V O L U M E 23, NO. 9, S E P T E M B E R 1 9 5 1
1229 current immediately past the end point in accordance with the results of Foulk and Bawden (4). COMBINATION OF TWO SYSTEMS I
If two reversible systems such as cericcerous and ferric-ferrous are placed with proper alignment of their respective voltage axes, a three-dimensional plot results as in Figure 5 . A potentiometric titration is seen t o follow curve ABCDE. B represents the point where the first system is 50% oxidized and D represents the point where the second system is 50% V O L T A G E oxidized. The voltages a t these points Figure 5. Three-Dimensional View, Showing Interaction of Two Systems correspond t o respective Eo’s if activities are neglected. The end point ocABCDE. Potentiometric curve JKC-CLM. Amperometric titration curve curs in region C. If a polarogram is run FGCHI. Polarogram of solution at endpoint a t the end point, a curve such as FGCHI would result. The FG wave represents the oxidation current for the higher voltage couple (cericpendent upon 2. The shape of this end point has been reported cerous) and the H I wave represents the reduction wave of the for the titration of metavanadate by ferrous ( 5 ) . If the k values lower voltage couple (ferric-ferrous). The amperometric titraare identical, the mid-point of the titration should give a value of tion end point is illustrated by the intersection of two straight da/dE = -nFkCo/4RT. As the previous equations were based lines, JKC and CLM. The coincidence of the potentiometric upon a rapid, reversible system, other approaches must be used and amperometric end points is seen a t C. for irreversible systems. The dead-stop end point has been applied for the most part to irreversible systems titrated iodometriLITERATURE CITED cally. Figure 3 (IO)shows an irreversible system such as arsenite Bottger, W., and Forsche, H. E., Mikrochemie, 30, 138 (1942). Cooke, W. D., Rellley, C. K.,and Furman, N. H., ANAL.CHEW, when titrated with iodine. In the initial solution, A , reduction 23, in press. of H1O+and oxidation of OH- may be the only reactions that Delahay, P., Anal. Chim. Acta, 4, 635 (1950). could occur to any appreciable extent. As such a small voltage Foulk, C. W.,and Bawden, A. T., J. Am. Chem. Soc., 48, 2045 (about 10 to 15 mv.) is usually applied, no current will flow due (1926). Gale, R. H., and Mosher, E., ANAL.CHEM.,22, 942 (1950). to the hydroxyl or hydronium ion discharge. Any irreversible Kolthoff, I. M., and Furman, N. H., “Potentiometric TitraRubstances present which are oxidizable or reducible a t the elections,” Kew York, John Wiley & Sons, 1926. trodes will give a curve as shown by the dotted line(s) in A. ThioKolthoff, I. hl., and Lingane, J. J., “Polarography,” Kew York, sulfate, for example, has been shown to be electrolytically ouiInterscience Publishers, 1941. Mitchell, J., Jr., and Smith, D. hl., “Aquametry,” p. 86, Kew dizable ( I ) . Thus, as the slope is about zero initially, and reYork, Interscience Publishers, 1948. mains so up to the end point [Figures 3 A and B ( I O ) ] , the current, RZiiller, Erich, “Electrometrische Rfassanalyse,” Dresden, T. d,, will also be about zero in this region. Any impurity, or traces Steinknopff, 1942. of iodine to couple with iodide, will increase the slope and give Reilley, C. N., Cooke, W. D., and Furman, N.H., ANAL.CHEM., 23, 1223 (1951). rise to a small current. Immediately past the end point [Figure Stock, J. T., Metallurgia, 37, 220-3 (1948). 3, C ( I O ) ] , the slope suddenly increases owing to the presence of Van Kame, R. G., and Fenwick, F., J . Am. Chem. Soc., 47, 19 excess iodine, and the current, di, increases rapidly. Thus, up (1925). to and a t the end point, the current is small, with a sudden rise in RECEIVED hIarch 30, 1951
+--
Variability in the Beckman Spectrophotometer W. 0. CASTER‘ Nutritional Chemistry Laboratory, Nutrition Branch, U.S . Public Health Service, Washington, D . C.
