Miniature On-Line Digital Computer for Multipurpose Applications Applications to Kinetic Analyses Russell A. Parker and Harry L. Pardue' Department of Chemistry, Purdue University, Lafayette, Ind. 47907 A miniature on-line digital (MOLD) computer employing stored programs and suitable for multipurpose use has been developed. It includes analog circuitry for preconditioning of analog signals and a memory bank for storing analytical data. Results are available as a numerical display in decimal format. Because of the low cost of the system, it is economically feasible to dedicate it to a single experiment. Since it involves little interfacing from one instrument to another, and since the operating program can be changed quickly, it can be applied to a variety of different problems. The system is applied to two types of kinetic analyses involving single and two-component systems using first-order reactions. Results are reported for organic and inorganic analyses.
ONE OF THE MAJOR MILESTONES in the development of analytical instrumentation was the commercial development in the late 1950's of operational amplifiers in pre-packaged forms which were easily and effectively used by chemists with a modest knowledge of electronics (I). The availability of these components has led to the development of a wide variety of special- and general-purpose analog computers to solve a variety of chemical measurement and computational problems. A second major milestone has been the development in the late 1960's of digital circuitry in pre-packaged forms which are easily used by chemists (2). The major thrust in research related to analytical applications of digital technology has been directed toward applications of the socalled small general-purpose computer (3). There has been much less emphasis on the development of miniature specialand general-purpose digital instrumentation than was the case with operational amplifiers and analog computers. Also, there has been surprisingly little effort reported on the development of hybrid analog-digital systems. Both of these areas offer the potential for fruitful research. Recent reports have demonstrated the utility of miniature digital and hybrid systems for kinetic (4-6) and electrochemical (7) applications. These miniature systems have been developed for the solution of specific problems and as such do not provide the option of multipurpose utility. This report describes the results of effort directed at the development of an economical hybrid analog-digital system with multipurpose capability. The interface between an analytical instrument and this computer involves the connection of two wires carrying the analog signal from the instrument to the computer. The system digitizes the analog Correspondence should be addressed t o this author (1) R. G. McKee, ANAL.CHEM., 42 (1 I), 91A (1970). (2) J. S. Springer, ibid., (8), 23A. (3) S. P. Peroneand J. F. Eagleston,J. Chem. Educ.,48,317(1971). (4) R. A. Parker, H. L. Pardue, and B. G. Willis, ANAL. CHEM.,42, 56 (1970). ( 5 ) S. R. Crouch, ibid., 41,881 (1969). (6) G. E. James and H. L. Pardue, ibid., 40,797 (1968). (7) R. G. Clem and W. W. Goldsworthy,[bid.,43,918 (1971). 1622
signal and processes it via a stored program to generate numerical readout of concentration data. In contrast to the so-called small general-purpose computers (3), which usually include several thousand words of core memory and a variety of peripherals, the present system includes sixteen words each of instruction and data memory and built-in numeric readout. The system is intended for routine types of computations and is believed to be applicable to a wide range of equilibrium and kinetic problems. Results are reported for kinetic analysis applications. The reasoning is that if the system can be successfully applied to the transient signals involved in kinetic analyses, then it surely can be extended to many equilibrium systems. Examples reported here demonstrate that the miniature on-line digital (MOLD) computer is readily and easily adaptable from one type application to another. Since the circuitry involved is quite extensive, this report is limited to a generalized description of the system, special characteristics of critical components, and analytical results obtained in the evaluation of the instrument. A more complete description of the system, including circuit details and programming procedures, will be made available to interested persons upon request. However, it should be emphasized at this point that the overall concept of a miniature stored program computer and the potential utility of such a system as demonstrated in this report are more important than the exact details of the specific unit. This is made doubly true by the fact that there have been major advances in component design since this project was initiated. Consequently, a unit constructed today likely would differ significantly from that described herein. This fact in no way invalidates the potential usefulness of this concept or the approach taken to implement it in this work. SYSTEM DESCRIPTION
Objectives. The system as described here is intended primarily for routine applications as opposed to general research. A major goal was economy of design, both in terms of cost and size. Another goal was simplicity of operation in all respects including interfacing to analytical instruments, programming, and real time usage. The attainment of these objectives involves some compromises in terms of certain characteristics such as ultimate accuracy, speed for some operations, and mathematical options. For example, a potential trade-off of accuracy for circuit simplicity and economy is made in the use of analog rather than digital methods for computing logarithms. General Description. Figure 1 represents a simplified block diagram of the system. It can be viewed as consisting of three major operational units. These are the analog section, the data processing and display section, and the control section. The analog input from an analytical instrument is first subjected to the selected manipulations by the analog signal conditioning circuitry. The resulting signal is then digitized and stored in the arithmetic unit (AU). The quan-
