dependent on NO concentration ranging from 2.8% a t 3000 ppm to 0.53% at 30 ppm although the ratio is not sensitive to the change of composition (within 5%). On the other hand if the exhaust gas is diluted by 1:lOO with Nz, the ratio F"/F, is not much dependent on the NO concentration, that is, the signal is reduced to 34 f 1%of F" in the exhaust gas, independent of the change in NO concentration and in composition. A signal decrease caused by dilution is compensated by an inciease of signal due to an increased N2 concentration. It is still possible to detect the fluorescence signal of 30-ppm NO in the exhaust after 1: 100 dilution where the signal becomes equivalent to 0.1ppm NO in pure N2. Thus the dilution of the exhaust gas by N2 provides an almost linear calibration curve for measuring NO in the exhaust in the range 30 to 3000 ppm. Dilution by N2 has the further advantage that the condensation of H2O can be avoided when the gas mixture is brought to near room temperature for the NO measurement. To minimize an interference by SO2 which may be present in the exhaust gas, a filter transmitting predominantly the NO fluorescence (230-300 nm) and rejecting most of the SO2 fluorescence (250-420 nm) may be required. Alternatively, if the exhaust gas is diluted by air or by oxygen, and a filter transmitting light of wavelengths 300 to 420 nm is used, it is possible to measure SO2 as well.
ACKNOWLEDGMENT The help of William H, Kirchhoff in the error analysis is gratefully acknowledged. The flow system run was performed by Ryna Joseph Marinenko of the Analytical Chemistry Division.
LITERATURE CITED (1) Air Quality Criteria for Nitrogen Oxides, EPA(US) Air Pollution Control Office, Washington, D.C., Publ. NO. AP-84, 1971. (2) D. R . Crosley and R. N. Zare, Bull. Am. Phys. Soc.,-12, 1147 (1967). (3) L. A. MeRon and W. Klemperer, J. Chem. Phys., 59, 1099 (1973). (4) R. W. B. Pearse and A. G. Gaydon, "The Identification of Molecular Spectra." John Wiley & Sons, New York, N.Y.. 1963. (5) A. B. Callear and M. J. Pilling, Trans. Faraday Soc., 66, 1618 (1970). (6) F. P. Schwarz. H. Okabe, and J. K. Whittaker, Anal. Chem., 46, 1024 (1974). (7) L. A. Melton and W. Klemperer, Planet. Space Sci.. 20, 157 (1972). ( 8 ) H. Okabe, P. J. Splitstone, and J. J. Ball, J. Air Poilut. Control Assoc., 23, 514 (1973). (9) Private communication from R. N. Zare of Columbia University to H. Okabe. (10) A. V. Kleinberg, and A. N. Terenin, Dokl. Akad. Nauk, SSR, 101, 1031 (1955). (11) "Outlook-Electric Vehicle Revival of the Fifty-Year-Old Memory," Environ. Sci. Techno/., 1, 192 (1967).
RECEIVEDfor review October 11, 1974. Accepted December 19,1974. This work was supported by the Measures for Air Quality Program at the National Bureau of Standards.
Automated Computer-Controlled Spectrophotometer System for Kinetic or Equilibrium Methods of Analysis K. R. O'Keefe and H. V. Malmstadt' School of Chemical Sciences, University of Illinois, Urbana, Ill. 6 180 1
An automated computer-controlled spectrophotometer system is described that is applicable for stopped-flow kinetic or equilibrium methods of analysis. The system provides rapid sequential analysis using rate measurements in the time range of milliseconds to minutes or accurate equilibrium absorbance measurements of stable sample constituents. Only small volumes of composite reagent and sample, about 0.17 ml of each, are required for each complete fill/ inject cycle of operation. Absorbance changes of 0.00004 A are readily measured in the 2-cm pathlength cell by the split-beam dual-detector system. The automated analyzer has been programmed for use in either a routine analytical mode or in a research investigative mode. New light source and beam splitter modules that are compatible with other commercial spectrometer modules are described. Experimental results with the complete system compare closely with the theoretical results calculated on the basis of photon statistics.
