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ANALYTICAL CHEMISTRY, VOL. 51, NO. 2, FEBRUARY 1979
Optimization of Precision in Dual Wavelength Spectrophotometric Measurement Kenneth L. Ratzlaff
and Hamzah bin Darus’
Department of Chemistry, The Michael Faraday Laboratories, Northern Illinois University, DeKalb, Illinois 60 1 15
The theory describing the precision of dual wavelength spectrophotometric (DWS) measurement is extended and validated using a DWS instrument fully under computer control. DWS measurement is shown to be effective in combatting uncertainty due to optical artifacts produced by samples and cells under non-ideal conditions. A method of controlling the light level makes possible measurement of analyte absorbance In the presence of several units of interferent absorbance.
Recently, a treatment (I) of the precision of Dual Wavelength Spectrophotometric (DWS) measurement produced several new conclusions concerning the conditions under which optimum precision could be obtained and made several comparisons with Single Wavelength Spectrophotometric (SWS) measurement. Among these are t h e following. (1)In t h e absence of interferents and sample presentation variations, S W S measurement will generally provide better precision than DWS measurement. (2) Employment of DWS measurement may reduce sample presentation variations; this may lead to better precision for D W S measurement t h a n for S W S when t h e sample creates distortions in t h e beam. (3) Although t h e absorbance of an interferent may be cancelled in DWS measurement (the primary advantage of DWS), the interferent seriously degrades the precision so that measuremeht is nearly prohibited in the presence of greater t h a n two t o three units of interferent absorbance. I n t h e investigation described herein, t h e theoretical treatment is expanded t o cover more carefully sample presentation variations and t o present a new mode of light intensity programming. With regard to the latter, the output signal of a spectrophotometer may be scaled in a variety of ways t o suit t h e measurement and the signal processing system. Commercially significant techniques for S W S instruments include programming the slit, which may degrade resolution, and programming the gain of the photomultiplier tube, which yields no improvement if the uncertainty in the measurement is signal shot-noise limited. Neither method is suitable for DWS measurement in the presence of serious optical interference. Consequently, new programming techniques must be investigated. T h e theoretical investigations must be validated by experimental studies. T o that end, the development of a highly flexible DWS spectrophotometer is described which is fully under computer control. The extent of t h a t control makes possible both t h e self-optimization of a wide variety of experimental parameters and the control and adjustment of those parameters where required to test their effect.
THEORETICAL As previously described ( I ) , the measured DWS value, AA, is t h e difference in the absorbances a t X1 and X2: AA = A1 - A2 = (e1 - < 2 ) b ~= (1 - ,/?)t,bc (1) *Present address, Department of Chemistry, Kansas State University, Manhattan, Kansas. 0003-2700/79/0351-0256$01 .OO/O
where el and t q are the molar absorptivities a t X1 and A,, and b, c, and /3 are length, concentration, and the ratio, t 2 / t l , respectively. Expressed in terms of the detected radiant powers, AA = -log ( @ 1 / @ 2 ) log K (2)
+
where a1and G2 are the transmitted radiant powers and K is the ratio of the incident intensities, sol, aOz, a t wavelengths XI and h p ,respectively. Where D is the absorbance or scattering of an interferent a n d is equal a t both wavelengths, t h e relative standard deviation in t h e measurement of AA was written as
where Eolis the photosignal resulting from t h e incident intensity a t A,; uI2and uz2are the variances in the photosignal resulting from the measurements of GIa n d 0,. When fl = 0 a n d K = 1, this equation describes S W S precision as well. The uncertainties in the photosignals, u1 and u2, are related to those photosignals in three possible ways: independent of, proportional to t h e square root of, and proportional t o t h a t signal. T h e relative standard deviation in t h e value of AA for independent uncertainty is
1 0 0 % (4) where q = g1 = u2 a n d a[/Eol is the uncertainty in any photosignal measurement relative to t h e reference signal. Equation 4 is plotted for various values of /3 as the dotted lines in Figure 1 where or/Eol= 0.5 X For square root uncertainty
100% ( 5 ) where the product PEolmay be considered t o be the number of photoevents in the measurement interval for Eel. The value of P may be calculated from operational parameters since P’ = 2 meRfAf where m , e , R,, and Af are P M T gain, electronic charge, feedback resistance of t h e OA current-to-voltage converter, and noise equivalent bandwidth. T h e proportionality factors involved in P are discussed in references 1 and 2. Equation 5 is plotted in various values of fl in Figure 2 for PEol = lo6. Finally for proportional uncertainty
