ACKNOWLEDGMENT T h e assistance of A. A. Clouston (Commonwealth Industrial Gases, Ltd.) and M. B. A. Crespi (Argentina AEC) is gratefully acknowledged for supplying the samples from Australia and Argentina, respectively. Thanks are due t o the Chemistry Department a t Brookhaven National Laboratory, especially t o R. Davis, Jr., and G. Friedlander, for their hospitality and for use of their facilities. V. Radeka and L. Rogers, also of Brookhaven National Laboratory, are thanked for their instrumentation support. Several helpful discussions and exchanges of results have taken place with H. Oeschger and H. Loosli of t h e University of Bern and with L. Machta of the National Oceanic and Atmospheric Agency.
LITERATURE CITED (1) W. F. Libby, "Radiocarbon Dating", University of Chicago Press, Chicago, Ill., 1952. (2) D. La1 and B. Peters, Handb. Phys., 46(2). 551 (1967). (3) L. Machta, R. J. List, M. E. Smith, and H. Oeschger, in Precipitation Scavenging 7970 (CONF-700601) p 465. (4) L. Machta, paper presented at the Noble Gases Symposium, Las Vegas, Nev., 1973. (5) H. Oeschger, J. Houtermans, H. Loosii, and M. Wahlen in "Radiocarbon Variations and Absolute Chronology". i. U. Olsson. Ed., Almqvist and Wiksell, Stockholm, 1970. (6) K. 0. Minnich and J. C. Vogel, Naturwissenschaften, 45,327 (1958). (7) R. Pannetier, J. Geophys. Res., 75, 2985 (1970). (6) L. A. Currie, Anal. Chern., 40, 586 (1968). (9) L. A. Currie, E€€ Trans. Nucl. Sci., NS-19, 119 (1972). (10) H. Erlenkeuser, 2.Naturforsch., TellA. 26, 1365 (1971). (11) B. Verhagen, "Rapid Isotope Enrichment of Gases by Thermal Diffusion for Nuclear Dating", pp 657-72 of "Radioactive Dating and Methods of
(15) (16) (17) (18) (19) (20) (21) (22)
Low-Level Counting", IAEA Symposium on Radioactive Dating and Methods of Low-Level Counting, Monaco, March 2-10, 1967: STIIPUB152 and CONF-670309. B. Th. Verhagen and J. P. F. Sellschop. "Proceedings of the Sixth international Conference on Radiocarbon and Tritium Dating, 1965", CONF650652, p 505. H. von Buttlar and B. Wiik. "Proceedings of the Sixth International Conference on Radiocarbon and Tritium Dating", CONF-650652, p 515. M. Shimizu and J. Ravoire, "Tritium Enrichment by Thermal Diffusion I. Calculation of an installation for Measuring Natural Tritium", CEA-R3015, Commissariat a I'Energie Atomique, Saclay. France, October 1966. 45 DD. W. MI Ruiherford, J. Chern. Phys., 53, 4319 (1970). J. H. Dymond and B. J. Alder, J. Chern. Phys., 51, 309 (1969). E. A. Mason and W. E. Rice, J. Chern. Phys., 22, 843 (1954). W. M. Rutherford, W. J. Roos, and K. J. Kaminski, J. Chern. Phys., 50, 5359 (1969). R. Davis, Jr., J. C. Evans, V. Radeka, and L. C. Rogers, "Proceedings of the Hungarian Physical Society, Neutrino '72", Vol. 1, Omkdk-Technoinform, 1972, pp 5-15. H. Loosli, personal communication. H. Loosli. H. Oeschger, R. Studer, M. Wahlen, and W. Wiest, Noble Gases Symposium, Las Vegas, 1973. J. M. Matuszek. C. J. Paperieilo, and C. 0. Kunz, "Characterization of Stack Effluents from Certain Nuclear Facilities", AEC Rep., COO-2222-4 (1973).
RECEIVEDfor review February 6, 1975. Accepted November 17, 1975. Mound Laboratory is operated by Monsanto Research Corporation for the U S . Energy Research and Development Administration under Contract No. E-33-1GEN-53. This research was supported in part by the Advanced Research Projects Agency of the Department of Defense and was monitored by HQ USAF (AFTAC), Patrick AFB, Florida 32925.
Exponential Dilution as a Calibration Technique J. J. Ritter* and N. K. Adams Inorganic Chemistry Section, National Bureau of Standards, Washington, D.C. 20234
Gas phase exponential dilution is frequently employed as a convenient calibration technique for gas detectors. The objective of the investigation was to examlne exponential dllution for its efficacy to provide demonstrably reliable detector callbratlons, particularly for air-pollution monltorlng instruments. An evaluatlon of representative types of exponential dilution flasks (EDF's) with regard to exponential behavior and slope reproducibility was conducted. Error propagation analyses on the data indicated Uncertainties in concentration measurement of the order of 4 to 8 % over a concentration range of 50-3 ppm. Inadequate gas mixing within the dilution flasks was a significant contributor to these uncertainties. A new, more efficient EDF was developed and extensively tested in connection with a flame ionization detector. Comparison calibration experiments performed with the new EDF and with propane-air mixtures of known concentration gave detector calibrations with an uncertainty of f l YO over the 50-3 ppm concentration range. In addition, it was demonstrated that the new EDF could provide an acceptable assessment of detector linearity. The basic principles of exponential dilution, some aspects of gas mlxing, dilution flask-detector interactions and EDF design features are discussed in detail. 612