ANALYTICAL CHEMISTRY, VOL. 44, NO. 9, AUGUST 1972
tity in the AU can be treated in a variety of ways. It can be stored directly in the data memory (DM), its decimal equivalent can be displayed, or it can be subjected to a variety of arithmetic operations with the result being stored in D M and/ or displayed. The operations performed on the quantity in the AU are controlled by the circuitry in the lower half of Figure 1, and in particular by the program stored in the instruction memory (IM). Each word in the IM contains information which controls the D M locations for reading and writing information, arithmetic codes which specify the mathematical operation performed on the data in the AU, and codes necessary for several decisions made during each program cycle. The following sections give information on the capabilities of subunits within each section. Subunit Descriptions. ANALOGSECTION.Signal Conditioning. The input to the computer includes an amplifier (Fairchild 741) which permits the signal level to be scaled to a level which is compatible with the ADC. Voltage suppression, if required, must be provided external to the computer. Log Converter. The logarithm of the ratio of the input voltage to an internal reference is generated by the log converter. The unit that produces this function (Model 751-N, Analog Devices) is temperature compensated, and adjustable to an accuracy of 0.1% over one decade change in input voltage. It responds with little degradation to sine wave variations of well over one kHz, and is thus suitable for stopped-flow, as well as intermediate and slow reactions. Scaling of’the output of the log converter by a variable gain amplifier (Fairchild 741) allows for establishing readouts directly in units of concentration. Sample and Hold. The primary function of the sample and hold amplifier is to provide signal averaging. The input voltage, after either scaling or log conversion, can be integrated for 1 / 6 ~second, whereupon the voltage across the integrating capacitor is sampled by the ADC. Timing for the various operations involved is provided automatically, and can be adjusted for input voltage integrating times over several decades. Linearity is as good as that of the ADC. Analog to Digital Conversion. The analog to digital converter (Computer Products, Fort Lauderdale Model AD 352C) produces the digital equivalent of the analog signal at the input. The unit is capable of making one 12-bit conversion every 100 psec. Accuracy is specified at *0.025% f 112 LSB, which, for a 0 to -4 volt full scale input, yields 1 MV resolution. Conversions are initiated by a short-duration “start” command, and an end-of-conversion level shift indicates the completion of each cycle. PROCESSOR-DISPLAY SECTION.Data Memory. The storage of all the information generated by the experiment is provided by the data memory. The array of memory chips (Fairchild 9033) is comprised of 16 words of 12 bits each. Each word can be addressed randomly in less than 50 nsec, and information can be written into the memory in approximately 50 nsec. The sequencing necessary for the actual addressing and storage operation ultimately determines the cycle time of the computer, and is adjusted for a cycle time of slightly less than 500 nsec. The outputs of any addressed word are available to the AU at all times, Arithmetic Unit. All programs involving analog to digital conversion, mathematical operations, or display of numbers in memory utilize the arithmetic unit (Texas Instruments, 74181). Addition, subtraction, transfer, multiplexing, and many other logical and mathematical functions are selectable by suitable codes in each instruction of a program. The three units, necessary for 12-bit accuracy, are wired for proper utilization of carry and borrow information. Multiply-Divide. The product or quotient of any two numbers in the D M can be computed in an average of 0.2 second with the M/D circuitry. The result of the operarion is stored in any of the available D M locations, and is simultaneously displayed. Multiplication and division are im-
Arithmetic Divide
Figure 1. Block diagram of miniature digital computer plemented by gated counters using techniques similar to those reported earlier ( 4 ) . The M / D unit is capable of handling both integers and decimal fractions and when division is performed, the result is displayed as the quotient times one thousand. The accuracy of the method employed averages low to the extent of one half of the uncertainty of the dividend, or the multiplier, whichever is appropriate. Display. The output from either the AU, or from the experiment timer, is continuously displayed on four seven segment readout tubes (RCA DR2010). The binary information used in normal data processing is converted to BCD every 0.01 sec without interrupting the operation of the computer. Decimal point location and zero blanking are included in the decoders which drive the filaments of the readout tubes. CONTROLSECTION.Instruction Memory. Nearly all of the sequencing, storage, and mathematical operations arz controlled by the instruction memory (IM). Each of the sixteen 16-bit words is programmed a bit at a time by a 4 X 4 array of momentary contact