096 e000116 ,000076
,1506 a2504 -3499 -4982 e4982 -6478 -7472 -8479
,1507 ,2506 -3500 -4983 -4983 -6473 ,7474 -8480
-1966 -3154 -4267 -5789 -5817 a7231 ,8076 -8904
EXPERIMENT 3 4 - I O N I Z A T I O N X-SECTION DETECTOR. PHILIPS,GAP I>TEST RUN 7 3 0 9 1 8 CARBON DIOXIDE/NITROGEN MIXES EX GAS MIXING PUMP IN ASCENDING ORDER O F CARBON DIOXIDE SPAN FRACTIONS. 11
2
24
MIX TIME NO. CODE 1 2 3
4 5
6 7
8
S.D. COL.26
1138 1107 1218 1015 1000 1204 1047 1126
-000132 m000155 -000236 ,080214 -000174 -000292 -000332 -000395
25
27
26
VOL. MOLE SPAN FRACT. FRACT. FRACT. -1513 ,2514 -3510 a4991 ,4991 a6477 -7475 -8480
-1519 a2523 ,3520 -4997 -4997 -6487 .7484 ,8466
-2009 -3118 -4158 -5620 e5677 ,7017 -7899 *E1754
Figures 8a and b. Experiments 30 and 34. Part of the output of the computer program C19. Column 24 figures represent the standard deviation of the Y values in column 26. Column 25 contains the corresponding X values
significance a t 5% or 1%levels. The null hypothesis applicable to the F test is seen to be a relation of form 9. The output table showed, but on a percentage basis, the residuals comprising the error sum of squares used for the F test (column 31), and the corresponding percentage difference between observed and calculated Y values (column or row 32). By reference to Figure 7 , and making a point by point comparison of columns 31 and 32, it will be observed that these transformations give the desirable attribute to the 1. This would percentage Y residuals of decreasing as X make possible a good estimation of the molar fraction (1 -
-
XI. The partial print-out of Figure 7 also shows the root mean sum of squares of the row 32 values, which represent the percentage residuals after application of the pump balance correction to the X data. Tables Ia, Ib, and IC show a summary of results from all the experiments, extracted mainly from the output of program C2. For example, most of the items under the experiment number 30 column head in Table Ib will be seen to originate from the partial computer output shown in Figure 7 . The detector current and component current response ratios are also listed. Inflections in the Characterization Curves. There was little reason to expect that detector response curves such as those plotted in Figures 4 and 5 should have points of inflection. If such inflections existed in a characterizing relation in the valid range of 0 to 1, there seemed to be three possible explanations. These were: 1) There may have been more than one detection mechanism occurring simultaneously. 2) The data were inaccurate. 3) The characterizing relation was unsuitable. The second derivative functions with respect to X were determined for relations 7 and 8. I t was found that the relation 7 curve had points of inflection in the 0 to 1 range in only two of the twenty-seven experiments, namely in experiments 34 and 35, a t X = 0.98 and X = 0.84, respectively. As these two experiments, involving nitrogen-carbon dioxide mixtures, were necessarily less precise, in terms of the Y measurement, than other gas mixing pump experiments, it was assumed that inaccurate data caused these inflections. On the other hand, roots of the second derivative function of relation 8 were found in the range X = 0 to X = 0.063 in the case of twenty-three of the twenty-seven reported sets of fitted experimental data. The exceptions were experiments 6 and 7 (no real roots) and experiments 34 and 35 (inflections outside the 0 to 1 range). As there 812
ANALYTICAL CHEMISTRY, VOL. 47, NO. 6, MAY 1975
were very little data taken a t the low values of X where these unacceptable inflections occurred, the characterizing relation 8 seemed also unacceptable. Pump Unbalance Corrections. The method used in the program C2 to correct the gas mixing pump asymmetry was as follows: 1) Coefficient sets A and B were fitted, using one or both of relations 10 and 11,to the data pairs as read from file C2F. 2) By reversing the pump gas feed connections a t the 1:1 mixing ratio, two Y estimates Y1 and Yz corresponding to the one X estimate X, had been obtained and were included in Y, X data of file C2F. 3) The program calculated dY/dX a t X = X, for relations 10 and/or 11. 4) The value(s) (Y1 - Yz)/((dY/dX)(2Xm))represented estimate(s) of the fractional inequality of the two pumps. 5 ) This value for the pump unbalance was used to correct the X values as extracted from file C2F, and the two pairs (Y1, X,) and (Yz, X,) were replaced with a single new pair ( ( Y l Y2)/2, X,). 