A
M J M B E R of approaches have been used in describing spectrophotometric error. Some workers ( 3 , 8, I S ) have concerned themselves primarily with estimating the highest degree of precision obtainable with an instrument under certain given conditions. Others ( I O , 20, 23) have been more interested in locating and estimating the magnitude of the errors introduced into their analytical data as a result of using a spectrophotometer. The latter approach can be criticized, in that it may not distinguish between errors traceable to the instrument and errors inherent in the technique. However, this approach yields over-all error values which are usually of more practical interest to the analytical chemist. As these approaches are accompanied by different testing conditions, it is not surprising that certain differences of opinion have ’Present address, Physiological Chemistry Department, University of Minnesota. Minneapolis, Minn.
arisen concerning the accuracy expected from a given instrument. It is reported that, under certain conditions, the Beckman quartz spectrophotometer is capable of yielding transmittance readings with a precision of 0.1% (6, 8), 3~0.07%(ZO), or 0.02% ( 5 ) transmittance. Ewing and Parsons ( I O ) reported that although individual Beckman spectrophotometers may give highly consistent results, there is a spread of several per cent between the analytical results obtained from a series of different instruments. In a collaborative assay ( 1 5 ) differences of as much as 10% were observed in the standardization of a series of Beckman spectrophotometers. By special techniques, Bastian (4,6) reported analytical errors smaller than 0.1% with the Beckman spectrophotometer. These widely differing results pose a real problem for the analyst. Under what conditions is it safe to report such values as 1742 ( I I ) , 27,450 (IQ), 4954 ( 2 5 ) ,and 14,704 (@), which imply
1230
A N A L Y T I C A L CHEMISTRY
accuracy to within 0.1% relative analytical error? Under what conditions may errors of several per cent appear in the data? The microanalyst has an even greater problem in this respect. As it is necessary to modify the Beckman spectrophotometer slightly to adapt it for micro work, it is possible that the accuracy has likewise been modified. Sevci a1 vitamin microprocedures ( 7 , I?’), using the Beckman spectrophotometer rquipped with microcells, are being used more extensivelv. In a study of vitamin niicroniethods it appeared advisable first to evaluate the performance of the Bcckmari spectrophotometer. The resulting data were studied by analysis of variance methods ( 9 1 ) . A number of distinct sources of variation were thus 10cated. The statistical procedures used are discussed by Alexander and Caster ( 1 ) . .411 the analytical work was carried out on a single Beckman spectrophotonieter (Model DU, Serial No. 1304, purchased in the fall of 1946). The microcells wed in this work are obtainable from the Pyrocell Manufacturing Co., 207 East 84th St., New York 28. They are not manufactured by or approved by the National Technical Laboratories ( I d ) . Preliminary results have been discussed (9).
In a study of vitamin micromethods it seemed necessary to evaluate the sources of variability in the Beckman spectrophotometer. Though duplicate determinations checked within 0.1 to 0.5$7”, consistent errors of as much as 3 to 59’0 were observed under different conditions. The largest variations were associated with the phototube or with factors such as slit width, lamp intensity, and aging which directly affected phototube response. Deviations from Beer’s law were found to depend upon a choice of phototube and slit width, and to change with age i n the same phototube. Other potential sources of error were located and statistically evaluated. These factors must be kept in mind in the interpretation of extinction coefficients and other absolute spectrophotometric values. They may also serve as a guide in the evaluation of instrumental procedures. The use of this instrument in establishing deviations from Beer’s law is questioned.
CELL CORRECTIONS
Four quartz microcells were carefully cleaned, filled with distilled water, and placed in the instrument. Exact agreement between cells was not observed. The data in Table I demonstrate the effect of changing wave length and optical density scale reading upon the apparent “cell correction” (6). .\fter each column of readings in Table I the slit width was changed to allow progressively smaller amounts of light to leach the phototube. In order to accomplish this, the optical density knob was adjusted in such a manner that the optical density srale reading-Le., the zero point for each series of four readings --\ias changed progressively from 0.000 to 0.100, 0.200, etc. Duplicate readings were made in each caae. For every slit width, one reading was made for each cell. When all single readings were completed a t both wave lengths, they were repeated, giving the duplicate results shown in Table I. As the duplicate readings were independrntly obtained, these data give an estimate of the repeatability of duplicate readings as ne11 as of the effect of changing wave length and optical density scale reading (or slit width) upon cell constants. The dark current drift was appro\imntely 1 scale division in 5 minutes when these readings were taben Readings were made a t approximately 30-second intervals. The analysis of variance summarized in Table I1 demonstrates that there are t F o distinct sources of variation represented in the data in Table I: differences between duplicate readings made
Table 1.
