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Chapter 6 Wide-Range Calibration Of Electron-Capture Detectors
119
Chapter 6
Wide-range calibration of electroncapture detectors R.E. KAISER and R.I. RIEDER
CONTENTS 6.1. Fundamentals of calibration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1.1. The two fundamental quantitation equations . . . . . . . . . . . . . . . . . . . . . . 6.2. Calibration by conventional laboratory techniques. . . . . . . . . . . . . . . . . . . . . . . . 6.3. Calibration by exponential dilution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4. Direct mode use of the exponential dilution technique with the “quantegg” . . . . . . . . . 6.5. Wide-range calibration by the “quantegg” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.6 Limitations of the “quantegg” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.7. Evaluation of data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.7.1. Data evaluation by manual measurements from a recorder display . . . . . . . . . . . 6.7.2. Data evaluation with a laboratory computer. . . . . . . . . . . . . . . . . . . . . . . . Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1 19 120 122 124 126 129 130 132 132 135 135
6.1. FUNDAMENTALS OF CALIBRATION There have been many detailed discussions of the quantitative use of electron-capture detector (ECD) data in gas chromatography and lengthy descriptions of how to use different ECDs in different modes, with different gases, in many analytical applications can be found in the literature. This paper offers an alternative procedure for optimizing and using ECDs for quantitative gas chromatographic (GC) analysis: the “black box” principle and absolute quantitation. For this purpose it is of no importance which type of detector is used in quantitative gas chromatography: any detector can be understood and treated as a black box for the production of correct, precisely repeatable quantitative analytical data. Therefore, we thought it might be acceptable to describe the quantitative detector behaviour in a way that is valid for a given instrument under constant (although optimized) analytical conditions of temperature, carrier gas composition (including trace contaminants), inlet pressure, outlet pressure, detector cell voltage, and amplifier, integrator and recorder conditions, without including a discussion of the theory of ECDs, as this is available elsewhere in this book. The principles discussed here are valid for any ECD, under any special conditions of practical use, if the fundamental requirement for quantitative GC analysis holds true, namely that the conditions remain constant throughout the whole working period between calibration and quantitative application.
WIDE-RANGE CALIBRATION OF ECDS
120
6.1.1. The two fundamental quantitation equations The quantitative GC signal can be given as the integral of
(A) voltage (volts) times flow (millilitres/second)
+
-
V ml/s
or
(B) current (amps) times time (seconds) + A-s Although any GC detector response i s based on moles of substance, it is more practical to relate the response to mass given in grams. Calibration allows conversion of all quantitative data to the basis of grams, volts, amps, millilitres and seconds. Therefore, we can write the two fundamental quantitation equations, first for a detector, which is “substance flow dependent”: as
(A) grams of substance X = 4
(6.1)
where q is the “quantity” or the response in amps times seconds, which the detector “produces” per gram of substance X,also known as the “gram-based substance-specific response”, and secondly for any detector which is “concentration dependent”:
v-ml (B) grams of substance X = 4
(6.2)
where q is the “quantity” or the response in volts per “concentration unit” given in grams per millilitre. These two q factors are different for A and B, but both describe quantitatively the function of the detector. Concentration-sensitive detectorslproduce a signal in volts from the unit concentration, grams/ml. Mass flow-sensitive detectors produce a signal in amps from the unit mass flow, grams/second. Different ECDs, under certain conditions of carrier gas, flow, pressure, temperature, voltage, etc., show neither pure mass flow- nor pure concentrationdependent behaviour, which fortunately is not a problem in quantitative analysis if all conditions remain constant between the time of calibration and the time of analytical application. This lack of problems depends, however, on the technique of calibration. The two fundamental quantitation equations both give a result in grams of substance X,i.e., both describe the GC peak area of substance X in terms of grams of the substance. Both equations are, at first sight, linear, provided that we consider the mass response factor q as a substance-specific constant. In fact, q is by no means a constant and is influenced by many physical and chemical factors, which make quantitation with ECDs difficult. This remark is immediately understandable if one considers the fundamental equations just as the substance-specific calibration line, giving the analytical signal function (see Fig. 6.1). q in Fig. 6.1 is the slope of the analytical signal function and its dependence on the specific nature of the substance and on the amount of substance can be seen; q is constant.
FUNDAMENTALS OF CALIBRATION
121
Signal (A)
Fig. 6.1. Substancespecific, analytical signal function. q,,2 = specific response.
It can be easily understood why the two fundamental quantitation equations A and B are interchangeable or can be used simultaneously: the quantitative GC signal can be expressed as peak area. This area can be approximated to peak height times peak width at half-height. One can measure the peak height in amps and the peak width in seconds, the peak area then being amps times seconds. Alternatively, one also can measure peak height in volts and peak width in millilitres (carrier gas passed during the peak width times period). Whether the signal is measured in amps times seconds (coulombs) or in volts times millilitre it is practically the same. Both measurements are correlated with the mass of the substance in grams. Although we have discussed quantitation as a “black box” model so far, it would be of some help to the practitioner, using more than one detector, to be able to compare the popular ECD with the equally popular flame ionization detector (FID). By giving the quantitative content of Fig. 6.1 in a different form, viz., the change of signal function slope with amount of substance in grams, we can better understand the quantitative differences between an FID and an ECD: Fig. 6.2 shows the result one most often finds in practice: the FID has a wider more-or-lesslinear range, but both detectors need precise calibration as both are never linear enough for accurate quantitative analysis. Although it is often stated that FIDs are linear over a range of seven orders of magnitude and (linearized) ECDs are considered to be linear over four orders of magnitude, one
1
G r a m s substance (CH2CHCI)
Fig. 6.2. Linearity (or deviation from linearity) can be expressed as the change of q with absolute amount, concentration or flow of analytical substance in the carrier gas, passing through the detector.
122
WIDE-RANGE CALIBRATION OF ECDS
has to compare this “linearity” with the analytical quantitative needs: do we want to. accept accuracy as less important than repeatability? If not, then the accuracy has to be as correct as repeatability within the statistically possible limitations, and therefore “linearity” becomes fundamental to our discussion. Linearity is what Fig. 6.2 shows: the change in q over the range of the mass of substance in grams. Many practitioners do not think in such terms and therefore do not measure q data. The quantitative measurement of correct 4 data is, in fact, the fundamental of calibration.
6.2. CALIBRATION BY CONVENTIONAL LABORATORY TECHNIQUES
A simple calibration technique consists of a few steps and their combination: (a) Take substance X(substance to be determined) and a standard substance R. (b) Make a quantitative mixture of both by means of volumetric or mass measurements. Preferably weigh W grams of X (= W x grams) to W grams R (= WR grams). (c) Make a homogeneous mixture of X and R in a suitable solvent, so that in each microlitre the mass ratio of X to R is constant and exactly equal to W X / W R . (d) Separate the substances X and R chromatographically and measure the integrals. Let us call the peak area of substance X A X and that of substance R A R . (e) Compare the mass ratio with the chromatographic peak-area ratio : Is (6.3) Possibly not. We now introduce correction factor, f, to correct the simple calibration equation 6.3. In any case it holds true that
-wx _ - - AX’f WR
AR
and therefore the correction factor is
which too often is considered to be a constant. However, f is never constant, if we consider constancy and linearity as strict quantitative expressions like chromatographic repeatability. The relationship peak area A x to the amount of substance X was defined as
CONVENTIONAL LABORATORY TECHNIQUES
123
Therefore qR =
WR ~
AR
and hence
~ f (for x substance X relative to R )
= qX/qR
Thus the simple laboratory calibration correction factor turns out to be the ratio of the two fundamental response data, q , for the two compounds used, X and R . As this is too simplified for more detailed discussion, we can add important comments. The simple correction factor, f, can never be a constant over a practically useful quantitative range if one of the response factors, q , of whichfconsists, changes. As there is no detector that is truly linear over the practical ranges in which we want to work quantitatively - considering linearity strictly as quantitative repeatability - the correction factor f is not constant: it depends on the absolute values of the amounts of X and standard substance in grams entering the detector. In practice we usually overload detectors, but many practitioners simply do not believe this statement, so a quantitative example will be given. Let us use the nearly “unlimited linear FID” for this example. FIDs are called linear over a range of at least 1 to lo6.Their quantitative working range starts at lo-’* g/s giving a measurable signal of about i = A. Linearity of six orders of magnitude means that the detector will also work at a level of g/s. If one uses a packed column, one normally injects between about 1 and 0.1 1.11 of sample, which is about 1-0.1 mg. Normally a rapidly eluted peak is about 1 s wide at half-height. This means that about lo-’ g enter the detector, which is about one order of magnitude above the linear range of the wide-range FID. Let us consider these conditions with an ECD. As its linear range is at least two orders of magnitude less than that of an FID and starts at a two-order smaller range level than that of an FID, one will have overloading with a even four orders of magnitude smaller sample injection. Who really takes care that not more than about 1 ng of substance enters the ECD? Only users of capillaries (sometimes) take care in this respect. We can repeat, therefore: with the practical range of modern chromatographic quantitation we normally tend to overload our detectors and therefore the correction factor f has to be considered to be non-constant. On the other hand, for trace amounts of substances, we are confronted with the problem of losses due to chemical sorption. This makes understandable Fig. 6 . 3 , which shows the dependence of the correction factor on the absolute amount of sampled compoundX. A classical rule states that one should choose internal standard compounds so as to be chromatographically as closely related to the substance under analysis as possible. The best would be for them to have identical polarities. Of course, the optimal solution would be to use the substance X itself as the standard. In practice, one tries to have X and R just sufficiently separated from each other, so the peak of X may be partly overlapped by the peak of R . In this case, undesirable sideeffects may occur in the detector. A s f i s composed of two responses, namely qR and q , we can understand the dependence of the
124 c
WIDE-RANGE CALIBRATION OF ECDS
2.00-
L
0 c U r
c
0 ';I 100-
tl
0 V
r'a"
r'a"
:do
Substance flow or concentration ( 9 1 s )
Fig. 6.3. Dependence of the correction factor f on the absolute amount, concentration or flow of analytical substance in the carrier gas, passing through the detector.
