Miniature digital computer for reaction rate analyses - Analytical

A Miniature Digital Computer for Reaction Rate Analyses Russell A. Parker, Harry L. Pardue,’ and Barry G . Willis Department of Chemistry, Purdue University, Lafayette, Ind. 47907

A method for computing reciprocal time for concentration determination in reaction rate analyses is described. The instrument utilizes digital circuitry in the computer, with a direct readout in units of concentration, or reciprocal time. Results from simulated response curves show standard deviations of 0.1% or less, limited by the integrator used in testing the device. Data for the determination of alkaline phosphatase show standard deviations and deviations from linearity of less than 1% over a ten-fold concentration range. SEVERAL recent publications have been concerned with instrumentation for the automation of the measurement step in reaction rate analyses. Measurement approaches developed and studied have included the constant time ( I , 2), the variable time (3-3, the derivative or slope (6-8), and the signal-stat (9) methods. The relative merits of these different approaches have been discussed (IO). The variable time approach, in which the time required for the reaction to proceed to a predetermined extent is measured, has proven to be a very versatile and useful method. If, for the species of interest, the reaction kinetics are first order and the measurement interval is sufficiently small to give zero order kinetics, then the reaction time is inversely proportional to concentration. Several instrumental developments directed at the automation of the measurement and computational steps have been described (3-5). Each of these methods, with the exception of that described by Crouch (3, has been based solely on analog computational methods. The computer described by Crouch is a hybrid analog-digital system. The reaction time is represented as an analog signal generated by an integrator. A voltage to frequency (V/F) converter generates a pulse train, the frequency of which is proportional to the analog signal. The period of the pulse train, which is inversely proportional to the analog signal and, therefore, to the reaction time, is measured and related to concentration. The system described here utilizes all digital circuitry to generate a frequency which is proportional to reciprocal time and to concentration. It eliminates the need for the analog time base and the V/F converter. Drift in the computer is limited by the drift of a crystal clock and the resolution and 1

Enquiries should be addressed to this author.

(1) W. J. Blaedel and G. P. Hicks, ANAL.CHEM., 34, 388 (1962). (2) E. M. Cordos, S. R. Crouch and H. V. Malmstadt, ibid., 40, 1812 (1968). ( 3 ) G . E. James and H. L. Pardue, ibid., 40, 797 (1968). (4) H. L. Pardue and R. L. Habig, Anal. Chim. Acta., 35, 383 (1966). ( 5 ) S. R. Crouch, ANAL.CHEM., 41, 881 (1969). (6) H. L. Pardue and W. E. Dahl, J. Electroanal. Chem., 8, 268 (1964). (7) H. V. Malmstadt and S. R. Crouch, J. Chem. Ed., 43, 340 (1966). (8) T. W. Weichselbaum, W. H. Plumpe, Jr., R. E. Adams, J. C. Hagerty, and H. B. Mark, ANAL.CHEM., 41,725 (1969). (9) H. V. Malmstadt and E. H. Peipmeier, ibid., 37, 34 (1965). (10) H. L. Pardue, “Advances in Analytical Chemistry and Instrumentation,” Vol. 7, Wiley, New York, N. Y . , 1969, pp 141-207.

56

e

bfi

Voltage Interval Detector

$2

Detector ond Analog Circuits

I To

I Sixteen Bit Binary

Frequency Meter

UP Counler

T I

I I

Reset

Figure 1. Block diagram of reaction-rate instrument

accuracy is easily varied by adding or removing binary stages from a pair of counters. The speed of the computer is limited primarily by the delay times in digital gates and counter and/or the clock frequency, whichever is slower, and can be much faster than any practical mixing system. The total reaction rate instrument includes a noise averaging capability not included in earlier designs. The system performance is evaluated using synthetic signals and using the alkaline phosphatase catalyzed hydrolysis of p-nitrophenylphosphate. GENERAL DESCRIPTION Instrument System. The operation of the analytical system is best understood using Figure 1. The detector and analog circuits generate a signal which varies with time, the rate of change being a well defined function of the concentration of the rate limiting species. A voltage interval detector (VID) senses when the signal passes two preselected signal levels SI and SZat times tl and tz. The VID controls the operation of the computer to evaluate the reciprocal of the time interval At = tz

- tl.