In recent years, the use of reaction rate methods of chemical analysis has become increasingly popular, especially in laboratories where advantages in speed and selectivity over equilibrium methods are important ( I , 2 ) . The current interest in rate methods is attested to by several recent reviews covering reactions that are useful for analytiSend reprint requests to this author.
cal purposes (3, 4 ) and instrumentation and methodology for rate measurements ( I , 5, 6). Routine reaction rate methods on time scales from several seconds to minutes have been available for many years (1-3), and rate methods on the millisecond-to-second time scales have been reported (7, 8). In addition, the introduction of automated systems for rate measurements has had considerable impact in this area (3,6). In this report, a new system for reaction rate measurements is described that is useful for both the fundamental characterization of chemical reactions and the application of both rate and equilibrium methods to chemical analysis. A dual-beam optical arrangement is used that eliminates source fluctuations as a source of photometric error in absorbance measurements. This allows the use of an unregulated high intensity source while still permitting high precision absorbance measurements. The measurement system for the spectrophotometer is described and is shown to introduce negligible error into the measurement. The sampling-mixing system is a new automatic stopped-flow head which requires no operator attention during normal use. All control functions are readily implemented, and are TTL-compatible. The stopped-flow head provides for thermostating of the mixing syringes and optical cell and thermistor measurement of the mixed solution temperature. Volumes of sample and reagent that are required for each sampling-mixing cycle are 0.17 ml. System dead time is 5 f 2 msec. The entire system is automated using a PDP-8/f miniANALYTICAL CHEMISTRY, VOL. 47, NO. 4 , APRIL 1975
*
707
BEAM SPLITTER
LlGhT SOURCE
TELETYPEWRITER
PDP 811 COMPUTER
Figure 1. Block diagram of automated spectrophotometer
computer as a control, communication, data acquisition, and data reduction device. Programming is implemented so that the operator can easily change between an investigative mode that is useful for initial studies and fundamental characterization of a chemical reaction and a routine mode that allows the repetitive analysis of solutions placed on a turntable by either rate or equilibrium absorbance methods. Rate measurements are made on time scales from milliseconds to hours using a modification of an integration technique (9) after a delay which is variable over the same time range. Equilibrium measurements are made either absolutely, by measuring the absorbance at some selected time after mixing, or differentially, by measuring the absorbance a few milliseconds after mixing and then again after a selected interval so as to obtain the absorbance change. Operator interaction is accomplished using a teletypewriter and an oscilloscope display.
INSTRUMENTATION A general diagram of the system is shown in Figure 1. In operation the sample solution is drawn into the stoppedflow head from the turntable and the reagent from a reservoir, then the two solutions are forced through a mixer into the observation cell. The output currents of the reference and sample channel photomultiplier tubes are sampled and the resulting signals are modified and stored in the computer memory. At the end of a data acquisition cycle, the computer processes the data and outputs results, displays the absorbance-time plot, etc. according to responses to an initial dialog.
