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Anal. Chem. 1984, 56,1750-1752
Control Algorithm for a Computer-Automated Coulometric Titrator Gary D. Howard* and Sherman Henzel'
Department of Chemistry, University of North Carolina at Charlotte, Charlotte, North Carolina 28223 Various control algorithms have been used for computercontrolled titrators (1-8). The control objective usually has been to reach the end point as fast as possible without overshooting it. The specific control strategy used appears to have depended upon the type of application and upon the resources available. The different methods used to determine the amount of titrant delivered include: fixed additions ( I ) , two speeds (6),proportional control (6, 7), differential control ( 4 , 5 ) ,and the reciprocal of first and second differentials (2, 3). Harrar and Pomernacki have developed a direct digitally controlled potentiostat that was used for constant potential electrolysis. They designed a proportional plus integral plus differential (PID) control algorithm, but only implemented the PI cbntrol concluding that the differential element was not important for maintaining a constant potential. Both volumetric (1-6) and coulometric (6-8) computer-controlled titrators have been reported. The goal of this work was to develop a coulometric titrator that could control the titration rate to produce a constant change in the p H readings vs. time, especially near the equivalence point. The evenly spaced ApH values would permit precise determinations of the end points. Although maintaining a constant rate of p H change before reaching the end point would require extra time, the resulting values would be particularly well suited for curve fitting analyses. Also, it is desirable to be able to titrate relatively large samples (up to 100 pmol samples vs. typical 0.1 to 10 pmol samples) in reasonable lengths of time but still retain control without overshooting in the region of the equivalence point. Reaching this goal required devising a control algorithm different from any previously reported (1-9) that had the necessary dynamic range, rapid response, and fine point control.
EXPERIMENTAL SECTION Instrumentation. The coulometric titrator consists of a titration cell, an electrochemical titrant generation system with a constant current source, an Orion 801A Ionalyser pH meter, a DEC PDP 8/E minicomputer,a teletype with a paper tape punch, and the necessary interface hardware to allow the minicomputer to control the titrant generation rate, acquire the data, and output them. The titration cell (Figure 1) is a 30-mL weighing bottle fitted with a rubber stopper modified to accommodate the electrodes and to permit N2 purging. The cell is thermostated at 25 "C by immersion in a constant temperature water bath. The working electrode is a 1 cm diameter platinum screen smelted to a platinum wire. The auxillary compartment consists of two concentric glass tubes each having Du Pont Nafion 125 membrane epoxied to one end. The auxiliary electrode is a platinum wire placed inside the inner tube resulting in a double barrier to unwanted ion migration. The constant current circuit is shown in Figure 2. The current across the generating electrodes in the feedback loop of the operational amplifier is controlled either on or off. The current was determined to be 8.00 mA, using a PAR Model 179 coulometer. The impedance of the cell used for these studies causes the output of OA3 (Figure 2) to voltage limit if significantly larger currents are used. The computer controls the titrant generation with digital signals at the ACID and BASE inputs. In addition to the optical isolation the potentiometric measuring circuit and the titrant generation circuit are also isolated from each other with respect Current address: Monroe Community College, Rochester, NY 14623.
to time. The software is designed so that the generation current is off while the pH is being measured. The DEC PDP-8/E minicomputer was used because it was available. Any of a number of microcomputers could have been used equally well. The software is interrupt controlled with the Orion busy/done flag providing the interrupt signal (Figure 3). The BCD encoded pH readings from the pH meter are gated into the accumulator in two bytes. The amount of titrant generated for each interval is controlled by the length of time the ACID or BASE input of the constant current source is held low. This length of time is proportional to a 12-bit number that the computer loads into a binary counter pulsed at 1O.ooO kHz (Figure 4). When the counter counts down to zero, titrant generation automatically stops. The state of the link latched at the time the counter is loaded determines whether acid or base is generated. Software. During the initialization phase of the program the operator enters the number of readings to be summed for each output, the number of readings to delay so that the solution can become more homogeneous, whether acid or base is to be generated, the desired pH change/reading, and the coefficients for the control algorithm. Over 2000 data readings were taken for most of the titrations; so typically 10 to 25 readings were summed for each datum output. For these titrations 0.003 pH unit was used as the desired pH change per reading. The closed loop control is based on a proportional plus integral plus differential plus squared (PIDS) algorithm that is used to calculate the time the titrant generation system should be on (TO) for each interval TO = LTO + (A*E B*E.JEJ + GAB + D*AB-JABJ)/(F*ApH/LTO)
+
(1)