Optical Densities
(Variations in cell correction observed when Kave length and slit 350 mp ,
Slit, rnm. Blank Cell 1 Cell 2 Cell 3
1.26
1 15
1.08
0.99
0.91
0.83
0.000 0.000
0.100 0.100
0.200 0.200
0.300 0.300
0.400 0,400
0.003 0.003 0.000 0.000
0.103 0.102 0.098 0.100
0.203 0.202 0.199 0.198
0.302 0.301 0.299
0,403 0.402 0.399 0,400
0.500 0.500 0.502 0,603
0.002 0.001
0.099 0 100
0.199 0 199
0.300
0.401
0.300 0.300
0.401
0.199 0.501 0.500 0.502
550 mp
Slit, mm.
0.13
Blank
0.000 0.000
Cell 1
0.000 +0.001 -0,001 0.000 -0.001
Cell2 Cell3
+0.001
0.12 0.100 0.100 0.099 0.100 0.099 0.099 0.099 0.099
0.10
0.09
0.08
0.07
0.200 0.200 0.201 0.200
0.300 0,300
0.400 0,400
0.500 0.500
0.301 0.301
0.400 0.400
0.500
0.199 0.199
0.299 0.300
0.399 0.399
0.500
0.198 0.200
0.300
0.398
0,300
0.399
0.502
0.500 0.500 0.500
under substantially identical conditions amounting to c = 0.00077 on the optical density scale; and consistent changes which appear in the cell correction factors m the wave length is changed from 350 to 550 mp, resulting in an observed variation of c = 0.00226 on the optical density scale (interaction of cells by wave lengths). In Table I1 the P-test values were obtained by the composite method ( 2 ) . Because one of the interaction terms was significant, and the second, though not significant, was somewhat larger than the between-duplicates mean ?quare, the first three variables were also tested by the approximate method ( 8 ) . The results of this are shown in Table 111, and are in good agreement with the conclusions of Table 11. By both methods it is concluded that none of the first three variations listed in Table I1 is significant. It is of particular interest to note that the variation betwen cells is nonsignificant. In other words, the apparent diffeiences between cells, or the cell corrections ( 6 ) , observed in these data are entirely explained by the two sources of variation described above (variations between duplicate readings, and cells by wive lengths’ interaction). Thus, general cell correction factors, for use a t all wave lengths and slit widths, would be of no value in improving the accuracy of these results. If cell correction factors are to be used a t all, they should be specifically determined for each wave length and slit width used. Whenever the cells are matched, under a given set of conditions, so as to show width were changed) a range of difference between thein no greater than 0.002 in optical density 0.64 0.77 0.70 value [a range of approximateIy 3 0.800 0.600 0.700 0.800 0.600 0.700 times the replicate standard deviation 0.803 0.603 0.703 (21, page %)], cell correction factors are 0.804 0.604 0.704 of questionable value. 0,800 0.600 0.700 rl repeatability between duplicates of 0.799 0.601 0.700 u = 0.00077 on the optical density scale 0.802 0.600 0.702 0.800 0.601 0.701 is little more than the error to be expected in reading the scale of the in0.05 0.06 0.06 strument. Assuming one had the im0,800 0.600 0.700 probable ability to estimate with com0,800 0.600 0.700 plete accuracy to l/looth of a scale divi0.600 0.702 0.800 0.600 0.702 0.800 sion and would record the result in each 0.798 0.600 0.700 case to the closest of a scale divi0.799 0.600 0.701 sion, the error in reading the optical 0.600 0.699 0.800 density scale would be c = 0.00015, 0.800 0.600 0.702 0.00030, and 0.00058 a t optical densi-
1231
V O L U M E 23, NO. 9, S E P T E M B E R 1 9 5 1 Table 11.
