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Capacitive Integration to Produce High Precision Isotope Ratio Measurements on Methyl Chloride and Methyl Bromide Samples John F. Willey and James W. Taylor" Department of Chemistry, University of Wisconsin, Madison, Wisconsin, 53706
Jackson and Young (8). In this system, the two ion beam currents are integrated and the output of the two integrators is inverted to obtain positive voltages which are ratioed using a digit digital voltmeter (DVM). This system has several advantages over the conventional circuitry including (a) improved precision due to the elimination of the high value resistors and averaging of ion beam fluctuations, (b) elimination of the need for manually drawing a "best" line through a noisy recorder trace to measure the off null residuals, and (c) the availability of data in a digital form for automatic printing or computer processing. A circuit similar to that of Jackson and Young has been constructed which avoids the use of voltage inverters. This paper discusses the various sources of error in this type of circuit and the selection of circuit components t o minimize these errors. Results of measurements on methyl chloride and methyl bromide gases are presented and discussed. These gases were selected for analysis because a procedure exists for the quantitative conversion of chloride ion into methyl chloride gas ( 5 ) ,and work in these laboratories has shown that a similar conversion of bromide ion to methyl bromide is possible (9).
A capacitive integration circuit for the measurement of ion current ratios In an Isotope ratio mass spectrometer is described. Sources of error and their effect on measurement precision are discussed. Results from the isotopic analysis of methyl chloride and of methyl bromide gases are presented. The relative standard deviation of measured ratios for methyl chloride was 13 parts In loe while that for methyl bromide was 7 parts in lo6.
T h e measurement of heavy atom kinetic isotope effects (KIE) is used t o elucidate reaction mechanisms ( I , 2) and to probe transition state structures (3. 4 ) . T h e precise measurement of isotope ratios, which are used to calculate KIE, is generally performed via isotope ratio mass spectrometry using a dual inlet, dual collector instrument specifically designed for this purpose ( 5 ) . Because t h e magnitude of the KIE is proportional to the relative mass difference of the isotopes involved, the determination of meaningful KIE values for increasingly heavier elements requires a corresponding increase in the precision with which isotope ratios may be measured. For example, chlorine leaving group KIE have a maximum value of approximately 1.01, and the instrumental precision with which chlorine isotope ratios have routinely been measured in our laboratories is 7 parts in lo5. Bromine, an element of significant mechanistic interest. should have a maximum leaving group effect of about 1.0033. Thus it would be desirable to increase the routine measurement precision to a t least 2 parts in lo5. It is primarily for this reason that we undertook to study the sources of error in isotope ratio measurements with t h e aim of increasing the measurement precision. Most modern isotope ratio instruments are based on the original design of Nier (6) with the modifications of McKinney e t al. (7). In these instruments, the larger of the two ion beam currents is converted t o a voltage using an operational amplifier with a large (typically 10" Q)feedback resistor and this voltage is fed to a Kelvin-Varley voltage divider. The output of the voltage divider is fed through a second large resistor t o produce a current which is nulled against the smaller ion beam current using the variation in the voltage divider to approach the null condition. A second operational amplifier is used t o sense accurately the approach to null, and differences smaller than the least significant digit on the voltage divider are interpolated by recording the output of the second amplifier on a strip chart recorder and measuring the residual off null signal from the chart tracings. T h e factors limiting the precision of this type of circuitry are t h e inherent noise of the large value resistors, the large voltage and temperature coefficients for these resistors, and the ability of the operator to draw reproducibly the "best" straight line through the recorder tracings and measure the off null signal. An alternate means of determining the ratio of the ion beam currents is a capacitive integration system described by 0003-2700/78/0350-1930$01 OO/O
