Direct-Reading, Response-Compensating Integrator for Chromatography Jack R. Barnes and Harry L. Pardue, Chemistry Department, Purdue University, Lafayette, Ind.
the areas R under the peaks is necessary for precise quantitative determination of ELIABLE MEASUREMENT Of
the composition of mixtures separated by chromatographic means. Several devices have been developed, of which a few are commercially available, to integrate the chromatographic output signal with respect to time. Some of these use such techniques as rotating ball and disks (S), low-inertia d.c. motors (9), voltage to frequency conand electrochemical procverters (1,6), esses (11). Although the use of most of these is widespread, each has shortcomings in the areas of accuracy, ease of operation, ease of data reduction, or cost, Kone of these, in their basic forms, permits readout in percentage or concentration units. Some of them depend upon a signal from a retransmitting potentiometer of a recorder, which may contribute significant error to the results. None of these has a convenient method to compensate for differences in detector response with different materials in a sample mixture. The work reported here resulted in the development of an integrating device which eliminates most of these shortcomings, while retaining reasonable accuracy and precision without becoming complex or costly. EXPERIMENTAL
The layout of the instrument is illustrated in Figure 1. The potential resulting from a chromatographic peak is connected a t Ed,and compensated for detector response by the sensitivity compensator. The signal is then integrated with respect to time and the integrated signal is stored. After all the peaks of a ohromatogram have been processed in this manner, the sum of Functional Layout.
INTEGRATOR
STORAGE
E5-U-a FOLLOWER
DIVIDER
DIGITAL READOUT
Figure 1. Functional layout for directreading, response-compensating integrator
156
ANALMICAL CHEMISTRY
all the stored signals is measured through the follower and the divider is adjusted until a reading of 100.00 is observed on the digital voltmeter (DVAl). As each of the individual signals is then sequentially measured, the digital voltmeter presents the data in the form of per cent composition. Complete Circuit Layout. The circuit layout illustrated in Figure 2 contains components which perform the functions described below. STORAGEOF INTEGRATED SIGNALS. Storage of individual integrated signals is accomplished by providing a bank of 10 capacitors (Cl, C2, etc.) which may be switched (SwBb) into the integrator circuit one a t a time t o receive the integration signal arising from the individual peaks. These capacitors must be closely matched in capacitance value and must be made with very lowleakage dielectric. Those used in this work are 10% tolerance Mylar, 2-rf. 200-vv.v.d.c., (Goodall) matched to within *0.5% by smaller parallel capacitors. RELATIVERESPOKSECOhfPEKSATOR. The signal from each peak must be modified t o compensate for differences in relative response of the detector to the different sample materials. This function is performed by a bank of ten 10-turn, 100-kilohm potentiometers (R1, etc.) used in the input to the integrator. These potentiometers are switched by a second set of contacts on the capacitor selector switch (Swn,) so that each potentiometer is always associated with the same capacitor. Response compensation is accomplished by setting relative response factors for each sample material on the potentiometer dial associated with the integration of the peak arising from that material. These relative response factors may be obtained from the literature @), calculated ( d ) , or obtained experimentally by running known composition samples. Either weight or molar factors may be used, resulting in readout in either weight or mole per cent, respectively. These potentiometers may be replaced by fixed resistors for routine applications in which repetitive determination of mixtures containing the same components are to be made. According to the integration equation
the output voltage is proportional to (l/R,,J and the output is increased by decreasing the input resistance for a given voltage-time integral. The effect of dialing the relative response factor on the input potentiometer is to increase the output potential for materials of less detector response so that the same weight of each material results in the storage of equal charges on the capacitors. INTEGRATOR. The operational amplifier (0.A.) is one section of a Heath Model EUW-19A operational amplifier system (Heath Co., Benton Harbor, Mich.) stabilized with a Philbrick K2-P chopper stabilizer. (Philbrick Researches, Boston, Mass.) Details of an integrator employing the Heath amplifier stabilized by a K2-P have been reported (8). This amplifier is connected in the conventional integrator configuration ( 7 ) with the above capacitors in the feedback to accumulate the integrated signal. FOLLOWER. Amplifier Kumber 1 of the Heath operational amplifier system used in a voltage follower configuration (FOL) provides a very high impedance t o the capacitors and a very low impedance to the digital voltmeter. This effectively isolates the capacitors and the voltmeter, preventing drainage of
