An Analog Computer For Reaction-Rate Analysis Gerald E. James and Harry L. Parduel Department of Chemistry, Purdue University, Lafayette, Ind. 47907 An instrument which facilitates the automatic measurement and computation of results in kinetic analyses is described. All measurements and computations are performed automatically to provide an output signal easily calibrated in desired concentration units. The instrument employs solid state circuitry throughout and, as such, has response speeds considerably faster than electromechanical systems described to date. The system has been evaluated for simulated kinetic response curves and for the determination of the enzyme, alkaline phosphatase. The instrument performs satisfactorily over the time range from 6 X to lo3 seconds. Measurement errors on simulated curves approach 2% at the shortest times and 0.5% for measurement times greater than a few seconds. Digital values of alkaline phosphatase activity read directly from the instrument are repeatable and have linearity (activity as output) to within 1%.
RECENTLITERATURE demonstrates a growing interest in the application of kinetics in quantitative chemical analysis. Kinetic methodology is being applied to the differential analysis of organic functional groups ( I , 2, 3), to the selective determination of organic species using enzymes (4), to the determination of enzyme activities (4), and to the determination of trace cations and anions using catalytic oxidation reduction reactions ( 5 ) and coordination chain reactions (6, 7). Accordingly, significant effort is being devoted to the instrumental problems associated with kinetic measurements. A major objective of this effort has been to develop automatic instrumentation which will render the kinetic measurement simple, rapid, and highly precise and accurate. Developments in this area have been surveyed briefly in recent reports (8, 9). Of the several approaches studied to date, the variable time method (9) appears to have significant advantages over the others in many situations (8). In this approach, the time required for the reaction to proceed to a predetermined extent is measured. Under controlled conditions the measured time is inversely proportional to the concentration of the rate limiting species. The principal advantage of the variable time approach is that it is applicable with equal ease to pseudo zero or first order reactions and to linear and nonlinear response curves so that a single instruCorrespondence to be addressed to this author. S. Siggia and J. G. Hanna, ANAL.CHEM., 33, 896 (1961). F. Willeboordse and R. L. Meeker, Ibid.,38, 854 (1966). D. Benson and N. Fletcher, Tuluntu, 13, 1207 (1966). G . G. Guilbault, ANAL.CHEM., 38, (5) 527R (1966). (5) K. B. Yatsimirskii, “Kinetic Methods of Analysis,” Pergamon Press, New York, 1966. (6) D. W. Margerum and R. K. Steinhaus, ANAL.CHEM., 37, 222 (1965). and J. J. Latterell, Ibid.. 39, (7) . , R. H. Stehl, D. W. Maraerum, 1346 (1967). (8) H. L. Pardue. Rec. Chem. Prowess. 27. 151 (1966). (9) W. J. Blaedel,‘and G. P. Hicks;“Advances in‘Anafytica1Chemistry and Instrumentation,” Vol. 3, Wiley, New York, 1964, pp 105-142.