simple correction factor of the substancespecific trace behaviour of different compounds as well as of side-effects which can greatly influence the response. Hence a situation arises that is no longer as simple as the process of simple laboratory calibration appears t o be. It is not only the relative composition of the calibration mixture, but also the absolute amount of the calibration mixture that is important. We now have non-linearity plus sideeffects. Non-linearity as such leads to problems in quantitative analysis as all quantitation equations - both absolute and relative functions, and internal and external standard techniques - depend on a linear correlation between the signal and the concentration or amount of substance. There is no doubt about the only way to handle non-linearity: measure repeatability correction factors or response data with many different absolute amounts of substance. Do we have enough time in routine analysis, where quantitatively correct data are important, to follow such time-consuming advice? We do not. Calibration by conventional laboratory techniques cannot handle effectively enough the problems of non-linearity. ECD analysis means non-linear analysis, and here calibration by exponential dilution is of help.
6.3. CALIBRATION BY EXPONENTIAL DILUTION If one dilutes a full pot of coffee (or any other substance in solution) with a constant flow of water (or any other diluent) and continues carefully to homogenize the dilution
(e.g., by stirring), the coffee will be diluted to half its concentration in a constant time. This holds true if the diluted coffee leaves the pot at the same flow-rate as that of the water being added. Let the starting concentration be Co (g/ml), the volume of the pot be V (ml), and the flowrate of diluent be F (ml/s), then the concentration C a t each time t (s) is given by the fundamental equation of exponential dilution: C
=
Co.exp(-Ft/V)
(6.4)
We built a glass bulb with a volume of about 10 ml and connected to it two capillaries of very narrow bore (less than 0.2 mm I.D.). With a flow-rate of about 10 mllmin of
CALIBRATION BY EXPONENTIAL DILUTION
125
Outlet; t o detector
0
Fig. 6.4. “Quantegg”, a glass bulb of several millilitres volume with platinum-iridium tubings (0.1 to 0.15 mm I.D.).
carrier gas through the glass bulb, as shown in Fig. 6.4), the stirring energy pumped into the bulb volume was sufficient to give good constant homogenization of the exponential dilution vessel in the bulb volume. In addition, the inlet capillary introduced tangential stirring. The outlet capillary was precisely centred in the middle of the bulb volume. Capillary i was connected with the (second) chromatograph injection port and capillary o was connected to the detector. We injected the calibration substance X (pure X diluted in an inert solvent) (preferably no solvent is used, but in practice carrier gas is used). Immediately after injection we obtained a maximum signal from the detector. The change in signal with time approximately followed the exponential dilution curve, but the discrepancy surprised us. We therefore thought at first that the 10-ml exponential dilution vessel was not functioning. To check for systematic errors we split the outlet gas via a dead-volume-free tee-connection into two parallel detector, one an ECD and the other an FID. The FID channel showed a nearly ideal exponential dilution signal with time, but the ECD channel failed at high concentrations, with certain carrier gas compositions, or both. Fig. 6.5 compares the two signals. Eqn. 6.4 is so simple that with any programmable pocket computer one could calculate the expected time for the “half-signal’’ value. If one knows the carrier gas flow-rate
0 Theoretical dilution
curve
-Practical dilution c u r v e
Injection
Time
Fig. 6.5. Comparison of theoretical, FID, and ECD experimental exponential dilution function curves.
126
WIDE-RANGE CALIBRATION OF ECDS
(which is easy to measure accurately enough) and the volume of the exponential dilution vessel (easy to measure: fill with water and weigh) the equation gives the required data. We therefore calculated the time necessary to measure over 3, 4,5 and more orders of magnitude. We call this (relative to quantitative calibration) a wide range and hence the procedure is a wide-range calibration technique. We call the whole procedure cahbration, as we know the theoretical value and can measure the practical signal; the ratio of the two is the linearity correction factor. We calibrate with substance X and then with substance R and use a laboratory computer to calculate all factors for all concentrations as well as for all absolute amounts of substance. As we no longer depend only on relative data, but on absolute data, we call the technique “direct mode” It is not indirect as with the other techniques. We never succeeded in making the exponential dilution vessel precisely symmetrical; it looked more like an egg. Nevertheless, one can work quantitatively with it, and therefore we call this tool a “quantegg”. 6.4. DIRECT MODE USE
THE “QUANTEGG”
OF THE EXPONENTIAL DILUTION TECHNIQUE WITH
Based on eqn. 6.4 the following time data are known, if one knows (a) the volume (e.g., 12.00 ml) and (b) the gas flow-rate (e.g., 10.00 ml/min = 0.167 ml/s): Half-time = 49.9 (s) l/lO-time = 165.8 (s) One can therefore calculate, independent of the type and amount of sample, the halfconcentration time and easily measure this on the chromatogram recorder simply by observing when the signal reaches the half-height level. This can be done n times, if the amplifier sensitivity switch covers a range of S = 2n positions. Procedure: Inject (milligrams, micrograms or nanograms of) any compound with a detector response into the quantegg under constant conditions of pressure, flow and temperature. Switch the detector signal to a low level of sensitivity, so that the maximum signal just can be contained by the recorder on-scale. Switch the sensitivity switch by two units just when the detector signal reaches 50% of full-scale, and measure the time difference from signal jump to signal jump. Do the successive readings seem equal? Fig.6.5 shows the power of this first quantitative information with respect to the linearity of the detector response, a basis for simple conditions of accurate quantitative analysis. One can make further observations. Are the peaks produced by the sensitivity jumps at equal heights? If not, this indicates (a) a bad manual response or, if the starting line for the 2-unit jump is precisely at the 50% full-scale level, this indicates (b) a defective sensitivity switch. Check the shape of the first peak: is it sharp? if yes, the detector is not (heavily) overloaded. Does it look round, as in Fig. 6.6? if so, the detector is overloaded. Considering precision, in Fig. 6.6 we draw a parallel to the recorder zero-signal line. We measure precisely that the time for each crossover with the signal line. Even if there had been imprecise timing for the 2 u n i t switching, we have precise signal versus time
EXPONENTIAL DILUTION WITH THE “QUANTEGG”
127
Fig. 6.6. Recorded result of a manual quantegg run. See the flat signal maximum, indicating heavy detector overload. The factors 64 to 2 are the manually adjusted amplifier sensitivity switch positions. The “delta’s” indicate systematic (hardware) errors of the sensitivity switch factors. The 3, to t, time values’’ have to be equal in the case of a linear detector or a linear detector working range. The 50% height level line offers the time data measuring scale. The time delay between injection (arrow, right side) and the sudden rise of the detector signal demonstrates the possibility of precise flow measurement, if done at the millisecond level, impossible by manual techniques, but simple for on-line computer techniques.