EXPERIMENTAL The capacitive integration circuit is shown schematically in Figure 1. The amplifiers are Teledyne Philbrick model 1702-01 (Teledyne Philbrick Co., Dedham, Mass.). These units have a specified bias current of 5 X A (max) with a temperature coefficient of 2 X A/"C. The output noise in the 0.016 to 1.6 Hz frequency range is 10 p V p-p. The amplifiers are mounted in Teflon insulated sockets (Teledyne Philbrick model 6123). The capacitors are hermetically sealed Teflon dielectric capacitors (Series DjlD, Component Research Co., Santa Monica, Calif.). Teflon capacitors were chosen because of their high insulation resistance, low dielectric adsorption coefficient, and low temperature coefficient. They are rated for 200 V and have a specified minimum insulation resistance of 1013Q. The reed relays were a custom order item (Coto-Coil Co., Inc., Providence, R.I., engineering number E-8246) and consist of a Hamlin model MRH-15 Form A relay (Hamlin, Inc., Lake Mills, Wis.) wound for 1 2 V dc operation and fitted with complete electrostatic shielding. They are operated at 8 V dc and are fitted with 1N48 diodes across the coils to suppress transients when the coils are de-energized. A 1000-R resistor is placed in series with each relay to limit the discharge rate of the capacitors and avoid dielectric strain. The manual switches were constructed as single pole, single throw switches with beryllium copper contacts which are isolated on Teflon standoffs. These switches were patterned after the zero check switch of a Keithley Model 602 solid state electrometer (Keithley Instruments, Inc., Cleveland, Ohio). The switch shafts are sealed with O-rings so that the circuit boxes can be desiccated. The open contact resistance of these switches was measured to he greater than 1014 R. The operating sequence is controlled by a cam actuated, motor driven timer (Model 540, Cramer Division, Conrac Corporation, Old Saybrook, Conn.) with six single pole, double throw switches. The total cycle time may be selected as 90: 135, or 180 s by changing the gear ratio. Each of the controlled events (eg., reed relay opening/closing, DVM data hold, gas valve switching, etc.) may be individually adjusted by the proper positioning of the cams
C
1978 American Chemical Society
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RESULTS AND DISCUSSION In isotope ratio work, it is the relotiue difference between the measured ratios for the standard and sample gases which is used in determining the isotopic composition of the unknown gas. This relative difference may be calculated using Equation 1.
R , .- R, Rs
Ru R,
relative difference = -- = 1 - -
Figure 1. Schematic of capacitive integration circuit
on the timer shaft. Typically a 135s cycle is used with a 60-s integration time. A typical operating sequence is as follows. (1)The reed relays are opened and integration begins. (2) After a delay to allow the plate circuit integrator to reach a voltage greater than 5 \' (the minimum reference voltage required by the DVM), the hold mode on the DVM is released and the ratio of the integrator outputs is displayed. (3) Sixty seconds after the start of integration, the hold mode of the DVM is actuated and the final ratio value is transmitted to the Teletype. (4) The reed relays are closed, thus discharging the capacitors. (5) The gas valve assembly is switched such that the gas from the other half of the dual inlet system is fed into the mass spectrometer source. The instrument is allowed to stabilize with this new gas for 75 s. (6) The cycle is repeated. The digital voltmeter is a Julie Model DM lOl0PM (Julie Research Laboratories, Inc., New York, N.Y.). This is a 61/2digit unit which operates on the principle of an auto-balancing reed switched Kelvin-Varley voltage divider. It has an accuracy in the ratio mode of better than 1 part in lo6, and thus will not be the limiting factor in the overall measurement precision. It is capable of ratioing negative voltages directly so inverters can be avoided. The output of the DVM is interfaced to a Comdata Modified ASR33 Teletype (ComData Corp., Skokie, Ill.). The mass spectrometer used for these studies was a Nuclide Model 6-60 RMS (Nuclide Corporation, State College, Pa.). It has been modified by the addition of an externally adjustable source slit assembly. This assembly consists of two fixed slits of 0.30-mm width with the second slit located 9 mm behind the first slit. Each of the slits may be independently translated by means of micrometers with bellows sealed feedthroughs. For the analysis of methyl chloride gases, the mass spectrometer is operated a t an accelerating potential of 4.0 kV and the source filament is regulated to maintain a constant source trap current of 200 FA. The source slits are centered. The sample and standard pressures are adjusted such that the ion beam currents for the m / z 52 ions (CH,"7C1)are between 1.99000 X and 2.00000 X lo-'' A and are matched to within 3 X A. This requires a sample inlet pressure of approximately 12 Torr. The