(1) (2) (3) (4)
796
ANALYTICAL CHEMISTRY
ment is easily applicable to a wide variety of chemical and detection systems with only minor modifications. Recent instrumental developments have demonstrated that it is possible to perform all measurements and computations automatically to yield output signals proportional to concentration (IO, I I ) . Each of these instrument systems has involved one or more mechanical operations in the measurement or computational circuits. Principal limitations of these systems are their limited response speeds and their tendency toward mechanical malfunction during continued use. This report describes an instrument system for automatic kinetic measurement which eliminates some of the problems and limitations inherent in previously reported systems. The following are the more important characteristics of the system. (a) All measurements and computations are performed completely automatically. The measurement step consists of mixing sample and reagents, activating the instrument, and recording the computed result. (b) The system is applicable to any pseudo zero or first order reaction which can be monitored continuously with a suitable signal system. (c) The system is applicable with equal ease to both linear and nonlinear response curves. The change from one reaction or signal system to another involves only a change in the preamplifier characteristics and a calibration. (d) The output is easily calibrated in any desired concentration unit, including absolute values of enzyme activity. (e) Critical parts of the control and computational circuitry function satisfactorily for times between 6 X and 103 seconds. This rapid response is achieved by using all electronic control and computer circuitry. The only mechanical operation is the reset switch at the initiation of each run. (f) The output is a nontransient analog signal which can be held for extended periods of time if desired. This permits the use of relatively inexpensive digital voltmeters to record data obtained on a rapid time scale. (9) Results are precise and accurate (in terms of time measurement) to about 1 relative. INSTRUMENTATION
The block diagram in Figure 1 will facilitate understanding the instrument system. In this diagram the solid lines represent operations implemented in this work, while the dashed lines represent operations which could be controlled using this circuitry, A suitable signal system continuously monitors the reaction proceeding in the reaction cell. The output from the detector is adjusted by the signal conditioning circuit (SCC) to have the proper amplitude, polarity, and direction of change to be compatible with the remainder of the circuit. The voltage interval detector (VID) selects the signal interval over which the reaction time is to be measured and serves to control the function of the other components. A principal function of the VLD is to start and stop an electronic timer in (10) H. L. Pardue, C. S. Frings, and C. J. Delaney, ANAL.CHEM., 37,1426 (1965). (11) H. L. Pardue and R. L. Habig, A n d . Chim. Acta, 35, 383 (1966).
r-----I Reaction Cell
.
I
I
A
I
L
Sample Handling
-
1 I
I k - - 7 i
---- ---a
I
t
'
I I
I I I
I I
I Signal System
-
Signal Conditioning Clrcult
-
Voltage Interval Detector
-
Reciprocal Time Computer
11
-
Readout
+ I
.___________________-I
the computer. The reciproal time computer (RTC) computes the reciprocal of the time interval which is determined by the VID. The solid arrow from the VID to the SCC represents an information path which resets the SCC to a standby condition at the end of a measurement interval. This, or a comparable function, is necessary to prevent recycling of the instrument while the sample is being changed in the sample compartment. The dashed line between the control circuit and the readout device represents an information path for triggering automatic recording of the results. Similarly the control system generates sufficient information to control automatic sample and reagent handling equipment. Signal Conditioning Circuit. The signal conditioning circuit is shown in Figure 2. Amplifiers OAl and OA2
serve to amplify the input signal to the proper level such that the voltage interval selected by the VID will correspond to the desired reaction interval. A bucking voltage (Es)obtained across Rzserves to adjust the output from OA2 to the desired starting point. The functions of SZand SCSz(silicon controlled switch) are discussed below. Additional details related to the SCC will be given after the characteristics of the VID and RTC have been established. Voltage Interval Detector. The VID is represented in Figure 3. The circuit is similar to that described by Todd (12). The voltage levels at which the VID starts and stops (12) C. D. Todd, Electronics, Sept. p 97 (1965).