data, provided that the switch factors are precise (some instrument manufacturers guarantee 0.02% accuracy for the sensitivity switch factors). Now calculate the theoretical signal for the time data one could measure for the baseline. The ratio of the theoretical to the measured signal is the linearity deviation factor. If this is equal to theoretical signal (for time t ) measured signal
=
1.000
then at this concentration level the detector response is linear. If it deviates from unity, we can correct the signal. Let the signal measurement be done by a computer on-line, and let the calculation be done in real time in the same computer. By this means we can use any non-linear detector quantitatively without any doubt about the accuracy. This is substance-specific autolinearization, which is not yet available commercially (but ready to be done with a suitable programmable integrator). Of course this necessitates constant conditions between the calibration run and the analysis run, a condition sine qua non for all sequential analysis techniques. Table 6.1 shows off-line calibration runs with detectors, integrators and computers
128
WIDE-RANGE CALIBRATION OF ECDS
TABLE 6.1 EXAMPLE FOR THE NON-AUTOMATIC USE OF THE QUANTEGC TECHNIQUE We used the chain: gas source -inlet - quantegg - detector - amplifier - integrator -printer/plotter. As integrator we used a Spectra Physics SP 4100, programmed for peak height measurement. The following SP-BASICS program was used and the signal height quantified every five seconds. The SP 4100 printerlplotter printed the peak height in units. The necessary time data are given as the number of data output times 5.00 in seconds. If an APPLAB interface is connected (IMI Interactive Microware, State College, PA, U.S.A.) t o an APPLE 2 home computer, 48 kbyte, and the amplifier signal is fed into the APPLAB interface, then auto-linearization is available. Only a few changes in the BASIC program in Table 6.5 would be necessary to correct the integrator signals automatically. !" interval in sec I = "; input A l : end P = PW: plot 1 run30 return plot off gosub 100 A = ((2.5*3peek#C142)/PW) - 1000 !$12. A; ifpeek#80C109=#80then 30 else end Y = 2peekK234 X=Y+A1 if 2peek##C234=>X then return else 120 gosub 2
SPECTRAPHY SICS BASIC program for SP 4100 (R.I. Rider)
Data print out: (one measurement per five seconds) Inject time 11: 26:54 107424 82521 51654 31992 19543 11859 7186 4362 2661 1632 1016 638 409 276 191 138 103 77 66 53 45 40 35 32 28 24 17 10
116902 76378 47772 29502 17993 10914 6611 4014 2450 1507 937 5 94 381 25 8 180 130 99 74 65 53 43 41 35 32 29 24 16 8
110375 70657 44144 27 170 16553 10037 6083 3697 2262 1392 867 548 358 244 168 125 93 70 60 52 44 35 35 32 27 24 16 8
103451 65456 40776 25 04 2 15229 9222 5600 3403 2083 1286 805 513 335 225 157 117 90 70 59 47 43 37 34 33 27 24 13 5
96374 605 18 37643 23042 14002 8499 5 149 3137 1921 1188 74 1 476 312 216 151 115 85 67 56 48 44 36 35 31 26 22 12 4
-
89243 55931 34742 21223 12879 7 806 4740 2889 1771 1094 686 440 293 20 3 144 109 80 66 57 46 42 34 34 31 26 21 12 2
WIDE-RANGE CALIBRATION BY THE “QUANTEGG”
129
available in 1981, for which there were n o commercially available instruments for on-line autocalibration. 6.5. WIDE-RANGE CALIBRATION BY THE “QUANTEGG”
Table 6.2 shows the experimental results. As the detector turned out to be reasonably non-linear, and as most users consider non-linear detectors to be less valuable, we have not revealed the manufacturers of the ECDs tested. In the future it will become much more important for detectors to have a flat optimal response range when the measuring TABLE 6.2 EXPERIMENTAL CONDITIONS Quantegg: home made (Institute for Chromatography, Bad Diirkheim, G.F.R.). Quantegg volume: 14.90 m l (measured by weight of water filling at known temperature) Carrier gas: nitrogen from direct liquid nitrogen evaporation; argon-methane (95:5, v/v) from Messer Griesheim, ECD quality. Temperature: between 25°C and 200°C tested. Gas flow-rate: between 5 ml/min and 50 ml/min tested. ECD scavenger gas at detector response ioptimum conditions or through gas by-passing. Pressure: between 0.1 and 3 bar. Detectors: ECD, different branches, made in 1980. Amplifier: Carlo-Erba electrometer Model 180. GC amplifiers used in DAN1 model 3900 or PerkinElmer model F22. Recorder: 0.5 to 200,000 mV f.s.d., 0.3 s recorder Servogor from GoerzlBBC. Sample: CH,CI,, or CHCI,, or a mixture of both in n-heptane (Merck) ranging over 1:100,000 starting with maximum concentrations of 10.’ g/ml down to the ECD noise level under normal experimental conditions. Extreme concentration levels until detector saturation have been tested as well.
TABLE 6.3 DEVIATION OF ECD LINEARITY Normal conditions, clean carrier gas argon-methane ( 9 5 5 , v/v), not oversampled, just dairy analytical conditions. The data show linearity deviations are not constant (S-shaped function for signal deviation from linearity), and remarkably large (-20%!!) for quantitative analysis. Quantegg volume = 14.9 ml; gas flow F = 14.3 ml/min; maximum signal height = 140,000. Time
SignaI height
Corr. factor
38.4 89.4 135 178.8 220.5 262.5 304.2 347.4 392.1 440.1
63539.2 31769.6 15884.8 7942.4 3971.2 1985.6 992.8 496.4 248.2 124.1
1.192 1.055 1.017 1.009 1.036 1.059 1.087 1.089 1.065 0.989
130
WIDE-RANGE CALIBRATION OF ECDS
conditions are changed ind for the absolute signal levels to remain constant rather than having perfect linearity: However, at present we use primitive integration techniques and primitive quantitation equations, both of which depend on perfect linearity (cf. Table 6.3). 6.6. LIMITATIONS OF THE “QUANTEGG”
The most important condition for quantegg cahbrations is a stable and known position of the real signal baseline. Another weak point is that the quantegg signal starts at a maximum, and that at first we may consider this C, value as being correct, until we realize that non-linearity applies. From there we have to calculate backwards. If there is no linearity, one has to start the calculation at the lowest signal level. For manual evaluation both are troublesome, but not for on-line or off-line computation, where we can start with any value. The quantegg function depends on constant conditions of flow-rate and pressure. Therefore, a constant flowrate is important, but in gas chromatography this can be guaranteed to at least 1%. The quantegg will give false results if systematic losses by chemisorption on the inner surface occur. However, the surface can be deactivated and heated to the optimal temperature. The quantegg does not correct systematic calibration errors due to substance losses in the chromatographic column, but one can ascertain their magnitude by using the pneumatic circuit shown in Fig. 6.7.
Fig. 6.7. Pneumatic circuit for combined or parallel use of quantegg and a chromatographic (or capillary) column. G = carrier gas source. PI,P, = pressure regulators. I,, I, = sample inlet systems. N , , N,, N, = needle valves (outlet split for the injection systems; N, = carrier gas flow regulator for quantegg. Q = quantegg. C = column or capillary. R = analytical gas flow resistor kept under constant temperature. P, allows, together with the gas flows from C and Q , adjustment of the gas flow optimum for detector D. Pressure P, < pressure P, .
LIMITATIONS OF THE “QUANTEGG”
131
The quantegg installation must be gas-tight. The homogenization must be perfect and remain so, but here we have to consider limitations. There is a limiting lowest acceptable flow-rate through the quantegg. Below this value the practical elution curve is steeper than the theoretical shape allows, and homogenization is non-ideal. The flow-rate through the quantegg must be known and be accurate. This is not easy, but a very precise dead-time measurement can be used for flow metering. As the quantegg itself does (theoretically) not allow any dead time to the signal delay, the flow-rate (F) could be calculated by
F =
volume of the quantegg capillary dead time
It is no problem to measure the quantegg volume exactly, but one has to consider the exact pressure within the bulb for precise time data calculations. It turns out that the quantegg offers simple solutions to the problems encountered in quantitative chromatography, but there are many data to be handled if one wants high accuracy. The data evaluation is not simple. We used an Apple 48 kbyte double disk laboratory computer and used its CP/M version for easy data transfer to and from floppy disks. TABLE 6.4 TEST OF LINEARITY OF AN ECD The ECD was run under equal conditions of sample, sample amount temperature, flow, voltage, etc., but with differing carrier eases: A: swer clean nitrogen: B: common mixture of areon-methane. Time* A
164.4 234.6 285.9 338.4 399.3 492.6
Signal height** 8192 4096 2048 1024 512 25 6
Corr. factor***
H-Theor. 8
3.003 2.065 1.892 1.703 1.348 0.652
24602.4 8456.4 3874.9 1743.4 690.3 167
Quantegg volume = 14.9 ml; gas flow F = 13.6 mllmin; maximum signal height B
27.9 73.5 116.4 158.7 200.1 242.1 284.4 375
31667.2 15833.6 7916.8 3958.4 1979.2 989.6 494.8 123.7
1.048 1.005 1.007 1.019 1.047 1.064 1.077 1.001
=
300,000
33176.7 159 16.4 7975.3 4035 2071.3 1053 532.8 123.8
Quantegg volume = 14.9 ml; gas flow F = 14.3 ml/min; maximum signal height = 52,000. *Time: since injection of sample into quantegg. **Signal height: signal height in units (sensitivity times volt times 1000). ***Corr. factor = correction factor to achieve linearity. SH-Theor. = signal height times corr. factor.
132
WIDE-RANGE CALIBRATION OF ECDS
6.7. EVALUATION OF DATA 6.7.1. Data evaluation by manual measurements from a recorder display Fig.6.8 compares two records and Table 6.4 contains data from some measuring positions. If one examines both sets of data the whole procedure becomes evident and does not need further comment here, with one exception. Both sets of figures represent wide-range calibrations with CHzClz, CHC13 in n-heptane* as the test substance. In both examples the same detector and the same amounts of substance were used, the important difference being the carrier gas composition. The practitioner can imagine how rapidly and simply he can check his own detector conditions with respect to linearity, depending on the working conditions.
+
+
Fig. 6.8.1 1
+
Fig. 6.8.21 I t
/ C o r r e c t i o n factor value C o r r e c t i o n f a c t o r value 100
P
-Theoretical Theoretical Practicol *
Time
*
*
.
A+ .+ -.
Time
Fig. 6.8.12
+
100
Theoretical
+’?\
Fig. 6.8.22
C o r r e c t i o n f a c t o r value
+
+
+
-
100
[+]Run away
\\Practica
+ Time
.
* Time
Fig. 6.8. 6.8.1 1-6.8.22: computer prints of graphical evaluation in on-line or off-line quantegg calibrations. 6.8.1 1: Heavily overloaded ECD, carrier gas nitrogen. Hopeless to correct anything. 6.8.12: No overloading, but ECD with nitrogen as carrier gas. Detector remains extremely non-linear. 6.8.21 : Qualitatively and quantitatively the same conditions as in Fig. 6.8.11, but argon-methane as the carrier gas. 6.8.22: Same as in 6.8.12, but argon-methane as the carrier gas. The measurements are delicate. The gas flow must have an accuracy of better than 99%. The BASIC program (Table 6.5) offers possibjlities to check for gas flow and maximum signal errors. The corrections can be checked graphically.
*Tests wjth many other ECD-active compounds run comparably. Results are supported by FID, HCD, in GC and many different detectors in HPLC.