The computer consists of a stable clock, a frequency divider, one up counter, one down counter, and some gating. Prior to the initiation of a run, the computer is preset (switch closure to ground) to the initial state. In the initial state the frequency divider flip-flops are all cleared (set to zero) and the up and down counter flip-flops are all preset (all sixteen bits set to logical “1”). During the time interval to to tl before the signal reaches the first trigger point, S1, the output from the VID (output of GI)is a logical “0” and gate Gz is inhibited so that the clock pulses reach neither the frequency divider nor the down counter. Therefore the down counter remains in its initial state (all sixteen bits true or logical “1”). The clock pulses do, however, pass through the up counter. Because the up counter was initially set with all sixteen bits true, the clock frequency is divided by unity. Each output pulse from the

ANALYTICAL CHEMISTRY, VOL. 42, NO. 1, JANUARY 1970

up counter enables the gated preset input of this counter to permit a parallel transfer of the current contents of the down counter to the up counter. Because the down counter is in the initial state with all bits true, the up counter is again set to this same state. Therefore, a frequency meter at the output of the up counter will measure the clock frequency unaltered so long as the signal is below the first trigger point. When the signal exceeds S1,the VID output changes to a logical “1.” This enables the gate Gz permitting clock pulses to pass through the frequency divider to the down counter. Thus, the contents of the down counter are decremented at a constant rate determined by the clock frequency and frequency divider. The up counter functions, as described above, with each output pulse triggering the transfer of the current contents of the down counter to the up counter. As the content of the down counter is being decreased continuously, the up counter will be preset to successively lower and lower values and the output frequency will decrease with time. It will be shown below that the output frequency is inversely proportional to the time interval during which pulses are gated to the down counter. The above described situation exists until the signal exceeds the second trigger point, SZ. At this point the VID output returns to logical “0,” gate GIis disabled, and frequency divided clock pulses are no longer passed to the down counter. Thus, the down counter contains a count equivalent to its initial value less the product of the divided clock frequency times the time interval A t = tz - tl. The frequency at the output of the up counter is therefore representative of this count and clearly is a function of the time, At, required to be overcome. The for the signal interval, A S = SZ - SI, exact relationship between the output frequency from the up counter and the time interval, At, is derived below. Mathematical Interpretation. The object of this section is to show that the output frequency from the n bit up counter is inversely proportional to the time interval the down counter operates. For a clock with frequency f o operating into an n bit binary up counter, the output frequency from the up counter fu is given by fu = f0/2”

(1 )

If, after each counter cycle, the up counter is preset to have some content, C,, other than zero, then the output frequency is given by the relationship where the maximum value for C, is 2” - 1. In the present instrument the up counter is preset to the current content of the down counter, CD. It follows then that the output frequency is given by fu = f0/(2’

- CD)

(3)

It is recalled that the contents of the down counter have the initial value of 2” - 1 counts and that it is decremented at a constant rate equal to the frequency, fD, at the output of the frequency divider for the period At = tz - tl. It follows that the content of the down counter at any time is given by

CD = (2” - 1) - f D A t

(4)

Substituting Equation 4 for CDin Equation 3 and rearranging gives fu

+

= f ~ / ( r ~ A t 1)

+15v

Figure 2. Schematic diagram of voltage interval detector OAl OA2 OA3

Philbrick SPZA Philbrick P65AU Motorola MC1709CG A,Pz 5K, ten turn Ps loOK, ten turn R,, R2, Ra, Ra, R5, Re,-15K, 10K, 50M, 10K, 1K and 180 ohm, respectively Cl,Cp 0.001 PA 0.Olpf Swl SPAD Toggle GI Raytheon Computer MDGZ (1)

