t h e glass or polyethylene substrate, even a t very low current densities. T h e generally larger diameters of t h e flexible electrode assemblies limited t h e needle size with which they could be used t o 23 gauge or larger.
C 0N CL U SIO N
It has been demonstrated that glass microbulb electrodes can be fashioned into a variety of rigid a n d flexible p H sensing assemblies. Dip and hypodermic type microsensors were evaluated in vitro and generally found t o have all t h e desirable characteristics of ordinary glass electrodes, suggesting their use for both routine a n d novel analytical measurements. While i t was not possible to test the various microprobes in vivo, it was evident t h a t they represent a n important improvement over t h e devices presently used for such life saving techniques as muscle p H monitoring. Furthermore, the adaptability of t h e microelectrodes t o new probe configurations should prepare the way for new biomedical techniques such as continuous fetal pH monitoring.
LITERATURE CITED (1) J. D. Czaban and G. A. Rechnitz. Anal. Chem., 47, 1787 (1975). (2) R. M. Filler and J. B. Das, "Muscle pH, pOn, pC02 Monitoring: A Review of Laboratory and Clinical Evaluations", in "Ion-Selective Microelectrodes", H. J. Berman, and N. C. Hebert, Ed., Adv. Exp. Med. Biol., 50, 175 (1974). (3) G. Gebert and S. M. Friedman, J. Appl. Physiol., 34, 122 (1973). (4) J. W. MacKenzie, A. J. Salkind, and S. R. Topaz, J. Surg. Res., 16, 632 (1974). (5) R. M. Bates, "Determination of pH, Theory and Practice", 2nd ed., J. Wiley and Sons, New York. N.Y., 1973, p 300. (6) R. Green and G. Giebish. "Some Problems with the Antimony Microelectrode", in "Ion-Selective Microelectrodes", H. J. Berman and N. C. Hebert. Ed., Adv. Exp. Med. B i d , 50, 43 (1974). (7) A. Wakabayashi, Y. Nakamure, T. Wooley, R. J. Mullin, H. Watanabe, 1. Ino, and J. E. Connolly, Arch. Surg.. 110, 802 (1975). (8) R. W. Beard, Pediafrics, 53, 157 (1974). (9) J. F. Roux, M. R. Neuman, and R. C. Goodlin, Crir. Rev. Bioeng., 2(2), 119 (1975). (10) H. J. Berman and N. C. Hebert, Ed., "Ion-Selective Microelectrodes", Adv. Exp. MedBiol., 50, 188 (1974) (11) G. J. Janz, in "Reference Electrodes", D. J. G. lves and G. J. Janz, Ed., Academic Press, New York, N.Y., 1961, Chap. 4. (12) D. M. Band and S. T. G. Semple, J. Appl. Physiol., 22, 854 (1967).
RECEIVEDfor review September 8, 1975. Accepted October 20, 1975. We gratefully acknowledge t h e financial support of a grant from the National Institutes of Health.
On-Line, Computer-Controlled Potentiometric Analysis System John M. Ariano and W. F. Gutknecht" Department of Chemistry, Duke University, Durham, N.C. 27706
A computer-controlled, direct potentiometric analysis system has been developed. During a typical analysis, a series of standard additions are made to an unknown solution in a cell containing an ion-selective electrode and a reference electrode. These additions are optimized in that the volume of each is automatically adjusted so as to yield an even distribution of resulting cell voltages. The cell voltages, which are acquired using a computer-optimized sampling technique, and the standard addition data are fit to the Nernst equation using the nonlinear least squares procedure. This system has been used to automatically analyze for potassiM, with um ion over a concentration range of lo-' to the resulting accuracy and precision both being about 2 YO.
Over t h e past several years, the small digital computer has become an almost commonplace instrument in many analytical laboratories. In most cases, however, the small computer has been used only for calculations, or relatively simple instrumental control and data acquisition (1-4). Little has been done in the way of computer-controlled real-time experimental alteration; that is, having t h e computer alter a n experiment during the course of t h a t experiment so as to optimize the analytical output. Perone e t al. ( 5 ) have described one such system, however, wherein stationary electrode polarographic measurements were optimized by means of real-time computer control. I t is in such applications t h a t the real power of t h e computer-in terms of its capabilities for rapid calculation, rapid acquisition of high precision data. and control of the instrumental system-is used to the fullest extent.