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T h e use of exponential dilution as a technique t o calibrate gas detectors was first described by Lovelock in 1960 ( I ) . Basically, the detector to be calibrated is coupled t o a gas blending device (exponential dilution flask, E D F ) through which a carrier gas is flowing a t a fixed rate ( r ) . T h e technique is based upon the expectation t h a t the concentration ( c ) of a calibrant gas after its introduction to the E D F will decay exponentially with time ( t ) according t o the expression c = c , e - a f . In this expression c , is the initial calibrant concentration, and CY = r/Vg where V , is the volume of gas within the E D F a t a specified pressure and temperature. Under ideal conditions, the detector response ( S ) is related t o the calibrant concentration ( c ) through the simple relationship S = IC, where I is a constant obtained from measureable system parameters. Since c for any time t can be calculated and be readily related to detector response ( S ) ,the exponential nature of the decay curve can provide a rapid and continuous detector calibration over a wide range of concentrations. T h e purpose of this investigation was t o assess the feasibility of utilizing exponential dilution as a rapid calibration technique for air pollution monitoring instruments. As a primary criterion, the EDF system was required to provide
CARRIER
--t
:
The calibrant gas used was propane, shown to be better than 99.5% C3Hs by gas chromatography (4-m, 2-mm i.d. column, 10% Apeizon L on 80-100 mesh inert support, operated at 25 “ C ) . Mass spectrometric examination of the calibrant confirmed the absence of Cd and higher hydrocarbons in concentrations above 0.1%. Carrier gas flow was regulated using a gas chromatographic flow controller capable of control to f0.3% of the instantaneous rate. The variation in laboratory temperature during individual EDF experiments was measured as fO.l OC from a mean temperature of 25 “ C . Carrier gas flow rates were determined with a positive displacement flowmeter consisting of a mercury-sealed polytetrafluoroethylene (PTFE) piston which traveled in a precision bore (12mm id.) glass tube. The time required for the displacement of a fixed volume of gas was determined using two fixed photocells to trigger a high speed electronic counter. The gas pressure during a flow measurement was monitored with an open tube water manometer while gas temperature was measured from a calibrated thermocouple installed in the flow meter. Typically, flow measurements ( r ) made with this apparatus were repeatable with a percent relative standard deviation % RSD = 0.3. With proper care and design, it is reportedly possible to obtain similar results with the commonly used soap bubble flow meter (2). The volumes (V) of the EDF’s were determined by weighing the flasks filled sequentially with air and then with water. For a typical volume of 150 ml, this procedure gave % RSD = 0.05. Classification of EDF’s. Exponential dilution flasks may be divided into four general types: I) Simple flow-through or passive mixing devices consisting of vessels (generally spherical and possibly containing flow diverting baffles) in which calibrant and carrier blending depends almost entirely upon normal gaseous diffusion. 11) Turbulent eddy devices (often spherical, cylindrical, or bell-shaped enclosures) which rely upon the turbulence generated by rotating solid flat paddles or vanes to augment the normal diffusional processes. 111) Unshrouded fan devices which utilize multiple identically pitched fans on a common shaft running in a cylindrical enclosure to effect mixing through turbulence, diffusion, and possibly through some degree of recirculation. IV) NBS developed EDF which employs division-recirculation technology to achieve mixing. Procedure for the Evaluation of Type I and I1 EDF’s. The published procedures ( I , 3-7) for using EDF’s were used to test flasks of types I and 11. Two flasks of type I and seven flasks of type I1 were evaluated with an FID. Flask volumes ranged from 50 to 300 ml and carrier flows were adjusted to give CY in the 0.2 to 0.5 min-l range. Rotor speeds for type I1 EDF’s were typically in the range from 300-1800 rpm. The relatively simple test system is shown schematically in Figure 1. Briefly, pure carrier gas whose flow is carefully regulated by a flow controller ( P ) is purged through the EDF ( A ) and into the FID
I
b
,a
Figure 1. Experimental arrangement used for the evaluation of types I and I1 EDF’s
calibrations which were demonstrably accurate and repeatable to f 1%. The work progressed through several phases: 1) An examination of the basic principles underlying exponential dilution. 2) The evaluation of conventional EDF’s installed in a model, yet relevant, detection system. Specifically, the EDF technique was examined for its possible application to t h e calibration of flame ionization detectors (FID’s) used to measure automotive hydrocarbon emissions. 3) The development of an improved exponential dilution flask. 4) An evaluation of the improved EDF. 5 ) A comparison of the EDF detector calibration results with those obtained from certified standard reference gas mixtures. T h i s report provides a detailed discussion of the many factors which influence gas phase exponential dilution and is intended to encompass the current stage of development of the exponential dilution flask as a measurement tool.
EXPERIMENTAL FACILITIES AND PROCEDURES General. The EDF to be evaluated was coupled to a commercial gas chromatographic FID. Hydrogen was used as a fuel and “zero” air used to support combustion. Standard Reference Material (SRM) mixtures containing propane were available only with air as a matrix gas. Thus, to facilitate direct comparison between FID responses to the SRM mixtures and to the output of the EDF’s, the EDF’s were operated with “zero” air as a carrier gas. Maximum detector response was obtained with equal flows of carrier and Hz.