switches arranged on the control panel. Each word of the IM is addressable by either toggling in the appropriate binary code, or for the actual running of a program, addressing is automatically provided for by the instruction increment counter. The IM word is divided into four major parts. The first row of four bits is the current address of the data memory, and the information stored in this address, with the proper “transfer” code to the AU, is displayed continuously. The second four bits represent a data memory address, and indicate the storage location in the data memory for information generated by the ADC, or the results of several mathematical operations. The third four bits and the “mode” bit in the last row of the 4 X 4 array provide the codes for the AU functions, including addition, subtraction, etc., and for the M/D sequence. The last three bits, plus the “mode” bit, supply the sequencing pulse generator with the logical decisions necessary for the various pulses to be directed to the appropriate “blocks”. An ADC/Latch bit controls a multiplexer, which determines the “B” input of the AU, and also provides other logical decisions. A “timer reset” bit resets the experiment timer at the beginning of each instruction with this bit enabled. Some slope-determining programs may have this operation occur several times. Lastly, a “wait” bit controls the incrementing of the instruction counter. When it is enabled (true), a “write” command generates the instruction increment pulse, and when it is disabled, the latch pulse does this. Since every instruction has either a “write” pulse or a latch pulse, in most cases the computer executes the program until the last instruction contains a “write” command with the “wait” bit low, so that the computer stops. Clock. The timing sections, display, S & H, and M/D are controlled by pulses from a crystal clock (10 MHz) with
ANALYTICAL CHEMISTRY, VOL. 44, NO. 9, AUGUST 1972
1623
Table 1. Simulated Response from Ramp Voltages Display Volts to output, Standard Run integrator, average deviation, 15 trials Error, no. mV
z
50 100 200 500
1
2 3 4
49.91 99.90 200.0 500.9
-0.1 -0.1
...
+0.2
0.34 0.09 0.09 0.2
BCD dividers providing frequencies through the 0.1 Hz range. A common reset was provided to eliminate the randomness of low frequency pulse trains used in certain circuits. Timers. The rate of data acquisition and the duration of certain other computer operations are controlled by several timers. Two thumbwheel controlled counters are used to generate ADC data-taking rates corresponding to 1 msec to 99 msec, and 100 msec to 9.9 seconds between data points. A third counter selects the number of data points to be taken. Also, the S & H integration period is provided by a fixed 16.68 msec timer. An independent counter-timer is used for reciprocal time measurements. An overflow auto-ranging circuit varies the rate at which this counter is incremented. It also controls certain reset decisions, and together, these provide a readout, over several decades of time, in units of concentration. The decimal point is moved automatically during the course of computation. Write Logic. The storage of the result of an AU operation, such as analog to digital conversion, multiplication, or division is handled by the write logic. A pulse is generated at the completion of any of the above events. The pulse triggers a precisely timed sequence that loads the information to be stored into a buffer, fetches the “write” address, and generates the write pulse for the memory elements. Within 500 nsec, the operation is complete, and the next instruction is initiated. PROGRAMMING CONSOLE.The operations for taking data, manipulating it, and providing the proper readout are controlled by the instruction memory. A program is stored in the IM to perform these operations in the proper sequence, and with the appropriate time relationship to the experiment. The first step in programming the IM is the enabling of the load switch. This prevents the instruction counter from functioning. The first address of the program is entered through a switch register. Then, the contents of that location are cleared, and “1” ’s are placed in the appropriate rows through momentary-contact switches arranged in a 4 X 4 array. The second instruction location is selected and the appropriate instruction is entered via the switch matrix. This procedure is repeated until all instructions are entered. Should a mistake be made, the instruction is cleared, and the correct code is entered. Upon completion of the programming, the load switch is disabled, and the instruction counter, which is now at the address of the last instruction, is cleared to location 0 with a momentary-contact switch. RESULTS AND DISCUSSION
The MOLD computer was evaluated using electronically simulated kinetic response curves and single and two-component analyses using first-order reactions. The general description, experimental conditions, and results for each application are presented below. Simulated Response. The primary objective of this set of experiments was to utilize carefully controlled signal characteristics to evaluate the ultimate reliability of the system. To accomplish this, a voltage ramp was generated using an integrator constructed from a high quality operational am1624
e