Analysis of Variance of Results Reported in
Table I
"Blank" cell valuea were subtracted from corresponding values obtained for the other three oells in Table I. These differences were multiplied by ,lo00 (to avoid many deoimal places) and 2 was added to each value (to eliminate negative valuee). The resultini \-allies \!-ere itudied by analysis of variance. hliniDegree. Eatimum of Mean F-Test mated Errora, Freedom Squares Values u 7% Varintion betwew Cella 2 12.50 4.05 ... Blank settings e t different slit widths 8 3.26 2.89 ... Wave lennthe 1 33.00 3.14 ,., Interactionof ... 1t j 0 44 0.74 Cells by blank settinp.. , 0 . .53 10.50 17.72** 2.'26 Cells by wave lengths Blank settings b y wave 1 12 1.9 ... 8 len ths Cells %y blank settings by ... 16 0.31 0.53 ... wave lengths Variation betmen duplicate 0.18 , . . 0.77 54 0 59 roadinm 0
x
100
1.Iinirnum yoerror = 434dignificant at 6% level (0.002 P > 0.011. ** Significant at 1% level ( P 5 0.011
n
.
Table 111. Results Obtained by lpplying Approximate Method (2) to Testing of Three Primary Variables in Table I1 Variable ~ Teated _.__. _ _ Variatiom between Celln Blank settings JVttve leDgths
Mean square 42.50
Degreeof freedom. 2
3.25
Calcd. Value for Use in Testing Degreen of >lean freedom square 10.62 2.0 8.9 2.3
1.25 11.31
8
1
33.00
.
ties of O.oo0, 0.400,and 0.800, respectively. miiiimum relative error term
F-test value 4.00 2.60 2.92
This sets the
readings X 100 __ ok, = u- of ~ _optical _ _ _density _ optical drnsity reading a t approximately
-
u =
0.07% in tliiq optical density range
(Light intensity decreased for each subsequent pair of readings) Optical Densities F+d Tube Ultraviolet tube Red tube Reading -0.087 O.Oo0 0.087 O.Oo0 0.190 0.103 0.100 0.200 0.300 0.400 0.500 0,600 0.700 0.800 0.900 1.m
0.293 0,397 0.497 0.600 0.702 0,800 0 I910 1.02 1.11
0.206 0.310 0.410
0,513 0.815 0.713 0.823 0.93 1.02
In Figure 1 thc N iring diagram ot the Bcck6ian spectrophotometer ( 6 , 8) had becn preqented in a greatly abbwviated form to facilitate the understanding of its action. One mplifying stage is omitted to siniplify the appearance of the diagram.
PHOTOTUBES
VOLTS
.2 VOLT OP. DENSITY
- 2 VOLTS
Table 1V. Comparison of Responses of Two Phototubes E x p o d to Same Amounts of Light
PHOTOTUBE CIRCLJT
GALVANOMETER
4-20 V P L T S
density of 0.434. The mean of all the readings in Table I m ~ s sufficiently close to this value so that essentially the sitme result would he fiecured by using the value 0.434 in calculating these percentages. Above 0.800, the variation in the optical densities increased with the increase in the optical density values, and for this reason valuec above 0.800 were not included in this report. Belotv 0.800, thiq effect was small. Taken altogethei, the error factors listed in Table I1 amount to only u = 0.00238 on the optical density scale, or a minimum relative error of o.%570. Though somewhat above 0.170, thk value is seldom a basis for serious concern. Hogncss, Zscheile, and Sidwell ( I d ) report that over the entire wave-length range obtainable by this inqtrunient a variation of 0.5% is R reasonable agreement to euptrt from specially made and carefully matched quartz cells. In the use of microcells serious errors may i~mltfrom iinproperly centering the cells, or from an attempt to use a volume of liquid that is too small for the measurcnients. It is very simple to produc e a 20 to 50% error in either of these way^. In centering the mirrowll~,care must be exercised to make certain that reasonably cwirt agreement between cella is obtained over the total rang(%of *lit width settings.