I
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I
I
-
Figure 2. Experimental arrangement used for the evaluation of a type Ill and IV EDF’s ANALYTICAL CHEMISTRY, VOL. 48, NO. 3, MARCH 1976
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Flgure 4. Photograph of the type IN EDF showing the internal components
Figure 3. Cross-sectional view of the type IV exponential dilution flask (to scale)
(F).Flow measurement is made by disconnecting the EDF exit tube at “ b ” and temporarily inserting the positive displacement flowmeter. After reconnecting (A) to (F), a measured amount of calibrant propane is introduced to the carrier stream by a gas syringe ( 0 )through the septum at “a”. The response of the FID to the calibrant is processed through an amplifier (K) and the resultant signal sent bath to a strip chart recorder ( N ) and to an electronic digitizer-integrator ( L ) resulting in a digital record and a corresponding punched tape from a teleprinter ( M ) . Least-square fits of log (signal) vs. time data were carried out on ca. 20 equally spaced points generally covering a concentration range from ca. 200 to 1ppm. The data from this procedure were used to assess the exponential behavior and slope reproducibility capacity of the various EDF’s.Because of the large number of data points involved, we present our results primarily in terms of the slopes and their uncertainties. Procedures for the Evaluation of a Type I11 EDF. An EDF of type 111was initially evaluated in the test system shown in Figure 1. An analysis of the preliminary In S vs. t data indicated improved straight line fits and better slope reproducibility when compared to those of types I and 11. Pressure and temperature monitoring facilities were added to the system to permit the determination of V , under operational conditions. The basic components, the flow controller ( P ) ,FID (F) and signal processing units K, L, and M shown in Figure 1were retained. With reference to Figure 2, the EDF (A’) was provided with a calibrated thermocouple (H’) and B water manometer ( J ) referred to atmospheric pressure. Calibrant gas (ea. 30 pl) was introduced with a gas syringe ( 0 )through a septum integral with the EDF. Carrier gas flow was regulated with the flow controller ( P )at 50 ml/min while the EDF was coupled to the FID (F) through a four-way, low-resistance PTFE valve (C).This four-way valve permitted convenient and rapid coupling of the EDF to either the FID or the positive displacement flowmeter (E). The SRM cylinders (Q)could be coupled to either the flowmeter or the FID. Eaperimentally, no alterations in EDF behavior were noted as a result of these modifications. The mixing fans were rotated at 1800 rpm so that both the fan-induced flow and carrier flow were codireetional as in the preliminary testing. It was discovered that the operational FID caused a backpressure in the EDF (typically CB. 0.01 atm when hoth carrier and H? flows were set at 50 mllmin) and thus affected the carrier flow through the EDF. To accurately measure the operational flow rate (I), it was necessary to simulate this condition during flow measurements by the adjustment of the needlevalve (0) above the piston in the flow meter. Both I and V , were subsequently calculated at STP (273 K, 1 atm) using the appropriate temperatures and pressures. Description of a Type IV (NBS) Exponential Dilution Flask. Design and performance data for EDF’s are notably sparse ( I , 5-9). There are no published critical design guidelines for EDF construction. Our evaluations of conventional EDF’s (vide infra) suggested that the basic requirement for true first-order behavior, continuous, perfect mixing, is not realized in a relatively simple mixing process. The type IV EDF (US.Patent 3,911,723) utilizes 614 * ANALYTICAL CHEMISTRY, VOL. 48, NO. 3, MARCH 1976
an improved mixing process wherein the bulk EDF contents are divided into parts, the parts combined, recycled, and redivided. Fluid dynamic and aerodynamic principles were applied to the design in an attempt to maximize mixing efficiency. As can he seen in Figures 3 and 4, the hasie EDF enclosure is spherical, with a volume of 150 ml. Since the sphere offers a uniform curved surface free of corners and obstructions, we hoped to minimize fluid stagnation near the flask walls. The principal gas mixing regions are designated 1-4 in Figure 3. In operation, the fan drive shaft 5 is driven by an air turbine and the sample and carrier gases are admitted through inlet tube 6. The incoming gas enters tangentially to the spiral flow pattern generated in the fluid between spinner memher 7 and its stationary shroud 8, as shown in Figure 3, to the region 1. Upon reaching the end of the shroud, the now pre-mixed inlet gas is divided into 16 separate streams by the 16 peripheral holes 9 and is discharged into region 2 where the first fan is located. In so doing, the streams must traverse the fluid being drawn into the fan and further blending is effected. Conical spinners 7 and 10 on the intake sides of fans 11 and 12, respectively, assist flow into the working region of the blades and reduce fluid stagnation near the fan hubs. Spacer 14 serves to displace fluid from both the fan hubs and shaft, thus minimizing fluid stagnation in these regions. The mixture is moved by the motion of fan 11 to the area at the far end of shroud 13 which has 16 peripheral holes therein and to face plate 15 which has 100 holes therein. At the same time, fluid mixture is being drawn past conical spinner 10 by fan blade 12 and is moved to face plate 16 and the far end of shroud 17. Thus the mixture, after it has moved past each of the fan blades, is suhdivided into 116 streams, 100 of which collide head-on at velocities of between 160 to 200 em/s in region 3 shown in Figure 3. The resulting blend is then forced, by pressure differential and the radial pumping induced hy the rotating shaft, to move outwardly towards the walls of,the sphere to region 4. In so doing, it must traverse a cross-fire of 32 streams emanating from the peripheral holes 18 and 19 of shrouds 13 and 17, respectively. The relative positions of 18 and 19 are arranged so that the streams do not collide but rather pass each other inducing vortex formation in the region of passing. Most of the fluid thus compounded is recycled while a small portion finds exit through one of the entrance ends of C-shaped tube 20 to the outlet 21. The probability of a short circuit developing between inlet and outlet is very low, since any gas entering the device must traverse all four mixing regimes before having access to the exit tubes. The effect of fluid stagnation near the walls and other stationary portions of the device are minimized by providing polished surfaces and gentle curves wherever possible. With this design, a high gas recirculation rate is desirable to foster efficient mixing. For our system, we found that a rotational rate of 5500 rpm afforded us a recirculation rate of the order of 20 times per second in a volume of 150 ml, good turbine stability with respect to speed, and a reasonable bearing life. Experiments at fan speeds of 7000 and 9000 rpm showed no particular improvement in the EDF performance, presumably due to the limitation in fluid recirculation rate imposed hy the natural resistance in the recirculation system. An insufficient number of experiments were conducted at rotor speeds below 5500 rpm to draw any definite conelusions concerning their effects upon EDF performance. Sample Introduction System. Among the requirements for a completely independent EDF calibration system is a reliahle cali-