where LTO is the previous TO, E is the error in the pH ( E = measured pH - calculated desired pH for the present reading), AE is the change from the previous E to the present E , ApH is the change in pH from the previous pH and A , B , C, D, and F are constants entered during the initialization phase of the program. These constants can be in the range of 1/4095 to 4095. The ApHILTO term is used to allow for the nonlinear behavior of pH vs. moles of titrant added. E , AE, and ApH are all multiplied by 1000 before being used in eq l. Small values are used for the coefficients of the squared terms so that these terms only become important when E or AE becomes relatively large. For the relatively flat parts of the titration curve, maximum titrant generation may produce a pH change of less than the specified amount. When the generation current used and the amount of analyte used create this situation, the software sets the desired pH equal to the last pH reading plus the specified change. Otherwise, the desired pH at any time is equal to the sum of an increment or decrement plus the first pH reading where TO is less than 4095. The increment or decrement for each desired pH reading is equal to the specified pH change per reading multiplied by the number of ensuing readings. For example, during the titration of a strong acid a maximum TO value of 4095 (titrant generation for 0.41 s) produces less than a 0.003 pH change when the pH is less than 3.5 or greater than 10.5. Control was maintained in the pH range from 3.5 to 10.5. The program was written in machine language, and double precision arithmetic is used for all calculations. A first in, first out (FIFO) rubber band storage routine is used to hold the data until they can be output to the teletype and paper tape punch. The output routine for the pH and TO data pairs is a low priority background program. The punched paper tape of the data is input into a DEC Edusystem 50 computer system which is programmed in BASIC to analyze the data and display them on a Tektronix 4010 graphics terminal. Hard copies of the displays are obtained on a Tektronix hard copier. A typical
0 1984 American Chemical Society 0003-2700/84/0356-1750$01.50/0
ANALYTICAL CHEMISTRY, VOL. 56, NO. 9, AUGUST 1984
747eT
1751
DS 37
OH Electrode
i"
Flgure 1. Thration cell.
Flgure 4. Thrani generation control circuit DS376 is a high going device select signal that the interface decodes from the computer's data and control buses. TP3 is a timing pulse generated by the computer. The data lines are connected to the computer's data bus.
Flgure 2. Constant current circult. 011 and 012 are 4N32 optoisolators. R1, R2. andd R3 are lOOK R variable resistors. R4 is a 1K f7 variable resistor. R5 is a 500 R variable resistor. OAl and OA2 are IM324 operational amplifiers. OA3 is a LH002iCK 1.OA operational amplifier. 10
20
Micromoles of Flgvre 5. Thration curve for HCIO,.
30
40
OH-Generated
I
c
?
.I I
~ I -
Figure 3. Interrupt control cicuit. DS371 is a high going device select
sigml mat ths interface d W & m ths computer's data and conkc4 buses. DS370. DS372, and DS373 are Mnesponding low gdcg device select signals. Init is an iniiiilkation pulse generated by the computer. Skip Line and Internal Request are signals sent to the computer's control bus. All device selects and the starred logic gates use open collector circuitry. titration required about 30 rnin with the analysis of the data taking about 5 min. Fisher 13-639-90combination glass electrodes which were etched in 10% HF for 2 min to improve their resmnse times (IO) were used for pH measurements. Reagents. The supporting electrolyte for the reaction compartment and the auxiliary compartment was 1.0 M NaNO? Aliouots of a standardized HCIO. solution DreDared from concentrated ~ ~ 1and 0 a, N ~ solution ~ ireiared c ~ with ~ dried analytical grade Na,CO, were used for the analytes. Boiled deionized water was used for all dilutions. Reagent grade chem-
. a
I a 0
Micromoles of OH- Generated
Flgure 6. First differential plot of the titration of HCIO,. icals were used for all preparations except where otherwise indicated.
RESULTS AND DISCUSSION The titration of a strong acid or base is the most stringent test of the effectiveness ofthe control algorithm. Therefore, five samples of 31.68 pmol of HClO, were titrated. The mean of the results was 31.44 &molwith a relative standard deviation
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Anal. Chem. 1984. 56. 1752-1753
of 0.84%. In the pH range between 3.5 and 10.5 the difference between the measured pH and the calculated desired pH was h0.002 pH units or less. Outside of this range full-on titrant generation produced a change in pH of less than 0.003 per reading. The plot of a typical titration is shown in Figure 5. The first differential of the data is shown in Figure 6. The ApH/ Amoles of titrant values were calculated directly from the sums of the time on values without using any averaging or smoothing routines. Titrations of four samples of 35.82 pmol of Na2C03produced a mean of 71.50 pmol of hydronium ion generated with a relative standard deviation of 0.27%. The titrator was less than full on in the pH regions of 3.3 to 5.3 and 6.8 to 8.9. In these ranges the measured pH was controlled to within f0.002 p H units of the desired values. The actual algorithm used was
TO = LTO + (1E+ 0.02EIEI
+ 35A.E + 0.2aElaEl)/(400ApH/LTO) (2)
Again, E , AE, and ApH were multiplied by 1000 before being used in the equation. If the hE term is omitted, or even when its multiplier is significantly decreased, T O values will oscillate around the correct control value. If the E term multiplier also is decreased to prevent this overshooting, T O will lag behind the correct control value. If only the E term multiplier is decreased or if the AE term multiplier is increased, TO will tend to be offset from the correct control value. The squared terms are necessary to bring the titrator under control rapidly without oscillations when the pH range is first reached where control
can be maintained, 3.5 for the titration of strong acids. With the indicated multipliers the squared terms have no effect within the control range. For the HC104 titrations in the 3.5 to 10.5 pH range the E value can accumulate for successive readings. In this range the standard deviation of the measured pH readings from the desired pH values was 0.0007 pH unit. With this precision the accuracy of the pH control is limited only by the accuracy of the pH measuring system itself. Without using the full algorithm we were unable to approach this degree of control. The titrator has the capability to back titrate if necessary. However, back titration only occurred when inappropriate coefficients were used in the control algorithm.