EVALUATION OF DATA TABLE 6.5
BASIC PROGRAM FOR QUANTEGG ]LIST
REM CLFAR
1 2 0
10 20
PUAllTLCC
RFM
40 50
6n 70
A3
70 1oc 101 102 110 11 1 11: 150
14"
150
163 IF Ff!L z "Y" UiLI! LOO 1L2 IF !! : ' ( 1." iTHEN 170 165
GOT? 1 l i PRINT : P R I l K " 4 YO!: 9NOU HALF TI!.IE 1 0 . 5 - T I b 5 ' ' ~ : HTAB 28: INPUT Y /PI 7" ; !I'? $ i,sr J t TRS = "I:" THEN PHIF!T : PRINT *I lili FIND HALF HEIGHT SIGNAL I': PRINT I ' -->L:OORCSP.lIb'E I S '0.5 - T I l i E ' 1 1 C PI'INT : PEINT " E W E R T l l I S VALUE HERE. .:!': IlTAB 28: INPUT ,' T . c, = ":I,, , ,-rr FPI!!T : PRI$T "-> YOU K!lOi THE QUANTECC VOLUVE?": HTAB 28: INPUT I( Y /hi 7";FR$ 21" :r w z = !*Y" P N P III > c ) TIIEII 250 71'f I' FR? = " t i " TIIEH 240 7 -?-Q 1 COT0120 123 COT0 ,~ PI'IKT: :P RF IRKI K"YOU ''YOwL!ST UWL!STKNOW KNOWT!IFT!IFVOLUI!E VOLUI!E I!: I!: PRINT PRINT"ECACTLY "ECACTLYBYBY +/-+/- 1 1 :'ir:)I? 1 PI'IKT PFI!IT: :PKINT PKINT"XEEASURE t'XEEASUREPRECISELY PRECISELY I ! ' !":":END END * * I !I"!:" :PFIIIT 'I: IITAU INPUTV V ?10 PETE!? : F r I ? ' T It EllTiI' VCL[!PF Ill t:L. 'I: t!TAU 35:35:INPUT 17fl
..
._
END / 10
TtX'F : H O X : POKE :Ll,2: INVERSE : FRIMT DATA INPUT WITII <-I> iion:+m : P r m T 'IQi VT,?R 2: !TAG 26: PRINT "3.5-? I " , l i Z : VTAC 4 : PRINT
'5'~
*
CORRECT
99:
(10 FiiR
:=
I IT1 10C
INPUT
I'
!ITAB 10: IIJPd?
INPUT
'I
f,40
PRINT I
(70
C(I) = IPiiIllT
CC "--)
II
"CORR.TIMC ( S ) T
CCRRCiT? THEN 'RETURN) EYl' ( (
C(TH)
z
-
E = ";E
SE::SIIIVITY
EIGHT ( Y M ) :
*
1) T(I) " ; I N T (10C
*
= ";II(I):H(I)
L
H(I)
E: IF
H(I)
I F T ( I ) < 0 THEN 6 j O OTllLR!4.<-1>'1;QU$: I F QU$ D "-1" THEN :" ; T ( I ) :
F / 'I)
C(I1 + ,005) / 100;" C ( P R ) = " ; H ( I !
134
WIDE-RANGE CALIBRATION OF ECDS
680 I F t l ( I 1 = 0 THE14 PRINT "VALUE CANNOT P,E >>ZER!3<<": GOTO 610 690 KF(I) = c ( 1 ) H ( I ) 7fl0 I F FB = "C" THEN K = N + 1 71C PRINT : PRIP!T * LINEARITY CORRECTIGN FACTOR = ',; I N T (100 KF(I) + ns, I ion 720 i f - H ( I > z.0 THEN 830 730 EIFXT 740 El T I 1
-
750
TEXT : PRINT : PRINT "CHANCE START SICN.IIEIGtIT ? (WAS I " ; C O ; " ) " : HTAB 30: INPUT " / Y , N > ? ";QU$ I T CU$ = "Y" THEN 780 PRINT : PRINT "CHANCE FLOh' VkLUE? WAS: 1,; I N T (100 * 60 F ) / 1 0 0 " "Y" THEN 767 ML/?^INl": tITAB 3 : INPUT " < Y , N > 7 ";QU$: I F QU$ GOTO 790 PRINT "CNTER IIEK VALUE FOR P!lASE FLOW": INPUT It F = ";F:F = F / 60:
760 7G5 766 167
GOSUB 1220 770 GOTO 790
780
PRINT ENlEH SENSITIVITY FACTOR E FOR 'C0' IL NCIU WAS- ";CO: INPUT IlEY P C 0 -VALUE PRINT tllt: PRINT : INPUT ,,+ PRINTOUT 'VALUES? U$ < > "Y" THEN 830
790 800
GOSUC
PRINT VALUE USED T I ";CO: GOSUB 1220 / < N > ";QU$: I F Q
IT:
1160
PRINT "** WANT TO CHANGE STIIORTINC SICN.HT.?": PRINT "OH WANT TO S E E GRAPHICS 7": PRIRT I,--> CHAIIGING: ENTER VALUE-< >": INPUT "-4 G <0> HERE ";W: I F W = 0 THEN 8 3 0 RAPHICS? ANTER 820 CO = W: GOTO 790
810
e3n REV
8JlO I F T(N) = 850 I F T ( N ) = 61.0 IF TOI) = 870 FIF. : U
< 2 22 < 3 ZZ < 4 * ZZ
THEN BE = 2: GOTO 8P.O THEN BE c 3: GOTO 880 TflEfl BE = 4
*
~
8110 FX = 250 / (RE Z2):FY = 157 / (CO P90 PRItiT : PRINT "GRAPHICS RANGES CVER CONCFNTRP.TION 'I: PRII!T 900
9lC 920
130 9110 950
IIIFFY: j w o c i C l i : IHCOLOR: 7 !ITLCT 11.0 TO 0,159: IIPLOT FOR 2 = 1 33 250 STEP 3 Y = FY CO 1 E l * EXP ( ( !PLOT Z , 157 - Y
El)
";6E:
PRINT "ORDERS OF MRGN. OF
TO 250,159
-
1)
*
F / Vl
FX)
(Z /
I6C NEXT
tIPL(IT 0,79 TO 21O,7? l C O FCR I z 1 TI\ N 190 IX z T C I ) FX:YP = FY lI(I) El in00 ~i = K K F ( I ) 1010 I F Y 1 > I 5 6 THEN Y l z 116 1020 I F Yl < 3 Tl!Ul Y 1 = j 1030 I F YP > 158 Tlikl; YP = 15: 1040 IF YI' < 2 T!iE!I YP = i I050 I F IX > 250 THEN I X z 250 1OGC I F IX < 2 nlEN IX 2 1070 tIPL0T I X + 1,151 - YP TC IX - 1,159 YP 1080 IIPLOT ? X , 1 5 1 - YP + 1 TO IX.159 - YP - 1 l09C IIFLST IX,15? - (Y1 + 21 TO IX,159 - (Y1 - 2 ) : HPLOT I X 2,159 - Y1 TC IX + 2,159 - Y 1 1 1 0 0 NFXT 1110 PRINT : PKII!T ' I ";EE" ORDERS OF MACN. RANGING; ---> T" I120 VTAB 22: II!PUT !'ADD DATA; E l X < C > ; OTHER 'F;CO'";F$ 170
-
I
1160 C$ = CIIRS.
T","tI-TIiFCR.":
rrn I
I190
rtm TFXT : IIOXE : cmo 750 FCR I = N + 1 TIC 1 0 0 : GOTO 6 1 0 **; RESTART 6Y 'GOTO 7 5 0 " ' : END
THEN
EYE
(ti):
PR?t:T D$;"PR'11": PRINT "TIME"," SICN.I!T.","CORR.FAC t'E?IIT ' 8 ________________________________________------
= I T C ~:I PQI?IT T ( T ) , I ~ ( T ) :!;T ,
IIK
lion
5) / 1c
-
( ~ ~ ( 1 1IOGC + .5) /
NfXl
10o0,
Iiir ( c ( I )
FiuW F = "; IPil ( F
1210 PRJIUT : I'RIIIT 1223 FOK I = I TO N:C(I) T CO * LXP 1 / II(1): IlEXT : PRINT "TI:;E
((
-
1) * r ( I ) SIGNdL
*
1u +
.
*
1
b0
F / Vl:I(F(Il 2(I CORR.LACTOR": PAIN7
o______________________________________,,
1230 1240 1250 1261:
FOR I = 1 TO N : PIIIf(? T ( I ) , t l ( I l , I N T (I00 I K F ( i ) ) / 100: EiEXT PHItlT : INPUT CONTIHbC ";$L$: I F PU$ = " Y " THEN HLTURlu IIETUAti
REE'
KCESSEP!
LITERATURE
135
6.7.2. Data evaluation with a laboratory computer Table 6.5 gives parts of the BASIC program (Applesoft Basic) as well as a program that runs under CP/M conditions, which we wrote to make calibration simple. If one can use an Apple 48 kbyte computer, one disk and a monitor for qualified graphics representation, one will have a screen display as shown in Fig. 6.5; it is much easier to read a picture than numbers in order to be able to make immediate decisions. If line L in Fig.6.5 (which represents the non-linearity correction factor) deviates by more than 1% from the middleline M, then non-linearity causes systematic analytical errors. We have never seen h e L coinciding with line M with any GC detector that we have checked during the past 2 years work with the quanteggs.