In the work presented here, a small digital computer has been used for t h e real-time control of a direct potentiometric analysis system. Several of t h e computer-controlled operations which are a part of this system were optimized so as to permit automated analyses, with the accuracy and precision of these analyses both being about 2%. In t h e system, a series of standard additions are made under computer control to a n unknown solution in a cell containing a pair of electrodes (ion-selective and reference). T h e volume of each of t h e standard additions is optimized under computer control. In general terms, this volume optimization involves increasing t h e volume of each successive standard addition so as to yield an even distribution of resulting cell voltage values. In addition, the cell voltage readings after each addition are acquired using a unique data sampling and averaging technique. T h e concentration of the unknown is calculated by fitting the standard addition data t o t h e Nernst equation
after a method described earlier by Brand and Rechnitz (6) In Equation 1, E , is the cell voltage, E o is the standard potential, C, is the concentration of the unknown, Vu is the volume of the unknown, C, is the concentration of an individual standard addition and V , is the volume of a n individual standard addition. Concentration could be used here in place of activity as the changes which occurred in t h e ionic strength of an unknown solution during analysis were minimized by making all solutions 0.5 M in an indifferent electrolyte, MgSOJ. The three unknowns determined in t h e fitting process are E " , RTInF, and C,. ANALYTICAL CHEMISTRY, VOL. 48, NO. 2, FEBRUARY 1976
281
I(+
CONCENTRATION,
Figure 1. Voltage response of the Corning cation-selective electrode. The K+ solutions used here were 0.5 M in MgS04
T h e technique used to fit the equation to the standard addition data is nonlinear, residual least squares ( 7 , 8). I n this technique, one determines those values of Aj (where Aj represents each of the unknown terms in Equation 1) for which the summation
is a minimum. At this minimum, A,, the best value of the unknown term, is approximated by the summation of A,,,, a n estimate of the unknown term, plus AA,, a small correction term. Here Yj represents the experimental data (Eiin this work) and Wi represents the weights of the residuals (8). (In this work W , was set equal to unity). The minimum is determined by calculation of the partials of Equation 2 with respect to each of the correction terms, AA;, and equating these partials to zero. The initial estimates of Aj (Le., Ai,.) are entered by the operator. T h e calculations of t h e partials of Equation 2 for the Nernst equation (Equation 1) result in three simultaneous equations. These equations are solved for t h e correction terms AAj. T h e values of AAj determined here are, however, only approximations of the final corrections since t h e term 2ik,l (aflaAj) ( S A , ) of Equation 2 constitutes a truncated Taylor series (9). Thus, the calculated values of the correction terms are added to the previous estimates of the unknown terms, these sums are used as new estimates for t h e unknown terms, and the entire procedure is repeated until the values of the correction terms become insignificantly small (about 0.01% of the current value of the unknown term).
EXPERIMENTAL Computer System. T h e computer used in this work was a Digital Equipment Corporation (DEC) PDP-8/L computer with 4096 words of memory. T h e computer is equipped with a teleprinter and a Tennecomp Model TP-1375 cassette tape system. Conversion of analog voltages t o digital values for computer processing is done with a Burr-Brown Model ADC 50-12-BIN 12-bit, 3 0 - j con~~ version time analog-to-digital converter. Two operational amplifiers, one wired as a follower and the other as a variable voltage a m plifier, are included in the interface for purposes of voltage modification prior t o analog-to-digital conversion. Precise timing for control and d a t a acquisition is achieved with a DEC Model M405 10M H z crystal clock counted down t o 100 Hz using DEC Model M204 flip-flop logic cards ( I O ) . All interface logic is constructed using DEC logic cards. T h e computer is used to control two components of the system, a magnetic stirrer and the standard addent delivery system. In the control operation, software is used to actuate two solid state relay drivers found on a DEC M040 relay driver card ( 1 0 ) . T h e external 282
ANALYTICAL CHEMISTRY, VOL. 48, NO. 2, FEBRUARY 1976
power of each relay (the relay driver acts as a current sink for an external supply) is provided by a Heath Model EUW17 transistor power supply. T h e DEC relay drivers in t u r n actuate 2 D P D T P o t ter and Brumfield Model K R P l l D G relays. These two Potter and Brumfield relays actuate, through connection of 110 volts ac, the magnetic stirrer and a solenoid-actuated valve. I t was found necessary to connect a 5-ohm resistor and a 0.01-jLf capacitor (connected in series) in parallel with the contacts of the relay. Without this RC circuit, noise from preclosure arcing and/or contact bounce upsets the timing circuitry in the general purpose digital interface. T h e addent delivery system consists of a 300-ml solution reservoir connected with Tygon tubing to a Skinner solenoid actuated valve, Model B2DA9052. T h e solution flow from the valve is fed through copper tubing to a stainless steel delivery tip having an i.d. of 0.5 m m . T h e distance from the center of the reservoir t o the delivery tip is 67 cm. T h e delivery rate for a n 0.1 M KC1-0.5 M MgSOd solution using this system was determined t o be 0.370 f 0.004 ml/s. Solution delivery rates were found to change less than 1.0% when measured over a range of 1.0 s total delivery time t o 14 s total delivery time. Cell and Electrodes. T h e electrodes used in this work were a Corning monovalent cation electrode, catalogue No. 476220, and a Beckman saturated calomel electrode (SCE). T h e response curve for this electrode system is shown in Figure 1. Connection between t h e unknown solution and the S C E is made with a fiber-tip secondary junction filled with 2 M MgSOd. T h e cell consists simply of an easily replaced IjO-ml plastic beaker. T h e voltage developed by the potentiometric cell is fed to a Beckman Research p H meter. T h e recorder output from the meter is connected to t h e input of a Keithley 160 Digital Multimeter, t h e analog output of which is in turn fed to the follower-amplifier combination described above. T h e Keithley DVM is used in t h e system in t h a t it provides a continuous visual display of t h e cell voltage. T h e overall gain of this analog system is set a t 20. Finally t h e output of t h e follower-amplifier combination is digitized as described above. Solutions. T h e solutions used for this work were prepared from reagent grade salts. All KCI solutions were made 0.5 M in MgS04 so that t h e solution ionic strength changes occurring during the course of the standard additions would be minimal. T h e water used was purified by passage through a mixed-bed cation-anion exchange resin followed by distillation. As the unknown solutions and addent were a t essentially t h e same temperature, no temperature control was deemed necessary.