where ( is the “flicker factor”, a proportionality factor between ,C 1979 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 51, NO. 2, FEBRUARY 1979
257
+
(2
' I
I
Substituting for u1 and X2 as f 1 and f 2 . UI
f.72
Absorbance (A,)
Flgure 1. Percent relative standard deviation ( % RSD) as a function of absorbance for various values of under conditions of independent uncertainty. The dashed lines and solid lines represent measurement without and with programmable attenuation, respectively. The lines are calculated from Equations 4 and 10, respectively, where u1/€,,, = 5 x 10-4 I
,.' 2
0
re
v1
Y 4
Absorbance (A,)
Figure 2. Percent relative standard deviation (YORSD) as a function of absorbance for various values of p under conditions of square root uncertainty. T h e dashed lines and solid lines represent measurement without and with programmable attenuation, respectively. The lines are calculated from Equations 5 and 11, respectively, where E,,,= 108
the signal and the uncertainty in t h a t signal; is considered here to be approximately equal for both wavelengths. Obviously, ( % uu)p monotonically decreases with A l so that it will seldom be limiting except a t low A I . In all the above cases, % uu is proportional to (1- 3)-' so t h a t the expected precision is poorer for DWS measurement than for SWS since a SWS measurement may be represented by setting p = 0. In Equations 4 and 5 , the dependence of % uu on D is very strong, drastically degrading precision when interferences are present. C o r r e l a t e d S a m p l e P r e s e n t a t i o n V a r i a t i o n s . In discussing the various contributions to proportional uncertainty in SWS measurement, Ingle and co-workers ( 2 , 3 )have pointed out that t h e most significant might be that due to variations in t h e optical qualities of the sample and cell, even in high quality cells. Where flow cells or cells of lower quality must be used, the problem is accentuated. In DWS, these variations are partially correlated however, and the suggestion has been made ( I ) t h a t their effect could be reduced. This may be shown somewhat more rigorously by adding to Equation 3 t h e covariance term of propagation of error mathematics ( 4 ) . This step is necessary since the two beams, whose radiant powers are ratioed in Equation 2, follow a nearly identical path; consequently, the optical variations are largely correlated. Equation 3 now becomes
u2,E
is specified separately a t X1 and
= t;lEollO-'D
+
'41)
= t2KEo110-(D
+
( % n u ) " = (2.3(1 - P)A1)-lltl
OA1)
- (21
X
100%
(8)
Although the term El - t2may approach n d l , the wavelength dependences of the phenomena which produce the variance will generally make it non-zero; these phenomena probably include light scattering by surfaces and suspended materials and refraction by oblique surfaces and gradients in the sample. In any case, by comparing Equation 8 (adapted t o S W S by setting p t o 0) with Equation 6, it is apparent t h a t the uncertainty due to sample presentation will be less for DWS than for S W S if (E1 - F 2 ) / ( l - p) < 2[. Precision with P r o g r a m m a b l e Attenuation. Where the magnitude of the reference incident power, ao1or aO2, is not limited by source intensity or the throughput of t h e optical system, an effective upper limit is determined by the detector and data acquisition system; a photomultiplier will fatigue if operated a t excessive photocurrent levels while multichannel detectors such as vidicons, photodiode arrays, and chargecoupled device photoarrays will saturate. Amplifiers and analog-to-digital converters also have an upper limit past which they no longer provide meaningful values. On the other hand, for each unit of absorbance by analyte or interferent, the signal is reduced by an order of magnitude resulting in decreased precision. Examination of Equations 4 and 5 suggests t h a t for optimum precision the photosignal should be kept as close t o Eol as possible. When making a DWS measurement, the values of both aOl and aoZare less than the incident radiant powers. Therefore, if the incident power could be increased a t both wavelengths by precisely the same factor so that the photosignal a t X1 or A, approaches the limit, the precision could be improved without loss of accuracy. T h a t factor would be the inverse of the transmittance a t the wavelength producing the larger signal; in this treatment, that wavelength has been considered to be As. In such a case both measurements could be made a t a higher signal level. The factor by which Eol can be increased is lC?)ldAso l that Equation 3 becomes
The prime indicates t h a t the intensity is programmed. Where the uncertainty is constant, uI = u1 = u2. ( % mAA')I =
01
[ 1 0 2 ( 1 -8)Ai
+ K-2]1/2 x
2.3(1 - P)AiEoi 100% (10)
Equation 10 is plotted for various values of in Figure 1.