Spectrophotometer. The spectrophotometer section of the automated analyzer is built by utilizing several modules in the GCA/McPherson 700 series for spectroscopy (GCA/ McPherson, Acton, Mass, 01720). Some modules are used unmodified, and the others are redesigned to fit within the 700 series system so as to retain the versatility associated with the modular approach. A modified light source module for the spectrophotometer is shown in Figure 2. It consists of a sample cell module (Model EU-701-11, GCA/ McPherson) which is modified to accept a high intensity tungsten lamp (type CPR, General Electric Company, Cleveland, Ohio 44112) and an adjustable collimating mirror mounted on the optical axis behind the lamp. The lamp is powered by an unregulated, LC filtered, 6.3-V, 20-A power supply. The new source module is also equipped with an automatic shutter that is under computer control. This source is suitable for use through the visible and down to 300 nm. For work lower in the UV, a deuterium source is used. Wavelength isolation is accomplished with a commercial monochromator (Model EU-700, GCA/McPherson). The beam splitter module, shown in Figure 2, was constructed by modifying a sample cell module (Model EU-701-11, GCA/McPherson). The sample cell module was reduced to a width of two inches to minimize the increase in pathlength from the exit slit of the monochromator to the sample channel photomultiplier (PM) tube. A pellicular beam splitter (National Photocolor Corporation, South Norwalk, Conn. 06854) was introduced into the light path at 45' to the optical axis so a fraction of the incident light beam is reflected parallel to the surface of optical bench, but at 90' from the optical axis, where it is intercepted by the reference channel P M tube. The remainder of the incident beam is transmitted and follows the original optical path through the observation cell to the sample P M tube. The pellicular beam splitter reflects 8% of the incident light onto the reference P M tube, and transmits 92%. The P M tube is a 1P28A selected to have a dark current of less than 2X A at 600 V. It is powered by the same high-voltage supply that is in the sample PM module. A variable series resistor is used to reduce the applied voltage to the reference P M as necessary to equalize the output currents. This connection, as well as the BNC output connector are located on the back of the module.
PM Tube Power
To Lamp Power
To Shutter
S~WIY
Spring Lwded Adjusting Screws Lamp Module
Lamp Mount ond Lamp
Figure 2. Light source and beam splitter modules for the spectrophotometer 708
ANALYTICAL CHEMISTRY, VOL. 47, N O . 4 , APRIL 1975
Pellicle Surface
Beam Splitter Mount
DIGITAL OUTP’ET
Figure 4. Logic waveforms for spectrophotometer interface
Figure 3. Spectrophotometer interface
The sampling and mixing system used in the present work is a prototype unit from GCA/McPherson (Model EU-730-11). The stopped-flow head includes two identical mechanically driven syringes, a multiport mixer, a 2-cm pathlength X 2-mm diameter optical cell, thermostated water jacket around the syringes and optical cell, a thermistor in the solution stream, and TTL-compatible electronics to activate the syringes and to indicate when the syringes stop moving after initiation of the mixing sequence. Solution introduction from the sample turntable and reagent reservoir is through Teflon tubing. The sample channel P M tube is a commercial module (EU-701-30, GCA/McPherson) that includes a 1P28A PM tube selected to have a dark current of less than 2 X A a t 600 V and a regulated power supply. Spectrophotometer Interface. The interface for the spectrophotometer is shown in Figure 3. The four functional blocks outlined in the figure provide sampling of the PM tube currents, signal conditioning and conversion of the data to a digital number, timing and flags for the interface functions, and control of the automatic shutter. The flag portion of the interface allows the computer to control the data acquisition and conversion sequence and to sense when the digital result is available. The clock and timing circuitry provides accurately timed logic pulses to control the analog electronics. The data acquisition and conversion circuitry consists of similar channels for the sample and reference information. In each channel, the P M tube current is converted to a voltage which is sampled a t a precise time and held by a sample-and-hold circuit until it can be converted to a digital number. The sample-and-hold voltages are alternately n~ultiplexed t o the buffer amplifier, OA5, and the output of the buffer amplifier is converted to a digital number. The shutter control circuitry allows the computer t o initiate a 2-sec interval during which the shutter in the lamp module is shut so a dark current measurement can be made. The entire interface was built in a Heath Computer Interface Analog Digital Designer (ADD) Module (Model EU-801-E, Heath Company, Benton Harbor, Mich. 49022) to provide an easily modified system. The interface waveforms for a typical data acquisition