ODlVf
1N2071
From Q4 (Flgura 3)
+15v
t -15v
Figure 2. Transducer signal conditioning circuit &-lo turn lOOK Helipot with dial; Rz-10 turn 5K Helipot with dial; R3-2 K trim pot; OAl-SP2A; OA2,OA3-P65AU; BI-P66A; SCSaC.E. 3N59; Sz-SPST Toggle VOL. 40, NO. 4, APRIL 1968
797
-1sv
To SCS1 i w e 4)
-1sv
0.lYf
-
-
-
Figure 3. Voltage interval detection circuit R4-lK, Rs-2K, R-1.5K (these resistors are trimmed to give desired intervals) Qi-Qa-2N1305, 01-Dr-IN3713
the electronic timer will be designated by E1 and 4, respectively. The diodes D1and Dzare tunnel diodes (13). Resistors R 4 and R6 are selected such that iplRl = El and ip& = 4 where ip1and ip2are the peak currents of the diodes. Therefore, for the input to the VID, Eo2, more positive than El, D 1will be in its low resistance state and the base of QI will be tied to ground and Ql will be in a nonconducting state. Similarly, for the input to the VID more positive than Ez, D2 will be in its low resistance state and Q2 will be nonconducting. However, when Em becomes more negative than El, D lswitches into its high resistance state SO that Qi is forward biased and conducts heavily, raising the collector voltage of Ql from -15 volts to about zero volts. This POtential is maintained until Eoz = Ez = R5ip2. At this point D2 switches into its high resistance state which drives QZ into conduction. The base of Ql is drawn to ground rendering it nonconducting and the collector potential of Ql changes abruptly to -15 volts. The output a t the collector of Ql is differentiated to give a positive pulse at E1 and a negative one at E?. These pulses are used to control the electronic timer in the reciprocal time computer. The voltage interval, E2 - El, was made equal to about 1 volt to minimize errors due to small variations in transistor leakage current. Reciprocal Time Computer. The reciprocal time computer is represented in Figure 4 . An integrator, OA4, generates a voltage proportional to the time interval. The amplifier, OA5, with a transistor connected in the trans-diode configuration (14) computes the logarithm of the output from OA4. This signal is summed with a constant voltage a t OA6. (13) “Tunnel Diode Manual,” General Electric Co., Semiconductor Products Dept., Liverpool, N. Y.,1961. (14) “Application Manual for Computing Amplifiers,” Philbrick Researches, Inc., Nimrod Press, Inc., Boston, Mass., 1966.
798
ANALYTICAL CHEMISTRY
The sum, with sign inverted, is fed through Q 6 to OA7. This combination computes the exponential (14) of the output from OA6 which is a function of the negative logarithm of the reaction time interval. The resultant output from OA7 is proportional to the reciprocal of the time interval. The input voltage to the integrator is controlled by SCS1. At El a positive pulse from the VID applied to the cathode gate (Gc) of SCSl turns it on applying a constant voltage to the integrator (OA4). The integrator generates an output.
where ei, is the constant voltage applied through SCSl to the input of the integrator. At Ez a negative pulse turns SCSl off, and
where At is the time required for Eoz to go from El to E2. The amplifier OA5 computes the logarithm of this voltage giving (3)
where Eo and Zlare characteristic of transistor Q5. The sign of eo4 is ignored except that it dictates the type of transistor is summed with a reference which must be used. At OA6, eO5 voltage, e,,f, to give an output, eo6 =
-[
+ Eolog (g)]
eref
At OA7 the analog is computed to give an output, eon
eo7=
-R,~I~IO~
(4)
From Oar (Figure 3)
L I
.
F I
-15V +15V
1N2071
+1sv
r -15V
R10
25pf
I
'51
I\
I\
I
Ib.
I '07
Rll
.. O.OO1pf
Figure 4. Reciprocal time computer circuit OA4-P25AUYOA5,OA6,OA7-P65AU; B2-P66A C1-2 pf polystyrene capacitor (Southern Electronics Corp.) Rr22M Rs-1OK Rs-100K (1 %) Rlo-lO-turn 1K Helipot &-5K trim pot Rlz-lO-turn lOOK Helipot with dial Q6 and QsPhilbrickPLIP matched transistors SCS1, SCSI-G.E. 3N59 where I2 is a characteristic of Q,. Equation 4 into Equation 5 yields
Substitution of eO6from
which can be rewritten (7)
Substitution for eO4from Equation 2 yields (9)
where all symbols have been defined above. There are several details of this circuit which merit additional discussion. When SCSl is conducting there is a constant voltage drop of about 0.7 volt across this device. Therefore, the effective integrator input voltage ei, is 0.58 volt. The leakage current IOfor the PLIP transistors used in this work is reported to be less than lo-'* ampere and was evaluated to be about 10-14 ampere at 25" C. The constant, &, was evaluated to be 0.0592 volt at 25 O C. Both IOand Eo are functions of temperature. The validity of Equation 5 for the antilogarithm configuration was evaluated over a range of voltages from zero to 0.6 volt. The exponential relationship was valid with high accuracy for voltages greater than 0.43 volt but failed below this level. Therefore, the function of erefat the input of OA6 is to maintain the output of this