as the solid lines
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ANALYTICAL CHEMISTRY, VOL. 51,
NO.2,
FEBRUARY 1979
As it was for Equation 5, square root uncertainty is treated by making ul a n d uz proportional to t h e square root of t h e signal. u1 = ~(lO-"-B'A')E,,/pJliz 02 (%UU)S
= (KE,,/P)'/2
+
= (2.3(1 - /3)A,)-' [lo'' - B'A'/EOIP (KE,lP)-']1;2 x 100% (11)
Equation 11is plotted for various values of p as the solid lines i n Figure 2. In t h e case of proportional uncertainty, t h e precision is independent of t h e magnitude of t h e photosignal. Consequently, controlling the intensity will have no effect. However, since the total variance of the measurement is the sum of the individual variances, measurements are usually limited by the independent or square root uncertainties which are usually higher than t h e proportional uncertainty. In comparing Equations 4 a n d 5 with 10 and 11, two significant differences stand out. First, the dependence of the precision on AI is weaker where p > 0 in Equations 10 and 11; this is easily observed in Figures 1 and 2. Secondly, and more significantly, the very strong dependence of the precision on D in Equations 4 a n d 5 is eliminated. It should be noted that t h e required capacity to increase radiant power by the factor of 10(D+BAl) is not readily obtained since, if increased radiant power was available, it might appear reasonable t o use it at all times. However, since t h e detection system will have an upper limit, the radiant power must be reduced from its maximum t o a level compatible with t h e detection system. The radiant power can then be increased as D and PA, increase. Alternatively, if an integrating detector or a voltage-to-frequency converter and counter is used, the integrated radiant power can be programmed by simply changing t h e integration period.
EXPERIMENTAL Instrumental. The system developed to test the principles developed above is based on a GCA McPherson EU-'721 spectrophotometer system and a microcomputer-based minicomputer system. The computer system is built around an 8080 and/or 2-80 microprocessor on the S-100 bus. Peripherals include floppy disk, CRT, and printer. Programs were written in BASIC with assembler subroutines. The computer system was described in detail elsewhere ( 5 ) . The original light source module was replaced with a high intensity light source module to obtain the requisite wide dynamic range in intensity necessary for the application of Equations 10 and 11. The module contains a 30-V, 375-W tungsten halide lamp (Sylvania DWZ) with a linear filament. A concave mirror collects and collimates the light, and the infrared radiation is removed by a heat-absorbing filter. A Kepco Ks36-30M regulated dc power supply is operated in the current-regulated mode, and current level may be controlled by the computer via an 8-bit digitalto-analog converter. A second mode of programming the intensity is accomplished by use of linear variable transmission wedges which are positioned in the beam by driving a precision rack (Berg No. RI-8) with a dc gear motor (Hughes (2-54). Unregulated *6-V power to drive the motor is switched with mechanical relays. Micro switches a t the limit positions limit the travel; these switches also signal the computer of limit condition. Using short pulses (about 100 ms) to the motor and reading the photocurrent between each, the light intensity can be adjusted under program control to within 10% of a present level in 1 s or less. An absolute shaft encoder (Norden ADC-13-BNRY-A), which generates 128 counts per revolution, is used to monitor the position of the attenuator. The value is read via parallel 1/0 ports. A 48-tooth, 64-pitch spur gear couples the encoder to the rack providing resolution of 0.47 mm per count. Several linear optical attenuators were tried in hope of finding one which attenuates equally over a wide wavelength region. The
