If the program diverges, one method is to improve the set of initial estimates and perhaps add more component peaks to the summation. An alternative remedy is to reduce the magnitudes of corrections before adding them to the parameters. For example, if all the corrections are reduced by a factor of ten and if the set of parameters is divergent, the adverse effect on S will be reduced by about a factor of ten and the calculation may recover on subsequent iterations. The price paid for this improved chance of convergence is that the convergence itself takes that many more iterations. Sample Results. A program has been written in FORTRAN for use on the time-sharing system of the CDC 3600 computer at the University of Massachusetts at Amherst through a teletypewriter linkage to the University of Massachusetts at Boston. (Program listing is available on request.) The program analyzes for a maximum of four Gaussian components. The analysis of an experimental ultraviolet spectrum of potassium squarate is shown in Figures 1 and 2. Although previously published by Ireland and Walton (3),
and the corresponding component peaks are shown in Figure 2. The summation of these peaks approximates the experimental spectrum with an average (RMS) deviation of
(3) D. T. Ireland and H. F. Walton, J. Phys. Chem., 71, 751 (1967).
RECEIVED for review March 4,1971. Accepted May 25,1971.
this spectrum was reproduced in this laboratory using a Cary 14 spectrophotometer. A fairly poor estimate of the parameters of three Gaussian components is as follows: Component € xo, lo3 cm-1 6 , IOa cm-1 1 2 3
85 74 50
36.4 40.8 62.5
1.06 2.00 9.17
These components sum up to the crude spectrum shown in Figure 1. Eventually the least-squares iterative calculation converged to the folldwing set of parameters : Component E XO 6 67.7 80.1 18.4
1 2 3
36.8 39.8 48.4
1.33 2.48 3.97
1.0%.
Solid State Pressure Transducer for Pressuremetric Titrations D. J. Curran and S. J. Swarin Department of Chemistry, University of Massachusetts, Amherst, Mass. 01002 A NUMBER OF REACTIONS of interest in analytical chemistry involve gases. Therefore the measurement of changes in the amount of gas present, particularly at the micromolar level, is of interest. In a recent paper ( I ) , we pointed out specific areas of application of this measurement technique and presented an electronic conductivity manometer for use in this field. Quinn and Posipanko (2) have demonstrated the use of a solid state pressure transducer called a Pitran (for Piezotransistor) (Stow Laboratories, Inc., Hudson, Mass. 01749) for monitoring the course of chemical reactions in a closed-system. As part of our studies of applications of pressure transducers in chemical analysis, we have undertaken a study of this unique device to determine its usefulness for the measurement of small pressure changes in reactions of analytical interest. Most transducers for the conversion of pressure to an electrical signal involve a variable but passive electronic circuit element such as a resistor, capacitor, or inductor. The Pitran is unique because it is the first transducer that involves an active circuit element. It is a silicon planar NPN transistor with a stress sensitive emitter-base junction. Pressure applied to the front side of the top of the transistor header produces a large reversible change in the gain of the transistor, i.e., the Pitran output is modulated by the mechanical variable. Holes in the physical base of the transistor permit access of the prevailing atmospheric pressure (or a set reference pressure) to the back side of the top of the transistor header. Thus the transistor header is a diaphragm responding to the difference in pressure between its front and back sides; and the output of the device is differential. (1) D. J. Curran and S. J. Swarin, ANAL.CHEM., 43, 358 (1971). (2) E. L. Quinn and T. Posipanko, Reu. Sei. Instrum., 41, 475 (1970).
1338
When the device is connected in a simple common emitter configuration (Figure l), it provides a dc output proportional to the mechanical input. The Pitran appears to have application in the areas we have cited previously: reaction kinetics, null point pressuremetry, and pressuremetric titrations ( I ) . We have demonstrated here the applicability of this instrument as an end-point detection device in pressuremetric titrations of 1,904- and 0.8694-mg samples of ammonium ion with electrogenerated hypobromite. Nitrogen is produced according to the following equations: Br-
2NH4+
+ 20H-
+
+ HzO + 2e+ 3Br- + 2H+ + 3Hz0
BrO-
+ 3Br0- + Nzt
(1) (2)
EXPERIMENTAL
Apparatus. The complete circuit diagram of the pressure transducer system is given in Figure 1. All of the components except the Pitran were mounted in a 51/4 X 3 X 2l/*inch aluminum chassis. The power supply was a nine-volt transistor battery. The Pitran was mounted as shown in Figure 2. Since the Pitran is mounted to fit into the transistor socket, it was connected to the circuitry by simply fastening the 18/9 ball and socket joints together. The Pitran used in this study was a Model PT-M2 which has a nominal linear pressure range of 0.25 psid. Pressure signals for testing the linearity and reproducibility of the transducer were supplied by a hydrogen-nitrogen coulometer designed according to the recommendations of Page and Lingane (3) and operated with a Sargent Model IV Constant Current Source. The recorder, constant temperature bath, submersible magnetic stirring motor, potentiometer, Ampot, (3) J. A. Page and J. J. Lingane, Anal. Chim. Acta., 16, 175 (1957).