plifier (Philbrick SP2A). The computer was used to evaluate the slope of the voltage ramp using the so-called “variable time” method so that data obtained could be compared directly with previously published data (4). The ramp voltage was amplified by a gain-of-ten amplifier with the result being fed to the voltage interval detection circuitry. The interval detector controlled the timer to measure the time required for the ramp voltage to change from 0.88 V to 0.90 V. The computer calculated and displayed the reciprocal of this time interval. The output computed in this way should be proportional to the slope of the voltage ramp. Since the resulting slope should be proportional to the voltage applied to the input of the integrator, the readout was calibrated in terms of this voltage. Results obtained in the different experiments are presented in Table I. The average values presented in the display output are reported to one more significant digit than was shown on the computer, except for run No. 3 in which the display had 4 significant digits. These experiments were designed to illustrate the linearity of the system. The agreement between input and calibrated readout is observed to be quite good, with a maximum error of 0.2 % throughout the tenfold range. Also, the repeatability of the results is good as demonstrated by the relative standard deviations. These results are comparable to those reported earlier ( 4 ) using a special purpose computer. The levels of error and irreproducibility observed in these experiments approach those expected for the analog integrator. Thus, it is not possible to separate the exact sources of error. However, it is apparent that the system is feliable at least to the 0.2 %level. Chemical Data. The computer was evaluated for chemical applications using single and two-component analyses based upon first-order reactions. SINGLECOMPONENT ANALYSES.The system selected for this study involves the reaction between Ni(I1) and thiolacids. Recent work in this laboratory has shown that this reaction produces a product [presumed to be a 1: 1 complex between Ni(I1) and the thiolacid (TA)] which absorbs radiant energy near 275 nm. There is no significant absorbance at this wavelength by any other species in the reaction mixture. Subsequent work has demonstrated that by careful control of conditions ([Ni(II)] >> [TA]), the reaction can be forced into pseudo-first-order behavior, depending only upon the TA concentration, The reaction is used for the determination of sub-millimolar concentrations of thiolactic acid (TLA) and cysteine (CYS). The reactions are sufficiently fast that stopped flow mixing is required. Since the method to be described here is general and can be applied to any first-order reaction, the mathematical treatment is presented for a general situation in which an unknown species B reacts with a reactant R to produce a product P. B+R+P
(1)
For a reaction that is simple first-order in reactant B, the following expression for the product concentration as a function of time (Pl) holds true;
P,
=
B,(1 - e&‘)
(2)
where ka is the first-order rate constant, Bo is the initial concentration of the reactant, and B, is the concentration of B remaining unreacted at time t. This expression assumes that there is no product at t = 0. If the concentration of PLis determined at times t l and h, the change in concentration is given as
ANALYTICAL CHEMISTRY, VOL. 44, NO. 9, AUGUST 1972
Table 11. Kinetic Determination of Thiolactic Acid. TLA added (M/l. X 4.016
x
107)
201 402 602 803
16
1004 2008 Condltions: NI(II) =
Deviation from linearity, MOLD H.P. 206 0 +3 200 -4 394 386 -2 -1 612 598 +1 -1 819 796 +2 1032 +4 +3 1044 2000 -3 0 1943 1.25 X 10-2M; Citrate = 1.58 X 10-2M; pH = 9.0; h = 275 mp, bandwidth
Relative standard deviation, MOLD H. P. 5 4 1 1
TLA found (M/L X 4.016 X 10') MOLD H.P.
which simplifies to AP(L2-i,,= B,(e-'t'1
-
e-'b'?)
(4)
Preliminary work with the Ni(I1)-TA reactions showed that the product of the reaction obeys Beer's law at 275 nm. Equation 4 can be written in terms of the change in absorbance (AAt2-fl = A,: - A f l ) as follows A A t j P t ,= €/B,(e-"Jfl -
e-'bf2)
(5)
where 6 is the molar absorptivity of the product a t 275 nm and I represents the cell length. Rearranging Equation 5 to solve for the initial concentration of B yields
Holding the measurement times tl and fz constant makes the exponential terms constant, and thus the initial concentration of B is directly proportional to the observed change in absorbance during the reaction time. The chemical procedure included the preparation of a stock 1.25 x 10-?M Ni(I1) solution in 1.58 X 10-*M sodium citrate, buffered to p H 9.0. Various dilutions of TLA and CYS, prepared in bufler solution at p H 9.0 and ranging in concentration from 5 x 10-5 to 5 X 10-4M, were prepared from 10-?M stock solutions. All solutions were prepared t o have an ionic strength of 0.3 using KCI. The pseudo-firstorder rate constants for the Ni(l1)-TLA and Ni(I1)-CYS reactions under these conditions are 11.0 sec-' and 21.0 sec-', respectively. The course of the reaction was monitored on the stoppedflow instrument described earlier (8). The fastest mixing time for the system is about 10 msec. Also, the reaction does not exhibit true first-order behavior until about 20 msec have elapsed. Accordingly, all analytical data were collected for reaction times exceeding 20 msec. The stopped-flow instrument generates a - 3 V to ground transition at the end of the syringe drive. This signal was used to trigger the computer at the completion of the mixing operation. The analog signal was taken from the 1-volt output of the stopped-flow instrument, and connected t o the input of the log converter in the MOLD computer. The output from the logarithmic converter is proportional to the absorbance of the product. The computer was programmed to take two data points, at 25 and 40 msec from f = 0. The difference between absorbance values during each run was used as a measure of TA concentrations. (8) B. G. Willis, J. D. Bittikofer, H. L. Pardue, and D. W. Margerum, ANAL.CHEM., 42,1340(1970).