LITERATURE R.E. Kaiser, Pittsburgh Conference 1980, Atlantic City, paper No. 111. R.E. Kaiser and R.I. Rieder, GITFachz. Lab., 24 (1980) 633-639.
Chapter 6
Wide-range calibration of electroncapture detectors R.E. KAISER and R.I. RIEDER
CONTENTS 6.1. Fundamentals of calibration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1.1. The two fundamental quantitation equations . . . . . . . . . . . . . . . . . . . . . . 6.2. Calibration by conventional laboratory techniques. . . . . . . . . . . . . . . . . . . . . . . . 6.3. Calibration by exponential dilution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4. Direct mode use of the exponential dilution technique with the “quantegg” . . . . . . . . . 6.5. Wide-range calibration by the “quantegg” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.6 Limitations of the “quantegg” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.7. Evaluation of data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.7.1. Data evaluation by manual measurements from a recorder display . . . . . . . . . . . 6.7.2. Data evaluation with a laboratory computer. . . . . . . . . . . . . . . . . . . . . . . . Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1 19 120 122 124 126 129 130 132 132 135 135
6.1. FUNDAMENTALS OF CALIBRATION There have been many detailed discussions of the quantitative use of electron-capture detector (ECD) data in gas chromatography and lengthy descriptions of how to use different ECDs in different modes, with different gases, in many analytical applications can be found in the literature. This paper offers an alternative procedure for optimizing and using ECDs for quantitative gas chromatographic (GC) analysis: the “black box” principle and absolute quantitation. For this purpose it is of no importance which type of detector is used in quantitative gas chromatography: any detector can be understood and treated as a black box for the production of correct, precisely repeatable quantitative analytical data. Therefore, we thought it might be acceptable to describe the quantitative detector behaviour in a way that is valid for a given instrument under constant (although optimized) analytical conditions of temperature, carrier gas composition (including trace contaminants), inlet pressure, outlet pressure, detector cell voltage, and amplifier, integrator and recorder conditions, without including a discussion of the theory of ECDs, as this is available elsewhere in this book. The principles discussed here are valid for any ECD, under any special conditions of practical use, if the fundamental requirement for quantitative GC analysis holds true, namely that the conditions remain constant throughout the whole working period between calibration and quantitative application.
WIDE-RANGE CALIBRATION OF ECDS
120
6.1.1. The two fundamental quantitation equations The quantitative GC signal can be given as the integral of
(A) voltage (volts) times flow (millilitres/second)
+
-
V ml/s
or
(B) current (amps) times time (seconds) + A-s Although any GC detector response i s based on moles of substance, it is more practical to relate the response to mass given in grams. Calibration allows conversion of all quantitative data to the basis of grams, volts, amps, millilitres and seconds. Therefore, we can write the two fundamental quantitation equations, first for a detector, which is “substance flow dependent”: as
(A) grams of substance X = 4
(6.1)
where q is the “quantity” or the response in amps times seconds, which the detector “produces” per gram of substance X,also known as the “gram-based substance-specific response”, and secondly for any detector which is “concentration dependent”:
v-ml (B) grams of substance X = 4
(6.2)
where q is the “quantity” or the response in volts per “concentration unit” given in grams per millilitre. These two q factors are different for A and B, but both describe quantitatively the function of the detector. Concentration-sensitive detectorslproduce a signal in volts from the unit concentration, grams/ml. Mass flow-sensitive detectors produce a signal in amps from the unit mass flow, grams/second. Different ECDs, under certain conditions of carrier gas, flow, pressure, temperature, voltage, etc., show neither pure mass flow- nor pure concentrationdependent behaviour, which fortunately is not a problem in quantitative analysis if all conditions remain constant between the time of calibration and the time of analytical application. This lack of problems depends, however, on the technique of calibration. The two fundamental quantitation equations both give a result in grams of substance X,i.e., both describe the GC peak area of substance X in terms of grams of the substance. Both equations are, at first sight, linear, provided that we consider the mass response factor q as a substance-specific constant. In fact, q is by no means a constant and is influenced by many physical and chemical factors, which make quantitation with ECDs difficult. This remark is immediately understandable if one considers the fundamental equations just as the substance-specific calibration line, giving the analytical signal function (see Fig. 6.1). q in Fig. 6.1 is the slope of the analytical signal function and its dependence on the specific nature of the substance and on the amount of substance can be seen; q is constant.
FUNDAMENTALS OF CALIBRATION
121
Signal (A)
Fig. 6.1. Substancespecific, analytical signal function. q,,2 = specific response.
It can be easily understood why the two fundamental quantitation equations A and B are interchangeable or can be used simultaneously: the quantitative GC signal can be expressed as peak area. This area can be approximated to peak height times peak width at half-height. One can measure the peak height in amps and the peak width in seconds, the peak area then being amps times seconds. Alternatively, one also can measure peak height in volts and peak width in millilitres (carrier gas passed during the peak width times period). Whether the signal is measured in amps times seconds (coulombs) or in volts times millilitre it is practically the same. Both measurements are correlated with the mass of the substance in grams. Although we have discussed quantitation as a “black box” model so far, it would be of some help to the practitioner, using more than one detector, to be able to compare the popular ECD with the equally popular flame ionization detector (FID). By giving the quantitative content of Fig. 6.1 in a different form, viz., the change of signal function slope with amount of substance in grams, we can better understand the quantitative differences between an FID and an ECD: Fig. 6.2 shows the result one most often finds in practice: the FID has a wider more-or-lesslinear range, but both detectors need precise calibration as both are never linear enough for accurate quantitative analysis. Although it is often stated that FIDs are linear over a range of seven orders of magnitude and (linearized) ECDs are considered to be linear over four orders of magnitude, one
1
G r a m s substance (CH2CHCI)
Fig. 6.2. Linearity (or deviation from linearity) can be expressed as the change of q with absolute amount, concentration or flow of analytical substance in the carrier gas, passing through the detector.
122
WIDE-RANGE CALIBRATION OF ECDS
has to compare this “linearity” with the analytical quantitative needs: do we want to. accept accuracy as less important than repeatability? If not, then the accuracy has to be as correct as repeatability within the statistically possible limitations, and therefore “linearity” becomes fundamental to our discussion. Linearity is what Fig. 6.2 shows: the change in q over the range of the mass of substance in grams. Many practitioners do not think in such terms and therefore do not measure q data. The quantitative measurement of correct 4 data is, in fact, the fundamental of calibration.
6.2. CALIBRATION BY CONVENTIONAL LABORATORY TECHNIQUES
A simple calibration technique consists of a few steps and their combination: (a) Take substance X(substance to be determined) and a standard substance R. (b) Make a quantitative mixture of both by means of volumetric or mass measurements. Preferably weigh W grams of X (= W x grams) to W grams R (= WR grams). (c) Make a homogeneous mixture of X and R in a suitable solvent, so that in each microlitre the mass ratio of X to R is constant and exactly equal to W X / W R . (d) Separate the substances X and R chromatographically and measure the integrals. Let us call the peak area of substance X A X and that of substance R A R . (e) Compare the mass ratio with the chromatographic peak-area ratio : Is (6.3) Possibly not. We now introduce correction factor, f, to correct the simple calibration equation 6.3. In any case it holds true that
-wx _ - - AX’f WR
AR
and therefore the correction factor is
which too often is considered to be a constant. However, f is never constant, if we consider constancy and linearity as strict quantitative expressions like chromatographic repeatability. The relationship peak area A x to the amount of substance X was defined as
CONVENTIONAL LABORATORY TECHNIQUES
123
Therefore qR =
WR ~
AR
and hence
~ f (for x substance X relative to R )
= qX/qR
Thus the simple laboratory calibration correction factor turns out to be the ratio of the two fundamental response data, q , for the two compounds used, X and R . As this is too simplified for more detailed discussion, we can add important comments. The simple correction factor, f, can never be a constant over a practically useful quantitative range if one of the response factors, q , of whichfconsists, changes. As there is no detector that is truly linear over the practical ranges in which we want to work quantitatively - considering linearity strictly as quantitative repeatability - the correction factor f is not constant: it depends on the absolute values of the amounts of X and standard substance in grams entering the detector. In practice we usually overload detectors, but many practitioners simply do not believe this statement, so a quantitative example will be given. Let us use the nearly “unlimited linear FID” for this example. FIDs are called linear over a range of at least 1 to lo6.Their quantitative working range starts at lo-’* g/s giving a measurable signal of about i = A. Linearity of six orders of magnitude means that the detector will also work at a level of g/s. If one uses a packed column, one normally injects between about 1 and 0.1 1.11 of sample, which is about 1-0.1 mg. Normally a rapidly eluted peak is about 1 s wide at half-height. This means that about lo-’ g enter the detector, which is about one order of magnitude above the linear range of the wide-range FID. Let us consider these conditions with an ECD. As its linear range is at least two orders of magnitude less than that of an FID and starts at a two-order smaller range level than that of an FID, one will have overloading with a even four orders of magnitude smaller sample injection. Who really takes care that not more than about 1 ng of substance enters the ECD? Only users of capillaries (sometimes) take care in this respect. We can repeat, therefore: with the practical range of modern chromatographic quantitation we normally tend to overload our detectors and therefore the correction factor f has to be considered to be non-constant. On the other hand, for trace amounts of substances, we are confronted with the problem of losses due to chemical sorption. This makes understandable Fig. 6 . 3 , which shows the dependence of the correction factor on the absolute amount of sampled compoundX. A classical rule states that one should choose internal standard compounds so as to be chromatographically as closely related to the substance under analysis as possible. The best would be for them to have identical polarities. Of course, the optimal solution would be to use the substance X itself as the standard. In practice, one tries to have X and R just sufficiently separated from each other, so the peak of X may be partly overlapped by the peak of R . In this case, undesirable sideeffects may occur in the detector. A s f i s composed of two responses, namely qR and q , we can understand the dependence of the
124 c
WIDE-RANGE CALIBRATION OF ECDS
2.00-
L
0 c U r
c
0 ';I 100-
tl
0 V
r'a"
r'a"
:do
Substance flow or concentration ( 9 1 s )
Fig. 6.3. Dependence of the correction factor f on the absolute amount, concentration or flow of analytical substance in the carrier gas, passing through the detector.