4-
Figure 1. Simplified Wiring Diagram of Heckman Spectrophotometer Showing dark current a n d sensitivity a d j u s t m e n t s . A n electricnl s w i t c h (not shown) i s coupled w i t h the s h u t t e r i n the optical s y s t e m . I n t h i s way the % t r a n s m i t t a n c e (or optical density) c o n n e c t i o n is grounded whenever the s h u t t e r i s closed. T h i s i s equivalent to setting the optical densit>- scale reading a t infinity (8)
In order to evaluate the different sources of variation in approximately equivalent terms, it is necessary to establish a base for the calculation of percentages. As the magnitude of the variation is expressed as optical density, it was decided to use the optical density associated with the minimum error. Twyman and Lothian ( M ) reported this minimum error to occur a t an optical
There is a potential drop from about +20 volts to + I volt through the galvanonieter and tube, 5". The a o u n t of current flowing through the galvanometer depends upon the tential a t the control grid of this tube. In the other branch o&e circuit there is a potential drop of about 20 volts through the phototube and resistance, R. R is a very high resistance ( 2 x 109 ohms). The phototube resistance, de ending upon the intensity of incident light, varies b e h e e n vayues of this order and values many times higher [I X 1 0 ' 3 ohms ( 1 2 ) l . The grid thus occupies a position intermediate across this voltage drop. As light strikes the phototub(,, the internal resistance of the phototube decvases, increasing the otential on thc control grid. To twmpensate for this the totafpotential diop through the system tan be varied by adjusting the potentiometer knob, which has a scale calibrated in terms of optical d m s i t r or per cent transmittance values. It is thus found that the phototube response is directly balanced against a potentiometer. The potentiometer is very precisely linear. The phototube response is undoubtedly linesr over a certain region (14). If recise linearity is not obtained over the total legion from comprete darkness (dark current) up to and beyond the light intensities enrountered in normd analvtical work, one might well evpect to find that different phototubcs will give different answers. Within each instrument there is an opportunity to check this possibility directly. The Beckman spectrophotometer contains two hototubes: a red-sensitive tube for use above 600 mp, and an ugraviolet-sensitive tube for use below 625 mp. Halves (1.9) reports that the No. 2342-1 ultraviolet-sensitive tube in the Beckman spectrophotometer is a cesium-antimony phototube having a spectral sensitivity essentially like that of the RCA
ANALYTICAL CHEMISTRY
1232 Type 935 (S-5 response), and the red-sensitive phototube KO. 156 is essentially identical in spectral characteristics with the RCA Type 919 (S1 response). The two tubes can be used, and properly compared, in the region between 600 and 625 mp (8). The readings reported in Tables IV to X I were made at 610 mp, Most of these findings have been checked a t one or more additional wave lengths close to 625 mp; in each case substantially the same effects were noted. The direct comparison of phototubes was made in two xays. Table IV shows the results obtained when the two phototubes were exposed to thz same amounts of light.
A single quartz cell was filled with distilled water and placed in the instrument. It remained in osition, untouched, throughout the complete set of readings. T l e ulbraviolet-sensitive tube was moved into position, the dark current balanced, and the slit width adjusted so as to give an optical density reading of 0.000. Without changing the slit width or sensitivity setting the redsensitive tube was moved into position, the dark current was balanced, and the corresponding optical density reading was recorded. To vary the amount of light reaching the phototubes between each of these pairs of readings, the slit width was adjusted in much the same fashion as described for the work reported in Table I. Though in each case both phototubes were balanced so as to give identical dark current readings, the red-sensitive tube consistently gave higher values than those given by the ultravioletsensitive tube when both tubes were exposed to the same light intensities. Initially this difference was 0.087. As can be seen by comparing the first and third columns in Table IV, the difference did not remain constant, but increased with the optical density value. This increase amounted to 2.8% on the average. Part of this nonlinearity may have resulted from the slit width changes in this procedure. The relation between slit width change and linearity is considered below.
Table V.
Optical Density of Copper Sulfate Solutions at 610 mp (As determined with two different phototubes)
Ultraviolet tube and 0.24-mm. slit Density Average (x'1000) Red tube andb.-Z6imm.slit Density Average E:Fm,(X 1000) Difference between phototubes, %
9%
water
ctk
c%th
cusoi
0.000 0,000
0.082 0.083 82.5
0.247 0.247 82.3
0.741 0.744 82.5
0,000 0.000
0.086 0.086 86.0 4.1
0.256 0.257 85.5 3.7
0.762 0.763 84.7 2.6
...
...
0
Some six months later the above readings were repeated. I t was found that the initial difference was 0.123 on the optical density scale, and the increase with narrowing slit widths amounted to 3.3% of the optical density reading. The distilled water was replaced with 9% cupric sulfate (which has a strong absorption through the yellow and red) and then with 10% potassium dichromate (which has a strong absorption through the blue) and the above process was repeated. While the initial difference between phototube readings with the distilled water had been 0.123, with the cupric sulfate solution this initial difference was 0.172, and instead of increasing with decreasing light intensities this difference progressively decreased to the extent of 1.470 of the optical density reading. With the 1070 potassium dichromate solution the initial difference was 0.179, and again this difference decreased with narrowing slit widths to the extent of 2.170 of the optical density reading. These discrepancies suggest the possibility of: a nonlinearity of instrumental response, a small change in that response with respect to time, and scattered light effects causing measurable changes in results. Another comparison of the phototubes was carried out under conditions which are closer to those used in routine work with this instrument.