first was a linear neutral density wedge (Edmund Scientific). A second wedge was produced by imaging a pattern in gold on quartz; the pattern consists of a 40-tooth comb, each tooth being a triangle approximately 0.64 mm by 330 mm. The 1:l photographic negative for the comb was also tested. A third mode of programming was the use of an iris, adjustable under program control. A geared pulley was mounted on the iris and coupled by a plastic belt to a pulley on a small stepping motor (HSI 36740-63) so that it may be closed in 180 steps. The fully open position is indexed via a micro switch, and a given aperture can be reproduced by counting a preset number of steps. The signal level but not the intensity could also be programmed via the gain on the photomultiplier tube or by a programmable gain amplifier; the former was used. A 0- to 10-V digital-to-analog converter controls the voltage on the photomultiplier tube in the EU-701-30 detector module. It should be noted, however, that programming the photomultiplier gain has no effect on the photon flux, and consequently it has no effect on square root uncertainty. However, it does provide a convenient method for initially adjusting the output current level to the input of the data acquisition system. The photomultiplier current is converted to a voltage using an operational amplifier (RCA 3140) with a 10-MR resistor in parallel with a 100-pf capacitor in the feedback loop. The relatively long time-constant eliminates the need for a sample-and-hold amplifier preceding the analog-to-digital converter. The analog-to-digital converter is a 10-bit successive approximation converter whose effective resolution was increased according to the technique suggested by Horlick (6); a sine wave generator was connected to the amplifier's summing point through a 108-Rresistor, thereby adding pseudo-random noise to the signal. The generator was adjusted at 1 kHz for approximately 1 V peak-to-peak output with 0.5 V offset. By summing 255 conversions for each measurement, the effective resolution is approximately 12 binary bits. The monochromator (EU-'700) is a Czerny-Turner mount grating monochromator. The wavelength control may be driven by either stepper motor or dc slew motor; each of these was interfaced to the computer so that it may be activated under program control. An encoder, coupled to the drive, produces pulses which were directed to an up/down counter in the computer interface so that the current wavelength is continuously available to the program. DWS wavelength modulation is performed by rotating the mirror which focuses the light from the grating onto the exit slit. The mount for the parabolic mirror was replaced by a precision mirror mount (Oriel, Model 1450); a precision spur gear was mounted on the horizontal rotation micrometer and coupled to a gear on a stepping motor (Superior Electric, Type SS25-1140) mounted outside the monochromator. Absolute indexing of the drive is possible by stepping to a limit switch. The motor is driven by pulses produced by a computer output port. The excursion of the wavelength modulation was limited by loss in intensity at SImore than about -20 nm, where K drops to about 0.3. A split beam module based on the design of Defreese and Malmstadt (7) was also used for some preliminary work to obtain simultaneous dual wavelength output. The exit folding mirror was replaced by a beam splitter so that radiation appears both a t the original exit slit and on the front focal plane. A carriage containing an adjustable slit and photomultiplier tube housing is positioned laterally along the focal plane by a stepping motor. Except where noted, this module was not used for the investigations described herein. A Programmable Sample Chamber (EU-721-11) was used. This module contains an oscillating cell holder which may be halted in either sample or reference position upon receipt of a Tl'L signal. Internal reed relay closures signal the computer when the holder has reached one position or the other. Reagents. A stock solution of K2Cr207dissolved in 0.1 M KOH was used to prepare a series of solutions of varying absorbances. These were used for studies of precision as a function of absorbance at the analytical wavelength pair 395 and 407 nm. At these wavelengths R = 0.292. For the studies of precision as a function of interferent concentration, a series of solutions were prepared in which varying amounts of p-nitrophenol were added to a constant amount of