simple correction factor of the substancespecific trace behaviour of different compounds as well as of side-effects which can greatly influence the response. Hence a situation arises that is no longer as simple as the process of simple laboratory calibration appears t o be. It is not only the relative composition of the calibration mixture, but also the absolute amount of the calibration mixture that is important. We now have non-linearity plus sideeffects. Non-linearity as such leads to problems in quantitative analysis as all quantitation equations - both absolute and relative functions, and internal and external standard techniques - depend on a linear correlation between the signal and the concentration or amount of substance. There is no doubt about the only way to handle non-linearity: measure repeatability correction factors or response data with many different absolute amounts of substance. Do we have enough time in routine analysis, where quantitatively correct data are important, to follow such time-consuming advice? We do not. Calibration by conventional laboratory techniques cannot handle effectively enough the problems of non-linearity. ECD analysis means non-linear analysis, and here calibration by exponential dilution is of help.
6.3. CALIBRATION BY EXPONENTIAL DILUTION If one dilutes a full pot of coffee (or any other substance in solution) with a constant flow of water (or any other diluent) and continues carefully to homogenize the dilution
(e.g., by stirring), the coffee will be diluted to half its concentration in a constant time. This holds true if the diluted coffee leaves the pot at the same flow-rate as that of the water being added. Let the starting concentration be Co (g/ml), the volume of the pot be V (ml), and the flowrate of diluent be F (ml/s), then the concentration C a t each time t (s) is given by the fundamental equation of exponential dilution: C
=
Co.exp(-Ft/V)
(6.4)
We built a glass bulb with a volume of about 10 ml and connected to it two capillaries of very narrow bore (less than 0.2 mm I.D.). With a flow-rate of about 10 mllmin of
CALIBRATION BY EXPONENTIAL DILUTION
125
Outlet; t o detector
0
Fig. 6.4. “Quantegg”, a glass bulb of several millilitres volume with platinum-iridium tubings (0.1 to 0.15 mm I.D.).
carrier gas through the glass bulb, as shown in Fig. 6.4), the stirring energy pumped into the bulb volume was sufficient to give good constant homogenization of the exponential dilution vessel in the bulb volume. In addition, the inlet capillary introduced tangential stirring. The outlet capillary was precisely centred in the middle of the bulb volume. Capillary i was connected with the (second) chromatograph injection port and capillary o was connected to the detector. We injected the calibration substance X (pure X diluted in an inert solvent) (preferably no solvent is used, but in practice carrier gas is used). Immediately after injection we obtained a maximum signal from the detector. The change in signal with time approximately followed the exponential dilution curve, but the discrepancy surprised us. We therefore thought at first that the 10-ml exponential dilution vessel was not functioning. To check for systematic errors we split the outlet gas via a dead-volume-free tee-connection into two parallel detector, one an ECD and the other an FID. The FID channel showed a nearly ideal exponential dilution signal with time, but the ECD channel failed at high concentrations, with certain carrier gas compositions, or both. Fig. 6.5 compares the two signals. Eqn. 6.4 is so simple that with any programmable pocket computer one could calculate the expected time for the “half-signal’’ value. If one knows the carrier gas flow-rate
0 Theoretical dilution
curve
-Practical dilution c u r v e
Injection
Time
Fig. 6.5. Comparison of theoretical, FID, and ECD experimental exponential dilution function curves.
126
WIDE-RANGE CALIBRATION OF ECDS
(which is easy to measure accurately enough) and the volume of the exponential dilution vessel (easy to measure: fill with water and weigh) the equation gives the required data. We therefore calculated the time necessary to measure over 3, 4,5 and more orders of magnitude. We call this (relative to quantitative calibration) a wide range and hence the procedure is a wide-range calibration technique. We call the whole procedure cahbration, as we know the theoretical value and can measure the practical signal; the ratio of the two is the linearity correction factor. We calibrate with substance X and then with substance R and use a laboratory computer to calculate all factors for all concentrations as well as for all absolute amounts of substance. As we no longer depend only on relative data, but on absolute data, we call the technique “direct mode” It is not indirect as with the other techniques. We never succeeded in making the exponential dilution vessel precisely symmetrical; it looked more like an egg. Nevertheless, one can work quantitatively with it, and therefore we call this tool a “quantegg”. 6.4. DIRECT MODE USE
THE “QUANTEGG”
OF THE EXPONENTIAL DILUTION TECHNIQUE WITH
Based on eqn. 6.4 the following time data are known, if one knows (a) the volume (e.g., 12.00 ml) and (b) the gas flow-rate (e.g., 10.00 ml/min = 0.167 ml/s): Half-time = 49.9 (s) l/lO-time = 165.8 (s) One can therefore calculate, independent of the type and amount of sample, the halfconcentration time and easily measure this on the chromatogram recorder simply by observing when the signal reaches the half-height level. This can be done n times, if the amplifier sensitivity switch covers a range of S = 2n positions. Procedure: Inject (milligrams, micrograms or nanograms of) any compound with a detector response into the quantegg under constant conditions of pressure, flow and temperature. Switch the detector signal to a low level of sensitivity, so that the maximum signal just can be contained by the recorder on-scale. Switch the sensitivity switch by two units just when the detector signal reaches 50% of full-scale, and measure the time difference from signal jump to signal jump. Do the successive readings seem equal? Fig.6.5 shows the power of this first quantitative information with respect to the linearity of the detector response, a basis for simple conditions of accurate quantitative analysis. One can make further observations. Are the peaks produced by the sensitivity jumps at equal heights? If not, this indicates (a) a bad manual response or, if the starting line for the 2-unit jump is precisely at the 50% full-scale level, this indicates (b) a defective sensitivity switch. Check the shape of the first peak: is it sharp? if yes, the detector is not (heavily) overloaded. Does it look round, as in Fig. 6.6? if so, the detector is overloaded. Considering precision, in Fig. 6.6 we draw a parallel to the recorder zero-signal line. We measure precisely that the time for each crossover with the signal line. Even if there had been imprecise timing for the 2 u n i t switching, we have precise signal versus time
EXPONENTIAL DILUTION WITH THE “QUANTEGG”
127
Fig. 6.6. Recorded result of a manual quantegg run. See the flat signal maximum, indicating heavy detector overload. The factors 64 to 2 are the manually adjusted amplifier sensitivity switch positions. The “delta’s” indicate systematic (hardware) errors of the sensitivity switch factors. The 3, to t, time values’’ have to be equal in the case of a linear detector or a linear detector working range. The 50% height level line offers the time data measuring scale. The time delay between injection (arrow, right side) and the sudden rise of the detector signal demonstrates the possibility of precise flow measurement, if done at the millisecond level, impossible by manual techniques, but simple for on-line computer techniques.