cycle are shown in Figure 4. When a data-collection cycle is initiated, two computer-generated pulses start the clock and timing circuitry. A STOP instruction is first issued, causing the output of nand gate 6 (G6) to go to logic level 0, which sets the Q output of flip flop 1 (FF1) to 1 and clears a four-bit binary counter ((21). This ensures that, when a data acquisition cycle begins, the reference channel information will always be converted first. Data acquisition is initiated when a STAIiT instruction is issued. This clears FF1, enabling C1. As C1 counts from 0 to 15 the 4-to-16 line decoder (DC1) integrated circuit decodes the 4 inputs to provide 16 sequential logic level 0 pulses on 16 separate outputs. Initially the “0” output of DC1 is logic level 0. F E T drivers 1 and 2 close the respective FET switches, and the voltages from OAl and OA2 are sampled. These voltages are proportional to the PM tube currents. When the clock toggles C1 the “0” output of DC1 goes to logic level 1 and FET switches 1 and 2 are opened. The sampled voltages are then held hy the capacitors preceeding F E T input OA’s 3 and 4. The reference channel F E T switch associated with F E T driver 3 is closed as long as the “D” output o f C 1 is logic level 0 and the sampled reference voltage is multiplexed to the input of the gain-of-two amplifier OA5 and is present a t the analog input of the A/D converter. When the “1” output of DC1 goes to logic level 0, the output of G2 goes to logic level 1 and monostable M1 is triggered and produces a 5-psec pulse. The trailing edge of this pu!se triggers M2 and a 1-psec logic 1 pulse starts the A/D converter. The 5-psec delay is to allow the sample-and-hold amplifier to settle to its final value. During the A/D conversion the end-of-conversion (EOC) output of the A/D converter is logic level 0. When it returns to logic 1, the A/D conversion is completed. When this occurs and the “7” hutput of DC1 goes to logic 0, the output of G4 goes to a logic 1. After issuing the START pulse, the computer enters a loop issuing the E N D instruction to wait for the end-of-conversion flag. When G4 goes to a logic 1, the ENII signal causes the SKP line to go to a logic 0 and the computer jumps out of the loop and the digital number resulting from the A/D conversion is strobed into the accumulator. When the D output of C1 goes to a logic 1 the signal held on the sample channel sample-and-hold is multiplexed to the A/D converter. A t the same time the “8” output of DC1 goes to logic 0 , the output of G2 goes to logic 1 and, as before, the A/D conversion is initiated 17.5 psec after the signal is multiplexed to the A/D converter. The END pulse is issued as in the reference portion of the cycle, and the sample information is taken and stored. This cycle repeats until all the required data are taken. ANALYTICAL CHEMISTRY, V O L . 47,
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1975
709
The shutter control closes the shutter for two seconds upon computer command so dark current data may be taken. When the dark current is to be measured, the computer issues a CLOSE instruction that causes a logic level 0 pulse to appear a t the output of G8. This triggers M3 and a two-second logic level 1 appears a t its Q output. This brings the output of G9 to logic 0, which sinks current through the light-emitting diode in the optical isolator (11) and causes it to emit. The resistance of the photocell in I1 is then lowered to a level that turns the triac switch (Tl) on, energizing the 6.3-V tranaformer. When the transformer is energized, a dc current passes through the shutter solenoid coil, and the shutter closes. Sampling-Mixing System Interface. The interface for the sampling-mixing system consists of a Heath Computer Interface ADD (Heath Co.) with associated circuit cards wired to provide control functions which are initiated by the computer and are decoded and optically isolated from the turntable and stopped-flow head. The basic functions associated with the interface are a computer-initiated 500msec pulse, OPR, that starts the sampling and mixing cycle of the stopped-flow head, a computer-initiated 1-sec pulse, INDEX, that causes the turntable to turn one position, and a stopped-flow flag, EOP, that indicates the mixing syringes have stopped moving. In a typical sampling-mixing cycle the following sequence of operations takes place: An INDEX pulse is issued that causes the turntable to turn to the proper sample. A flush sequence consisting of several OPR pulses purges the system of the previous sample. This sequence may consist of 2-5 cycles depending upon the physical characteristics of the solutions used and spacial arrangement of turntable, reagent reservoir, and stopped-flow head, and requires 0.34-0.85 ml of reagent and sample. After the flush sequence is completed, an OPR pulse is issued to take up 0.17 ml each of sample and reagent and mix and drive them through the optical cell. When the syringes stop, a portion of the mixed solution remains in the optical cell and the EOP flag is set. The computer is now looking for the flag and, when it is detected, the computer enters a data-collection mode. If more data are to be taken on subsequent samples of the present solutions, the analytical cycle repeats when exit from this mode occurs. If a new solution is to be analyzed, the entire process, starting with INDEX, is repeated. The time required for the complete cycle, from INDEX to the computer’s entry into the datacollection mode, is typically 8 sec. Subsequent analytical cycles require about 2 sec from the initiation of the cycle via OPR to the start of data acquisition after EOP. Computer. The computer used for automation is a Digital Equipment Corp. PDP-8/f (Digital Equipment Corporation, Maynard, Mass.) with 4 K of memory. Associated peripheral devices are an ASR 33 Teletype, magnetic tape 1/0 (Tennecomp Systems, Inc., Oak Ridge, Tenn.), and an oscilloscope display.