brant introduction system. Gas tight syringes afforded poor reproducibility at the 20-50 p1 level, most probably due to losses from the needle between loading and injection. Our experience with the EDF-FID system and various types of introduction techniques indicated that a workable device must embody the following: 1) provision for accurate and precise measurement of p l quantities of calibrant and 2) a facility for rapid calibrant introduction without altering or interrupting the carrier flow. Figure 5 shows the design used with the NBS dilutor. Basically, it consists of a stainless steel plunger ( A , dia. = 0.952 cm) into which has been milled a rectangular slot (s). The plunger is arranged to move coaxially within a brass barrel ( B ) so that the slot (s) will correspond to either the calibrant purge ports (g) or the carrier purge ports ( d ) . The plunger ( A ) is sealed in the barrel with three “0” rings ( 0 ) .A closely fitted PTFE wiper ( W ) is used to retain the sample in the slot during its transit from g to d . The dimensions of this slot can be varied to alter the quantity of calibrant injected. It is important, however, that the slot height be approximately 0.5 of the center “0” ring diameter to eliminate calibrant seepage into the carrier stream during the injection stroke. Typical dimensions giving V = 20 pl are 0.0762 X 0.952 X 0.276 cm. The slot is readily calibrated with mercury to four significant figures with % RSD = 0.2. Annular spaces ( a ) permit uninterrupted carrier and calibrant flow for any plunger position. The unit is coupled directly to the EDF ( E ) through, short, low-volume passageways. At a carrier flow of 30 ml/min, it is estimated that a 2O-pl sample can be completely transferred into the operational EDF in about 0.3 s. This estimate is based upon the time required for the slot and passages beyond to be flushed three times with carrier. In operation, the slot is placed in correspondence with the calibrant ports (g) and flushed with pure propane at about 15 ml/min for 10-15 min. Waste propane is vented to atmosphere and calibrant temperature recorded from a thermocouple ( T ) .During this loading process, pure carrier is continuously purging the EDF. The calibrant flow is stopped and the plunger depressed fully, bringing the loaded slot into a “line of sight” flow configuration with the carrier, thus effecting injection. Procedure for the Evaluation of t h e Type IV (NBS) Exponential Dilution Flask. Experiments with this EDF ( A )were conducted with the apparatus depicted in Figure 2, initially with calibrant introduction by gas syringe rather than by sample injection system ( E ) to maintain comparability with tests made on the type I11 EDF. Generally the EDF was operated with a rotor speed of 5500 rpm and the carrier flow adjusted to give 01 = 0.20 min-’. Carrier flow rate measurements were made under simulated FID back-pressure conditions as in the case of the Type I11 EDF. Under these conditions, and with the introduction of ca. 20 pl of propane (affording a concentration range of about 120-0.02 ppm), an exponential calibration could be completed in about 45 min. A single standard reference propane-air mixture (SRM) introduced directly to the detector established a fixed point (So,c,) on the exponential curve. Three other SRM’s were treated as unknowns and using the sigF from ~ E D F= k/cu and the equation c nal levels (SI,~ E D calculated = c,(S/S,)~’”EDF their respective propane concentrations were computed (cf., Equation 2, Mathematical Relationships in EDFFID Systems). Each concentration was then compared with the respective known SRM value. The alternative procedure whereby the EDF is filled with a known high-level propane--air mixture and this subsequently diluted out exponentially, was found to have several disadvantages. This procedure requires twice the calibration time and uses a considerable quantity of SRM gas. In addition, the extended calibration time leads to greater uncertainties in the data resulting from instrumental variations such as base-line drift. Subsequent experiments were conducted using the sample injection system ( E ) and integrating the areas ( A ) under the exponential curves. Integrated areas under the exponential curves for experiments in which the injection system was employed were repeatable with a % RSD = 0.5. Signals ( S ) from several SRM’s were measured as before and their concentrations calculated from the EDF data using the equation below (cf., Equation 3, Mathematical Relationships in EDF-FID Systems). c = No/’Vg(SVg/Arn)’’nEDF All gas volumes and flow rates used in this computation are expressed at STP. In general, the most consistent and useful data were obtained
VENT
CARRIER
_C
W
Figure 5. Cross-sectional view of the injector system used with the type iV EDF
when EDF calibrations and SRM signal levels were recorded within a single working day. Procedure for FID Calibration with Standard Reference Material Mixtures. The schematic arrangement used for SRM calibration of the FID is shown in Figure 2. Used in this fashion, the FID is a “total hydrocarbon” detector. Calibrated gas mixtures from a cylinder ( Q ) were taken through a stainless steel-PTFE regulator (c), a needle valve ( d ) , capillary tube ( e ) , (1-m X 0.15mm i.d.) and into a 100-ml surge volume ( b ) . The flow could be directed by means of switching valve, C, either into the FID ( F ) or into the flow meter ( E ) . For comparison calibration experiments, the SRM flow was matched to within *0.5% to the EDF carrier flow. The effect of FID flow resistance upon the operational SRM flow was again simulated at the flow meter during SRM flow measurements. Four SRM’s (nominally 95,45, 9.5, and 3 ppm) were used. A signal level ( S ) for each was recorded over a period of 5-7 min after the response maximum had been reached. Five repetitive determinations were made for each SRM. Typically signal levels for a given SRM were found to be repeatable with oh RSD = 0.5. Values for detector linearity ( R S R M ) were obtained from the slope of leastsquares fits of log S vs. log CSRM (cf., Equation 1, Mathematical Relationships in EDF-FID Systems).