Three copper sulfate solutions, 1.000, 3.000, and 9.00%, were prepared and were placed in the instrument together with a distilled water blank. Readings were made a t 610 mp with each phototube. Before each set of readings the phototube circuit was carefully balanced both for dark current and for 100% transmittance (with distilled water). The sensitivity knob remained three turns from the clockwise limit and the slit width was adjusted as required. The procedure followed was that used in routine analytical work with this instrument (6). The results are shown in Table V. The difference in E:?m. values given by the tn-o phototubes is again seen to be around 3%, though this difference is not constant for solutions of different copper sulfate concentration. Further insight into the nature of these differences may be obtained by a consideration of Tables VI and VII. Table VI. Effect of Changing Slit Widths, Phototubes, and Copper Sulfate Solution Concentrations on Measurement of E:%e,.(X 1000) at 610 mp Ultraviolet-Sensitive Tube Slit >vidth, Concentration mm. 1% 3% 9% 0.24 82.5 82.3 82.5 0.28 83.0 82.7 82.2 0.32 83.5 83.7 83.3
Table VII.
Red-Sensitive Tube
::&, mm. 0.26 0.30 0.34
Concentration 1% 3% 9% 8 6 . 0 85.5 8 4 . 7 8 7 . 0 8 8 . 7 85.9 8 8 . 0 8 8 . 2 86.8
Summary of Analysis of Variance Findings Obtained from ,Data of Table VI
[F-test values for first three terms obtained by composite method ( B ) ] Degrees Estiof Mean mated Freedom Square F-Test Source u Mean Variation between 2 3.96 3.36 ... Slit widths 2 1.36 1.51 ... .. Concentrations 1 6 7 . 2 9 57.03* 2 . 7 3 3.23 Phototubes Interaction of Concentrations by slit 0.30 1.43 widths Slit widths by photo1.18 5.62 tubes Concentrations by 0.90 4.29 phototubes Concentrations by slit 0.21 0.46 0 .54 widths by phototubes * Significant at 5% level (0.05 2 P > 0.01). ** Significant at 1% level ( P 5 0.01).
e
...
...
...
...
..
To obtain the data in Table VI the effective intensity of the initial light source was varied by inserting a variable aperture between the lamp housing and the monochromator case. As the effective intensity of the light source decreased, the slit width in front of the cell was increased to bring the instrument back into balance. This allowed the work to be repeated with different slit width openings. In the case of the red-sensitive phototube the wider the slit width adjustment required, the higher the E!?m. value obtained, That this did not also hold true for the ultraviolet-sensitive tube, however, may be seen in Table VII, in which it is noted that the between-slit-widths variation is nonsignificant, The average values shown were obtained from duplicate sets of measurements made in succession. During all these readings the same solutions remained in the instrument. Table VI1 summarizes the sources of variation in the data of Table VI. The concentrations by slit widths by phototubes interaction, amounting to u = 0.54y0, gives an approximation of t h e repeatability between duplicate measurements. In order to compare this value with the minimum error value obtained in Table 11, it should be corrected for the use of averages and comDared with the same mean value. This gives a value of u = 0.54 x 4 5 x 100 = 0.18%. The F-values for the other effects 434 were determined by the composite method ( 2 ) . Only the difference between phototubes, u = 3.23%, was significant. The effect of changing the intensity of the light source had no signifi-
V O L U M E 23, NO. 9, S E P T E M B E R 1 9 5 1 Table VIII.
Summarv of Results Obtained when analysis of variance was applied t o K values ( X 100) of
Ewing a n d Parsons ( I O ) at two wave lengths. D a t a used are from seven instruments for which a t least four replicate values are presented. As two of the interaction terms in the analysis are significant, the approximate method ( 8 ) is used to test the first three sources of variation Degrees u x 100 of Mean F-Test mated Source Freedom Square value u Mean Variation between Instruments 6 299.33 8.00** 5.72 1.09 Samples 3 12.67 0 . 9 2 ... ... Wave lengths 1 653,184.00 29,300a*** ,, ... Interaction of Samples b y instruments 18 16.11 4.75** 2.52 0.48 Instruments b y wave lengths 6 24.67 7.28** 2.31 0.44 Samples b y wave lengths 3 1.00 0.30 ... ... Samples b y instruments b y wave lengths 18 3.33 ... 1.82 0.35 * Significant a t 5% level (0.05 2 P > 0.01). ** Significant a t 1% level {P 5 0.01). a Not meaningful in this instance; see text.