data, provided that the switch factors are precise (some instrument manufacturers guarantee 0.02% accuracy for the sensitivity switch factors). Now calculate the theoretical signal for the time data one could measure for the baseline. The ratio of the theoretical to the measured signal is the linearity deviation factor. If this is equal to theoretical signal (for time t ) measured signal
=
1.000
then at this concentration level the detector response is linear. If it deviates from unity, we can correct the signal. Let the signal measurement be done by a computer on-line, and let the calculation be done in real time in the same computer. By this means we can use any non-linear detector quantitatively without any doubt about the accuracy. This is substance-specific autolinearization, which is not yet available commercially (but ready to be done with a suitable programmable integrator). Of course this necessitates constant conditions between the calibration run and the analysis run, a condition sine qua non for all sequential analysis techniques. Table 6.1 shows off-line calibration runs with detectors, integrators and computers
128
WIDE-RANGE CALIBRATION OF ECDS
TABLE 6.1 EXAMPLE FOR THE NON-AUTOMATIC USE OF THE QUANTEGC TECHNIQUE We used the chain: gas source -inlet - quantegg - detector - amplifier - integrator -printer/plotter. As integrator we used a Spectra Physics SP 4100, programmed for peak height measurement. The following SP-BASICS program was used and the signal height quantified every five seconds. The SP 4100 printerlplotter printed the peak height in units. The necessary time data are given as the number of data output times 5.00 in seconds. If an APPLAB interface is connected (IMI Interactive Microware, State College, PA, U.S.A.) t o an APPLE 2 home computer, 48 kbyte, and the amplifier signal is fed into the APPLAB interface, then auto-linearization is available. Only a few changes in the BASIC program in Table 6.5 would be necessary to correct the integrator signals automatically. !" interval in sec I = "; input A l : end P = PW: plot 1 run30 return plot off gosub 100 A = ((2.5*3peek#C142)/PW) - 1000 !$12. A; ifpeek#80C109=#80then 30 else end Y = 2peekK234 X=Y+A1 if 2peek##C234=>X then return else 120 gosub 2
SPECTRAPHY SICS BASIC program for SP 4100 (R.I. Rider)
Data print out: (one measurement per five seconds) Inject time 11: 26:54 107424 82521 51654 31992 19543 11859 7186 4362 2661 1632 1016 638 409 276 191 138 103 77 66 53 45 40 35 32 28 24 17 10
116902 76378 47772 29502 17993 10914 6611 4014 2450 1507 937 5 94 381 25 8 180 130 99 74 65 53 43 41 35 32 29 24 16 8
110375 70657 44144 27 170 16553 10037 6083 3697 2262 1392 867 548 358 244 168 125 93 70 60 52 44 35 35 32 27 24 16 8
103451 65456 40776 25 04 2 15229 9222 5600 3403 2083 1286 805 513 335 225 157 117 90 70 59 47 43 37 34 33 27 24 13 5
96374 605 18 37643 23042 14002 8499 5 149 3137 1921 1188 74 1 476 312 216 151 115 85 67 56 48 44 36 35 31 26 22 12 4
-
89243 55931 34742 21223 12879 7 806 4740 2889 1771 1094 686 440 293 20 3 144 109 80 66 57 46 42 34 34 31 26 21 12 2
WIDE-RANGE CALIBRATION BY THE “QUANTEGG”
129
available in 1981, for which there were n o commercially available instruments for on-line autocalibration. 6.5. WIDE-RANGE CALIBRATION BY THE “QUANTEGG”
Table 6.2 shows the experimental results. As the detector turned out to be reasonably non-linear, and as most users consider non-linear detectors to be less valuable, we have not revealed the manufacturers of the ECDs tested. In the future it will become much more important for detectors to have a flat optimal response range when the measuring TABLE 6.2 EXPERIMENTAL CONDITIONS Quantegg: home made (Institute for Chromatography, Bad Diirkheim, G.F.R.). Quantegg volume: 14.90 m l (measured by weight of water filling at known temperature) Carrier gas: nitrogen from direct liquid nitrogen evaporation; argon-methane (95:5, v/v) from Messer Griesheim, ECD quality. Temperature: between 25°C and 200°C tested. Gas flow-rate: between 5 ml/min and 50 ml/min tested. ECD scavenger gas at detector response ioptimum conditions or through gas by-passing. Pressure: between 0.1 and 3 bar. Detectors: ECD, different branches, made in 1980. Amplifier: Carlo-Erba electrometer Model 180. GC amplifiers used in DAN1 model 3900 or PerkinElmer model F22. Recorder: 0.5 to 200,000 mV f.s.d., 0.3 s recorder Servogor from GoerzlBBC. Sample: CH,CI,, or CHCI,, or a mixture of both in n-heptane (Merck) ranging over 1:100,000 starting with maximum concentrations of 10.’ g/ml down to the ECD noise level under normal experimental conditions. Extreme concentration levels until detector saturation have been tested as well.
TABLE 6.3 DEVIATION OF ECD LINEARITY Normal conditions, clean carrier gas argon-methane ( 9 5 5 , v/v), not oversampled, just dairy analytical conditions. The data show linearity deviations are not constant (S-shaped function for signal deviation from linearity), and remarkably large (-20%!!) for quantitative analysis. Quantegg volume = 14.9 ml; gas flow F = 14.3 ml/min; maximum signal height = 140,000. Time
SignaI height
Corr. factor
38.4 89.4 135 178.8 220.5 262.5 304.2 347.4 392.1 440.1
63539.2 31769.6 15884.8 7942.4 3971.2 1985.6 992.8 496.4 248.2 124.1
1.192 1.055 1.017 1.009 1.036 1.059 1.087 1.089 1.065 0.989
130
WIDE-RANGE CALIBRATION OF ECDS
conditions are changed ind for the absolute signal levels to remain constant rather than having perfect linearity: However, at present we use primitive integration techniques and primitive quantitation equations, both of which depend on perfect linearity (cf. Table 6.3). 6.6. LIMITATIONS OF THE “QUANTEGG”
The most important condition for quantegg cahbrations is a stable and known position of the real signal baseline. Another weak point is that the quantegg signal starts at a maximum, and that at first we may consider this C, value as being correct, until we realize that non-linearity applies. From there we have to calculate backwards. If there is no linearity, one has to start the calculation at the lowest signal level. For manual evaluation both are troublesome, but not for on-line or off-line computation, where we can start with any value. The quantegg function depends on constant conditions of flow-rate and pressure. Therefore, a constant flowrate is important, but in gas chromatography this can be guaranteed to at least 1%. The quantegg will give false results if systematic losses by chemisorption on the inner surface occur. However, the surface can be deactivated and heated to the optimal temperature. The quantegg does not correct systematic calibration errors due to substance losses in the chromatographic column, but one can ascertain their magnitude by using the pneumatic circuit shown in Fig. 6.7.
Fig. 6.7. Pneumatic circuit for combined or parallel use of quantegg and a chromatographic (or capillary) column. G = carrier gas source. PI,P, = pressure regulators. I,, I, = sample inlet systems. N , , N,, N, = needle valves (outlet split for the injection systems; N, = carrier gas flow regulator for quantegg. Q = quantegg. C = column or capillary. R = analytical gas flow resistor kept under constant temperature. P, allows, together with the gas flows from C and Q , adjustment of the gas flow optimum for detector D. Pressure P, < pressure P, .
LIMITATIONS OF THE “QUANTEGG”
131
The quantegg installation must be gas-tight. The homogenization must be perfect and remain so, but here we have to consider limitations. There is a limiting lowest acceptable flow-rate through the quantegg. Below this value the practical elution curve is steeper than the theoretical shape allows, and homogenization is non-ideal. The flow-rate through the quantegg must be known and be accurate. This is not easy, but a very precise dead-time measurement can be used for flow metering. As the quantegg itself does (theoretically) not allow any dead time to the signal delay, the flow-rate (F) could be calculated by
F =
volume of the quantegg capillary dead time
It is no problem to measure the quantegg volume exactly, but one has to consider the exact pressure within the bulb for precise time data calculations. It turns out that the quantegg offers simple solutions to the problems encountered in quantitative chromatography, but there are many data to be handled if one wants high accuracy. The data evaluation is not simple. We used an Apple 48 kbyte double disk laboratory computer and used its CP/M version for easy data transfer to and from floppy disks. TABLE 6.4 TEST OF LINEARITY OF AN ECD The ECD was run under equal conditions of sample, sample amount temperature, flow, voltage, etc., but with differing carrier eases: A: swer clean nitrogen: B: common mixture of areon-methane. Time* A
164.4 234.6 285.9 338.4 399.3 492.6
Signal height** 8192 4096 2048 1024 512 25 6
Corr. factor***
H-Theor. 8
3.003 2.065 1.892 1.703 1.348 0.652
24602.4 8456.4 3874.9 1743.4 690.3 167
Quantegg volume = 14.9 ml; gas flow F = 13.6 mllmin; maximum signal height B
27.9 73.5 116.4 158.7 200.1 242.1 284.4 375
31667.2 15833.6 7916.8 3958.4 1979.2 989.6 494.8 123.7
1.048 1.005 1.007 1.019 1.047 1.064 1.077 1.001
=
300,000
33176.7 159 16.4 7975.3 4035 2071.3 1053 532.8 123.8
Quantegg volume = 14.9 ml; gas flow F = 14.3 ml/min; maximum signal height = 52,000. *Time: since injection of sample into quantegg. **Signal height: signal height in units (sensitivity times volt times 1000). ***Corr. factor = correction factor to achieve linearity. SH-Theor. = signal height times corr. factor.
132
WIDE-RANGE CALIBRATION OF ECDS
6.7. EVALUATION OF DATA 6.7.1. Data evaluation by manual measurements from a recorder display Fig.6.8 compares two records and Table 6.4 contains data from some measuring positions. If one examines both sets of data the whole procedure becomes evident and does not need further comment here, with one exception. Both sets of figures represent wide-range calibrations with CHzClz, CHC13 in n-heptane* as the test substance. In both examples the same detector and the same amounts of substance were used, the important difference being the carrier gas composition. The practitioner can imagine how rapidly and simply he can check his own detector conditions with respect to linearity, depending on the working conditions.
+
+
Fig. 6.8.1 1
+
Fig. 6.8.21 I t
/ C o r r e c t i o n factor value C o r r e c t i o n f a c t o r value 100
P
-Theoretical Theoretical Practicol *
Time
*
*
.
A+ .+ -.
Time
Fig. 6.8.12
+
100
Theoretical
+’?\
Fig. 6.8.22
C o r r e c t i o n f a c t o r value
+
+
+
-
100
[+]Run away
\\Practica
+ Time
.
* Time
Fig. 6.8. 6.8.1 1-6.8.22: computer prints of graphical evaluation in on-line or off-line quantegg calibrations. 6.8.1 1: Heavily overloaded ECD, carrier gas nitrogen. Hopeless to correct anything. 6.8.12: No overloading, but ECD with nitrogen as carrier gas. Detector remains extremely non-linear. 6.8.21 : Qualitatively and quantitatively the same conditions as in Fig. 6.8.11, but argon-methane as the carrier gas. 6.8.22: Same as in 6.8.12, but argon-methane as the carrier gas. The measurements are delicate. The gas flow must have an accuracy of better than 99%. The BASIC program (Table 6.5) offers possibjlities to check for gas flow and maximum signal errors. The corrections can be checked graphically.
*Tests wjth many other ECD-active compounds run comparably. Results are supported by FID, HCD, in GC and many different detectors in HPLC.