EDF THEORY Basic Concepts in Exponential Dilution. If one considers the instantaneous introduction of a fixed quantity of calibrant ( N o )into an E D F in which perfect mixing occurs, then the instantaneous rate ( - d N / d t ) a t which the sample elutes from the E D F is proportional to the amount of sample ( N ) in the flask a t t h a t instant. Thus, -dN/dt = a N where a = a constant characteristic for the EDF. T h e quantity of calibrant ( d N ) passing through the E D F a t carrier flow rate ( r ) in time d t is d N = rcdt. Since c = NIV,, then d N = (r/V,)N d t and a = r/V,. Upon integration, we obtain N = N,e-Ot or dividing through by V,, c = c,ecat. Since exponential dilution is a continuous, dynamic process, involving a steady influx of pure carrier gas and corresponding efflux of mixture, the blending of incoming carrier gas with the contents of the E D F must be continuously instantaneous, Le., there should be no time delay for mixing. In practice, to achieve mixing, gas must be moved from one part of the E D F t o another and this requires time. Any condition short of instantaneous mixing will be reflected in the observed decay curve. Other workers (3, 7) have noted departures from ideal behavior in their EDF’s after the sample concentration had dropped to some level below the initial level. They obtained further calibration by introducing an amount of sample which approximated the concentration a t which the departure occurred and repeated this process as required down t o the limits of detectability. T h e precise reasons for this behavior are not totally clear, but some insight may be gained by considering t h e superimposed fluidic processes which occur within an EDF. These are: 1) turbulence, a randomizing process generally ANALYTICAL CHEMISTRY, VOL. 48, NO. 3, MARCH 1976
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induced by rapidly rotating vanes or fans, 2) diffusion, a randomizing process which can require minutes to develop, and 3) carrier gas flow, which a t the rates commonly used in E D F experiments (20-60 ml/min), contributes little to the randomization processes directly, but does determine the exposure time of the sample t o processes 1 and 2. In the initial stages of a dilution experiment, most of the mixing is achieved by the turbulent flow patterns rapidly developed by mechanical agitation. These are undoubtedly supplemented by the diffusion patterns which develop some minutes later. If there are regions within the EDF, such as near or on the container walls or any corners or pockets which are not effectively swept by the turbulent eddies, then movement of gas into or out of these can be relatively slow, diffusion controlled processes. Such regions can act as “sinks” for small quantities of sample or alternatively act as “sources” of relatively pure diluent gas. In the initial stages of dilution experiment, these effects, the temporary loss of some sample or the addition of relatively pure diluent gas t o the “effective mixing region”, can be insignificant compared to the concentration of sample eluting a t t h a t time. As time progresses, the concentration of sample in “effective mixing region” becomes lower. When the flux of sample or diluent gas into or out of these “sink and source” regions significantly alters the sample concentration of the effluent mixture, departure from ideal behavior is observed. If the flow of gas through the E D F is very rapid, the sample residence time is reduced, thus decreasing the probability for good mixing. This effect can conceivably be counteracted by operation a t lower flow rates, although this route prolongs the calibration experiment and places rigid demands upon the stability of the detector and its associated components. If the EDF design is such t h a t a path, poorly swept by turbulent or diffusive eddies, can develop between the gas entrance and exit, then this path (the fluidic analog of an electrical “short circuit”) provides a route by which some of the incoming gas can escape proper blending. T h e effect is, of course, departure from ideal behavior. Cholette and Cloutier (IO)have performed a detailed mathematical and graphic treatment of these fluidic phenomena for the case of continuous flow systems involving liquids. We have noted similarities between the calculated curves reported in the above work and those which we obtained from various types I and I1 EDF’s. These similarities suggest t h a t comparable phenomena may occur in continuous flow gas phase systems. Adsorption and desorption of sample from exposed E D F surfaces can also contribute t o non-ideal behavior ( I , 3 ) . For propane, the sample material used in this work, these effects are considered minimal ( I ) .
Mathematical Relationships in EDF-FID Systems. In order to fully assess exponential dilution as a detector calibration technique, it is necessary to consider not only the E D F itself but also the characteristics of the detector under calibration. For the specific case of the flame ionization detector (FID), several workers ( I I , I 2 ) have suggested the following equation relating detector response (S)and sample concentration ( c ) .
s = IC“ where I is a constant and n is a measure of,detector linearity. When n = 1, the detector is truly linear. If this relationship is combined with the simple first-order decay equation, c = c,e-at then,
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In S = (In I
+
+ n In c),
- net
where (In I n In c,) is a constant and a = r/Vg.This expression is of the form y = a br, indicating t h a t a plot of In S vs. t should yield a straight line with a negative slope k = na. Thus, we have the rather interesting result t h a t if an ideal EDF is used t o calibrate a nonlinear FID, a plot of In S vs. t will still be linear but its slope k will now be ncr. Moreover, if r, V,, and k can be determined with sufficient accuracy, then an estimate of detector linearity ( n ) can be obtained as a result of the EDF calibration experiment since n = k V g / r . Most FID’s are not truly linear. McNair and Bonelli ( 1 1 ) have found n to vary from 0.95 t o 0.99, while the manufacturer’s specification for the FID used in this work gives n in the range of from 0.99 t o 1.01. T h e signal to concentration proportionality constant I is related to system parameters as follows. If one considers an ideal EDF, c = c,e-Ot, then the detector will give a curve which is described by a similar expression, S = SAe-kt. Upon combining these two equations we obtain,
+
s = (So/C,n)Cn
(2)
I t can be seen from Equation 2 t h a t I = S,/con. Although c , can be readily calculated from the quantity of calibrant ( N o )introduced and V,, this concentration is never achieved in practice since no technique has yet been developed for the instantaneous introduction of and the simultaneous blending of calibrant with the total quantity of carrier in the EDF. Consequently, the corresponding signal S o is not observed. This problem can be circumvented in two ways: 1) T h e EDF can be purged with a preanalyzed mixture of calibrant and carrier whereby c , is then defined and S o is measured. The mixture is diluted out of the E D F with pure carrier and the detector calibrated for all concentrations below c,. 2) A fixed quantity of calibrant is introduced into the operational E D F and the decay curve recorded. A single point on the decay curve is determined by purging the detector directly with a preanalyzed calibrantcarrier mixture such as a Standard Reference Material (SRM) under identical operating conditions. Since the FID response is proportional t o mass flow, the E D F carrier flow and S R M flow must be carefully matched. With So and c , thus determined, other c values along the decay curve may be calculated. While the above method of determining I requires a preanalyzed gas mixture, the following alternative procedure is totally independent of this requirement. Let N o = pmol calibrant introduced a t time t. N = pmol calibrant in E D F a t any time t after to. As we have shown previously, for an ideal EDF, N =
N,e-at. T h e FID response is given by S = I N n = I N o e - a n t , T h e area under the exponential curve is given by A = J”; S d t and A = I N , e-antdt. Upon integration and rearrangement, we obtain I = AcYn/Non.Thus S = ( A a n / N O n ) N n . Since N = cV, and cr = r/V,, then
1;
c = N,/V,(SV,/Arn)l/n
(3)
T h e integrated area under the decay curve and an accurate means to measure N o are required for this method.