amplifier w i t h the exponential range of L.3 transistor, Qa, throughout the anticipated time interval. In practice, eraf is selected such that the transistor is operating somewhere near the upper limit of its exponential range for an integration (OA4) time of a few seconds. The output from OA5 then decreases the input to Q e at a rate of 60 mV per decade of time (at 30" C). Note that the effective range from 0.43 0.17V or 3 decades of time. to 0.6 volt corresponds to 0.06 V/decade Note that at zero time and indeed until the input to VID reaches E,, the output from the integrator (OA4) is zero volts. If the input to OA5 is permitted to go to zero, then this amplifier limits. This results in an unsually large voltage applied to Q,. As a result, this transistor tends to heat up giving instability in the computer which may last several minutes after OA5 is driven out of limit. The signal applied through SCS3 is designed to prevent the input to OA5 from ever having a value of zero. At the beginning of each run S1 is closed momentarily. Among other things, closing this switch activates the cathode gate of SCS3 and turns this switch on applying sufficient voltage at the input of OA5 to prevent saturation of this amplifier SCS3 remains on until a positive pulse arises at the anode gate from Q 3 of the control circuit. Referring to Figure 3 it is noted that the current limiting resistor R6 for tunnel diode D3 is between the values corresponding to the "on-oK"leve1s (E1 and E2)of Ql. Therefore, SCS3 will be turned off part way between El and E*. During this time, the integrator will have developed sufficient voltage to prevent saturation of OA5. The voltage applied through SCS3 also provides a means of checking the computer calibration between runs. Once Rlz has been set, em should always read the same when this signal is the only input to OA5. If, for some reason, em should drift from the calibrated value, recalibration is achieved by adjusting ere!with Rlo until em reads the correct value. VOL 40, NO. 4, APRIL 1968
799
The amplifier used for the integrator (OA4) should have low current offset and drift. A Philbrick P25 A was found quite satisfactory for this purpose. It was observed that Mylar capacitors exhibited some “memory” effects after being charged to several volts for several minutes. Therefore, a polystyrene capacitor which exhibited no “memory” effects was used as the integrating capacitor, C2. All variables in Equation 9 can be evaluated in practice. However, because some of these variables are subject to change with time, and from one transistor to another, it is more convenient to employ empirical calibration procedures. Resistors Rlo and Rlz are calibration controls. With this in mind, and assuming that the temperatures of Q sand Q e are maintained constant, Equation 9 reduces to
-
-
l*O
(15) G . W.Bowers and R. B. McComb, Clin. Chem., 12,70(1966).
800
ANALYTICAL CHEMISTRY
/
”i
/
IO0
a C
/
=,Vt // I 0
where K is equal to the quantity in brackets in Equation 9. It will be demonstrated later how R12is utilized to calibrate the output in desired units. Combined Operation. Adaptation of this control-computer system to different reactions and signal systems requires only that the signal be conditioned to be going negative at a rate to overcome the 1-volt interval (Ez - El) with the desired measurement interval. The system has been evaluated for the colorimetric determination of alkaline phosphatase using the reaction reported by Bowers and McComb (15). The signal conditioning circuit required for this measurement is represented in Figure 2 and discussed briefly above. Amplifier OAl (Philbrick SP2A) converts the phototube current to a voltage which is summed at the input of OA2 with a constant bucking voltage. The bucking voltage is used to adjust the output of OA2 to a level compatible with the VID as discussed above. As the reaction proceeds, the transmittance decreases and the phototube current decreases so that the output from OA2 is going negative. R1 is adjusted so that the transmittance range over which the measurement is to be made correspond to a change of - 1 .OO volt as required by the VID. The photometer sensitivity is adjusted to yield exactly 1.OOO volt at the output of OAl at 100.0% T. The time is measured for the transmittance to change from 95 to 90% T. This corresponds to a change of f 5 0 mV at the output of O A l . With Rl set at 20K, OA2 will have a gain of - 2 0 giving a change of - 1.00 volt at the input of the VID for this 5x T change. R1 is adjusted to give an output of +1.000 volt from OA3 to compensate for the output from OAl at the