q OFF
i
(Y), Figure 2. Circuit layout for directreading, response-compensating integrator
charge from the capacitors during readout. DIVIDER.The divider is a 10-turn, 100-kilohm potentiometer (R) which permits the sum of the charges on the capacitors to be adjusted to give a loo.OO~o reading on the digital voltmeter during the calibration step. DIGITALREADOUT.A DigiTec Model 100 (United Systems Corp., Dayton, Ohio) digital voltmeter with a 1.0000volt full-scale range is used to convert the analog data into digital data. This is done for ease of reading and to enable the data to be printed out if a compatible printer is available. Evaluation Procedures. The following procedures were used t o evaluate the performance of the completed system. INTEGRATION OF RECTANGULAR SIGNALS. Known rectangular signals were generated by applying to the input of the integrator a known potential for a measured length of time. The input signal was obtained from a 1.35-volt mercury battery with a 100-ohm 10turn potentiometer as a voltage divider. A signal of 45 mv. was supplied to the integrator input for 30 seconds as measured by stopwatch. The divider was adjusted to give a reading of about 1000 on the DVM. COMPARISON WITH DISCINTEGRATOR. A sample mixture of hydrocarbons was chromatographed and the detector signal was alternately integrated with a Disc integrator (3) and the directreading integrator. A Wilkins Aerograph Model 202 (Wilkins Instrument and Research, Inc., Walnut Creek, Calif .) vapor-phase chromatograph with thermal conductivity detector was used. The five-component hydrocarbon mixture was prepared from n-pentane, n-hexane, cyclohexane, methyl cyclohexane, and n-octane. The integrators were not run directly in parallel because it was necessary to attenuate the detector signal for presentation to the Disc integrator, whereas the directreading integrator utilizes the unattenuated detector signal. Injections of 0.1 pl. were used with the Disc integrator and 1 pl. with the direct-reading integrator. Since the Disc integrator has no response-compensation capability except manual calculation, this feature of the instrument described here was nullified by setting all the potentiometers to full scale (lOOO), representing a response factor of 1.000 for all materials. I n this manner direct comparison between the Disc integrator and the direct-reading integrator was possible. ANALYSISO F KNOWNCOhfPOSITIOlr MIXTURES.Known composition mixtures of the hydrocarbons used earlier were prepared by weighing into rubberseptum-covered serum bottles various amounts of each of the five liquids used. Relative weight response factors were experimentally determined by chromatographing known-composition binary mixtures of one of the sample liquids with each of the others used in the sample mixture. The factors were then calculated from the weight ratios and the signal ratios observed a t
the DVM. Factors determined in this manner were then dialed on the appropriate potentiometer of the response compensator. The proper times to switch from one capacitor to the next as integration of one peak was completed and before the integration of the next peak began were determined by observing a trial chromatogram on a recorder and measuring the proper times for switching. RESULTS
Integration of Rectangular Signals. The relative standard deviations obtained in this evaluation show t h a t the precision of integration into each potentiometer-capacitor combination is about 0.5%. The 10 potentiometer-capacitor combinations are also matched to about 0.57,. Comparison with Disc Integrator. The results of this evaluation are summarized in Table I. These data show t h a t the two integrators have essentially the same precision. The similarity of results by these two instruments may indicate t h a t this is a measure of the precision of the chromatographic system and t h a t both integrators may be capable of better results if provided better data from the chromatograph. This possibility is further substantiated in the case of the Disc integrator by the findings of Sawyer, et al. (10) who report an average per cent deviation of 0.5% for the integration of rectangular signals by this type of instrument. The present work indicates similar results are observed with the direct-reading integrator. Analysis of Known Composition Mixtures. Experimental d a t a obtained for two different sample mixtures are summarized in Table 11. These data are typical of many other samples run. The experimental values reported are averages of values read from the digital voltmeter for replicate runs. The integrals have been compensated for relative response by
Table 11.