.
cant effect in the over-all case. Houever, this apparent lack of difference may have been due to the fact that the two tubes b e haved differently in this respect. Considering the values from the rad-sensitive tube by themselves, a tentatively significant effect resulting from this change in light source ( F = 11.01’ with 2 and 4 degrees of freedom, for which O.OB > P > 0.01) was found which amounted to a 1.32% error. A difference between a series of ultraviolet-sensitive phototubes was reported by Ewing and Parsons (IO). Their data were studied by analysis of variance methods, and the results are summarized in Table VIII. The repeatability of duplicate readings in this work, as measured by the final iiiteraction term, was u = 0.35%. The variation in K-values for the different instruments between wave lengths is easily seen in their data by noting that the instrument reporting the highest K,,,. is not t.he one reporting the highest Kmin,,etc. This instruments-by-wave-lengths interaction points out an inconsistency in instrumental response which results in an additional error of u = 0.447,. The variation with sample values between the different instruments was u = 0.48%. This is effectively a direct estimate of the mechanical errors in making up solutions for these readings in the different instruments, and is in rough agreement with their estimate of “considerably less than 0.5%.” The variation betmen instruments was u = 1.09%. Consistent interlaboratory differences in glassware, state of sample, etc., could conceivably account for all or part of this error. However, in view of the large variation found between different phototubes (see Table VII), it is considered more probable that this 1.09% represents a direct measure of the variation to be expected between a series of ultraviolet-sensitive phototubes. The between-wave-lengths mean square is marked as being not meaningful in this case. As K,,,. and &,in, are known to be different, the significance of this effect adds no useful information to thz analysis. Even larger variations were noted in the data reported by Kemmerer (15) from a collaborative assay of the Association of Official Agricultural Chemists. Four Beckman spectrophotometers (collaborators 7 , 10, 12, and 13) were checked a t three different wave lengths with 0.02% potassium chromate. On submitting these data to analysis of variance it was found that the between-instruments mean square was significant ( F = 7.52* with 3 and 6 degrees of freedom for which 0.05 > P > 0.01), and this amounted to a u = 5.37% error. Again, consistent errors in making up solutions may account for a portion of this error. Aside from this term, however, there was an instruments-by-Jyavelengths interaction of u = 3.6icG error. DARKCURRENT
The dark current must be very constant before one can expect to obtain useful readings. If it is erratic or drifting rapidly,
1233 there is little point in proceeding further until this condition has been corrected. Dark current stability is strongly dependent upon the condition of the hatteries. Two well-charged storage batteries connected in parallel are used as a source of power. In locating a source of instability, the lamp and battery connections should not be overlooked. One useful test is to move each of the wires and connections back and forth slightly, and notice if this procedure has any effect upon the galvanometer needle. Battery terminals and clips should be cleaned and checked frequently. Rawlings and Wait ( 2 0 ) reported that the first sign of failure of the B batteries was an erratic response which results in a fivefold increase in replicate standard deviation. During most of the present work there was a slow but consistent dark current drift which amounted to between 1.0 and 1.7 scale divisions in 5 minutes. Under these conditions there is but small chance of large random errors resulting from dark current drift. A reasonable question may still be raised concerning the possibility of introducing consistent errors into the results by an inexact adjustment of the dark current setting. Table I X shows the
Table IX.