start of the reaction. The above discussion has assumed that the triggering points of D1 and D2, El and E,, are exactly -1.00 and -2.00 volts, respectively. As the nominal values of peak current are specified to + l o % it is necessary to trim Rd and R S to give the desired triggering points. Alternatively of course, the gain of OA2 and the bucking voltage can be adjusted so that intervals other than 1.00 volt can be used. When reagents and samples are being added to or removed from the sample compartment, the output from the photometer fluctuates causing the VID to go through a portion, or all, of its cycle before the reaction is started. To prevent this recycling, SCS, is utilized to remove the bias voltage from the circuit during the time the sample is being changed. This is accomplished by introducing a positive pulse from Q4 into the anode gate of SCS,. Note in Figure 2 that Q4 operates in parallel with and conducts at the same time as Q2. Therefore, the bias voltage is removed at the end of each run. At the start of each reaction, after all reagents are added and the solution is stirred, S2 is closed momentarily, applying a positive voltage at the cathode gate of SCSZ, turning it on and reapplying the bias voltage.
t
I
020
I
I
1
I
I
am
ow
R11.llwe
E n i y ~Cen6.nIi.Ilm
I
I
0 10
I
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Figure 5. Computer output vs. relative activity of alkaline phosphatase
Obviously the exact nature and settings of the SCC will differ from one reaction and/or one detection system to another. For example, if one were detecting a voltage from a potentiometric cell, OAl could be operated in a follower configuration to provide a high input impedance. For a signal which is going positive at the input of OAl it will be necessary either to use the noninverting input of OAl or to introduce another inverter stage. To obtain a negative bucking voltage at the input of OA2 it is necessary to use the noninverting input of OA3. Considering the operation of these circuits, it will be noted that after sample addition the only manual operation which is required is the momentary closure of switches SI and S2. The switch S1simultaneously discharges Ca,switches on SCSI, and removes the anode voltage of SCS1, while Sz activates SCS2. The former, S1, may be used alone, before sample addition, if a calibration check is desired. Otherwise, both are closed simultaneously after sample addition and mixing are complete. The physical design of the computer utilizes printed circuit boards such that any circuit changes or additions which may be necessary, especially as were mentioned with regard to the SCC, may be made easily and without disturbing the other computer components. CALIBRATION OF COMPUTER OUTPUT
Calibration will be described for the case where the sample is an enzyme. The procedure is essentially the same for other systems, Enzyme activity is defined in terms of a reaction rate--i.e., quantity of substrate reacted per unit time per milliliter of sample, or, activity
AS At
= - C,
where S = substrate and C = factor for dilution, temperature, etc. Substituting At from equation 10 into Equation 11 and rearranging yields CAS activity = Rlz K
The constant C is known, A S is selected precisely by selecting the proper transmittance levels corresponding to El and Ez, and K is determined as described below. Note that AS, the change in substrate concentration, is determined from the preset transmittance interval and the molar absorptivity of the species being detected photometrically (see reaction 15 below).
A voltage ramp generator is connected at the input of the instrument and an oscilloscope is connected to the collector of Q1. The triggering pulses of the VID are observed as the input signal changes, the time between pulses is measured with 1 a timer, and em is noted. A plot of em us. - gives a straight At line having the slope = R1& Rlz is known, and thus K. can be calculated. This constant need be determined only once for the computer. The calibration resistor RIPis then set so that
where x is a positive or negative integer. Substituting Equation 13 into 12 above gives activity
=
10Zeo7
(14)
Therefore, multiples of enzyme activity are read directly from a digital voltmeter. It will be noted that this calibration procedure is not based upon any enzyme standard but rather upon the more accurately defined and determined molar absorptivity of the absorbing species (p-nitrophenol in this work). This is one of the stronger merits of the variable time method of measuring rate data. In situations where good standards are available-such as with most substrates and inorganic systems-the calibration procedure can be as simple as running a standard and adjusting R12until the output voltage is a multiple of this standard.