6) The regression analysis(es) was run again on the recalculated set(s) of Y, X data and new estimates made of the A and B for one or both relations of type 10 or 11. In experiments 42 to 45 there were two separate estimates for each alternative gas connection mode a t the 1:l mixing ratio, and the numerator (Y1 - Yz) in step 4 above, became ( ( Y l Y2)/2 - (Y3 Y4)/2)), In these cases, the original four 1:l observation pairs were replaced with two new pairs. Analysis of Errors. In these experiments, standard deviations of observations and observation means were carried through the Y and X data processing streams to give estimates of the standard deviation of the final Y , X pairs used in the regression analyses. Figures 8a and 8b show sample outputs of the computer program C19 which was used with the gas mixing pump data. Column 24 in each case shows standard deviations for Y which are larger in the case of the carbon dioxide-nitrogen mix than for the nitrogen-hydrogen mix because the carbon dioxide-nitrogen signal span is only about half that of the latter pair. In the gas mixing pump experiments, the X errors are difficult to predict. The typical low standard deviations for Y as in Figure 8a indicate that, once the pump is operating near its equilibrium oil temperature, the blend composition is stable, but the spread of the pump unbalance estimates makes it uncertain that the same gear ratio will reproduce the same blend after a run-stop-run sequence. From the standard deviation of the pump unbalance estimate, standard deviations of the blend composition a t each X value can be calculated, on the somewhat uncertain assumption
+
+
+
that the pump unbalance estimate and its standard deviation are independent of the pumping speed of the variable speed half of the system. These calculated standard deviations of X are presented in the relative form in Table I1 and seem to be comparable to the percentage Y residuals presented in column and row 32 of Figure 7 , as a typical example. Sensitivity Limits for X . Relations 6, 7 , and 8 can be solved analytically for X. The solution for equation 6 is
x= f o r Equation 7
AY 1 - (1 - A)Y
(15)
X = (1/2B)(B - A
- 1/Y
+
+
JT]4 - B
1 / Y - 1)'
where
Z = 4A/Y
+
4A2 + B2 - 4A
4AB)
+
and f o r Equation 8 X = 4A2/(B2 - 2BZ'"
+
+
1+ (16)
Z) (17)
4AB
With relation 15, taking the first derivative w.r. to Y
This gives the inverse slope of the characterizing curve, and a t the values Y = 0 and Y = 1, this slope has the values A and 1/A. Similarly the slope d X / d Y a t Y = 0 and Y = 1 for relation 16 is A and 1/(A B ) and for relation 17 is A and 1/(A B/2). Knowing the standard deviation of a Y value based on a t least five observations, the smallest detectable change in Y following another five observations can be defined, a t the 90% probability level, to be about two standard deviations. This value can be converted to an X detection limit by multiplying by the d X / d Y slope a t the particular value of X. Table I11 shows the calculated X detection limits at X = 0.15 and X = 0.85 for experiments 29, 30, 34, and 41, using slopes calculated from the first derivative w.r. to Y of relation 16. Note that the Y standard deviations first used are less than those shown in column 24 of the output of the program C19 (e.g., see Figures 8a and 8b). The column 24 standard deviations are those of Y mean values when Y is estimated by the difference of a mixture mean and the light component mean divided by the heavy component-light component span. Thus, the column 24 standard deviations give X detection limits applicable to the least detectable X difference to be found from one detector calibration to the next using the same reference mixes. The generally lower X detection limit applies to the situation where the detector is sensing a reference gas and the feed mixture is changed directly to the comparison gas. Comparison of the MXD with the Thermal Conductivity Detector (TCD). These lower sensitivity limits of 50-100 ppm can be compared with those for a typical TCD (141, used as a continuous monitor, which could be expected to detect a 1-ppni impurity in a helium or hydrogen stream. The linear range of the TCD has been extended by constant filament temperature (15) and constant current (16) operation. Even with these linearity improvements, however, the TCD would appear to be about one order of magnitude less predictable than the MXD, over the full 0-1 molar fraction range, in terms of percentage deviation of predicted response (as span fraction) from actual response. The foregoing predictability comparison assumes, of course, a characterizing relation in each case with not more than two regression coefficients. It follows that these recently modified versions of the TCD will have a better useful dynamic range than the MXD as characterized in this paper for mixtures containing hydrogen as one component.