which establishes the desired reciprocal relationship. INSTRUMENTATION

Details of the design of the total system are presented in this section. Photometer. Reaction-rates were followed using a highlystabilized photometer system similar to those described earlier (11,12). The present photometer utilizes an interference filter to isolate the desired wavelength band. The alkaline phosphatase results reported are obtained using a band near 404 nm isolated using the interference filter and a visible cutoff filter. As with previously reported instruments, the drift of the photometer seldom exceeds 0.02 % T per hour. The reaction cell is thermostated at 25 -I 0.02 “C by circulating water from a constant temperature bath through a jacket surrounding the cell. Analog Amplifier and Voltage Interval Detector, The analog amplifier for the sample beam of the photometer and the voltage interval detector are represented in Figure 2. The output from the phototube (1P39) is connected to a currentto-voltage converter with a sensitivity of 50V/pA. This signal is amplified further by an amplifier of variable gain to yield an output of 10.0 V at 100% T . The output from this amplifier drives the input of a voltage comparator (Voltsensor Model 555-01 manufactured by California Electronic Manufacturing Co., Inc., Alamo, Calif. 94507). The input is compared (in two separate circuits) to the reference voltages across P1and PB. When the input signal is above the reference value at P1 or below the reference value at Pz,the output transistor is turned on and the output goes to +5 V. The positive NAND gate connected to the output of the volt sensor inverts this to give a logical “0” output. When the input signal is between the two set points, the output transis-

(5)

If the frequency f D and time interval are selected such that fDAt >> 1, then it follows that

(11) H. L. Pardue and P. A. Rodriguez, ANAL.CHEM.,39, 901 (1967). (12) H. L. Pardue and S. N. Deming, ibid., 41,986 (1969). ANALYTICAL CHEMISTRY, VOL. 42, NO. 1, JANUARY 1970

57

tor is off and the output from the NAND gate is logical “1.” This signal is used to gate clock pulses into the frequency divider and down counter. The switching point of the voltage comparator is reproducible to better than 1 mV. An objective in this work is to measure transmittance intervals as small as 1 % with maximum errors of 1 %. In other words, the 1 mV limit of the voltage of the comparator should represent only 0.01 X 0.01 or total signal at 100% T . Therefore, the 100% T voltage is amplified to l o 4 x V or 10 V. Although the trigger points are reproducible to better than 1 mV, there is an appreciable difference (several millivolts) between the reference voltage(s) and the input voltages at the trigger point(s). Therefore, the set points must be set empirically. A detailed procedure is given below. The output of the Voltsensor is modified slightly by inclusion of resistors in the collector and emitter circuits of the output transistor. The 180 ohm resistor in the collector circuit minimizes interaction between the Voltsensor and the analog amplifiers at the switching points. The 1K resistor in the emitter provides the level changes required to control gate GI. Computer. The computer is constructed on a modular logic patchboard system using standard logic modules (Logic Master System, Raytheon Computer, Santa Ana, Calif. 92704). Interconnections on and among modules are made with patchcords. The wiring diagram for the computer is represented in Figure 3. Modular components (counters, clock, gates, etc.), are identified by the manufacturers module number. Module MUCl is a four-stage counter wired as a ripple-carry binary counter; MUC2 is a dual four-stage counter wired to give two decades of ripple carry binary coded decimal counting; MBCZ is a four-stage counter wired as a ripple-carry binary down counter. All gates (MDG2) are positive NAND gates (+5V, OV nominal logic levels). Only those pin numbers to which connections are made are shown. Detailed descriptions of these modules are given in Bulletin SP-230C supplied by the manufacturer. In most of the work shown here a 1-MHz crystal oscillator (MCGI) was used as the clock. In some cases discussed below an astable multivibrator (MMV1) was used to obtain a continuously variable frequency source. The clock output drives a sixteen bit binary up counter constructed from four MUCl modules. The clock output is also gated (under VID control) to a six decade frequency divider constructed from three MUC2 modules. The 10 and 100 Hz outputs were used in most of this work. At the initiation of a run the preset switch is pressed momentarily removing logical “0” from pin 16 of each of the MBC2 modules and applying logical “0” to pin 18 of the clock, pins 23 and 25 of each MUC2 module and pin 12 of each MUCl module, Removal of logical “0” from pin 16 of the MBCZ modules enables the preset enable input and causes this counter to be reset to a full count (216-1). The logical “0” applied to the clock, the MUC2 and MUCl counters inhibits the clock output during the preset operation, clears the frequency divider counters to zero, and enables the transfer of the down counter (MBC2) contents into the up counter (MUCl). Because the down counter has just been set to a full count, this operation presets the up counter to a full count. The Transfer and Preset lines into the MUCl modules merit additional comment. Pins 12 and 13 are the two inputs of an auxiliary two input NAND gate and pin 11 is the output of the gate. Pin 25 is the preset enable for the counters in this module and requires a logical “1” to be enabled. There58