COMPUTER PROGRAMS The computer programs for this system were developed using PAL 111, an assembly level language supplied by Digital Equipment Corporation. The programs allow operation in two basic modes, investigative or routine. The investigative mode provides flexible data taking options, oscilloscope display of data, extraction of rate or equilibrium information from various portions of the absorbance-time curve and is generally used for initial characterization or fundamental studies of a reaction of interest. The routine mode provides determination of a working curve from standards placed in the turntable and subsequent analysis of 710
ANALYTICAL CHEMISTRY, VOL. 47, N O . 4, APRIL 1975
samples in the turntable. Either rate or equilibrium methods may be selected in the routine mode. Upon program initialization, the computer asks the user which mode he wishes to use. When the user replies, the proper mode program is read into memory from the magnetic tape unit and control passes to the mode program chosen. In the investigative mode, the user is then instructed to manually flush solvent into the optical cell. The user responds when this is done, and the computer takes dark current and 100% T data. An error message is printed if these values are outside preset limits, and operator intervention is required to change some instrumental parameter such as slit width or P M tube voltage. When the 100% T and dark current data are successfully acquired, the computer asks the number of points to be taken, the number of individual A/D conversions to be summed for each point, the time interval between taking points, and the delay time after the EOP flag is raised to begin taking data. Times may range from 0 to 1.5 hours in increments of 0.001 sec. Reagent and sample are then flushed through the sampling-mixing head and the A/D conversions are acquired and summed according to the parameters previously set. Using the 100%T and dark current factors previously obtained, the raw data are reduced to transmittances using Equation 11 and then to absorbances, and are displayed on the oscilloscope readout. After examination, the user terminates the display and can select output of the individual absorbances, output of the average rate of change of absorbance over a portion of the curve, or the final absorbance value attained. The datataking and display can be repeated, if desired, and average values of the above quantities output for multiple runs. Rates are calculated and determined using an integration technique, primarily because of its good noise immunity (9). The user can change to the routine mode on command, retaining the current 100% T and dark current factors for the routine analysis. In the routine mode, except when entered from the investigative mode as noted above, the user is instructed to put a sample cup containing solvent in the turntable. When that is done, the user responds, the turntable indexes to the solvent position, solvent is flushed through the samplingmixing head, and 100% T and dark current data are taken. The user is then asked to select whether an equilibrium or a rate method is to be used for the analysis. He then responds to a series of questions setting measurement parameters: delay time, measurement interval, number of standards, standard concentrations, and number of runs to average for each standard. In a rate measurement, the average rate of change of absorbance over the measurement interval is determined. This measurement starts after the delay time selected has occurred. In an equilibrium method, an initial absorbance measurement is usually made a few milliseconds after mixing, and a final absorbance is taken as the average absorbance over the measurement interval, which starts after the delay time. After the parameters are set, the turntable indexes to the first standard, the solution is flushed through the sampling-mixing head a preset number of times to rinse the system, and a final sampling-mixing cycle mixes the standard and reagent and a measurement is made. This sampling-mixing cycle and subsequent measurement are repeated for the number of measurements to be averaged. Individual measurements and/or the average value can be printed on the teletype. This cycle is then repeated for all the standards. When all the standards are done, a least-squares line is fit to the average measurement values and the associated standard concentrations, and slope, intercept, and correlation coeffi-