The reaction of interest is given in Equation 15.
+ HzO
alkaline ____f
phosphatase
OzNoO-
-
+ HP0,2- + H+
(x)
113 87.7 64.7 43.5 21.6 11.0
109 87.9 64.8 43.7 21.6 11.0
0.63 0.74 0.96 0.71 1.43 1.11
0.92 0.65 0.93 1.00 1.18 0.64
3.67 0.28 0.15 0.46 0.00 0.00
Table 11. Computer Response at Short Time Intervals Proportionality Integrator Computer constant Dev from Re1 std input (volts) output (volts) X 104 av(%) dev(%) 0.0400 0.0501 0.0600 0.0699 0.0900 0. 100 0.111 0.120 0. 13OU
0.602 0.785 0.925 1.08 1.38 1.50 1.66 1.82 1.97
664 638 648 648 652 666 661 660 660 Average 655
+1.4 -2.6 -1.1 -1.1 -0.5 +1.7 +0.9 +o. 8 +0.8
0.42 0.39 0.23 0.66 0.51 1.22 1.35 0.39 0.62
Corresponds to time interval of about 6 mseconds.
seconds) 0.10 ml of sample is added rapidly along the side of the cell. After the solution is thoroughly mixed (about 3-5 seconds) SIand Sz are closed momentarily. The computer output is read from a digital voltmeter. The performance of the instrument was evaluated by comparing results determined in this fashion with results obtained from recorder traces obtained simultaneously.
PROCEDURE FOR ALKALINE PHOSPHATASE
OzN\)OP03Z-
Table I. Comparison of Computer Output with Recorder Data for the Determination of Alkaline Phosphatase in Reconstituted Blood Serum Activity (mV) Re1 std dev Computer Recorder Computer Recorder Re1 diff (Z)
(15)
Preparation of Equipment. A Spectronic 20, modified so that the phototube output was sampled directly by OAl, was used to follow the increase in concentration of p-nitrophenolate ion at 404 mp. The cell compartment is modified to permit thermostating water to be circulated around the cell. The solution in the cell is stirred by a magnetic stirrer. The cell and all reagents are thermostated to 30" C before any determinations are made. The transistors Q S and QB are kept at 30" C by circulating water from a constant temperature bath through a brass block in contact with the transistor caps. The intensity control is adjusted until the output of OAl is 1.000 volt with a substrate-buffer blank in the cell. The output from OAl was also recorded on a 100-mv strip chart recorder. Potentiometer R 3 is adjusted to give exactly 2.00 volts across RP. Then the 10-turn dial on Rz is set at 5.00 turns. Potentiometer R1 is set at exactly 20K. These settings result in a change from 95% T to 90% T being detected by the VID. The sample was Versatol-E reconstituted blood serum. Dilutions were made with 0.9% saline solution. Procedure. The reaction cell is emptied by an aspirator tube and rinsed with deionized water. The stirrer is started and 2.70 ml of buffer and 0.20 nil of substrate solution are added to the cell. When these reagents are mixed (a few
RESULTS AND DISCUSSION
Determination of Alkaline Phosphatase. Parameters which affect the determination of alkaline phosphatase using p nitrophenyl phosphate have been studied in detail ( I S ) . The data presented demonstrate that activities evaluated from recorded curves of absorbance us. time are reliable. Therefore, the instrument system described above was evaluated by comparing results from the computer with results obtained from recorded curves. Table I lists typical computer values of enzyme activity (em, mV) along with values obtained from simultaneously recorded curves. There is no significant difference between the relative standard deviations of the two methods, both having magnitudes of about 1%. With the exception of the one result at the highest activity level, the results are in agreement to 0.5% relative or better. The above data show good agreement between the recorded data and computer data. The data in Figure 5 demonstrate the linearity of the computer output with enzyme concentration. Deviations of all points from linearity are well within 0.5%. Clearly then, this instrument system provides results consistent with those obtained by manual methods. The measurement time for the highest activity shown in Table I was about 12 seconds and that for the lowest activity was about 120 seconds. Results obtained for electricallyVOL. 40, NO. 4, APRIL 1968
* 801