RESULTS Evaluation of Types I and I1 EDF’s. T h e data from type I and I1 EDF’s were generally evaluated over a con-
Table I. Error Propagation Analysis for a Type I1 EDFa t, min
c, Ppm
0 7 15 30 45
300 40.6 4.14 0.057 0.00079
%RSD,
... 3:5 7.4 14.8 22.2
a k = 0 . 2 8 9 min-’, u k = 0.005, a r ( m i n ) = 0.0016, n = 1.012. T h e percentage variation (7cRSDc) anticipated in t h e calculation of c for these data is given b y : % R S D c = 1 0 0 / n ( t z u ~ 2 ) y 2 .
centration range of ca. 200 t o 1 ppm. An examination of the least-squares fits of the In S vs. t data indicated t h a t the points were better represented by a simple curve rather than by a straight line. T h e possibility t h a t cumulative errors in the data were responsible for the observed curvature was ruled out after the application of a cumulative error test procedure described by Mandel ( 1 3 ) . Thus, we concluded t h a t these data could not be adequately described by a simple first-order exponential decay equation. If this discrepancy is ignored (as is evidently the case in t h e published work on EDF’s), we found t h a t the slope values ( k ) obtained from the least-squares fits of runs made over several-day periods exhibited a relative standard deviation of a t best 2%. In most of the published works in this field a’ = r/V ( V = E D F volume) is used in lieu of k to calculate concentrations. However, k is a more realistic indicator of actual system behavior since i t is a function of carrier flow through the E D F , detector linearity, and amount of gas involved in t h e mixing process, For t h e ideal system, k = ( r /
V,)n. T h e effect of variations in k upon calculated concentrations can be estimated from a n error propagation analysis on the equation c = c , e - ( k / n ) t (14). An example of this error propagation, using data from a typical type I1 E D F is given in Table I, which shows how a relatively small uncertainty in k rapidly propagates large uncertainties in concentrations. On these bases, EDF’s of types I and I1 were judged inadequate for the ‘calibration of flame ionization detectors with a degree of uncertainty acceptable in air pollution work. Evaluation of a Type I11 EDF. T h e evaluation of type I11 E D F was conducted over a calibrant concentration range of from 120-1 ppm a t a rotor speed (1800 rpm) and carrier flow rate t o give a = 0.20 min-l. T h e results were as follows: 1) Least-squares fitting of In S vs. t data showed t h a t these data are adequately represented by a straight line. 2) T h e slopes of these lines ( k ) obtained from repetitive experiments were reproducible with a %RSD = 0.5. 3) T h e k values were, on the average, about 13% higher than those predicted from r/V,. When a was reduced t o 0.12 min-’, then the k values were only 3% higher than a. T h e mathematical treatment of t h e EDF-FID system described previously suggested t h a t the discrepancies in 3) could result from a radical change in detector linearity with change in carrier flow rate. Independent determinations of the FID linearity utilizing SRM’s a t 95, 45, 9.5, and 3 pprn propane-in-air conducted a t the flow rates used in this E D F evaluation showed t h a t n did not vary by more than f0.7% from mean value of 1.006. Moreover, a careful evaluation of the uncertainties in flow, pressure, volume, and temperature measurements used in these studies showed t h a t combined, they were insufficient t o account for the disparity between k and a . T h e most probable explanation involves the supposition that, a t a given high flow rate, only
Table 11. Comparison of FID Calibrations by SRM and by EDF, Initial Results CSRM, p p m C,H, in air v/v
CEDF
‘CED F
93.9 46.3 9.51 2.96
89.8 43.8 9.41 2.86
0.1 0.3 0.04 0.02
part of the gas within the E D F is actively involved in the mixing, whereas a t lower flow rates, sufficient time is available for more of the gas to become involved bringing k closer t o a. In effect, one can visualize an “effective mixing volume’’, V , < V , within the E D F wherein active blending occurs. T h e expanse of this region is flow rate dependent. At a given high flow rate, the magnitude of V , is reflected in k . As V , approaches V,, k is observed t o approach a to the extent allowed by the detector linearity ( n ) .Bartok and coworkers ( 1 5 ) have reported a similar partitioning of blending regions in a jet-stirred reactor designed for gas phase reactions. However, because of the flow geometry, V , for t h e Bartok reactor was found to be independent of flow rate. It is of interest t o note t h a t neither the exponentiality nor the reproducibility [as indicated in 1) and 2) above] of the results obtained from the type I11 E D F are adversely affected. Thus, the type I11 E D F cannot be effectively used to assess the detector linearity except possibly a t very low flow rates. Operation a t very low flow rates both prolongs the calibration experiment and requires concomitant detector and amplifier stability for satisfactory calibration. Since an assessment of detector linearity is an integral part of detector calibration, the type I11 E D F was judged inadequate for the rapid calibration of flame ionization detectors used for air pollution work. Evaluation of the Type IV (NBS) EDF. Evaluation of t h e type IV E D F was conducted over a calibrant concentration range of approximately 120 to 1 ppm with a rotor speed of 5500 rpm and carrier flow adjusted t o give a = 0.20 min-’. T h e results were as follows: 1) T h e least-squares fit of In S vs. t data indicated t h a t the points were adequately represented by a straight line. 2) T h e slope of these lines ( k ) obtained from repetitive experiments were reproducible with %RSD = 0.5. 3) T h e k values were on the average 1 t o 2% higher than a , Le., in the region predicted by the value of n obtained from S R M calibrations for this detector. Values for n obtained from the exponential curves were repeatable with %RSD = 0.5. These results indicated t h a t the new design was operating closer to ideal performance than any of its predecessors. I t is believed t h a t the positive division and recirculation features incorporated into the type IV design greatly increases sample randomization. T h e high performance of the type IV dilution flask suggests t h a t it also be used as a dynamic blending device for two or more gas streams. Moreover, initial calculation of t h e sample residence time spectrum according t o the method of Weber (16, 17) indicated t h a t this E D F has some potential as a continuous-flow reactor for gas phase reactions. Comparative FID calibrations were conducted utilizing four propane-air SRM’s and the NBS E D F operating with air as a carrier gas and measured amounts of pure propane calibrant. T h e results are given in Table 11. From Table 11, it will be noted t h a t all of the c values obtained from the E D F are consistently low compared to the certified SRM values. Investigations into probable causes for this, disclosed t h a t the carrier air contained about 6% ANALYTICAL CHEMISTRY, VOL. 48, NO. 3, MARCH 1976