cient are printed. The user then inputs the number of samples to be run and the above sampling and measurement cycle is repeated for each sample. As the results are obtained for each sample, a sample identifier, the average rate, and the concentration corresponding to that rate from the least-squares fit are printed. An additional option in the routine mode allows occasional automatic resetting of the 100% T and dark current parameters. Basic Relationships Inherent in the New Measurement System. The measurement of absorbance or transmittance, T , is based upon the definition T = PalPowhere Po and Pa are the radiant powers transmitted by an optical cell filled with solvent or solvent plus absorber, respectively. For this relationship to be valid, all optical and electrical characteristics of the encoding and decoding systems, notably the incident radiant power, must remain unchanged during the time interval in which the measurements are made. These requirements can be reduced considerably if the radiant power incident upon the optical cell is measured a t the same time as the transmitted radiant power. This leads to a new definition of T
where A is the gain and V, is the voltage offset of the analog signal conditioning circuitry. It is important to note that while no signal integration is explicit in the above relationship, in the actual measurement system a short integration time is provided by RC time constants in the analog circuitry. The number, B, resulting from the A/D conversion is B = P'(AgP + A i , + V,) (4) where 1 is the resolution of the A/D converter. Because of the nature of the A/D conversion process, B is a binary integer and as such is a discrete representation of a continuous variable, V. To increase the time over which the signal is integrated, a number of such conversions can be summed. The resulting number, N , summed over M such conversions is M
N =
l-'(AgP
+
Ai,
+
V,),
Examination of Equation 5 shows that if a similar relationship is written for a case with no light reaching the PM tube, a dark number, Nd, is obtained Y
Nd =
P1(Ai0+ V,),
i=l
In this equation Pi,, and Pi,a are the incident radiant powers measured at the same time as the radiant power transmitted with solvent and solvent plus absorber, respectively. In the new measurement system, the incident and transmitted radiant powers are measured simultaneously by positioning a beam-splitter in the optical path between the monochromator exit slit and the optical cell, and by using two P M tubes to detect the two beams of light. The radiant power, P,, of the exit beam from the monochromator is split into two parts. One fraction, radiant power P , = aP,, is reflected to the reference P M tube and another fraction, radiant power Pi = PP,, is incident upon the optical cell. Thus, the radiant power reaching the reference P M tube is proportional to the radiant power incident upon the optical cell, since Pi = (p/a)Pr.The beam incident upon the optical cell passes through the cell and the transmitted radiant power, P,, is detected by the sample P M tube. The definition of T can therefore be written in terms of measurable quantities, giving
where the first subscript indicates measurements made with absorber (a) or solvent (0)in the cell and the second subscript indicates radiant power incident upon the sample or reference P M tube. The assumption that the ratio a/@is constant over the time of interest is made in deriving this equation. The new measurement system is a radiation-to-number converter that provides binary integers related to reference and sample radiant powers. Two such measurements, one made with solvent and the other made with solvent and absorber in the cell, along with a measurement of system offsets allow the determination of T . The relationship between the radiant power, P, incident upon either P M tube and the resulting current output, i, is i = gP + io ( I O ) , where g is a gain factor that includes several P M tube parameters and io is an output current present even with no radiant power incident upon the P M tube. The resulting P M tube current is converted to a voltage, and the voltage is periodically sampled and converted to a binary integer by an A/D converter. The voltage input to the A/D converter, V, is V = Ai + V , = AgP + Ai, + V , (3)
If A, io, and V, are constant over the measurement time, this result can be substituted in Equation 5 , yielding N = CP'(AgP), + PINd = AZ"C(gP),
+ P I N d (7)
which is rearranged to give
'kP)i=
Z(N -
A
Avd)
(8)
The index, M , for the summation has been omitted for brevity. Returning to Equation 2 , the equation defining T in terms of measurable quantities, the ratio Pa,,/Pa,,can be expressed in terms of Equation 8, since