cup circuit and plate circuit capacitors are 0.0018 FF (1.8nF) and 0.0056 pF (5.6 nF), respectively. For the analysis of methyl bromide samples, an accelerating potential of 3.8 kV is used and the source trap current is regulated at 200 PA. The slits are narrowed by moving the front slit 0.18 mm toward the center of curvature of the ion path and the rear slit 0.01 mm away from the center of curvature. The sample and standard pressures are adjusted such that the ion beam currents for the m / z 96 ions (CH381Br)are between 2.49000 X and 2.50000 X A and are matched to within 3 X A. This requires an inlet pressure of approximately 7 Torr. The cup circuit and plate circuit capacitors are 0.0018 IF (1.8 nF) and 0.0027 IF (2.7 nF), respectively. Upon the initial introduction of either methyl chloride or methyl bromide gas to the instrument, it is observed that the intensity of the ion beam currents drifts steadily downward. The rate of drift decreases with time and it has been found necessary to allow a 2-h stabilization period before any ratio measurements are made.
(1)
where R, is the measured ion current ratio for the unknown gas, and R, is the measured ion current ratio for the standard gas. Instrumental Factors Affecting Precision. In the capacitive integration circuit, the precision of the relative difference is limited by variations in the amplifier bias currents, leakage currents, switching transients, and amplifier input voltage noise (flicker). The theoretical limit to the precision arises from statistical variations in the ion beam intensity. The influence of each of these factors on circuit design and performance will be discussed separately. In this context the errors considered here are only those associated with the electronic processing of the detector responses. Other factors such as peak overlap, valve leakage, and background pressure will also affect the measurement results and have been discussed in detail by Deines (10) and by Mook and Grootes ( 1 1 ) . Bias Currents. The operational amplifier bias currents are integrated along with the currents from the detectors and will thus constitute a source of error. T h e output of the integrator may be expressed as
where I , is the ion beam current, Jb is the amplifier bias current, t is the integration time (in seconds), and C is the capacitance (in farads). From typical values for the ratios and ion currents and by using the manufacturer's specification of A for the bias current, it can be shown that the f5 X bias currents contribute equally to the integrations for both the sample and standard gases and, thus, introduce no error at the part-per-million level provided the bias currents remain the same during the period in which the ratios for both t h e standard and sample gases are measured. Leakage Currents. The transfer of charge to or from the input of the operational amplifier via any path other than from the detector or the active feedback component will give rise to an error signal. T o minimize these currents, all elements were insulated with Teflon and components of the feedback loop were selected to provide maximum insulation resistance. In addition, the circuit was thoroughly degreased after assembly. Further, because surface conduction across insulators increases with high relative humidity, the circuit box was sealed and desiccated with Drierite (calcium sulfate). Switching Transients. Switching transients may occur as the reed relays open to initiate the integration cycle. T h e reed relays were constructed with electrostatic shielding to minimize this but, when initially tested, shifts in the integrator output upon reed opening of up to 2.5 mV were observed using a Biomation Model 802 Transient Recorder. Reduction of t h e coil voltage from 12 V to 8 V anti the addition of diode coil suppression reduced these shifts to below the limits of detectability (estimated to be 0.05 mV). Amplifier Voltage Noise. Fluctuations in the input offset voltage (input voltage noise) will cause corresponding fluctuations in the output voltage. The specified input noise for the Teledyne Philbrick model 1702-01 amplifier in the low frequency range (0.016 to 1.6 Hz) is 10 pV peak to peak. The measured ratio value would be most affected if the error in
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ANALYTICAL CHEMISTRY, VOL. 50, NO. 13, NOVEMBER 1978