+
+
Table 11. Calculated Relative Standard Deviations of X vs. X for Mixing Pump Blends x mole fract 0.15 0.25 0.35 0.50 0.65 0.75 0.85
R e l . std d e v , 5:
0.28 0.25 02 2 0.17 0.12 0.084 0.050
Practical Laboratory Use of the MXD. The relation 10 can be applied to calibrate an MXD for a gas mixture of two known components as follows: 1) The detector current is recorded for the pure components of the binary mixture. 2) The current is recorded for at least two accurately known blends (heavy component molar fractions = Xi) of these components. 3) The span fractions (Yi) of these blends are calculated, using the data from steps 1 and 2, and the previous definition of span fraction. 4) The variables Pi = (1 - Yi)/Yi and Qi = (1 - Xi)/Xi are calculated for each of the blends of step 2. 5) A set of values Ri = PJQi are calculated, and fitted to a relation of the form R = A + B X
(19)
(see also relation 10). 6) If two intermediate blends were used in step 2, then the coefficients A and B are found by solving the simultaneous equations. Otherwise a least squares estimation of A and B should be made, after setting up the normal equations, or by using a suitably programmed desk calculator or computer. 7 ) The A and B coefficients may then be used in relation 16 to calculate X, the molar fraction corresponding to observed Y values for unknown mixtures of the same components. The A and B coefficients will be subsequently influenced by changes in detector pressure, temperature, and radiation source strength. Hence, it is advantageous to minimize such changes. An ionization source with a slower decay rate than tritium would be better, providing of course that such a detector can be characterized in the same way. The most difficult part of the above calibration procedure is in step 2, the preparation of the known calibration blends; however, the predictability of the detector response makes it possible to use only two blends of fairly amenable ratios. Thus, such blends can be prepared dynamically with gas mixing pumps, by infusion pump driven gas-tight syringes, or by soap film meter or thermal mass flowmeter measurement. Otherwise, calibration mixes may be gravimetrically prepared in pressure cylinders, blended by accurate pressure measurement, or blended and subsequently analyzed. The MXD as a Gas Chromatography Detector. The characterizing relations developed here for the MXD are directly applicable to the measurement of gas blend compositipns. In the GC situation, the integration of calculated composition vs. time would not be an exact analog of the quantity of component corresponding to a chromatographic peak because of the surge effect (17), which modifies the (carrier plus sample) detector gas flow during peak evolution. In normal practice, gas chromatography detectors are calibrated in the chromatographic system, and the surge effect will be included in the overall detector response curve. ANALYTICAL CHEMISTRY, VOL. 47, NO. 6, MAY 1975
813
Table 111. Typical X Detection Limits Experiment KO.
29
Components at A’= 0.15a dX/d Std dev ET Limit, ppmC Std dev Y (col. 24)d Limit ppmd at X = 0.85 dX/d Y Std dev Ir Limit ppm Std dev Y (col. 24) Limit ppm
30
N,:H?
COZ:H?
41
34
CO?:N?
CO*:H?
0.7572 0.000026 39 0.000034 51
0.8050 0.000043 69 0.000043 69
0.8252 0.000083 137 0.000132 218
0.5569 0.000075 84 0.000079 88
1.3926 0.000028 78 0.000073 204
1.2954 0.000037 95 0.000076 197
1.1850 0.000229 54 1 0.000395 937
2.6329 0.00005 1 269 0.000068 363
a X = molar fraction of heavier component. Derivative of relation 16. For sequential observations (see text). For isolated observations with same references.