where the first subscript refers to the measurement with absorber in the cell (a) or a dark measurement (d), and the s or r subscript refers to sample or reference, respectively. If the ratio (gs/gr)iis constant over the measurement interval and if the ratio Z(P8,s)/Z(Pa,r)can be expressed as the sum of an average ratio and a sum of small error terms, conditions which are met in this measurement system, the LHS of Equation 9 is closely approximated by (g,/g,) (Pa,,/Pa,,)where the barred ratio represents the average ratio, and Equation 9 is rewritten as
-
A similar result is obtained for the ratio of average radiant powers measured with solvent in the cell. If the gain ratio , constant, Equation 2 can be rewritten as term A g g , / A , g is
where the subscript o indicates the result of a measurement with solvent in the cell. The resulting transmittance is an average value over the measurement interval. The absorbance is then obtained by taking the negative base 10 logarithm of this quantity. For computational purposes, the second term on the RHS of Equation 11 is evaluated once after the initial dark current and 100% T measurements and is considered a constant in subsequent calculations. ANALYTICAL CHEMISTRY, VOL. 47, NO. 4, A P R I L 1975
711
E r r o r s in the Absorbance Measurement. The sources of error in a given absorbance measurement include invalidity of the assumptions made in deriving the measurement equations, fluctuations in the reference and sample beam that are described by photon statistics, and quantization errors in the digitization of the photon data. Assumptions made in deriving the measurement equations include the gain ratio, the invariance of the beam splitter ratio, (YIP, g,A,/g,A,, and the measurement system offsets over the time interval of interest. Each of these terms is constant over times from milliseconds to hours except the gain ratio term. Although A, and A, are stable, long-term drifts in the g, and g , terms are Dot exactly matched, so ratio term drifts of typically 0.5% per hour are observed. The shortterm gain variations due to power supply ripple track very well, however. The drift in the gain ratio term results in an sec-l a t 0 absorbance. absorbance drift of about 0.4 X This drift is usually negligible in rate measurements, since the rates normally measured are several orders of magnitude greater than this and since absolute absorbances are not important. The drift is important, however, if absolute absorbance measurements are to be made over times greater than 15 minutes, so provisions are made to automatically reset 100% T values occasionally in cases where such long times are used. The assumption that the ratio term Z(Pa,s)JZ(Pa,r)j is constant except for a small error term is satisfactory since the time interval for a measurement is selected so as to be small enough that even in rate methods, the net absorbance change is very small. Photon statistical fluctuations thus largely account for the error terms. Photon statistical fluctuations set a fundamental limit on the signal-to-noise ratio that can be achieved in a photometric measurement (10) and, as such, limit the precision with which an absorbance can be measured. Since the current output is proportional to the rate of photon arrival a t the P M tube, statistical variations in the photon flux are reflected in the current output, although the signal-tonoise ratio is reduced by the less-than-unity quantum efficiency of the photocathode (10). I t has been shown (11) that the photon limited variance, urn, for a photometric measurement is = (1 + 2B/S)/(St) (12) where t is the measurement time, S is the signal rate, and B is the background rate. These rates are photoelectron emission rates, and are proportional to P M tube currents. Because of the finite resolution of the A/D converter, the process of digitizing the photon information introduces errors in addition to those already discussed. If the system noise on a signal is greater than twice the quantization level of the AID converter, I, the variance, uq, of the sum of Nconversions of the signal S is (12)
=2 (13) 12NS In the dual beam arrangement, the independent cumulation of the photon statistical and quantization errors results in a transmittance measurement variance, U T , of UT
=
L'a,r +
vq,r
+
um,s
+ z'g,s
(141
where the subscripts r and s indicate reference and sample channel. Since the variance of an absorbance measurement, u A, is u~/(2.303A)' ( I 1 ), deviation in absorbance expected from the measurement system is
712
ANALYTICAL CHEMISTRY, VOL. 47, NO. 4, APRIL 1975
In Equation 15, the quantity tlt,, where t , is the time between A/D conversion for a given channel, is the number of A/D conversions summed to obtain the absorbance measurement.