I Figure 3. Schematic diagram of reciprocal time computer Clock MCGl or MMVl Frequency Divider Three MUC2 modules connected to give six decades of frequency division Delay MOSl set for 300 mec delay G1 Raytheon Computer MDG2 (1) Sw2 Push button, spring return, DPDT

fore a logical “0” at either pin 12 or 13 enables the transfer of information from the down counter to the up counter (uiu pins 18,21,23, and 26). After the computer is preset to its initial state it is ready to compute reaction rate. A logical “1” from the VID enables gate GB,permitting clock pulses to enter the frequency divider with each pulse from the frequency divider decrementing the down counter by 1 count. The clock output passes into the up counter continuously. Each time the count capacity of the up counter is exceeded the “1” to “0” transition at the output of the last flip-flop in the string triggers the monostable multivibrator (MOSl), so that the inverted output goes from a logical “1” to a logical “0” and remains there for the delay time of the oneshot. This logical “0” at pins 13 of the MUCl modules enables transfer of the current content of the down counter to the up counter. Initially both counters contain their full count and the clock frequency at the output is divided by unity (see Equations 5 with At = 0). However, when the detector signal reaches the measurement interval (SIto Sz) and the VID enables gate Gz,then the count content of the down counter is decremented continuously and the output frequency from the up counter decreases continuously. When the signal passes the second trigger point, the VID disables Gz and the output frequency becomes constant at a value proportional to the reciprocal of the time GZremained enabled. Noise averaging is possible with this system because of the very low hysteresis of the Voltsensor. If noise pulses carry the signal level into the measurement interval prematurely, the down counter will be enabled only for the amount of time the noise pulse is in the measurement interval. Similarly, if noise pulses bring the signal out of the measurement interval, the down counter is disabled for that amount of time. So, if the noise pulses are random in both the positive and negative directions, the excursions are effectively cancelled by this averaging through the trip points. EXPERMNTAL

The alkaline phosphatase catalyzed hydrolysis of p-nitrophenylphosphate was selected as a model system on which to evaluate this instrumental system. This reaction has been


well characterized (13) and all reagents and enzyme samples are prepared according to procedures outlined in this work. Alkaline phosphatase is determined in Versatol E reconstituted serum. Calibration of Computer. The computer system is easily calibrated to read directly in multiples of enzyme activity expressed in IUB units. The calibration can be performed in either of two ways, one assuming a constant clock frequency and the other assuming a continuously variable clock frequency. If the clock frequency is to be maintained constant, then the signal interval over which the reaction time is measured is varied to provide calibration. If the clock frequency is varied, then the signal interval need not be varied, In each case the readout can be in milliunits per ml of test solution (reconstituted serum). The calibration at constant clock frequency (1 MHz) is considered in detail below It is desired that a reading of 100.0 on the frequency meter represent an enzyme concentration (in serum sample after reconstitution and before dilution in the cell) of 100 mU/ml. It is also desired that the enzyme activity level require a 10.0 second measurement time and that the output frequency for this measurement time be 1000 Hz. The frequency meter is set on a one-second gate time so that the readout is in units of Hertz (1000 Hz = 100.0 milliunits). These requirements dictate the frequency into the down counter and the signal interval over which the reaction time is to be measured. The frequency into the down counter is evaluated from Equation 5 (or 6 to a very good approximation). Substituting fu = 1 x l o a Hz, fo = 1 X lo6 Hz, and At = 10.0 sec, it

- 1)/10or99.9Hz. Avalue of : : (: 100 Hz is selected. The analytical procedure outlined below follows thatfn

=

~

calls for 0.100 ml serum in a total reaction volume of 3.00 ml. For a 100 mU/ml sample the total change in concentration of substrate (and product) during the ten-second reaction interval is AC

=

(0.1 ml) (100 X l o 3 pmoles/min) (10 sec) (60 sec/min) (3 x lo-%)