Hydrocarbon
Taken
Table 1.
Comparison with Disc Instruments Integrator
Disc Instruments integrator Rel. std. Calcd., %a Std. dev. dev., % 16.57 21.38 24.52 16.60 20.96
0.27 0.34 0.30 0.38 0.36 Av. 0.33
1.63 1.59 1.22 2.29 1.72 -1
Direct-reading integrator Rel. std. Read, %b Std. dev. dev., % 16,68 20.94 24.67 16.30 21.23
0.19 0.47 0.32 0.37 0.26
Av.
*
1.14 2.24 1.30 2.27 1.22 1.63
0.32’
Av. of 5 runs each. Av. of 5 runs read from the digital
voltmeter.
setting experimental response factors on the appropriate potentiometer dials, The possible effect of various sample sizes was tested by varying the injection volume in the range 0.1 to 5 PI., in running sample Number 1. KO significant difference in accuracy or precision was observed between these results and those of the other samples in which all injections were 1p l . The overall average standard deviation for five different samples with ratios of the individual components varying hetween 7 and 55% is 0.25. This represents a relative standard deviation of 1.61% for all the sample runs. The overall average difference of 0.30 represents an average relative error of 1.82% for all the sample runs. DISCUSSION
This integrating device has accuracy and precision a t least equivalent to those of the ball and disc type integrator, with the favorable advantages of simple compensation for relative detector response and direct digital readout in percentage composition units.
Experimental Data Summary
Rt., yc Found
Std. Dev.”
n-Pentane 17.58 18.37 n-Hexane 10.65 10.88 Cyclohexane 16.62 16.33 Methylcyclohexane 25.43 24.97 n-Octane 29.73 29.70 n-Pentane 12.40 12.63 n-Hexane 15.63 15.50 Cyclohexane 24.34 24.49 hlethylcyclohexane 9.98 10.12 n-Octane 37.65 37.49 a The first set of data represents averages of 15 runs. averages of four runs.
0.29 0.18 0.17 0.22 0.19 0.20 0.07 0.11 0.49 0.73
Difference +0.79 $0.23 -0.29 -0.46 -0.03 $0.23 -0.13 f0.15 +0.14 -0.16
The second set represents
VOL. 38, N O . 1 , JANUARY 1966
157
It is reasonable to believe that the accuracy and precision of this instrument for integration of a n input signal can be increased by a factor of two by the use of precision-matched capacitors, a chopper stabilizer on the follower amplifier, or high quality soIid state amplifiers. These possibilities will be the subject of future investigations. Applications of this instrument for densitometry in paper and thin layer chromatography and electrophoresis may also be found. The work of Seligson, et al. (6) illustrates the application of a similar system to electrophoresis. The system described in that work requires a separate amplifier for each chromatographic peak being integrated. I n addition, each integrator is operating throughout the entire separation and measurement operation. In
the system described here, the integrating capacitors are switched into the amplifier circuit only during the period of the peak to be integrated. As a result, only one integrating amplifier is required irrespective of the number of peaks being integrated. I n addition, integration error resulting from amplifier offset is limited to that occurring during the period of the peak. ACKNOWLEDGMENT
The authors acknowledge discussions with Willard Faulkner of the Cleveland Clinic which provided inspiration for the initiation of this work. We also acknowledge the assistance of Jonathan University Amy of the Purdue Chemistry Department during the conduct of this research.
LITERATURE CITED
(1) Consolidated Electrodynamics Corp., Pasadena, Calif., Bull. 34210-1, Nov.
1963. (2) Dal Nogare, S., Juvet, R. S. Jr., “Gas Liquid Chromatography,” p. 198, Interscience, New York, 1962. (3) Disc Instruments Inc., Santa Ana, Calif., Bull. 200. (4)Hoffman, E. G., ANAL. CHEY. 34, 1216 (1962). (5) Infotronics Corp., Houston, Texas, Product Data Sheet CRS-11. (6) Lotito, L. A., XcKay, D. K., Seligson, D., Clin. Chem. 11, (3) 386 (1965).
