through the molten material. The susceptor thus approaches or falls away from the plane of the coil as the melting point of the sample mixture changes. Therefore, the zone length remains constant at the selected speed. RECEIVED for review February 28, 1968. Accepted April 29, 1968. Presented in part, Division of Petroleum Chemistry,
American Chemical Society, March 1966, Pittsburgh, Pa, Work upon which this report is based was done under cooperative agreements between the Bureau of Mines, U. S. Department of the Interior; the American Petroleum Institute; and the University of Wyoming. Reference to specific brand names is made for identification only and does not imply endorsement by the Bureau of Mines.
Linearization of Electron Capture Detector Response by Analog Conversion D. C. Fenimore Texas Research Institute of Mental Sciences, Houston, Texas 77025
Albert Zlatkis and W. E. Wentworth Department of Chemistry, University of Houston, Houston, Texas 77004
THERELATIVELY NARROW linear response range of the electrpn capture detector is often a disadvantage when this device is used in quantitative gas chromatographic analyses. This problem is particularly acute in multicomponent analyses where the electron capture coefficients and concentrations of the individual compounds can differ by many orders of magnitude. To improve the accuracy and facility of electron capture quantitation, we have devised an analog converter by which the amplified detector signal may be recorded as a linear function of sample concentration over an appreciably extended range. The electron capture detector responds to the presence of species having an affinity for thermal electrons by exhibiting a decrease in detector current ( I ) . This is normally displayed by subtracting the detector current, I,, from a constant applied current, 1 0 , of a magnitude equal to 1 8 when only the carrier gas is flowing through the detector-ie., 10 - I, = 0 when no capturing species are present, and sample response is then recorded as a departure from zero base line. The response is quite linear with sample concentration if Ib - I , is very small with respect to l a , but when l a - l e exceeds approximately 1.0% of the value of 10, nonlinearity becomes apparent. As the response approaches the value of the total deRctor current, further increases in sample concentration produce undiscernible changes in response and the detector is said to be saturated. Unfortunately, this region of nonlinearity is the most useful portion of the response curve with regards to absence of detector and electronic noise. Originally the relationship between vapor concentration and the observed current change in the pulse sampled electron capture detector was believed to be similar to that of Beer’s law for light absorption (2). In studies of the kinetics of this mode of operation, however, Wentworth and his coworkers (3) derived the following expression : (Ib
- le)/Ie = Ka
(1)
where K is the electron capture coefficient of a given substance and is similar to the relative coefficient described by Lovelock, (1) J. E. Lovelock and S. R. Lipsky, J. Am. Chem. SOC.,82, 431 (1960). (2) J. E. Lovelock, ANAL.CHEM., 35, 474 (1963). (3) W. E. Wentworth, E. Chen, and J. E. Lovelock, J. Phys. Chem., 70,445 (1966). 1594 *
ANALYTICAL CHEMISTRY
8 .O
7.0 6.0
5.0
4.0
3.0
2.0 I .o
0
1.0
2.0
3.0
CONCENTRATION(ARBITRARY UNITS)
Figure 1. Fraction of standing current, (Ib - Is)/&, and linear response function, (I* - Ze)/Io us. concentration and a is the instantaneous sample concentration. A comparison of the above function with the normally displayed l a I , is shown in Figure 1. Here, for the purpose of illustration, the Wentworth function is assumed to be linear and the normal response is derived and shown as (IO - Ie)/Io, i.e., as a fraction of the total standing current. At small values of - Ze the two functions are seen to converge, but when Ib - Ie is 10% of the total standing current, this response is in error by 10% compared with the linear function. A chromatographic fraction is eluted in a finite time, and the vapor concentration varies during this interval. Conversion by means of the above expression should therefore be per-
1
PK
IOOK
4. SCALE
FACTOR
Figure 2. Schematic diagram of analog converter
formed continuously in order to reproduce faithfully the chromatographic peak, and this computation is readily accomplished by analog operations. The results using an analog instrument were described in a previous publication ( 4 ) . In this device the signal from a vibrating reed electrometer was converted to the (Ib - &)/le signal followed by analog integration. The integral was displayed on a conventional potentiometric recorder and hence was limited to the range of the recorder. In addition this previous instrument provided no means by which the converted signal could be displayed as a conventional chromatographic peak before integration. A display of the converted signal is an advantage in analytical gas chromatography because this signal gives the true shape of the gas chromatographic peak. Small shoulders and asymmetry of the peaks can be more readily discerned with such a display. The analog device described in this paper permits recording of the converted signal, or, if used with a digital integrator, the full dynamic range of the detector could be utilized without attenuation. From the function defined in Equation 1, it can be seen that the only mathematical operations required for conversion are subtraction and division, and only one quantity, le,is variable during the elution of a chromatographic fraction. It is then a simple matter to arrange the appropriate amplifier circuitry to perform these operations. EXPERIMENTAL
A schematic drawing of the analog converter is shown in Figure 2. The detector current, I,, is amplified by a chopperstabilized, parametric amplifier (Philbrick Model SP2A) operated as a current-to-voltage transducer with feedback resistance selected for an output of approximately 1 volt at maximum input current. This initial amplifier functions as would the electrometer in normal electron capture detection. The output voltage of this amplifier, which is proportional to le,is then fed to the inverting input of a differential amplifier. A variable voltage representing I b and sup-