or 5.55 X 10-l pmoles/liter. The molar absorptivity of p-nitrophenol for the photometer system used was evaluated to be 1.621 X l o 4 liter/mole-cm. Therefore the concentration change corresponds to an absorbance change of (5.55 X loT7)(1.621 X lo4)or 9.01 X The detector readout is in %T, therefore this absorbance interval is converted to a transmittance interval. To allow adequate time for mixing and temperature equilibrium to be established, the signal Tz interval is begun at 90% T. It follows that A A = log T2 Ti or 9.01 X = log - and that TZ= 0.8815. The VID 0.90 is set to trigger at these transmittance values, Tl = 0.9000 and TZ= 0.8815, using potentiometers P1and P2. Calibration using a variable frequency clock for the up counter follows a similar pattern except that any %T interval can be selected and the clock frequency is varied to provide readout in desired units. Procedure. PREPARATION OF EQUIPMENT. The photometer and analog circuits are permitted to warm up for at least one half hour prior to use. For highest reliability work these systems are left on continuously. A blank solution containing all reagents and reactants except the enzyme is used in the calibration step (equivalent volume of water substituted for the enzyme sample). With the blank in the cell and S w l in the 100% T position, P 3 in Figure 2 is set to its maximum resistance, and then turned until G Ijust changes state (it is convenient to observe the (13) G. N. Bowers and R. B. McComb, Clin. Chem., 12, 70 (1966).

Table I. Experimental Results for Electronically Simulated Response Curve Input to Digital integrator readout Normalized Rel. std. Dev. from (mWa (Hz)* readout” dev. (%) mean 2.00 154.I d 1541 0.4 -0.06 4.00 307.64 1538 0.2 -0.26 5.00 386. Od 1544 0.0 +O. 13 10.00 770. jd 0.02 -0.06 1541 20.00 154.2e 1542 0.0 0.00 40.00 308. le 1541 0.2 -0.06 80.00 618.0e 0.0 +o. 19 1545 100.00 772. 6e 1545 0.02 +O. 19 200.00 154.21 1542 0.0 0.00 Average 1542 a VID interval is 300 mV. Average of three determinations. All values normalized to the value at 20.00 mV. Normalization factor includes ratio of frequency to down counter (notes d-f). Frequency to down counter 10 Hz. e Frequency to down counter 100 Hz. 1 Frequency to down counter 1000 Hz.

(x)

state of this gate with a suitable light indicator). The switch Swl is then set to “run” and the 100% T voltage is measured accurately. Potentiometer P3 is adjusted until the output of OA2 is equal to 0.900 times the 100% T voltage established initially. Then Pi is adjusted until the output of G1 just goes to logical “1.” Then P3 is adjusted until the output of OA2 is equal to 0.8815 times the 100% T voltage and P2 is adjusted until the output of G Ijust goes to logical “0”. When these operations are completed, PIis adjusted until the output of OA2 is the 100% T level established initially. This calibration procedure assumes a 1.00 MHz clock frequency into the up counter in Figure 3, a 100.0-Hz frequency into the down counter, a frequency meter set with a 1-sec gate time, a molar absorptivity of p-nitrophenol of 16.2 X lo3, and a sample size of 0.100 ml. If these criteria are met, then the instrument reads directly in milliunits per milliliter. Owing to the long term stability of the system, this calibration step is performed only at infrequent intervals. Reagents and samples are equilibrated at 25 “C prior to performing analyses. Measurement Step. The reaction cell is emptied using an aspirator tube and rinsed with deionized water. The stirrer is started and 2.70 ml of buffer and 0.20 ml of substrate solution are added to the cell. After these reagents are mixed, 0.1 ml of sample is added and the preset switch is pressed momentarily. Results are recorded after the measurement step is completed. RESULTS AND DISCUSSION

The instrument system is evaluated using simulated rate curves from an electronic integrator and for the determination of alkaline phosphatase based upon its catalysis of the hydrolysis of p-nitrophenylphosphate in alkaline solution. Simulated Rates. An electronic integrator with an R C time constant of 2.4 sec was utilized to simulate highly reproducible response curves. The slope of the response curves was varied by changing the input voltage. Typical experimental results for a 100-fold range of slopes are given in Table I. To cover this range with highest accuracy, the input frequency to the down counter was increased by one decade for one decade change in slope as noted in Table I. It is observed that the relative standard deviations for all runs are 0.4% or less and most are better than 0.1 %. The results are normalized to the value at 20 mV integrator input. Deviations from linearity approach 0.1 %.


59

Table 11. Experimental Results for Purified Enzyme Added to Reconstituted Serum Containing Normal Alkaline Phosphatase Activity

Vol. enzyme added (ml) 0.00 0.10 0.25 0.50

1 .OO 2.00

Readout freq. (Hz/lO) Exp.” Pred.b

Normalized conc. pure prep. (rnU/ml).