3
3
2
1 2 4
1 3 =
7.4 mp.
A Hewlett-Packard 21 15A general-purpose computer, with 8k of memory, was run in parallel with the MOLD computer to provide a comparison with those obtained with the latter system. The 2115A utilized the Savitsky method ( 9 ) to calculate a smoothed 10-point derivative of the reaction response curve. The resulting derivative data were processed to provide printout of data which are linearly related to TLA and CYS concentrations. Equation 6 and a comparable equation, which can be developed for the derivative method, predict a proportionality between the absorbance change (or derivative) and concentration of the rate-limiting species. In actual practice, there are slight deviations from the ideal situation such that a linear equation with a small but finite intercept best describes the data. Thus, the data for each measurement system were fitted to the best straight line plot of concentration cs. readout. A linear equation of the form TA=mD+b
(7)
was determined. In this equation, D represents, for each data set, the datum for each instrument, and m and b represent the slope and intercept of the plot. The linear equation, with appropriate constants, was programmed into the MOLD computer to yield direct readout of concentration data. In order that a maximum number of significant figures could be read for the concentration range examined, the readout was calibrated to represent the molar concentrations of the thio acids multiplied by 4 x 107 for TLA and 2 x lo6 for CYS. The resulting values for m and b, respectively, for TLA were 1.05 and -48 for the MOLD computer and 1.06 and -69 for the general-purpose computer. Comparable values for CYS were 1.08 and - 2 2 for the MOLD computer and 1.12 and -31 for the general-purpose computer. The constants for the two methods are not expected to be identical since one system in effect utilizes a chord measured after the reaction has proceeded for some time while the other method utilizes a slope measured as near zero reaction time as is possible. The concentration values obtained by the two systems are the data which should be compared. Table I1 presents the results for the determination of TLA. Comparisons of the concentrations of TLA taken with those which were found are shown for both computers. The results indicate that there is very little difference in overall precision and accuracy between the two sets of data. An investigation of each run of any one concentration shows small but noticeable anomalies in the absorbance curve, possibly due to improper mixing, temperature gradients, or other causes. Despite the differences in the computational (9) A. Savitsky and M. J. E. Golay, ANAL.CHEM., 36,1627 ( 1964).
ANALYTICAL CHEMISTRY, VOL. 44,NO. 9, AUGUST 1972
1625
Cysteine added (M/I. X 2 X lo6)
100 200
300 400 500
loo0 Conditions: Ni(I1) =
Table 111. Kinetic Determination of Cysteine. Cysteine found (M/L x 2 x 106) Deviation from linearity, Relative standard deviation, 2 MOLD H.P. MOLD H.P. MOLD H.P. 100 102 0 +2 7 4 199 197 0 -1 1 2 300 292 0 -3 1 1 416 401 +4 0 3 2 515 499 +3 0 1 2 963 1010 -4 +1 1 2 1.25 X 10-2M; Citrate = 2.19 X 10-211f; pH = 9.0; X = 275 m p ; bandwidth = 7.4 mp.