plied by a voltage divider is fed to the noninverting input, and the output of the stage is then proportional to b - I,. The input and feedback resistances of this amplifier are selected for unity gain. The l b - le voltage together with the original I , voltage then enters a logarithmic multiplier-divider based on the design of Paterson (5). An additional voltage is inserted at the multiplier-divider to provide a continuously variable scale factor. In this device, the output of the individual input operational amplifiers are logarithmic functions of the input voltages. By adding and subtracting these voltages and then extracting the antilogarithm, multiplication and division can be accomplished. Philbrick Model P85AU operational amplifiers were used throughout this circuit, a Philbrick Model PPL2 Dual Logarithmic Transconductor furnished the nonlinear feedback elements, and a Philbrick Model PR-300 power supply furnished the proper operating voltages. A four position switch permits any of the voltages representing I,, (Ib - le),( l a - le)/le, and scale factor to be selected for recording, and a voltage divider provides attenuation of 1, 10, and 100. The output of the final amplifier is then a voltage equal to the product of the ( l b - I,) voltage and the scale factor voltage divided by the I, voltage. The converter is operated by first applying a scale factor voltage of a magnitude such that the maximum converter output voltage will be of a convenient value for a given recorder sensitivity. With the detector collection pulse potential applied, the I b voltage is adjusted so that ( Z b - le) is zero when carrier gas only is flowing through column and detector. With the function switch at (& - Ze)/Ze and with appropriate attenuation the converter then provides a signal to the recorder which is linear with respect to sample concentration within the limits discussed previously. The electron capture detector used in this study was of coaxial geometry and contained a 1.04 curie tritium foil (Hastings Radiochemical Works, Houston, Texas) which produced a standing current of 5.6 x 10-8 ampere with argon/lO% methane carrier gas and collection pulses of 1 psecond width, 30 volts amplitude, and 1000 psecond interval. Pulses were supplied by a Datapulse Model 102 pulse generator. Samples were introduced into the chromatographic column by means of a 0.25-pl liquid sampling valve supplied by Biotron, Inc., Houston, Texas.
(4) W. E. Wentworth and E. Chen, J . Gas Chromatog., 5 , 170 (1967).
( 5 ) W. L. Paterson, Rev. Sci. Instr., 34, 1311 (1963). VOL. 40, NO. 10, AUGUST 1968
0
1595
MOLES
DICHLOROBENZENE x 169
Figure 3. Per cent standing current, (I* concentration of o-dichlorobenzene
-
le)/& (loo), us.
RESULTS AND DISCUSSION
Chromatographic peaks obtained from various concentrations of o-dichlorobenzene as normally displayed by electron capture detection are shown in Figure 3. The marked nonlinearity of response resulting when I b - Ze approaches Zb is readily apparent. The converted response of the identical sample concentrations is shown in Figure 4. Here the peak heights are quite linear with sample concentration, and the peaks assume the shape normally associated with linear response. The noise level of an electron capture detector with a tritium ampere (6),and by consource is approximately 1 X vention the lowest detectable signal is two times the noise level. If the standing current of a detector is 5 X lo-* ampere, and if we assume the normal response, 10 - I,, is linear to 1% of saturation, a value that can be verified by application of the response function (Equation l), we find that the range of linearity is 250. By making use of the region between l and 90% of saturation through response conversion, the linear range is increased to 2.25 X lo5. This value may be difficult to attain in actual practice because of instability of electronic components, column bleed, carrier gas impurity, etc., but the range of converted response can be at least two orders of magnitude greater than normal response. The response to a range of concentrations of o-dichlorobenzene is shown in Figure 5 . Here the linear range is 2.5 X lo4. The upper limit for the employment of the response converter was about 90% of detector saturation. Definite departure from linearity was observed at higher values, and this is probably caused by the error introduced in computing 1 0 - ZJZ, when 1, is very small compared to 10. In extending the conversion to 90% of detector saturation and above, it is well to remember the error propagation on to the converted function. Let f = (10 - Ze)/Ze, then the relative error in f (which is equal to the relative error in concentration) is given by
where gY is the error in the converted measurement. Because (Ia - I,) can be made a maximum by attenuation, the (6) G. R. Shoernake, D. C. Fenimore, and A. Zlatkis, J. Gus Chromatog., 3, 285 (1965).
1596
ANALYTICAL CHEMISTRY
1.5
1.0
0.5
2.5
2.0
MOLES 2- DICHLOROBENZENE x
ti9
Figure 4. Analog converted response us. concentration of odichlorobenzene 10.0 I
O.OO'
I
t /
0.0001
I
I
I
I
1~1613 1~1618 l X d l
I
I
J
1x160 1~169
MOLES p-DICHLOROBENZENE
Figure 5. Logarithm graph of analog converted response us. concentration of o-dichlorobenzene term in brackets governs the error propagation. In the linear region of (10 - I,) the ratio of 1b/1e is approximately unity, and At 90% c a p the square root of the term in brackets is ture the ratio is 9 and the square root of the term in brackets is or an increase in standard error of 6.4. However, at 99% capture the ratio is 99, the term in brackets is also approximately this value, and there is an increase in total error of IO. The analog conversion of an electron capture response to a linear function of concentration has increased the utility of the electron capture detector in gas chromatographic analyses. This conversion produces a peak which accurately represents the sample concentration. The quantitative aspects of this approach should prove quite useful in the analysis of pesticides and electron capturing derivatives in biomedical analyses.
h.
RECEIVED for review February 29, 1968. Accepted April 19, 1968. Work supported in part by Public Health Service Grant Number AP 00308-04 and also by AEC Contract Number AT-(40-1)-3541.