EVALUATION OF DATA TABLE 6.5
BASIC PROGRAM FOR QUANTEGG ]LIST
REM CLFAR
1 2 0
10 20
PUAllTLCC
RFM
40 50
6n 70
A3
70 1oc 101 102 110 11 1 11: 150
14"
150
163 IF Ff!L z "Y" UiLI! LOO 1L2 IF !! : ' ( 1." iTHEN 170 165
GOT? 1 l i PRINT : P R I l K " 4 YO!: 9NOU HALF TI!.IE 1 0 . 5 - T I b 5 ' ' ~ : HTAB 28: INPUT Y /PI 7" ; !I'? $ i,sr J t TRS = "I:" THEN PHIF!T : PRINT *I lili FIND HALF HEIGHT SIGNAL I': PRINT I ' -->L:OORCSP.lIb'E I S '0.5 - T I l i E ' 1 1 C PI'INT : PEINT " E W E R T l l I S VALUE HERE. .:!': IlTAB 28: INPUT ,' T . c, = ":I,, , ,-rr FPI!!T : PRI$T "-> YOU K!lOi THE QUANTECC VOLUVE?": HTAB 28: INPUT I( Y /hi 7";FR$ 21" :r w z = !*Y" P N P III > c ) TIIEII 250 71'f I' FR? = " t i " TIIEH 240 7 -?-Q 1 COT0120 123 COT0 ,~ PI'IKT: :P RF IRKI K"YOU ''YOwL!ST UWL!STKNOW KNOWT!IFT!IFVOLUI!E VOLUI!E I!: I!: PRINT PRINT"ECACTLY "ECACTLYBYBY +/-+/- 1 1 :'ir:)I? 1 PI'IKT PFI!IT: :PKINT PKINT"XEEASURE t'XEEASUREPRECISELY PRECISELY I ! ' !":":END END * * I !I"!:" :PFIIIT 'I: IITAU INPUTV V ?10 PETE!? : F r I ? ' T It EllTiI' VCL[!PF Ill t:L. 'I: t!TAU 35:35:INPUT 17fl
..
._
END / 10
TtX'F : H O X : POKE :Ll,2: INVERSE : FRIMT DATA INPUT WITII <-I> iion:+m : P r m T 'IQi VT,?R 2: !TAG 26: PRINT "3.5-? I " , l i Z : VTAC 4 : PRINT
'5'~
*
CORRECT
99:
(10 FiiR
:=
I IT1 10C
INPUT
I'
!ITAB 10: IIJPd?
INPUT
'I
f,40
PRINT I
(70
C(I) = IPiiIllT
CC "--)
II
"CORR.TIMC ( S ) T
CCRRCiT? THEN 'RETURN) EYl' ( (
C(TH)
z
-
E = ";E
SE::SIIIVITY
EIGHT ( Y M ) :
*
1) T(I) " ; I N T (10C
*
= ";II(I):H(I)
L
H(I)
E: IF
H(I)
I F T ( I ) < 0 THEN 6 j O OTllLR!4.<-1>'1;QU$: I F QU$ D "-1" THEN :" ; T ( I ) :
F / 'I)
C(I1 + ,005) / 100;" C ( P R ) = " ; H ( I !
134
WIDE-RANGE CALIBRATION OF ECDS
680 I F t l ( I 1 = 0 THE14 PRINT "VALUE CANNOT P,E >>ZER!3<<": GOTO 610 690 KF(I) = c ( 1 ) H ( I ) 7fl0 I F FB = "C" THEN K = N + 1 71C PRINT : PRIP!T * LINEARITY CORRECTIGN FACTOR = ',; I N T (100 KF(I) + ns, I ion 720 i f - H ( I > z.0 THEN 830 730 EIFXT 740 El T I 1
-
750
TEXT : PRINT : PRINT "CHANCE START SICN.IIEIGtIT ? (WAS I " ; C O ; " ) " : HTAB 30: INPUT " / Y , N > ? ";QU$ I T CU$ = "Y" THEN 780 PRINT : PRINT "CHANCE FLOh' VkLUE? WAS: 1,; I N T (100 * 60 F ) / 1 0 0 " "Y" THEN 767 ML/?^INl": tITAB 3 : INPUT " < Y , N > 7 ";QU$: I F QU$ GOTO 790 PRINT "CNTER IIEK VALUE FOR P!lASE FLOW": INPUT It F = ";F:F = F / 60:
760 7G5 766 167
GOSUB 1220 770 GOTO 790
780
PRINT ENlEH SENSITIVITY FACTOR E FOR 'C0' IL NCIU WAS- ";CO: INPUT IlEY P C 0 -VALUE PRINT tllt: PRINT : INPUT ,,+ PRINTOUT 'VALUES? U$ < > "Y" THEN 830
790 800
GOSUC
PRINT VALUE USED T I ";CO: GOSUB 1220
IT:
1160
PRINT "** WANT TO CHANGE STIIORTINC SICN.HT.?": PRINT "OH WANT TO S E E GRAPHICS 7": PRIRT I,--> CHAIIGING: ENTER VALUE-< >": INPUT "-4 G <0> HERE ";W: I F W = 0 THEN 8 3 0 RAPHICS? ANTER 820 CO = W: GOTO 790
810
e3n REV
8JlO I F T(N) = 850 I F T ( N ) = 61.0 IF TOI) = 870 FIF. : U
< 2 22 < 3 ZZ < 4 * ZZ
THEN BE = 2: GOTO 8P.O THEN BE c 3: GOTO 880 TflEfl BE = 4
*
~
8110 FX = 250 / (RE Z2):FY = 157 / (CO P90 PRItiT : PRINT "GRAPHICS RANGES CVER CONCFNTRP.TION 'I: PRII!T 900
9lC 920
130 9110 950
IIIFFY: j w o c i C l i : IHCOLOR: 7 !ITLCT 11.0 TO 0,159: IIPLOT FOR 2 = 1 33 250 STEP 3 Y = FY CO 1 E l * EXP ( ( !PLOT Z , 157 - Y
El)
";6E:
PRINT "ORDERS OF MRGN. OF
TO 250,159
-
1)
*
F / Vl
FX)
(Z /
I6C NEXT
tIPL(IT 0,79 TO 21O,7? l C O FCR I z 1 TI\ N 190 IX z T C I ) FX:YP = FY lI(I) El in00 ~i = K K F ( I ) 1010 I F Y 1 > I 5 6 THEN Y l z 116 1020 I F Yl < 3 Tl!Ul Y 1 = j 1030 I F YP > 158 Tlikl; YP = 15: 1040 IF YI' < 2 T!iE!I YP = i I050 I F IX > 250 THEN I X z 250 1OGC I F IX < 2 nlEN IX 2 1070 tIPL0T I X + 1,151 - YP TC IX - 1,159 YP 1080 IIPLOT ? X , 1 5 1 - YP + 1 TO IX.159 - YP - 1 l09C IIFLST IX,15? - (Y1 + 21 TO IX,159 - (Y1 - 2 ) : HPLOT I X 2,159 - Y1 TC IX + 2,159 - Y 1 1 1 0 0 NFXT 1110 PRINT : PKII!T ' I ";EE" ORDERS OF MACN. RANGING; ---> T" I120 VTAB 22: II!PUT !'ADD DATA
-
I
1160 C$ = CIIRS.
T","tI-TIiFCR.":
rrn I
I190
rtm TFXT : IIOXE : cmo 750 FCR I = N + 1 TIC 1 0 0 : GOTO 6 1 0 **; RESTART 6Y 'GOTO 7 5 0 " ' : END
THEN
EYE
(ti):
PR?t:T D$;"PR'11": PRINT "TIME"," SICN.I!T.","CORR.FAC t'E?IIT ' 8 ________________________________________------
= I T C ~:I PQI?IT T ( T ) , I ~ ( T ) :!;T ,
IIK
lion
5) / 1c
-
( ~ ~ ( 1 1IOGC + .5) /
NfXl
10o0,
Iiir ( c ( I )
FiuW F = "; IPil ( F
1210 PRJIUT : I'RIIIT 1223 FOK I = I TO N:C(I) T CO * LXP 1 / II(1): IlEXT : PRINT "TI:;E
((
-
1) * r ( I ) SIGNdL
*
1u +
.
*
1
b0
F / Vl:I(F(Il 2(I CORR.LACTOR": PAIN7
o______________________________________,,
1230 1240 1250 1261:
FOR I = 1 TO N : PIIIf(? T ( I ) , t l ( I l , I N T (I00 I K F ( i ) ) / 100: EiEXT PHItlT : INPUT CONTIHbC
REE'
KCESSEP!
LITERATURE
135
6.7.2. Data evaluation with a laboratory computer Table 6.5 gives parts of the BASIC program (Applesoft Basic) as well as a program that runs under CP/M conditions, which we wrote to make calibration simple. If one can use an Apple 48 kbyte computer, one disk and a monitor for qualified graphics representation, one will have a screen display as shown in Fig. 6.5; it is much easier to read a picture than numbers in order to be able to make immediate decisions. If line L in Fig.6.5 (which represents the non-linearity correction factor) deviates by more than 1% from the middleline M, then non-linearity causes systematic analytical errors. We have never seen h e L coinciding with line M with any GC detector that we have checked during the past 2 years work with the quanteggs.
LITERATURE R.E. Kaiser, Pittsburgh Conference 1980, Atlantic City, paper No. 111. R.E. Kaiser and R.I. Rieder, GITFachz. Lab., 24 (1980) 633-639.