methods, run-for-run correlation for the two systems was very good. Table I11 represents the results for C Y S . These data are quite similar to those described above for TLA and do not merit additional discussion. Although the relative errors range up to about 4 %, it should be noted that the maximum absolute concentration error observed is 1.5 x 10-6M. These results demonstrate the applicability of the MOLD computer to systems involving transient signals in the millisecond time range. TWO-COMPONENT ANALYSIS.The final step in the evaluation of the MOLD computer was to apply it to a two-component kinetic analysis using pesudo-first-order reactions. This represents one of the more complicated applications of kinetics to quantitative analysis in current usage. The reaction chosen for study involves the interaction of CN- with nickel ethylenediaminediacetic acid (EDDA) and nickel nitrilotriacetic acid (NTA). The rate of change of the product, Ni(CN)4*- has been shown to be proportional to the amount of NiL2-" present and the reaction can be used for the determination of the ligands EDDA and NTA (10). Conditions were adjusted so that the reactions of interest exemplified good first-order kinetics. There were several reasons for this choice. First, the NTA ligand has become important in ecological sciences as a potential pollutant. Second, the mixture employed here (EDDA NTA) behaves very well, in that two non-interacting pseudo-first-order reactions produce a highly colored product. Also, the ratio of rate constants for the two reactions was large enough to permit the determination of each reactant, yet small enough to require judicious selection of experimental procedures. The procedure developed for handling the two-component mixture is described here. Although the two reactions are kinetically independent of each other, there is potential interference of one reactant on the other due to the fact that both are producing product simultaneously. The approach taken in this work is to make initial concentration determinations assuming no interference between the components, and then to apply necessary corrections using these initial estimates. It will be observed later that the slower reacting component (NTA) can be determined reliably without applying any correction, but that the faster reacting component (EDDA) does xequire a correction to compensate for the contribution from NTA. The mathematical treatment demonstrating the computational method is developed for the general situation in which two species, B and C, react with a common reagent, R, to produce a common product, P. Reactant B is assumed to
+
(10) L. C. Coombs, J. Vasiliades, and D. W. Margerum Department of Chemistry, Purdue University, Lafayette, Ind., 1971, unpublished data. 1626
have the larger rate constant. The general procedure involves the measurement of the changes in absorbance over two time intervals tl to t2 and t3 to t 4 where tl < t2 < t3 < r4. The intervals are selected so that the first yields primary information on component B and the second yields primary information on component C . Since both reactions are assumed to proceed by fmt-order kinetics, Equation 5 from the previous section is an accurate representation of the situation for each component reacting alone. This equation is rewritten here for the two general components and two time intervals. AA(12-ll)= dB,(e-kbll - e-kbt*) AA(13-l,)= ~ l C , ( e - ~-~ ~eckc14) 3
(8b)
These equations, rearranged in the form of Equation 11, were used for the initial estimates, B', and C'o, of the concentrations of ihe two components as follows :
The estimated values were stored in memory and appropriate corrections were applied as described below. The correction of the initial estimate for component B involves a compensation for the contribution from component C during the interval t 2 - t l . If the two reactions are additive, then the following expression represents the actual situation for the two-component sample : AA(12-ll) = d[B,(e-kbtl - e-kblz)
+ C,(e-'Ct1
-
e-Lc12 )I
(10)
Dividing both sides of the equation by the quantity d(e-kbble-'b'Z) yields
The quantity on the left side of the equality is observed to be equal to the initial estimate, B'o, of component B as represented by Equation 9a. A similar equation can be written for the slower reacting component:
Comparing the quantities on the left side of these equations with Equations 9a and 9b, it is clear that in each case, a second approximation of the concentration of each component can be made by subtracting the quantity at the extreme right of each expression from the initial concentration estimate stored in memory. In a general situation, a series of successive
ANALYTICAL CHEMISTRY, VOL. 44, NO. 9, AUGUST 1972
approximations could be carried out if the situation required it. For the system being examined in this work, the ratio of rate constants is sufficiently large that it is possible to select a measurement interval for the component with the smallest rate constant during which the interference from the faster component with the largest rate constant is insignificant. Consequently, it is necessary to apply only one correction to the estimate for the latter using Equation 1la. Some discussion of the calibration procedures involved to yield direct readout in concentration units is in order. As indicated above, it is desirable to select the measurement interval for component C so that there is no contribution from component B. Once this time interval has been selected, then the computer gain adjustments can be set so that the readout is calibrated