the output of one amplifier were f 5 pV and that of the other amplifier were -5 pV at the time when the final ratio value was recorded. If, a t the end of the next integration period, the offset voltage values were reversed (-5 p V and +5 pV), then the maximum error in the relative difference value between these two ratios would be observed. Cnder these conditions, and assuming typical current and voltage values for methyl bromide samples, the value calculated for the relative difference would be in error by 0.000002. S t a t i s t i c a l Variation in Ion Beam Intensity. The ultimate limit to the measurement precision is the statistical variation of the ion beams. The random distribution in time of the ions gives rise to fluctuations in the instantaneous currents. The uncertainty in the measurement of the ion beam current is related to the number of ions collected (N) according to Equation 3 (12). UN
=
fi
(3)
Q,
to a line described by Equation 7 where x is the order (time) variable
y = a x 2 + bx
The integrator voltage is related to N by Equation 4
V=-N C
Table I. Measured Ratios f o r a Sample of Metllyl Bromide entry standard ratios sample ratios 1 0.956 889 0.955 813 2 0.956 660 0.965 802 3 0.956 882 0.955 795 0.955 783 4 0.956 881 5 0.956 870 0.955 768 0.956 859 0.955 756 6 7 0.956 850 0.955 743 0.956 827 0.955 729 8 0.955 713 9 0.956 805 10 0.956 795 0.955 705 0.956 790 0.955 693 11 12 0.956 771
(4)
where Q, is the charge per ion (1.6 X C per ion for singly charged ions) and C is the capacitance in farads. Thus, by propagation of errors (13),the relative error in the integrator voltage is
Similarly, because the measured ratio is the ratio of the two integrator voltages, the relative uncertainty in the ratio is given by
Under normal operating conditions for methyl bromide, the output voltages a t the end of the integration cycle are approximately 9.3 V and 9.7 V for the cup and plate circuits, respectively. From Equation 4,the values of N1 and N 2 are calculated to be 1.0 X 10l1and 1.6 X loll. The statistical limit to the relative uncertainty in the measured ratio values calculated from Equation 6 is then 4.0 parts in lo6. The uncertainty in the relative difference values (which are calculated from the ratio of these ratios) would then be about 5.5 x 104. Statistical T r e a t m e n t of Data. The measured ratios for one sample and standard of methyl bromide are listed in Table I. It can be seen that the ratios for both the standard and sample drift downward during the course of the measurements. This is typical of the results although occasional data sets show an upward drift or a reversal. The drift for both, however, is always in the same direction. The origin of this drift is unknown but is believed to be related to the drift in ion currents. The presence of this drift complicates somewhat the procedure for calculating the relative difference between the sample and standard ratios. In the absence of a technique for random switching, it is possible to correct for this drift mathematically by fitting all of the ratios for both the standard and sample to a quadratic line using a least squares fit with a dummy shift variable (14). In this method, the data are fit
+ c + dz
(7)
such that x = 1 for the first measured ratio, x = 2 for the second measured ratio, etc. The dummy shift variable, z , is assigned a value of 1 for each standard ratio and 0 for each sample ratio. The values of y used for the fit are y1 = I?,/!?,, where R, is the average of all of the ratios measured for the standard gas. The effect of this fitting process is that the ratios for both the standard and sample gas are fit to a single line by selecting the value of d which shifts the standard ratios to fit with the sample ratios. The resulting value for d is the average relative difference between the sample and standard ratios. This type of regression analysis is possible using the Minitab I1 statistical package developed a t Pennsylvania State University, Department of Statistics. Using this program provides not only the value of d but the standard deviation of 3’ about the regresson line, the standard deviation of d , and a table of the standardized residuals. (The standardized residual is the residual, y observed - y predicted, divided by the estimated standard deviation.) Also a “scatter plot” of standardized residuals vs. x and a histogram of the standardized residuals is provided as a convenient visual check for systematic errors and outliers. Outliers, ratios which are widely deviant from the least squares line, are occasionally observed. Entry 2 of column 1 in Table I is an example of one such point. The most common source of these is believed to be irreproducible valve seating in the glass ball valves which are used to select which of the two gases in the dual inlet system is introduced into the mass spectrometer. T o determine when a data point is sufficiently deviant to be discarded, a Dixon Test (15) is applied to the standardized residuals a t the 0.05 level of significance. The frequency of occurrence of outliers is about 270, that is, 15 outliers were found in a total of about 900 data points representing 45 analyses on methyl bromide. Methyl Chloride. Four samples of methyl chloride which had previously been