ANALYTICAL CHEMISTRY, VOL. 51,
potassium chromate. At the analytical wavelength pair employed for potassium chromate, (3 for p-nitrophenol is 1.00, and AA = 0. S t u d y of the Programmable Attenuator. It was first necessary to determine whether or not the intensity could be precisely programmed; this was done by measuring the wavelength dependence of each of the programming techniques. For each technique, the value of K was determined as a function of attenuation a t the 3951407 nm wavelength pair. This was performed by programing the light source power supply, by varying the position of the attenuator with each type of optical wedge, or by varying the aperture of the iris. K could also be determined as a function of encoder or stepper position for future use. S t u d y of Sample Presentation Variations. To determine the extent to which DWS measurement can correlate the sample presentation variations, it is useful to increase those variations by using a flow cell with nonhomogeneous contents or a poor quality conventional cell; a plastic cell was used. With the cell position fixed in the cell holder, both A, and 1A were measured by making a set of 20 measurements, averaging, and computing the standard deviation. This procedure was repeated 20 times with the cell removed and replaced between each set. The 20 averages were then averaged, and the standard deviation of that population was determined and compared with the average standard deviation of the 20 sets. The standard deviation of the averages would, in the absence of positioning variations, be expected to be equal to the average standard deviation of the 20 sets divided by v%. The extent to which those values are different is then a measure of the effect of sample presentation uncertainty on both SWS and DWS measurement. S t u d y of DWS Uncertainties. DWS measurements were made both as a function of A , and of D in order to compare Equations 4 and 5 with 10 and 11. Each datum consists of the standard deviation of 20 measurements with the cell in a fixed position. The programmed sequence for DWS operation will be briefly described. Upon initialization, the computer closes the attenuator to a minimum light level, zeroes the dual wavelength stepper drive, and queries the operator for the current monochromator wavelength, hl, the desired hl and AX, and LMODE. If LMODE = ‘ YES ’, the computer will later optimize X, for the particular interferent. If it is necessary to search for X1, the slew motor is activated in the appropriate direction and stopped when the encoder value indicates that the monochromator is close to A,. The number of steps required to reach A, is then computed and the monochromator is stepped to Xl f 0.01 nm. The photomultiplier voltage is then optimized under program control so that the larger signal of those corresponding to the incident intensities a t XI and X2 will produce a current such that the A/D converter will approach full-scale. If LMODE = ‘ YES ’, the operator is requested to place a sample of pure interferent in the sample chamber. The computer adjusts X1 (and consequently A,) by determining K , moving the interferent sample into position, determining AA,and changing X1 if the absolute value of AA exceeds the uncertainty of the measurement. The reference is again positioned in the beam and K is determined. The operator is then requested to place the sample in the chamber, and that sample is moved into the beam. A t this point, the computer positions the attenuator until one beam, I , or Z2,produces a near full-scale analog-to-digital converter reading. Then the rack encoder position must be read or the stepper position must be noted so that the value of K may be corrected by the value of the relative transmission computer from the data which was stored. A t that point, 20 values of AA may be determined, and the average, standard deviation, and relative standard deviation are determined. A new sample is then requested. If an SWS measurement is to be made, the attenuator must be kept a t a constant position since the reference intensity is constant.