in units of concentration of component C. The gain settings so established apply also to component B and, as such, dictate the magnitude the quantity (e--libtl ekLr2) must have to yield readout in concentration units. Thus, only one of the two times, tl and t 2 , over which the absorbance change must be measured can be selected without restriction. The other must then be selected to provide the correct numerical value of the exponential quantity. It may be that there are practical reasons why the resulting time interval is not a desirable one. For example, it may be too short to achieve satisfactory resolution of the absorbance change or, in the case of the MOLD computer, it may not be possible to provide the required time resolution. Consequently, an alternative may be desirable. Examination of Equations 9a and l l a demonstrates that the exponential quantity involving time is a proportionality constant. It follows that any change in this quantity can be compensated for by introducing an appropriate proportionality into the equation. In this manner, additional freedom can be exercised in the selection of t1and t2. This is the procedure used in this work. Thus, the expression used to compute the displayed value of the B component is
where Y represents the adjustable proportionality constant. The pseudo-first-order rate constants for the NiEDDA and NiNTA reacting with CN- under the conditions of these experiments are 17.3 sec-' and 0.349 sec-', respectively. If t 3 and t 4 are selected to be 1.0 sec and 2.0 sec, respectively, then this corresponds to the NiNTA concentration decreasing from roughly 70% to 50% of its initial value. The amount of NiEDDA remaining to react during this time period is less than of the amount present initially. Consequently, little or no interference from EDDA is expected for reasonable concentration ratios of the two species, The times tl and t2 for the determination of EDDA were selected somewhat arbitrarily at 40 and 80 msec. During this time interval, the NiEDDA concentration changes from about 50% to about 25% of its initial value. During the same period, NiNTA changes from about 98.6 to about 97.2 % of its initial value. Thus, for equal concentrations of the two species, the NT.4 reaction would contribute about 6 to the absorbance change observed between 40 and 80 msec. The error would increase as the ratio [NTA]/[EDDA] increases. Thus, it is necessary to apply the correction as implied by Equations l l a and 12. The analyses were performed using a commercial stoppedflow instrument (Durrum Instrument Corp., Palo Alto,
Table IV. Kinetic Determination of Ethylenediaminediacetic Acid and Nitrilotriacetic Acida Relative EDDA, standard EDDA, NTA added NTA found deviation, (M/I. X lo6) (M/L X lo6) Error, 9.65 -1.8 1.8 EDDA 9.82 NTA 10.25 9.10 -11.3 3.0 EDDA 3.26 3.38 +3.6 3.9 NTA 10.25 10.33 .8 2.8 EDDA 0.816 0.78 -3.8 3.0 2.80 $9 2.1 NTA 2.56 oconditions: [CN-] = 4.7 X'10-4M; pH = 11.0; X = 267 nm; bandwidth = 4.5 mp. " 1
/"
+
Calif.). The molar absorbtivity for Ni(CN)42- measured at 267 nm is 2.14 x 104; the cell length is 2 cm. The MOLD computer was interfaced to the stopped-flow spectrophotometer in the same fashion as described in the previous section, using a +4 V to 0 V trigger pulse and the 1-volt analog output. The analog signal (% T ) was applied to the log input of the MOLD computer for conversion to absorbance values. In principle, it should be possible to utilize known or determined constants to evaluate theoretical values of all the proportionality constants in Equations 8, 11, and 12. Since there is some day-to-day variation in the exact experimental conditions used, it would be necessary to re-evaluate each of these constants daily. An alternative approach which was used in this work was to establish the net proportionality and correction terms empirically using concentration standards. The MOLD computer was calibrated to read the concentration of NTA directly using a single NTA standard. Then the exponential correction term and the Y term in Equation 12 were determined using EDDA standards. These constants were entered into the MOLD computer for computation of EDDA concentrations. Analytical data for the determination of mixtures of EDDA and NTA are given in Table IV. The relative errors observed for EDDA are quite good, relative to results reported for other species using differential kinetic methods (11, 12). The results for NTA are not so good as those for EDDA, but they compare favorably with results obtained using a linear regression program and a small general-purpose computer (10). In fact, these results compare quite favorably with results obtained for single component analyses of this species at this concentration level (IO). It is probable that the observed errors are a function of the chemical system rather than the computer. The programming to resolve this problem utilized fifteen of the available sixteen instruction locations. Thus, this application approaches the limit of the MOLD computer, and it would not be possible to carry out a series of successive approximations to compensate for interactions between overlapping reactions. Thus, this example illustrates that the miniature computer can be applied to reasonably complicated computational examples and also presents some measure of the limitations of the system. The "constant time" method was used for all chemical analyses reported above. Although other computational (11) J. B. Pausch and D. W. Margerum, ANAL.CHEM.,41, 226
(1969). (12) D. W. Margerum, J. B. Pausch. G. A. Nyssen. and G. F. Smith, ibid., p 233.