LITERATURE CITED (1) Gampp, H.; Maeder, M.; Zuberbuhler, A.; Kaden, T. Talanta 1980, 2 7 ,
5 13-5 18. (2) Martin, C.; Freiser, H. Anal. Chem. 1979, 51, 803-807. (3) Christiansen, T. F.; Busch, J. E.; Krogh, S . C. Anal. Chem. 1976, 48, 105 1-1 056. (4) Leggett, D.J. Anal. Chem. 1978, 50, 718-722. (5) Smit, J. C.; Smlt, H. C.; Stelgstra, H.; Hannema, U. Anal. Chim. Acta 1082, 143, 79-94. (6) Wu, A. H. B.; Malmstadt, H. V. Anal. Chem. 1078, 5 0 , 2090-2096. (7) Earle, W. E.; Fletcher, K. S . , 111 Chem. Insfrum. ( N . Y . ) 1976, 7 ,
101-121. (8) Harrar, J. E.; Pomernacki, C. L. Chem. Instrum. ( N . Y . ) 1978, 7 , 229-240. (9) Pomernacki, C. L.; Harrar, J. E. Anal. Chem. 1975, 4 7 , 1894-1905. (IO) Adams, R. E.; Betso, S. R.; Carr, P. W. Anal. Chem. 1978, 4 8 , 1989- 1996.
RECEIVED for review December 21,1983. Accepted March 15, 1984. This work was supported in part by funds from the Foundation of the University of North Carolina at Charlotte and from the State of North Carolina.
Teflon Tubing as a Removable Replacement for Steel Ferrules in High-pressure Liquid Chromatography James L. Meek Laboratory of Preclinical Pharmacology, St. Elizabeths Hospital, National Institute of Mental Health, Washington, D.C. 20032 Most modern liquid chromatographs use 1/16 in. 0.d. steel tubing to connect the pump, sample injector, column, and detector. A leaktight s e d is made by compressing steel ferrules onto the tubing. Unfortunately, the compression fittings made by different manufacturers are incompatible. When columns or other components from different sources are interchanged, adapters may be required for each combination. An alternative to nonremovable steel ferrules is to use a plastic material as part of the fitting to grip the tubing and form a seal. Teflon ferrules can be used for this purpose but are limited to about 1500 psi. “Universal”adapters are now available from Alltech Associates, Deerfield, IL, and Rainin Inst, Woburn, MA, that can be used to 5000 psi. These adapters are rather expensive for use throughout an HPLC system and are too bulky to use in some cases (e.g., on Rheodyne sample valves). A less expensive solution that will work both with external threaded fittings (e.g., Swagelok) and with internal fittings (e.g., Waters, Rheodyne, Valco, Parker, SSI) can be made without machining from the ordinary Teflon tubing used in the inlets to most HPLC pumps. A Teflon tubing seal will withstand a t least 5000 psi, is reusable and removable, and allows ready interchange of different types of fittings, even This article not subject to
those which have been damaged by scratches or overtightening.
EXPERIMENTAL SECTION A Teflon sleeve is made by inserting Teflon tubing (l/s in. o.d., 1/16 in. id.) into the female part of the fitting and cutting it off flush with a razor blade. The tubing is removed. An additional 1-2 mm is cut off and discarded. The remaining Teflon sleeve is slipped over the steel tubing to be connected and inserted into the fitting, and the fitting is tightened slowly. The Teflon sleeve is thereby compressed and flows into and fills both a portion of the threaded part of the fitting and the space normally occupied by the ferrules. Maximum pressure tolerance develops if the fitting is retightened after a few minutes to allow completion of the flow. When the fitting is disassembled, the sleeve remains with the female portion of the fitting. The tubing can be removed from the sleeve and reinserted 10 or more times if, after loosening the nut, the tubing is wiggled in the sleeve to enlarge it. When the steel tubing is then reinserted, only moderate care is needed to center the tubing in the sleeve and avoid shaving off a piece of Teflon. A fitting can be used alternately with both conventional steel ferrules and Teflon sleeves since the latter can be removed by unscrewing them with a small Phillips head screwdriver (without damage to the sleeve) or with a flat screwdriver or a small
U.S.Copyright. Published 1984 by the American Chemical Society