ANALYTICAL CHEMISTRY, VOL. 43, NO. 10, AUGUST 1971
I
I
I
1
I I
-
I
l
I
l
A d RECORDER
Figure 1. Circuit diagram of pressure transducer system Figure 2. Photograph of mounted Pitran
and titration vessels used in this study have all been previously described ( 4 , 5). For work at high sensitivities a Heath EUW-16 Voltage Reference Source (Heath Co., Benton Harbor, Mich.) was used to null out the initial 1.0-volt collector-emitter signal and thus make recording of the output more convenient. Reagents and Solutions. All chemicals used were reagent grade. Laboratory distilled water which was redistilled from alkaline permanganate was used for all solutions. Stock ammonium sulfate solutions, 1.062 X lou2and 0.4828 x 10-2M in ammonium ion were prepared by dissolving 0.3509 and 0.1595 gram of the dried material in 500-ml volumetric flasks, respectively. Hypobromite was generated from an anolyte solution containing 10.0 grams of sodium tetraborate decahydrate and 200 grams of sodium bromide in 500 ml of redistilled water. The pH of this solution was adjusted to 8.6 i 0.1 (Corning Model 7 pH meter) by adding solid sodium hydroxide. In order not to evolve a gas at the cathode, a solution which was 1.OM in ferric chloride hexahydrate dissolved in 2.ON sulfuric acid was used as the cathodic depolarizer. Procedure. To determine the accuracy of the pressuremetric end-point technique using this pressure transducer system, the amperometric titration procedure of Christian, Knoblock, and Purdy (6) was used as a check method. The same samples and anolyte were employed in both methods. The procedure for pressuremetric end-point detection was similar to that previously described (1).
9 8
A. lS/9 ball joint into which the Pitran was epoxied B. lS/9 socket joint containing the transistor socket C. 12-mm 0.d. glass tubing containing flexible shielded cable (2-
wire with grounded shield) for connection from transistor socket to circuitry D . Epoxy seal to isolate reference side from atmospheric fluctuations E. 12/5 ball joint for connection to reference reactor F. l2/5 ball joint for connection to working reactor
9
,'Or
1
G 2
RESULTS AND DISCUSSION
The linearity, reproducibility, and hysteresis of the Pitran pressure transducer system were tested using a hydrogennitrogen coulometer to generate known quantities of gas in a system of known volume. The unit performed well within the specifications which are & 0 . 5 x for these variables. However, upon calibrating the unit, it was found that the linear pressure range was 0.39 psid compared to 0.25 psid specified. It is felt that this loss in sensitivity was due to distortion of the device caused by the epoxy mounting. Because of its design, the Pitran is very sensitive to lateral stresses and can be easily damaged in unpacking, handling, and mounting. However, Pitran Holders are now available, and Pitrans may also be purchased as mounted units which should alleviate this problem (Stow Laboratories, Inc., Hudson, Mass. 01749). (4) D. J. Curran and J. E. Curley, ANAL.CHEM., 42, 373 (1970). (5) D. J. Durran and J. L. Driscoll, ibid., p 1414. ( 6 ) G. D. Christian, E. C. Knoblock, and W. C . Purdy, ibid., 35, 2217 (1963).
0
A Pressure
*
-0.
PsIi
Figure 3. Input pressure-output voltage diagram for Pitran pressure transducer system
The input pressure-output voltage relationship for this pressure transducer system is shown in Figure 3. The output voltage corresponding to the linear pressure range of the Pitran is specified to be 20% of the applied voltage. However, this output voltage is referenced to an initial collector-emitter voltage of 1.0 volt in this case. Thus the linear pressure range for this unit was -0.195 to +0.195 psid. If one is dealing strictly with positive pressures, it is convenient to null out the initial VCE with the Voltage Reference Source in the sum-difference mode before recording the output. Table I summarizes the results of the coulometric titrations of ammonium ion utilizing the pressuremetric end-point technique with this transducer system. The theoretical
ANALYTICAL CHEMISTRY, VOL. 43, NO. 10, AUGUST 1971
1339
Table I. Titration Re-sults with Pressuremetric End-Point Detectiono Taken, mgb Found, mg No. of detn 1.904 f 0.007 1.906 6 0.8694 f:0.0030 0.8688 6 a Ammonium ion titrated with coulometrically generated hypobromite. Ir Based on check method.