This surge effect will become more important in affecting detector response as the peak concentration in the carrier gas increases. Preliminary results were gathered in this laboratory from a normal gas chromatographic system (e.g., experiments 1-3), where known gas compositions were injected by means of a gas sampling valve and relation 10 was fitted to peak area data. Although the percentage residuals column 32 of the program C2 output (e.g., see Figure 7), over 11 experiments showed a maximum absolute value of 1.4%, there seemed to be a detectable pattern in the residuals column which will require further investigation. A more promising approach to MXD operation as a quantitative device a t the outlet of a GC column would seem to be the use of a detector pre-calibrated with mixtures so that the A and B coefficients of relation 10 are known for each appropriate component-carrier gas mixture. The correct expression for X,,the molar fraction of a component in the sample is: (20)
where X is the instantaneous molar fraction of this component in the carrier gas (from relation 16), f is the instantaneous (carrier plus sample) detector molar gas flow rate, t is the elapsed time from sample injection, S, is the molar sample volume and T represents the integration time limits set by an appropriate peak window. Van de Craats ( I 7) showed that the surge effect could be allowed-for by first evaluating the above integral assuming f = F,, the constant quiescent molar carrier gas flow rate. Then, on the assumption that the peak approximated a Gaussian curve, an appropriately weighted flow correction factor, f 2 , was found to be:
where X, is the molar concentration a t peak maximum, Vp, the uncorrected retention volume, and V G the gas holdup volume. Thus, a more convenient form of expression 20 for this situation is:
(22) Using this relation, linearity and flow surge corrections can 814
ANALYTICAL CHEMISTRY, VOL. 47, NO. 6, MAY 1975
be applied to MXD peaks with the assistance of a data logger/computer system. An obvious application of the MXD is its operation a t high component concentrations, carried in a constant flow of “second” carrier gas, after a palladium transmodulator (18).A suitable second carrier gas would be helium plus 3% methane (2). In this case, the value, f , in relation 20, is independent of column parameters and can be evaluated: where F , is now the second carrier gas flow rate.
CONCLUSIONS The results for experiment 30 as shown in Figure 7 and Table Ib are typical of the more accurate data sets accumulated with the gas mixing pumps. The results show that: 1)Relations of the form 10 and 11 give significantly better fits of the experimental data than relations of the form 9. 2) I t is reasonable to conclude that relations of the form 9 give significantly better fits than the simple linear form 14 even for molar concentrations of the heavier component as low as 0.25. For example, if a relation of form 9 is fitted to the two lowest pairs of ( Y , X ( 1 ) ) data points of experiment 30, Figure 7, namely (0.1966, 0.1500) and (0.3154, 0.2496), an A coefficient of 0.72152 is determined on the basis of minimizing the sum of squares of fractional deviations of the transformed dependent variable about the regression line. The predicted Y values of 0.19652 and 0.31554 are -0.04% and +0.04% in error, respectively. A fit of the simple linear form 14 to the same data pairs produces an A coefficient of 1.28635 and predicted Y values -1.86% and +1.80% in error, respectively. This order of improvement of the fit of relation 9 over relation 14 is typical of experiments 28 to 33 which used the most linear narrow gap configuration and choices of binary pairs which favored comparatively small experimental errors. Further reference to Tables Ia, Ib, and IC allows the following five further conclusions to be drawn. 3) As plate spacing diminishes, the response characteristic tends to relation 9. It seems unlikely that a linear relation would be a reasonable assumption, except over a very small range of X, with practical cross-section detectors using tritium foil source(s). I t can be anticipated that linearity could be improved by sources giving @-particles of higher energy (e.g., 63Ni) plated on machined surfaces, so