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Table 111. Comparison of FID Calibrations by SRM and EDFa CSRY
CEDF
93.9 46.3 9.51 2.96
90.4 45.4 9.48 3.01
Table IV. Comparison of FID Calibrations by SRM and EDFa OCEDF
0.8 0.3 0.11 0.05
a S R h l diluent air a n d E D F carrier gas of comparable 0, c o n t e n t ,
more oxygen than the S R M diluent air. Carrier air of comparable 0 2 content was obtained and the calibrations were repeated. T h e results are shown in Table 111. T h e data in Table I11 show t h a t the agreement between the certified S R M values and the EDF values is now improved except a t the high level where a bias still persists. T h e contents of the SRM cylinders were reanalyzed using gas chromatographic methods, and by comparison to standard gravimetric CsHs-air mixtures, shown to be essentially unchanged. During the reanalysis it was also demonstrated t h a t the use of the S R M delivery system (gas regulator, needle valve, and capillary tubing, shown in Figure 2) did not affect the delivered propane concentrations. T h e results of calibrations using the alternative method based upon an exponential curve and a single S R M calibration point on t h a t curve are given in Table IV. A bias a t the high propane concentration is again indicated. If the EDF were a significant contributor to this bias, one might logically expect the effect to be reflected in all CEDF values. The results more directly suggest a possible alteration in FID linearity a t relatively high propane concentrations. If this were the case, then one could expect the change in linearity to manifest itself in the slopes ( k ’ s ) of the exponentiar curves in the 50-120 pprn region. However, a detailed examination of the slopes of the decay curves showed the k values to be identical (within t h e standard deviation) in the 100, 50, 10, and 3 ppm regions. We suspect t h a t the difficulty may be related to differences in FID behavior whether subjected t o a constant high propane level as in the S R M determinations or t o transient propane levels as in the E D F experiments. Thus, the source of this bias becomes a problem for further investigation. Detector Linearity. The linearity ( n ) of the FID used in this work was determined from both the E D F experiments and from S R M data. For ~ S R M this , involved leastsquares fitting of six sets of data, each containing four points while ~ E D Fwas obtained directly from the k and cy values as described previously. T h e mean values and their standard deviations (u,for a single measurement) are given below: ~ E D F = 1.020, UEDF = 0.005,34 measurements (VEDF) ~ S R M= 1.006, USRM = 0.013,6 measurements (VSRM) Student’s t-test (18) was employed to determine whether or not the mean values above are significantly different. For the present case
t=
nEDF
& :(;;
- nSRM I ~ R M ) ~ / z VSRM
T h e above data gave t = 2.60, indicating t h a t ~ E D Fand ~ S R M are significantly different. I t can be shown t h a t when t I 1.96, the mean values are significantly different (95% probability), whereas when t 5 1.96, the mean values are not significantly different. T h e data associated with the 94 ppm S R M were eliminated from each of the six sets of data and the remaining three S R M points in each set were refitted by the leastsquares method. T h e FID linearity (&& obtained from 618
ANALYTICAL CHEMISTRY, VOL. 48, NO. 3, MARCH 1976
cSRM
CEDF
93.9 46.3 9.51 2.96
92.0
‘CEDF
0.7
Calihra tion m i x t u r e
9.62 2.97
0.05 0.05
a 4 6 p p m SRM used t o establish a reference point on t h e e x p o n e n tial curve.
this procedure was 1.012 with USRM = 0.016. T h e nEDF and ~ ; R Mvalues were subject to the “t” test with the result t h a t t = 1.21, which indicates t h a t the values for ~ E D and F ~SRM are not significantly different. The statistical testing suggests the presence of a systematic error in ~ S R M This . error arises from the signal ( S ) obtained from the 94 ppm S R M under our experimental conditions. Since the propane concentration of the 94 ppm S R M has been duly verified, we believe the error to originate in the FID. T h e presence of a systematic error has been previously noted in the calculation of CEDF for the 94 ppm SRM.
CONCLUSIONS A basic and critical approach was used t o study the exponential dilution process. T h e elementary requirements for a true first-order exponential decay process, continuous and perfect mixing, are inescapable. In practice, the behavior of an EDF is determined by how closely this requirement is approximated. Our work with types I and I1 EDF’s has indicated how significant errors in concentration measurement can result from using first-order treatment on essentially non-first-order data. Whereas, the data obtained from the type I11 E D F could be adequately described with a first-order exponential equation, the dependence of the “effective mixing volume” (V,) upon carrier flow presented a serious obstacle in complete detector calibration, Le., detector linearity could not be readily assessed. Braun and co-workers (6) have pointed out that linear behavior of In S vs. t data of itself does not demonstrate detector linearity ( n ) unless k and cy are in agreement. We have developed the mathematical dependence of n upon a and k for the case of the FID and verified this relationship experimentally. In so doing, we have shown how an EDF may be utilized t o calibrate a nonlinear detector. Our investigation has clearly demonstrated t h a t EDF design features have a significant effect upon EDF performance and t h a t the EDF-detector combination must be treated as an interactive system. For meaningful results, the effect of carrier gas flow rate upon calibrant residence time and mixing efficiency, the possibility of blending region partitioning, as well as the effect of the operational detector upon the carrier flow must be considered. Flame ionization detector calibrations performed with the type IV EDF have been shown to be repeatable t o f l % . I t has been further shown t h a t the FID can be calibrated in the 50- to 3-ppm region with acceptable accuracy without reference to any precalibrated gas mixture by charging the E D F with a minute quantity of pure calibrant gas. Although the potential of the EDF as a calibration device has been demonstrated, an extension of the verifiable calibration range would be highly desirable. Further work with the FID and with other detectors will assist towards the achievement of this goal.