TEST METHODS AND RESULTS Spectrophotometer Characteristics. The linearity and precision of the spectrophotometer and measuring system were tested by introducing dye solutions of known concentration into the optical cell through both the reagent and sample ports of the sampling-mixing head. The dye used was p-nitrophenol in 0.1M tris(hydroxymethy1)aminomethane buffered a t pH 10.5. Absorbance was measured a t 400 nm with a monochromator bandpass of 1.0 nm. The absorbances of the test solutions were also measured on a GCA/McPherson Model 721 spectrophotometer calibrated vs. NBS absorbance standards. The results of this test are presented in Tables I and 11. The absorbances presented in the column labeled FA in Table I and that labeled absorbance in Table I1 were calculated from Equation 11 and the relationship A = -log T. Five thousand individual A/D conversions were summed for each measurement to give a 1-second integration time. The results of Table I, notably the correlation in the column labeled FA, show that the spectrophotometer exhibits excellent linearity up to an absorbance of 3. The ratio of the slope of the absorbance-concentration curve for the new instrument to that for the 721 is 2.041, which is the pathlength of the optical cell in cm. This is in reasonable agreement with the nominal value of 2 cm. The agreement between the intercepts for the least squares fits of the absorbance-concentration curves for the two instruments indicates that the new measurement system exhibits no appreciable absorbance offset. Similar results are obtained a t other wavelengths. Table I1 illustrates the excellent measurement precision of the spectrophotometer. The RSD's expected from photon statistics were calculated on the basis of Equation 12 with the conditions noted in footnote b, Table 11. Those expected from the measurement system include photon statistical and quantization considerations and were calculated from Equation 15 with t / t , = 5000 for a 1-second integration. The expected relative standard deviations show that, for these conditions, the measurement system contributes little additional error to that expected from photon statistical considerations. The agreement between measured and expected relative standard deviations also demonstrates that additional sources of noise in the spectrophotometer have been effectively eliminated. Measurement precision for other measurement times are predicted by Equation 13 to be inversely proportional to the square root of the measurement interval. This variation is important since measurement intervals from milliseconds to several seconds are routinely encountered. Photometric precision as a function of measurement time is shown in Table 111 with the expected RSD calculated from Equation 15. These results show that very precise results can be obtained on the millisecond time scale using an intense source. The leveling off of measured relative standard deviation above a 1-second integration time is due largely to linearity limitations of the A/D converter. Sampling-Mixing Head Characteristics. Two important characteristics of the sampling-mixing head are the precision of the volumes of solutions that are mixed and the dead time of the mixing system. The precision of volume delivery was determined by mixing water and a dye solution and measuring the absorbance of the resulting solution. Using p-nitrophenol buffered a t pH 10.5 as the dye, a relative standard deviation of 0.12% was obtained for sets
Table 111. Photometric Precision as a Function of Measurement Time=
Table I. Linearity of the Spectrometer and Measurement System
.Measurement
Absorbance
P-Yit~openol
time (mrec)
concn (nominal, m:n)
721 ( 1 - c m cell)
FA (2-cm cell, nominal)
0.0075 0.0150 0.0300 0.0450 0.0600 0.0900
0.129 0.261 0.518 0.777 1.030 1.522
0.2670 0.5282 1.0436 1.5612 2 .oa29 3.1096
16.90 0.009 0.99984
34.491 0.0087 0.99999
Least Squares Fits
Slope Intercept Y2
Measured
5 10 100 1 03
y6
RSD
Expected
0.23 0.12 0.046 0.019 0.011 0.010
104
105