basis of this technique has been presented previously (4, 7). Briefly it involves monitoring the pressure change in a closed system due to the evolution or consumption of a gas by the reaction of analytical interest. Utilizing this pressure transducer system, accuracies and precisions of a few parts per thousand were obtained. Generally it is felt that the Pitran may offer some advantages in the monitoring of small pressure changes associated with chemical reactions of analytical interest. The system is simple, inexpensive, and provides a dc output suitable for recording. We have shown that the Pitran is capable of highly accurate and precise analytical data. Although they do not possess a multirange capability, Pitrans are (7) D. J. Curran and J. L. Driscoll, ANAL.CHEM., 38, 1746 (1966).
Re1 std dev,
z
0.4 0.4
RelbAcc
z
+o.
1 -0.1
Total gas, pmoles 53 24
available in many pressure ranges (9 models from 0.1 to 20 psid) and their relatively low cost may permit the purchase of several units depending on the range of pressures to be studied. In addition, the unit possesses the advantages of high overload capability (700% of the linear range) and very small size (TO-46 header, 0.2-inch diameter and 0.07-inch height). Finally, with a battery power supply as used in this study, the unit is capable of field operation. ACKNOWLEDGMENT
We wish to thank D. K. Roe for calling our attention to the Pitran. RECEIVED for review February 12, 1971. Accepted April 27, 1971.
System for Continuous Pumping of Solvent at Low Flow Rates Gary 0. Nelson and Robert D. Taylor Lawrence Radiation Laboratorq , University of California, Livermore, Calif. 94550 PRECISION, NONPULSING PUMPS for dispensing solvent at low flow rates (10 to 0.005 ml/min) are often required for both routine and research applications, but such pumps are not commercially available. Diaphragm, cam-actuated, and piston pumps may specify a certain flow, but their output is generally the average of peaks and valleys, which makes them unacceptable in many instances. Peristaltic, finger, and kinetic clamp pumps also exhibit surges and lapses in output flow as a result of the rollers which alternately rise from and depress a resilient tubing. Tubing deterioration and variations in system pressure are also factors which cause inconsistencies in the output flow rate. Syringe-type pumps presently seem to offer a method of continuous, low-flow solvent pumping. If liquids must be slowly added over long periods, a reciprocal syringe pump appears to be the most appropriate. Often, such pumps have a liquid flow routing control which consists of solenoidactivated clamps which alternately depress and release some type of soft tubing. Here again, tubing deteriorationthrough swelling, dissolving, and splitting when in contact with incompatible solvents-proves to be a major problem. Also, diffusion of the solvent through tubing walls can cause losses of up to 50z with many solvents. Hence, it is not uncommon to have errors of 10 to 90% between the theoretical volume (as predicted from syringe capacity and rate of plunger advance) and the actual volume delivered. This paper describes a liquid routing control which has none of the disadvantages just described and can be easily adapted to any Sage Instrument Inc. Model 220 syringe 1340
pump. All tubing, valves, and fittings can be purchased commercially and easily fabricated, The liquid comes in contact with only the Teflon (Du Pont) materials, and there is no measurable diffusion, pulsing, or deterioration with any solvent yet studied. EXPERIMENTAL
A schematic diagram of the system is shown in Figure 1. Basically, it consists of dual syringe injectors, inert tubing and routing control valves, and an air-driven valve control unit. Commercial syringe injectors normally come complete with the plunger advance and reversing switch controls. As one syringe fills from the reservoir, the other empties at a predetermined rate. The filling cycle of our pump is slightly faster than the infusion cycle; thus the reserve syringe is always filled before the delivery syringe empties. The switchover is then free from any backlash, since both syringes are actually moving forward momentarily, one of them pumping back into the reservoir just before switchover occurs. The solvent is routed through a network of 0.076-inch i.d. Teflon tubing with Kel-F female h e r fittings at both ends. The routing control system consists of two 4-way Kel-F values with male h e r fittings. All T and X connectors are Kel-F with male and female h e r fittings as required. A manually operated recycling valve allows for liquid recirculation (90' counterclockwise) during the priming process and provides for a quick shutoff during periods when solvent delivery is unnecessary. The routing control valves are attached to the pinion gear of a rack and pinion arrangement. The gear can rotate back and forth through an angle of about 45". The rack is
ANALYTICAL CHEMISTRY, VOL. 43, NO. 10, AUGUST 1971