analyzed on this instrument using conventional null detecting circuitry were analyzed using the capacitive integration circuitry. The results are listed in Table 11. A plot of the relative difference values determined via capacitive integration vs. those determined via null detection had a linear least squares slope of 1.05 (standard deviation = 0.06) and a correlation coefficient of 0.996. These results indicate that the relative differences obtained from both circuits are equivalent. The average standard error for the null detecting circuit was 3.02 x while that for the capacitive integration circuit was 5.25 X lo4. This represents an improvement in precision of better than a factor of 5 . Methyl Bromide. Forty-five samples of methyl bromide have been analyzed. The average standard deviation of y
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Table 11. Results for Methyl Chloride Samples Analyzed via Null Detecting and Capacitive Integration Circuitry calculated relative difference values* (and standard errors)b SampleC null detecting
1
0.010 261 (0.000 034) 0.010 1 7 9 (0.000 005)
2 0.009 972 (0.000 031) 0.009 926
3 0.009 655 (0,000 030) 0.009 720
4 0.008 758 (0.000 026)
capacitive 0.008 7 7 0 integration (0.000 005) (0.000 005) (0.000 006) a The reported relative differences were calculated using the least squares regression, with shift variable, as described in the discussion of Equation 4. The standard error values are the standard deviations of the calculated shift variable. All data sets contained 1 0 to 12 ratio measurements for each of the two gases (sample and standard), These samples represent various fractions of reaction so the actual measured ratios are not expected to be the same for each sample. Table 111. Results of Day to Day Precision Study on Methyl Bromide relative differences (and standard errors) sample 1 sample 2 sample 3 day 1 0.001 149 0.001 157 0.001 153 (0,000 003) ( 0 , 0 0 0 003) (0.000 003) day 2 0.001 149 0.001 136 0.001 147 (0.000 003) (0.000 003) (0.000 003) day 3 0.001 137 0.001 154 0.001 149 (0.000 004) (0.000 002) ( 0 , 0 0 0 003) about the regression line (from Equation 7) was 7.6 x This corresponds to a relative standard deviation of the measured ratios of 8 parts in lo6. The average standard deviation of the shift variable was 3.4 X lo4. Comparison of these results with those obtained for methyl chloride indicates that the experimental precision is better for the data obtained on methyl bromide. The errors reflected in these data are a combination of the errors inherent in the electronics, the statistical fluctuations in t h e ion beam intensities, and the errors introduced by other instrumental factors such as peak overlap and background pressure. Since the error inherent in the electronics should be the same regardless of the nature of the ions which make u p t h e ion beam current, and the contribution from ion beam fluctuations is nearly the same (3.7 parts in lo6 for methyl chloride vs. 4.0 parts in lo6 for methyl bromide), it seems probable that the difference in the precision observed for the two gases arises from instrumental factors relating to the mass spectrometer itself. This is especially likely in light of the fact that a great deal of effort was expended in maximizing the instrumental performance for methyl bromide while the methyl chloride data were obtained with the instrument operated under the same conditions normally used with the null detecting circuitry. T o test the day to day repeatability, three identical bromide samples were converted to methyl bromide and were run on each of three days. T h e results are presented in Table 111. A one-way analysis of variance with the data grouped according to day run was carried out using the procedures described by Wetherill (16). The calculated F value to test the null hypothesis t h a t the groups all have the same mean was 1.36. The F (2, 6) value a t 5% from the F-table (17) is 5.14. Thus there was no significant difference between the values obtained on t h e different days. The standard deviation of the nine values in Table I11 was 7.2 X lo4. This is larger than the average of the standard deviation of the shift variables of the 45 analyses cited above (3.4 X 10')). This indicates that there is a run to run variation which is larger than the variation within a single run. The largest single factor contributing to this variation is believed to be the matching of the sample and standard gas pressures
prior to the run and the amount of pressure mismatch which develops during the time that the ratios are being measured (45 min for 20 ratios). The effects of pressure mismatch have been studied by Mook and Grootes (11)with the conclusion that changes in ion beam broadening caused by ion molecule collisions are a major contribution t o this effect.