NO. 2,
FEBRUARY 1979
259
Table I. Sample Presentation Uncertainty
sws
DWS ( A h = 1 2 n m )
A , = 0.8207
AA = 0.5809
20 measurements without changing cell %a = 0.12% %a = 0.15% 20 repetitions of above, replacing cell between each %o = 0.15% %a = 0.05% The measurement can be forced into conditions whereby i t is limited by independent, square root, or proportional uncertainty by control of slit width and signal processing parameters. For study under conditions of independent uncertainty, the limiting uncertainty in this system lies within the data acquisition system, possibly a somewhat artificial though not atypical situation. Square root uncertainty is reduced by opening the slit somewhat so that the feedback loop reduces P M T gain voltage to about 350 V while maintaining full-scale photocurrent; this ensures a high photon flux and low square root uncertainty. The independent uncertainty is primarily due to the 10-bit analogto-digital converter. The technique for expanding its resolution as described earlier is defeated primarily by reducing the number of conversions to 16 and by reducing the sine wave frequency so that it may not approximate random noise as well. For study under conditions of square root uncertainty, the slit width is closed to about 160 pm. The consequent reduction in photosignal with the attenuator closed causes the computer to increase the detector voltage to about 1000 V. This corresponds to a photoelectron rate of roughly lo8 photons-s-’ producing a full-scale analog-to-digital conversion (8). The time required for 255 conversions is 38 ms, and since the current-to-voltage amplifier time constant is about 1 ms, the measurement interval can be taken as roughly 38 ms. Consequently, a measurement represents the detection, at full scale, of roughly 3 X lo6 photons. This estimate is of sufficient accuracy only to provide confidence that the measurement precision under these conditions must be limited by square root uncertainty. For study of proportional uncertainty, other sources must be greatly reduced so that they are not limiting; this is accomplished by opening the slit to 900 pm and performing the signal processing in the normal mode. However, since this relative standard deviation monotonically decreases while the relative standard deviation due to other uncertainties increases with absorbance, it is difficult to create conditions in which the photoelectron rate is so high and independent uncertainty is so low that proportional uncertainty is limiting over a wide range; no attempt to do so was successful.
RESULTS A N D DISCUSSION P r o g r a m m a b l e Attenuation. Three modes of attenuation were attempted. In n o case was K constant with intensity. T h e technique of programming the light source current was rejected because of the slow response. Because of the thermal inertia of the tungsten-halide lamp, u p t o 40 s were required for the intensity t o be constant within t h e uncertainty of the measurement; this created a problem in t h e critical function of reducing t h e radiant power in order t o remain within t h e range of t h e electronics inputs. T h e dynamic range of t h e remaining modes was limited since the intensity could not be continuously reduced to near zero; t h e various linear attenuators and the iris had intensity ranges of 100 t o 200. T h e iris proved t o be t h e method of choice since i t is not vulnerable to dirt on an optical surface. A look-up table of K values for each discrete stepping motor position can readily be produced for the analytical wavelength pair. S a m p l e P r e s e n t a t i o n V a r i a t i o n s . In this study the results, summarized in Table I, indicate t h a t sample presentation variations are significant in SWS measurement, but less significant in DWS measurement. For the measurements made without moving t h e cell, Equation 3 predicts that t h e
260
ANALYTICAL CHEMISTRY, VOL. 51, NO. 2 , FEBRUARY 1979 l o
r
h I
0 0
1
I
I
1
I O
10
*,'
I
I
I
I
I
I
I
J
1
I n t n r t n r e n t A b s n r b a n c n (01
2
A b s o r b a n c e (A,)
Figure 3. Experimental study of precision as a function of interferent absorbance ( D ) . (A) Independent uncertainty conditions ( 0 )with no attenuator, (B) square root uncertainty conditions ( + ) with no attenuator, (C)independent uncertainty conditions (A)with attenuator, (D) square root uncertainty conditions (+) with attenuator relative standard deviation for DWS measurement should be greater than t h a t for SWS by a factor of (1 - 3 ) Since 3 = 0.29, the increase should be by a factor of 1.4; this is approximately the case. When the values for each of the 20 sets are averaged, the relative standard deviation, exclusive of sample presentation uncertainty, should be decreased by a factor of 20-"'. For the DWS case, the resultant relative standard deviation is only slightly larger than the predicted 0.034% indicating that the sample presentation uncertainty is less than { (0.05)2 (0.034)2)1/2or 0.036%. For t h e S W S case, the predicted relative standard deviation of the averages should be 0.027 7% indicating t h a t the sample presentation uncertainty is about 0.13%. These results indicate that where sample presentation uncertainty is significant, it can be largely correlated in the D W S measurement. This experiment was also attempted using the split beam module; however, the results were less positive indicating that the deflections of the beam by the sample had different effects on t h e two detectors; this result should have been expected