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approaches could have been used, the “constant time” method was used since it should provide highest reliability results for the pseudo-first-order reactions used in this work (13). The simulated response data were analagous to zero-order data, suggesting the use of the “variable time” method (13). These two groups of data, demonstrate that, when appropriate, the MOLD computer can be used for either the “variable time” or the “constant time” methods. CONCLUSIONS
The data reported above demonstrate some of the capabilities and limitations of the miniature on-line computer. The study of transient species was chosen to indicate the versatility in data acquisition and handling. There are possible applications for this system in static measurements. Atomic emission and absorption instrumentation could easily be interfaced, and programmed with as few as two instructions or, with averaging and scaling, as many as fourteen or fifteen instructions to provide direct concentration readout. With minor modifications, GC integration with direct mass readout could be achieved. It is probable that overlapping peaks could be resolved to the same extent that they can be determined graphically from a recorder chart. It should be obvious, however, that this instrument is not applicable to every situation. A tentative assignment for the MOLD system must be evaluated in terms of the sacrifices that might be encountered in simplifying the data handling procedure. Not only are there a limited number of mathematical operations available, but because of the small instruction memory, they can be applied only a few times. Still, the benefits gained with fast, easily obtained results could outweigh the possible loss of a small percentage of accuracy and/ or selectivity. There are at least two general situations in which such systems could be very attractive. One situation is that in which the number of routine computations is too (13) J. D. Ingleand S. R. Crouch, ANAL. C H E M . ,697(1971). ~~,
large to be handled manually, but is too small to justify a small general purpose-computer with required peripherals. The other situation is one in which a general-purpose computer is available, but the demands on its time for other purposes such as preparing requisitions, fling data, preparing reports, etc. are such that all of the routine computations required in the laboratory cannot be conveniently accommodated. The minature system would supply single valued data, in concentration format, either for manual recording or for computer recording and would minimize or eliminate the processing of raw data by the central system. An additional advantage of “back-up” data processing capability would be realized in the second situation during any down-time of the central system. Thus, in one situation the miniature system can serve as an alternative to the analog- and/or generalpurpose digital computers in current usage, while in the other it serves to complement the latter. In either situation, the system would be totally dedicated to a single task at one time. The cost of the system is such that multiple units could be afforded by most laboratories and the versatility is such that a single unit could perform many different duties at different times during a work-day. It is hoped that this report will help to stimulate interest among other chemists in the applicability of the digital components which are so readily available so that this field will enjoy a growth rate and general utility comparable to that observed for operational amplifiers during recent years. The estimated hardware costs for the system as constructed originally amounted to $650. At the time of this writing, it is estimated that a similar system could be constructed at a cost of about $300 for hardware and three weeks of construction time. RECEIVED for review December 13, 1971. Accepted March 30, 1972. This investigation was supported in part by PHS Research Grant No. GM 13326 from the National Institutes of Health and in part by a fellowship (RAP) from Phillips Petroleum.
Determination of T,race Quantities of Volatile Fluoride in Uranium Hexafluoride Using an Infrared Spectrophotometer Raymond Aubeau, Gerard Blandenet, and Guy Brogniart Commissariat L’energie Atomique, Centre de Pierrelatte, Boite Postale no 16, 26 Pierrelatte France This study describes a determination of volatile fluoride in uranium hexafluoride by infrared spectrophotometry in the range 0.1 to 1weight parts per million (wppm). The instrument used is a spectrophotometer equipped with a 50-cm-long dual path cell. According to the test accomplished and the sensitivity required, three versions are available: direct analysis; differential analysis; and analysis after absorption on sodium fluoride. These different technologies allow the contents of weight parts per million to be determined with a precision of 5 to 10%.
DETERMINATION OF GASEOUS impurities occurring in the form of traces in UFs is generally made using chemical methods based on long and delicate processes (1). (1) “19 Methods for Uranium Hexafluoride Determination,” Head
Laboratory,C.E.A., Pierrelatte(1971). 1628
For industrial control, quicker and generally more reliable physical methods of analysis must be used. In our case, we have considered the three techniques most used in the range of gas analysis : gas-liquid chromatography, mass spectrometry, and infrared spectrophotometry. Gas-liquid chromatography of corrosive fluorinated compounds does not allow the results obtained with organic compounds, especially when determining traces. Polymer supports give very low efficiency columns. It seems, however, likely to develop considerably in the near future (2). Mass spectrometry is a costly technique rather badly suited for the analysis of such compounds. Indeed these compounds (2) G. Blandenet and R. Aubeau, 111 European Symposium on Fluorine Chemistry, Aix en Provence, 14/17 September, 1970.
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