RESULTS AND DISCUSSION In this system, the computer controls two operations such t h a t they are optimized. These are t h e standard addition operation and the data acquisition operation. The exact nature of this optimization is best described in a discussion of a typical analysis, which is outlined in Figures 2 and 3. The first operation is the entry of the experimental parameters into the computer via t h e teletype. Table I shows a typical input. The “Total points” refers to the total number of cell voltages to be acquired. This value is equivalent to one more than t h e number of standard additions since the first cell voltage arises from the unknown solution alone. The meanings of parameters 3, 4 , and 5 on the list are obvious. T h e last three parameters on t h e list are the original estimates of the unknown terms of the Nernst equation described above. T h e meanings of the remaining parameters in this list will be explained in t h e ensuing discussion. After the unknown solution is placed in the cell, the program is continued with its first operation being t h e activation of the magnetic stirrer for 15 s. After t h e stirrer is stopped, data acquisition is begun. (This process is outlined in Figure 3.) T h e computer first obtains one cell voltage reading. After a preset amount of time, S (usually 1 s; see Table I, entry 8) a second reading is obtained. After N (see Table I, entry 7 ) readings of the cell voltage have been gathered, the computer’s interrupt system (111 is enabled, and a calculation of the relative standard deviation (RSD)
G E N E R A L PROGRAM FLOW
ENTER PARAMETERS, INCLUDING ESTIMATES
EQUATIONS FOR CORRECTION
, FOR Eo, RT/nF AND C
TERMS FOR ESTIMATES LADDRESS POINTER = 1
-
I CALCULATE PARTIAL 1
ADD CORRECTION TERMS TO ESTIMATES TO OBTAIN IMPROVED ESTIMATES
DERIVATIVES AND
CALCULATE SUMS OF PARTIALS, RESIDUALS,
[HALT]
M K E ADDITION
L-s'
ADDRESS POINTER
OBTAIN DATA POINT
Figure 2. Flowchart for the computer-controlled potentiometric analysis operation
D A T A ACQUISITION SCHEME
I STIR
15 SECONDS
I
TAKE 4 (10-50) VOLTAGE READINGS
-S (USUALLY
Q
I N T E R R U P T SCHEME
1) SECONDS
APART
4
I -VOLTAGE R ~ D I N G S COUNTER I
SET INTERRUPT SYSTEM ON ,CALCULATE RELATIVE STANDARD DEVIATION (RSD) OF
E VOLTAGE
VALUES
I
TO DATA BUFFER AS N TH VOLTAGE VALUE
k TAKE AVERAGE OF
ROTATE VOLTAGE DATA STORAGE BUFFER, DROPPING VOLTAGE F I R S T OF VALUES I N BUFFER
I
[HALT:
T h E OVERFLOW1
1
"SELECT" DATA POINT
1CLOCK PULSES Figure 3. Flowchart for the computer-controlled data acquisition operation ANALYTICAL CHEMISTRY, VOL. 48, NO. 2, FEBRUARY 1976
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Table I. Typical Values of Experimental Parameters Entered by the Operator Prior to Computer-Controlled Analysis Total points Between-points voltage range: Volume of unknown s o h : Concn of std solution: Buret delivery rate: First volume : Number readings t o be averaged Time between readings Maximum re1 std dev for readings Estimate, E” : Estimate, RT/nF Estimate, C :
80
5 20 (mV) 50 (ml) 0.1 ( M ) 0.370 (mlis) 0.50 (ml) 10 1(s) 0.01 (decimal percent) 0.0 (mV) -30 (mV) 0.00001 (M)
2
.:
60
0 < 40 -8