since the beams for t h e two wavelengths travel a much less identical path than they do when the wavelength is modulated by t h e mirror. DWS Precision as a Function of D . As Equations 4 and 5 suggest, the precision of DWS measurement in the absence of a programmable attenuator is a strong function of D ; for independent and square root uncertainties, the relative standard deviations are proportional to loD and loD$?, respectively. However, with the attenuator, the dependence on D is eliminated (Equations 10 and 11). T h e experimental dependence on D is shown in Figure 3. For these data, = 0.29, and A I = 0.22. A linear regression analysis shows that curve A, corresponding to Equation 4, has a slope of which is quite close to the theoretical value of Similarily, curve B, corresponding to Equation 5 : has a slope of compared with the theoretical 10'"'. However, when the programmable attenuator is utilized, the slope is nearly zero for both independent uncertainty (curve C) and square root uncertainty (curve D). T h e programmable attenuation technique is limited by the dynamic range of the attenuator; in this case, a range of 1 0 5 1 in incident intensity was used limiting the sum of PA + D to a maximum of about log,,(105) or 2.07. DWS Precision as a Function of A In the examples shown for both independent and square root uncertainty, employment of the programmable attenuator yields marked improvement in precision a t higher absorbance for measurements limited either by independent uncertainty or by
Figure 4. Experimental study of precision under conditions of independent uncertainty as a function of absorbance. (0)No programmable attenuator. (A)With attenuator. The dashed and solid lines are calculated for 8 = 0.29, K = 1.0 from Equations 4 and 10
Ic tP,
~
'.
5
E
I
I
I
I
I 1
I
I
I
I
I 1
Absorbance (A,)
Figure 5. Experimental study of precision under conditions of square root uncertainty as a function of absorbance. ( 0 )No programmable attenuator. (A)With attenuator. The dashed and solid lines are calculated for 3 = 0.29, K = 1.0 from Equations 5 and 11 square root uncertainty. In Figures 4 and 5 , the curves drawn through the experimental points are theoretical curves for K = 1.0 and $ = 0.29, and the fit is sufficiently good to substantiate the predictions generated by the theory. It should be noted that K is not constant as a function of A I when the programmable attenuator is used. T h e consequent changes in the curves are, however, less than the uncertainty in determining the precision; therefore, they are ignored.
CONCLUSIONS Two important conclusions can be drawn from this investigation. (1) U'here sample presentation variations are a serious problem, they may be significantly reduced by DWS measurement since the variations producing these uncertainties are largely correlated. The need for cells of high optical quality has recently been emphasized (2). However, except where pathlength variations might occur, this requirement might be relaxed for DWS measurement. Furthermore, in cases where the sample itself degrades optical quality, the DWS measurement might also be advantageous; such cases would include analyses of samples in flow cells where turbulence and density gradients can induce flicker. These data also support the assertion (2) that sample variations are not due to changes in pathlength since such changes would not be cancelled by DSVS measurement. (2) T h e range of molecular interferent concentration over which the value of 1 A may be precisely measured is greatly increased. In principle, if there was unlimited control over
ANALYTICAL CHEMISTRY, VOL. 51, NO. 2, FEBRUARY 1979
incident radiant power, measurements could be made in the presence of several units of interferent absorbance without loss in precision. Here the results may a t first appear artificial; radiant power was attenuated a t low @ and D rather than being increased a t high D or @ > 0.0. However, it must be remembered t h a t P M T fatigue a t excessive light level and electronic over-range a t high input current present real limits to the dynamic range. Furthermore, the detector signal can be integrated over longer periods of time by using integrating detectors or by using an analog-to-frequency converter and counter. Although the range of allowable molecular interferent may be very great, when the interferent is a scattering substance, one must be much more cautious. As has been discussed previously (9),the effect of a scattering interferent cannot ever be completely suppressed by application of Equation 1. This is d u e t o the fact t h a t scattering of radiation monotonically decreases with wavelength so t h a t no wavelength pair exists where the scattering would exactly cancel. T h e instrumental work in this investigation illustrates the types of adaptations and corrections which may be made when an instrument is under complete computer control. For example, the addition of attenuator and encoder was a relatively simple task entailing t h e construction of only very simple additional circuits and the addition of a few statements in BASIC. However, although the methods of programming the attenuator and of modulating wavelength were imminently suitable for an investigation as this, they might not be preferred for routine work. A servo motor could probably be used to bring the attenuator to balance more rapidly, and other techniques for obtaining dual wavelength modulation have been discussed previously (10) and may be preferred for particular applications.