simulated rate curves demonstrated comparable reliability for measurements up to about 800 seconds. No attempt was made to evaluate the system for longer times. Evaluation of Response Speed. One of the stated objectives of this work was to design a system to yield improved response speed over existing automated equipment. The following modifications and procedure were followed to evaluate the response speed of the instrument. The rate of integration of OA4 was increased by a factor of l o 3 by decreasing R7 from 22M to 22K. Capacitor CI was removed from OA2. Amplifier OA 1 was converted to an integrator (a voltage ramp generator) with a variable input to give ramps having slopes of from about 1 V/second to 5 V/ second. The gain of OA2 was left at 20.0 so that an interval of 50 mV at the input of OA2 gives the required 1 volt triggering interval at the input of the VID. The time between VID pulses was approximated with an oscilloscope. The computer output, eo7,was observed as a function of the input to the integrator, QAl. Using OAl as an integrator, it is easily shown that the computer output should be proportional to the input voltage to the integrator. The performance of the instrument was evaluated by determining em at several values of input voltage and computing the proportionality constant. Results of these experiments are given in Table 11. The largest and smallest values of Vi, correspond to time intervals of about 6 mseconds and 18 mseconds, respectively. The relative standard deviations are about l and the deviation of the maximum and minimum values of the computed constant is about 4% relative with the deviation from the average being about 1 . 2 x . No attempt was made to calibrate the computer in reciprocal time for these short intervals. However, the data in Table I1 demonstrate that with such standardization, computation of reciprocal time in this range can be made accurately. Therefore, this computer system should be applicable to reactions with rate constants considerably larger than has been possible with existing instrumentation. It should be noted that it is not necessary that either the logarithmic circuit or the digital voltmeter operate on this time scale. After the time information is stored in the integrator the computer and read out device can operate at a slower pace to perform the computation and read out the
802
ANALYTICAL CHEMISTRY
result. It would, of course, be necessary to utilize fast mixing systems to take advantage of this increased response speed. The potential user should keep the following points in mind. The transistors used to generate the logarithmic and exponential functions are temperature dependent and must be thermostated. The nominal switching levels of the tunnel diodes are only approximations and the exact switching levels must be determined in order to establish or select the exact voltage interval detected. Once established, the switching levels of the tunnel diodes are quite reproducible and need not be redetermined. Amplifier OA4 must have a low offset current drift. Otherwise, the integrator will drift continuously introducing an error into the output. Voltage levels are selected such that the characteristics of the other amplifiers in this figure are not so critical. If these points are observed, the limitations of the method will lie principally in the reliability of the chemical and detector systems being utilized. Currently, work is being initiated to apply this system to moderately fast reactions. Also, the instrument system is being extended to provide multiple measurements on a single reaction. This is desirable from the point of view of kinetic studies as well as for obtaining improved precision on analytical data. RECEIVED for review November 15, 1967. Accepted January 25, 1968. Investigation supported by PHS Research Grant No. GM 13326-01 from the National Institute of Health.
Correction Potentiometric Tit ration of Fluoride with Tetraphenylantimony Sulfate In this article by James B. Orenberg and Michael D. Morris [ANAL.CHEM.,39, 1776 (1967)] an error appears in the text on page 1778, column 1, line 8, of the Reagents section. The sentence should read “Tetraphenylarsonium carbonate was prepared from tetraphenylarsonium chloride (City Chemical Corp.) by treating aqueous solutions with silver carbonate to obtain soluble tetraphenylarsonium carbonate.”