Rel. std. dev. (73

Dev. from predicted value ( %)

50.8 50.5 50.9 49.9 49.3

0.0 0.7 0.4 0.2 0.6 0.8

+0.49 +o. 34 +O. 95 -0.69 -1.72

...

5.20 10.28 17.83 30.63 55.1 103.9

10.23 17.77 30.34 55.48 105.7

Average 50.28 Average of three determinations. * Predicted value is the sum of the experimental value for the serum plus the average of the normalized values for the purified enzyme multiplied by the appropriate volume ratio. The normalized concentration of the purified preparation is the difference between the experimental frequency readings for the serum with and without added enzyme divided by the appropriate volume ratio, Table 111. Experimental Results for Several Dilutions of a Reconstituted Serum Containing an Elevated Alkaline Phosphatase Activity

Dilution factor 10 8 6 5 3

Measured activity (mU/ml X 10) 192, 234, 238 321, 324, 388, 629,

Normalized activity (mU/ml)

Rel. std.

19.23

0.3

+0.4

18.96

0.9

-1.0

19.31 19.25 18.90

0.9 0.7 0.2“

+o. 8 +0.5 -1.3

193, 192 239, 237, 318, 325, 320 384, 383 631

dev. (%I

Dev. from norm. value

(z)

Average 19.15 Q

Average deviation from mean.

Other experiments were performed in which up to twenty measurements and computations were performed over periods of one hour. Three successive sets of experiments of this type yielded relative standard deviations of 0.04, 0.06, and 0.05 %. These data demonstrate that the instrument system is capable of very high precision and linearity. The principal limitation on the accuracy of the system is the frequency of the clock, and because a crystal clock is used, it can be inferred that accuracy in time measurements comparable to the precisions and linearity of the data given in Table I can be achieved. Alkaline Phosphatase. Having demonstrated the capability of the system for simulated signals, it was extended to a practical chemical system. Results for the determination of alkaline phosphatase over a twenty-fold concentration range are given in Table 11. In these experiments variable amounts of purified alkaline phosphatase were added to identical volumes of a reconstituted serum in which the residual alkaline phosphatase activity was measured. The data in the column headed “Exp” represent the averaged values of the measured frequency for each sample. The concentration (mU/ml) of enzyme added was computed as the difference between the measured frequency (Hz/lO) and the residual activity with no enzyme added (5.20 mU/ml). The results were normalized to that at 1.00 ml of purified enzyme added and then normalized values are reported. The average of these normalized values was used to compute the amount of enzyme added to each sample yielding the “Predicted” concentration given in this table. The predicted value computed in this manner agrees with the experimentally determined values to within about 1 % over a ten-fold concentration range 60

and to within 2 % over the entire 20-fold concentration range reported. Relative standard deviations of all results are observed to be within 1 %. Table I11 presents data obtained on several dilutions of a reconstituted serum containing elevated levels of alkaline phosphatase. This table contains the raw untreated data as read from the frequency meter as well as normalized values, The maximum deviations to be expected in a series of runs is apparent. This is a typical set of data representing neither the best nor the worst performance observed during several months of testing of the instrument. One disadvantage of the variable time measurement approach is the fact that the analysis times for low concentrations can be long. This effect is enhanced by variable absorbance in samples requiring that the first trigger point be set low to allow adequate mixing time prior to the measurement interval for highly absorbing samples. To evaluate this effect on practical analyses, alkaline phosphatase levels were measured in several serum samples using the procedure outlined above. The average analysis time per sample was about three minutes with average measurement and computation times of about 90 seconds. The noise averaging capability of the instrument was discussed earlier. Many of the data in Tables I1 and 111 were obtained from signals upon which a low-frequency noise level exceeded 10% of the interval detected by the VLD. Highly reliable results were obtained in all cases. It should be noted that this noise averaging capability is achieved at the expense of a latching capability as the signal passes the trigger points. This latching capability would be desirable in a completely automated system to provide information that the current measurement and computation are completed. This


capability can be built in by incorporating circuitry which latches the circuit in a measurement completed mode when the signal has remained beyond the second trigger level for some predetermined time. General Comments. The resolution of the computer is dependent upon the frequency into the down counter. Referring to Equation 5, it is obvious that for the reciprocal function to be accurate to within I%, f D A tmust be equal to or exceed 100. It follows that for a given time period, the accuracy of the computation can be improved by increasing f D . However, as f D is increased, the number of binaries in the up and down counters must be increased to acconiodate the increasing accumulation of counts; also, the gating time required on the frequency meter to obtain an accurate measure of the frequency from the up counter increases. The frequency meter will have an uncertainty of i l count. Therefore, a compromise must be made between the accuracy of the computation and the amount of hardware and measurement times. The data presented above demonstrate that relative errors of 0.1 are practical.