that interelectrode separation can be reduced. However, in view of the good fits obtained in this work, it seems there may not be very much to gain by aiming for a simpler characterizing relation than 9 which can be fixed by a minimum of three observation pairs. 4) Relation 10 is, overall, a more satisfactory characterizing relation than 11. T h e relation 11 gives a comparable fit of the data to relation 10 a t the minimum electrode gap, but 10 fits markedly better as the gap is increased. The root mean square of the percentage Y residuals, as summarized in Tables Ib and IC beside the Col./Row 32 heading are fairly constant, despite changes in electrode gap and concomitant linearity. This conclusion is supported by the previous consideration of the location of points of inflection in these alternatives. 5) Experiments 42 and 44 were performed to check the applicability of the characterizing relations to the hydrogen-free residue of a typical palladium transmodulator second carrier gas (18).This gas was a prepared blend of helium + 3.5% methane. I t is interesting to note by reference to Tables Ib and IC that the regressions fitted to data gathered by blending this mix with nitrogen as the heavy component gave suspiciously low F ratios compared to the other F ratios a t the 0.5mm detector gap (experiments 37, 3 8 ) , corresponding to the closest A coefficients. This fact, together with the observation of the X == 0.15 location of the maximum absolute percent Y residual of about -0.5%, suggests that a 3.5% methane addition may not be completely effective as a quenching agent to shorten the life of metastable helium atoms. 6) Boer ( 7 ) developed and tested a response factor (f) relation for the strontium-90 cross-section detector as used in gas chromatography. This had the form
8,
- Qc
(24) = 'W, where Q, and Qc are the molecular ionization cross-sections a t the mean source 6-particle energy for compound and carrier gas, respectively, and M , is the molecular weight of the compound. Lovelock et al. ( I ) implied that a response factor of this form, incorporating molecular ionization cross-sections applicable to the mean energy of tritium pparticles, was appropriate to the tritium MXD. The nonlinearity of response shown in this work, and the decrease in coefficient A as the electrode gap is increased, are clear evidence that, assuming the validity of Equation 19, the mean P-particle energy bet>weenelectrodes is too non-uniform to allow practical use of published molecular ionization crosssections for calibration of the tritium MXD. 7 ) A correlation was sought between the coefficients of the characterizing relation 10 and the pure component response ratios of Tables Ia, Ib, and IC. The response ratios f
were used for this correlation, rather than the much more uncertain electrode gaps. No generally useful mathematical correlation of this kind was found. Finally, Table 111shows that, under favorable conditions, and depending on the two-mixture components, the X detection limit or sensitivity will be as low as 50-100 ppm. The combinations of component pairs which can be measured with this detector are limited by the current discrimination between the components and by possible reactions with the foil surface (e.g., the case of propane). Outside these limitations, it can thus be concluded that the tritium ionization cross-section detector can be used, together with the characterizing relations described, as an accurate twocomponent composition monitor.
ACKNOWLEDGMENT The assistance of A. J. Kairaitis, W. M. Patterson, C. V. Robertson, T. H. Spurling, and I. Strudwick is gratefully acknowledged. LITERATURE CITED (1) J. E. Lovelock, G. R. Shoemake. and A. Zlatkis, Anal. Chem., 3 5 , 460 (1963). (2) G. R. Shoemake, Dissertation Ref. 66-71 12, University Microfilms, Inc., Ann Arbor, MI. (3) J. E. Lovelock, "Gas Chromatography 1960", R. P. W. Scott, Ed., Butterworths, London, 1960, p 16. (4) D. J. Pompeo and J. W. Otvos, U S . Patent 2641710 (1953). ( 5 ) P. F. Washbrooke, Gas Chromatography Discussion Group (U.K.) informal symposium, London, March 12, 1965, as summarized by D. R. Browning, Nature, 207 (5002), 1137-1 138 (1965). (6) C. H. Deal, J. W. Otvos, V. N. Smith, and P. S.Zucco, Anal. Chem. 28, 1958 (1956). (7) H. Boer, "Vapor Phase ChromatoqraDhy". D. H. Desty. Ed.. Butterworths, London, 1957, p 169. (8) P. F. Deisler, Jr., K. W. McHenry, Jr., and R. H. Wilhelm, Anal. Chem., 27, 1367 (1955). (9) W. Jost, "Diffusion in Solids, Liquids and Gases", Academic Press, New York. NY. 1960. D 411. (10) E. A. Mason and T. H. Spurling, "The International Encyclopedia of Physical Chemistry and Chemical Physics", Topic 10, Volume 2, "The Vlrial Equation of State", Pergamon Press, Oxford, 1969. (11) J. H. Dymond and E. B. Smith, "The Virlal Coefficients of Gases. A Crltical Compilation", Oxford Science Research Papers 2, Clarendon Press, Oxford, 1969. (12) Publication 51 l E , H. Wosthoff O.H.G., D463, Bochurn, West Germany, page 3. (13) N. R. Draper and H. Smith, "Applied Regression Analysis", John Wiley 8 Sons, New York, NY, 1966. (14) J. C. Sternberg, "Gas Chromatography", Lewis Fowler, Ed., Academic Press, New York, NY, 1963, p 161. (15) R. T.Wittebrood, Chromatographia, 5, 454 (1972). (16) R. B. DeLew, J. Chromatogr. Sci., I O , 600 (1972). (17) F. van de Craats, "Gas Chromatography 1958", D. H. Desty, Ed., Butterworths, London, 1958, p 248. (18) J. E. Lovelock, K. W. Charlton, and P. G. Simmonds, Anal. Chem., 41, 1048 (1969).
RECEIVEDfor review September 6, 1974. Accepted December 30, 1974. 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.
ANALYTICAL CHEMISTRY, VOL. 47, NO. 6, M A Y 1975
815