CONCLUSIONS The ability of capacitive integration to increase the precision with which relative isotope ratios may be determined has been demonstrated for methyl chloride and methyl bromide. In addition to increased precision, the use of capacitive integration also has the advantages that the data are available in a digital form for automatic printing or computer analysis, and the need for manually drawing the "best" line through a noisy recorder trace and making measurements from these tracings is eliminated.
ACKNOWLEDGMENT The authors express their appreciation to Paul Bender and Ted DiFiore for their aid with the isotope-ratio instrument and to Ted Weigt for his circuit design and aid in t h e interfacing t o the teletype.
LITERATURE CITED A. Fry in "Isotope Effects in Chemical Reactions", C. J. Collins and N. S.Bowman, Ed., Van-Nostrand Reinhold, New York, N.Y., 1970. D. G. Graczyk and J. W. Taylor, J . Am. Chem. Soc.. 96, 3255 (1974). R. C. Williams and J. W. Taylor, J . Am. Chem. Soc.. 96, 3721 (1974). R. L. Julian and J. W. Taylor, J . Am. Chern. Soc., g8, 5238 (1976). J. W. Taylor and E. P. Grimsrud, Anal. Chem., 41, 805 (1969). A. 0. Nier, Rev. Sci. Instrum.. 18. 398 (1947). C. R. McKinney, J. M. McCrea, S.Epstein. H. A. Allen, and H. C. Urey, Rev. Sci. Instrum., 21, 724 (1950). M. C. Jackson and W. A. Young, Rev. Sci. Instrum., 44, 32 (1973). J. F. Willey and J. W. Taylor, Department of Chemistry, University of Wisconsin, Madison, Wis., unpublished work, 1977. P. Deines, Int. J . Mass Spectrorn. Ion Phys.,4 , 283 (1970). W. G. Mook and P. M. Grootes, Int. J . Mass Spectrorn. Ion Phys., 12, 273 (1973). W. J. Dixon and F. J. Massey, Jr., "Introduction to Statistical Analysis", 3rd ed., McGraw-Hili. New York, N.Y., 1969. p 248. H. D. Young, "Statistical Treatment of Data", McGraw-Hill, New York, N.Y., 1962, p 96-101. N. R. Draper and H. Smith, "Applied Regression Analysis", John Wiley & Sons, New York, N.Y., 1966, p 134-137. W. J. Dixon, Biometrics, 9, 74 (1953). 0. 6. Wetherill, "Elementary Statistical Methods", Chapman and Hail, London, 1972, p 270-271. Ref. 12, p 470.
RECEIVED for review J u n e 5, 1978. Accepted July 24, 1978. T h e authors gratefully acknowledge the support of the National Science Foundation (Grant MI'S 75-21059). Purchase of the mass spectrometer and digital voltmeter was made possible through funds from the Wisconsin Alumni Research Foundation and from the Chemistry Department. Portions of the work were presented a t the American Society for Mass Spectrometry Meeting in Houston, Texas, May 1975.