( 7 ) Malmstadt, H. V., Enke, C. G., Toren, E. C.,“Electronics forscientists,”~.356, W. A. Benjamin, Inc., New York, 1962. (8) Pardue, H. L., Dahl, W. E., J. Electroanal. Chem. 8 , 268 (1964). (9) Perkin-Elmer Corp., Wilton, Conn.,
Bull. 990-9089. (10) Sawyer, D. T., Barr, J. K., ANAL. CHEM.34, 1213 (1962). (11) Self-organizing Systems, Inc., Dallas, Texas, Bull. 105, Sept. 1963.
A Simple Graphical Method for locating the End Point of a pH or a Potentiometric Titration Stephen R. Cohen, Department of Neurology, College of Physicians and Surgeons, New York, N. Y.
T
10032
method for finding the end point of a p H or a potentiometric titration is to plot ApH/AV or AE/AV as a function of V , the volume of titrant, and to take the value of V at the maximum as the end point. This graph consists of two parts, one for volumes less than the end point and one for greater volumes, which are extrapolated to intersect at the end point. Because these branches are curved and increase rapidly as the end point is approached, the intersection is poorly defined and, even with precise data, the end point is uncertain by several times the reading error of the buret. In addition, because p H or E changes very rapidly with V near the end point the values of ApH/AV or AE/AV in the critical region around the end point often have scatter which greatly increases the uncertainty of the end point. The following graphical procedure can be used t o find the end point precisely even with moderate experimental scatter. It is easier to use than Gram’s methods ( I ) . Unlike them, it can also be applied to differential titrations where ApH/AV or A E / A V , rather than p H or E , is measured as a function of V . Plot the values of ApH/AV or AE/AV against V as usual. Draw the separate curves through the data points before and after the end point. These curves should be smooth, but need not be fitted to the data with more than reasonable care. Curves drawn by eye are adequate. It is not necessary to extend HE MOST COMMON
158
ANALYTICAL CHEMISTRY
them beyond the data points to find their intersection. Select several values of pH/AV or AE/AV, and read the corresponding volumes from these two curves. Call them L for the volume taken from the left-hand curves (before the end point), and R for the volume taken from the right-hand curve (after the end point). Compute M = l/* ( L R ) ,the average of these two values; and D = R - L , the difference between these two values. Graph 211 as a function of D and extrapolate to D = 0 to find the end point. With reasonable care it will be located to within the reading error of the buret. This graph should be a well defined, straight line. Inaccuracies in drawing two curves of the ApH/AV us. V graph will produce a slight scatter in the values of M, which will have a negligible effect on the end point. The above procedure can be derived theoretically. For titrations such as acidbase titrations, which have a titration curve that is symmetrical about the end point, M is theoretically independent of D . I n practice some slight dependence may sometimes be found, but the slope of the graph 111 us. D will be small If the titration curve is not symmetrical about the end point, M will still vary linearly with D , but the slope will not be zero. This will not introduce any systematic error, but may reduce the precision of the extrapolated end point. This slight difficulty with unsymmetrical titration curves can be removed if
+
desired, and M made independent of D, by using a weighted average of L and R for 111. Let A be the reacting chemical species being titrated-Le., the species present in excess before the end pointand let B be the reacting chemical species being added; let n, and nb be the number of equivalents per mole of A and B , respectively, for the reaction
1
-A 120
+ nb-1 B
+
Products
at the endpoint. Compute D as before, but use the weighted average M =L nbD/(n, nb) for -11. [M may be seen
+
+
to be a weighted average by rewriting this expression as M = (n,L+nbR)/(n, nb).] -4s before, graph this modified value of J1 as a function of D and extrapolate to D = 0 to find the end point. The slope of this graph will be essentially zero. When this weighted average is used for X , it is important that na and ?& be taken from the stoichiometry for the end point reaction and not from the stoichiometry of the overall titration. For example when Na2C0g is titrated with HC1 to the CO, end point, the end point reaction is HCOa- H+-, COz HzO,and, therefore, n.ya2COI = 1 and not 2.
+
+
+
LITERATURE CITED
(1) Gram, Gunnar, Acta Chem. Scand. 4, 559 (1950); Analyst 77, 661 (1952).