261
We should point out that in addition to extending the range of the DWS technique, a significant application of the work described herein should be the weighting of points used for a calibration curve. I t is now clear t h a t the precision of a measurement may vary widely with AI, p , and possibly D, and low precision data points should not be valued as strongly in a calibration curve. Consequently, when executing a linear or polynomial regression analysis of calibration curve data, the data should be weighted according to their reliability ( 4 ) . This could be readily written into a program which would either store both absorbance and precision as a function of concentration or use relative weighting factors computed from equations presented here.
LITERATURE CITED K. L. Ratzlaff and D. F. S. Natusch, Anal. Chem., 49, 2170 (1977). L. D. Rothman, S.R. Crouch, and J. D. Ingle, Jr.. Anal. Cbem.,47, 1226 (1975). J. D. Ingle, Anal. Chim. Acta, 88, 131 (1977). Philip R. Bevington, "Data Reduction and Error Analysis for the Physical Sciences", McGraw-Hill, New York, 1969. Kenneth L. Ratzlaff, Am. Lab., 10, (2). 17 (1978). Gary Horlick, Anal. Chem.. 47, 352 (1975). J. D. Defreese, K. M. Walczak, and H. V. Malmstadt. Anal. Chem., 50. 2042 (1978). RCA Photomultiplier Manual, RCA Electronic Components, Harrison, N.J., 1970. K. L. Ratzlaff and D. F. S.Natusch, "Theoretical Assessment of Accuracy in Dual Wavelength Spectrophotometric Measurement", submitted to Anal.
_ _
Chem
K. L Ratzlaff, F. S. Chuang, D. F. S Natusch, and K R. O'Keefe. Anal. Chem , 50, 1799 (1978).
RECEIVED for review August 14, 1978. Accepted November 20,1978. Paper presented in part a t the Great Lakes Regional American Chemical Society Meeting, Stevens Point, Wis., 1977. Partial financial support provided by the Research Corporation.
Reduction of Matrix Interferences for Lead Determination with the L'vov Platform and the Graphite Furnace Walter Slavin" and D. C. Manning The Perkin-Elmer Corporation, Main A venue, Norwalk, Connecticut 06856
The addition to the graphite furnace of a thin pyrolytic graphite plate (L'vov Platform) on which the sample is deposited, makes it possible to atomize the sample at more nearly constant temperature conditions. This reduces analytical interferences that arise from a variation in the appearance temperature for Pb when it is present in different matrices. I n addition, this platform makes it possible to volatilize the sample into a gas that is hotter than the surface from which the sample is volatilized. This reduces the interference resulting from the volatility of Pb halides. Using the platform, we can determine Pb in matrices which contain chloride, sulfate, and phosphate without resorting to matrix modifications. It remains necessary to carbide-coat the platform surface to reduce its reactivity with Pb.
We have studied ( I ) the potential interference effects that occur in atomic absorption graphite furnace analyses. Our 0003-2700/79/0351-0261$01.00/0
initial work used P b as a test element because it appears to be the most widely determined in the furnace. We used a chloride matrix because the literature indicated t h a t the chloride matrix introduced the greatest problems in t h e determination of Pb. We showed that P b can be determined in a chloride matrix using ",NO3 as a matrix modifier additive to permit removal of a large proportion of the chloride in the charring step prior to atomization of the Pb. In addition, it was necessary to control the surface of the graphite tubes (we used molybdenum coating on pyrolytic tubes), t o use signal integration to avoid errors due to changes in peak shape, and to use an atomization ramp which separated in time the residual background signal from the P b signal. With these precautions, we were able to detect less than 20 pg of P b in solutions containing 1% NaCl or MgC12. While the method of additions has been widely used to quantitate analyses where interferences are present, this procedure involves extrapolation from the observed results. I t would be distinctly preferable to use simple standards with 1979 American Chemical Society