ACKNOWLEDGMENT The authors express their gratitude for encouragement and many helpful discussions to T. D. Coyle, W. D. Dorko,
E. E. Hughes, John Mandel, J. R. McNesby, R. C.Paule, a n d W. Spangenberg. Special thanks are extended t o W. D. Dorko, Analytical Chemistry Division, NBS, for his invaluable assistance in providing propane and oxygen analyses and various gas mixtures.
LITERATURE CITED (1) J. E. Lovelock, "Gas chromatography", R. P. W. Scott, Ed., Butterworths, Inc., Washington, D.C.. 1960, p 26. (2) A. Levy, J. Sci. hstrum., 41, 449 (1964). (3) Richard Dick and C. Harold Hartrnan, Varlan Aerograph Tech Bull. 133-67 11966). (4) J. E. Lovelock,'Anal. Chem., 33, 162 (1961). (5) J. Krugers, Instrumentation in Gas Chromatography", J. Krugers. Ed., Centrex Publ. Co., Eindhoven, The Netherlands, 1968, p 24. (6) W. Braun, N. C. Peterson, A. M. Bass, and M. J. Kurylo, J. Chromatogr., 55, 237 (1971). (7) H. P. Williams and J. D. Winefordner. J. Gas Chromatogr.. 4, 271 (1966).
(8) G. Greco, Jr., F. Gioia, and F. Aifani, Chlm. lnd. ( M a n ) , 53, 1133 (1971). (9) Arthur Fontijon, Albert0 Sabadell. and Richard J. Ronco. Anal. Chem., 42, 575 (1970). (10) A. Cholette and L. Cloutier, Can. J. Chem. Eng., 37, 105 (1959). (11) H. M. McNair and E. J. Bonelli, "Basic Gas chromatography", 5th ed., Varian Aerograph, inc.. Palo Alto, California, 1969, p 88. (12) "Gas Chromatography", A. B. Littlewood, Ed.. Adlard and Son, Bartholemew Press, Dorking, Surrey, England, 1966, p 431. (13) J. Mandel, "The Statistical Analysis of Experimental Data", lnterscience Publishers, New York, 1964, p 295. (14) Ref. 13, p 72. (15) W. Bartok, C. E. Heath, and M. A. Weiss, AlChE J., 6, 685 (1960). (16) A. P.Weber, Chem. Eng. Progr., 44, 26(1953). (17) A. P. Weber, Chem. Eng., 76,79 (1969). (18) . . J. Mandel. Ref. 13. o 118.
RECEIVEDfor review August 8, 1975. Accepted December 8, 1975. This work was f u i d e d in part by the Office of Air and Water Measurement a t NBS.
Development and Characterization of a Computer-Controlled Vidicon Spectrometer T. A.
Nieman' and C. G. Enke"
Department of Chemistry, Michigan State University, East Lansing, Mich. 48824
A computer-controlled spectrometer using a silicon vidicon multichannel detector has been developed to examine the operating characteristics of imaging devices as spectrometric detectors. Under computer control, the number of electronic channels in the wavelength window can be set between 32 and 4096. The readout beam can be deflected to any channel at random, made to scan them sequentially, or inhibited to Increase the target's integration time and enhance weak signals. The system has a single scan SIN of 220 which has been extended to I O 4 with signal averaging. SIN increases linearly with target integration time up to at least a 20-fold enhancement. The detector responds linearly to the Incident light level over at least 3% orders of magnitude with nonlinear response above 60% of target saturation. With a wavelength window of 230 nm, resolution is about 4 nm with wavelength linearity better than 0.3%. Scan limes as fast as 2 ms per frame were used.
T h e use of multichannel spectrometric detectors employing imaging devices has become widespread. Detectors employing tubes like the silicon vidicon or photodiode arrays have been used for atomic absorption (1-3), atomic emission (4-9), molecular absorption (10, I I ) , and rapidscan monitoring of reaction kinetics (9, 12, 13) and dc arc processes (14).Recently, a pair of articles (15, 16) has surveyed t h e various types of imaging device detectors applicable t o spectrometric use. Much of the work by analytical chemists with imaging devices has been with commercial instruments (2-6), although some work has been reported with instruments interfaced to a minicomputer for data acquisition and analysis ( 1 , 7-14). Despite the growing use of imaging device detectors, i t is still difficult for the analytical chemist t o gain a clear appreciation of their strengths and weaknesses relative t o current detectors. Present address, School of Chemical Sciences, University of 11linois, Urbana, Ill. 61801.
We wished t o gain experience with the use of imaging devices in chemical measurements and t o examine the performance characteristics of imaging device detectors. T o accomplish this, we have developed a computer-controlled multichannel spectrometer which uses a silicon vidicon tube as t h e detector. Besides using t h e computer for data storage and analysis, we have placed the deflection of the readout electron beam under computer control. T h e computer can position the beam a t any wavelength a t random, or cause the beam t o scan a wavelength region a t any of several possible wavelength axis resolutions. In addition, t h e computer can enable or disable the reading beam t o control the target integration time. This instrument has been used extensively in our laboratory both for conventional spectrometric detection in the visible region and for investigations of reaction kinetics (17).Having the instrument under computer control allows t h e user t o easily alter the operating parameters t o optimize a particular measurement. This computer control also proved invaluable to studies of the instrument performance characteristics since the computer could cause the instrument t o cycle through its combinations of operating parameters with a flexibility not available to hard-wired instruments. In this paper, we wish t o report on the design of the instrument and on experiments performed to extend the understanding of how the operating characteristics of imaging devices affect their performance as spectrometric detectors. Future papers will report on chemical applications.
EXPERIMENTAL A block diagram of the instrument can be seen in Figure 1. The basic units are 1) the power supply, 2) the vidicon tube, deflection assembly, and supporting circuits, 3) the instrument interface, 4) the computer and computer-interface buffer, and 4) the optical path and the dispersion system. Computer System. The computer around which this system was developed was a Digital Equipment Corporation PDP 8/I minicomputer with 12K words of memory. Standard peripherals ANALYTICAL CHEMISTRY, VOL. 48, NO. 3, MARCH 1976
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