x

The shortest time interval measured in this work was about 0.5 second. However, the instrument system should be applicable to shorter time periods by increasing f D as the time period decreases. It is probable that the Voltsensor with an operation time of 10 ksec is the limiting component in the total system as described here. The system likely could operate on a millisecond time interval with 1 reliability. Current work is being directed at extending this system to include automatic ranging for a wide range of reaction rates, multiple measurements on each sample and simultaneous processing of results from multiple instruments. With minor modifications the circuitry described above can be utilized to compute other mathematical functions of time such as t1l2,t-’/’, and In t.

x

RECEIVED for review September 19, 1969. Accepted November 6, 1969. This investigation supported by PHS Research Grant No. G M 13326-03 from the National Institutes of Health.

Short-Time, Spatially-Resolved Radiation Processes in a High-Voltage Spark Discharge R.D. Sacks’ and J. P. Walters2 Department o j Chemistry, University of Wisconsiii, Madison, Wis.53706 Time-resolved radial and axial intensity measurements have been used to study the interaction of the spark channel with the expanding cloud of cathodicallyejected electrode material. Observed intensity patterns divide into those showing time control and those showing current control. Comparisons of spatially resolved intensity maps for electrode and plasma species indicate charge-transfer excitation in the discharge channel and stepwise relaxation on the channel boundaries to be probable radiation controlling processes. The consequences of proposed excitation mechanisms to an analysis are presented in terms of the channel-vapor cloud temporal and spatial interaction.

RADIATION PATTERNS observed in the high voltage spark are strongly influenced by the interaction of vaporized electrode material with the current conducting plasma species in the discharge channel. The nature of these interactions should depend on the instantaneous dimension of the channel, its chemical composition, its current density, and the spatial and temporal distribution of electrode material in the discharge volume. An understanding of the above interactions will lead to definitive conclusions about important spectrochemical problems. Examples include defining the instantaneous nature of matrix effects, the origin of analytical radiation, and the spatial and temporal distribution of background radiation. Such information also should lead to the development of nonempirical methods for obtaining chemical and instrumental control of relative line intensities, as well as the development of new analytical methods based on the nature of the chemical system involved in the analysis. 1 Present address, Department of Chemistry, University of Michigan, Ann Arbor, Mich. 48104 a To whom requests for reprints should be sent.

In recent years, time resolved emission spectroscopy has proved extremely useful in obtaining information on the current sensitivity of certain classes of spectral lines. However, the high voltage spark exhibits considerable spatial heterogeneity as well as temporal complexity. Thus, it is necessary to observe the time dependent radiation patterns in various spatial regions of the discharge to obtain more fundamental information about phenomenological as well as state specific reaction mechanisms. The introduction of axial zone discrimination (1) allowed measurements to be made on cathode jet velocities for different classes of lines, and also yielded valuable information regarding the interaction of the axially expanding cloud of electrode material with the current conducting plasma. With sufficiently high axial zone resolution (2), it has been possible to probe the complex space charge regions just off the electrode surfaces. Information from these space charge regions is important for two reasons. First, radiation patterns show the most drastic changes in these regions. Second, all sampled electrode material must pass through these space charge regions before arriving at any other point in the discharge. Hence the space charge conditions will be experienced by all electrode material, independent of its direction of movement. A thorough understanding of space-charge radiation patterns, however, requires intensity measurements with radial as well as axial differentiation. Since electrode material is moving away from the point of sampling with a radial as well as an axial velocity component, different reaction mechanisms and subsequent radiation patterns should occur for electrode material that is within the region of the current conducting (1) J. P. Walters and H. V. Malmstadt, ANAL. CHEM.,37, 1484

(1965).

( 2 ) J. P. Walters, %id., 40, 1540 (1968).


0

61

Miniature digital computer for reaction rate analyses - Analytical

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