Change in Reading Due to Error in Dark Current Balance
Values are expressed as per cent deviation from readings obtained when dark current was correctly balanced. Dark current balance point values are in scale divisions t o the right (+) or left ( - ) of center Concn. of CUSOI Dark Current Phototube 1% 37, 9% Balance Point Sensitivity Knob at Clockwise Limit Ultraviolet -0.8 -1.1 -0.2 - 10 +0.4 -0.3 +0.9 10 Red 4-0.4 4-0.4 -1.4 - 10 +0.8 +0.7 +1.5 10 Sensitivity Knob 7 Turns from Clockwise
+ +
Ultraviolet Red
-1.9
f2.3
-2.9 f3.8
-2.9 $1.8 -3.6 4-4.0
-5.3 +3.8 -6.7 f7.6
+-- 101010
f10
effect upon a set of values resulting from adjusting the dark current slightly to the right or left of zero, and then proceeding to make readings as though it were correctly set. The sensitivity adjustment was set 7 turns from the clockwise limit. On the average, an error of 3.995 per 10 scale divisions (or 0.4% per scale division) resulted from a drift or an inexact adjustment of the dark current. I t was possible to reduce this error to nearly one fifth of this amount by working with the sensitivity set a t its clockwise limit. These sensitivity settings fall on both sides of the recommended setting (6). There was a noticeable difference in the rate a t which the two phototubes warmed up and became stable. The red-sensitive phototube adapted to changes in light intensity somewhat more rapid]) than its ultraviolet-sensitive partner. This was particularly true in adjusting the dark current, or in working with very low light intensities. Routinely, after the instrument warmed up, the dark current drift was checked and about 90 seconds were allowed for the dark current to become stable and to be brought into exact balance. rlbout 30 seconds were allowed for stabilization before each reading was taken. In such a system of operation it is conceivable that the differences noted between phototubes could be traced to a consistent difference in dark current balance, resulting simply from the difference in the rate a t which the two tubes adjust to darkness. I t was hoped, however, that these periods were sufficiently long to minimize any such effect. Since, as seen in Table I X , there is a manyfold change in the effect of dark current imbalance as the sensitivity setting is changed by a large increment, one way of checking this point would be to compare the readings given by the two tubes a t widely different sensitivity settings. Thus, if the differences noted between phototubes can be attributed to a difference in
ANALYTICAL CHEMISTRY
1234 ..
~
~~
~
~~
~~
-~ c u s z i o t i - of s p e c t r o p h o t o m e t r > -o r
Table X.
Effect of Changing Sensitivity Settings upon E:?,. Values
( X 1000)
errore in colorinietric methods, the error due to turbidity varrants further attcsn(For CUSOIsolutions at 610 m r . Each w r i e i- mean of three readings) tion. Red hiinus Comparing the values in Tablc \‘I UltravioletUltraviolet with the values in Table XI for the new ___ Sensitive c ~Tube. - - - .___-___. Ked-Sensitire Tube __ Values Position of Slit u s 0 1 Concn. . slit CuSO4 Concn. CuSOa Concnstandard or the centrifuged old sttlnd:ird, Sensitivity Knob xidth 1% 3% 9% width 1% 3% 9% 1% 3% 9% it was found that, significant instrumental Clockwise limit 0 34 88.0 85.6 83.4 0.41 9 2 . 0 89.8 87.1 4 0 4 . 2 3.7 changes had taken phce Over the &c 31/2 turns from elockwise limit 0 . 2 2 89 0 86.3 8 4 . 5 0 29 9 0 . 7 8 9 . 1 87.0 1.7 2.8 2,: nlont]~ period. The nature of t,h,tse 7 turns from clockwise limit 0 . 1 7 8 8 . 0 86 0 8 5 . 6 0.20 80.0 87.9 85.4 1.o 1 9 - 0 .~ .2 changes v a s verv different in the caw of the trvo phototubes-which is additional .-__ proof that the changes noted are attribTable XI. Comparison of E:?,. ( X 1000) Values utable to the instrument and not the (From t x o different sets of CuSOa solutions at 010 solutions. \Vhen the readings taken with the red-sensitive t i h e hefore and after centrifuging) were considered, the between-periods mean square w&s signiiiUltravioletKed-Sensitive cant a t the 5% level [V, = 30.3 for which, by the composite Sensitive Tube -. Tube 1% 3% 9%’ 1% 3% 9% nirtliod ( 2 ) ,F = 10.58*with 1 and 3 degrees of freedom]. In the case of the readings made with the ultraviolet-sensitive tube, Beforu centrifuging Old standarh 88.0 8 6 . 0 83.2 88.0 87.2 84.8 the between-pcriods mean square was definitely nonsignific-ant Xes standards 85 0 83.7 81.2 8,5.0 83.5 8 4 . 2 ( V p = 0.02 for which F < 1.0); hoqever, the concentrations-hyAfter centnf uging Oldatandards 8 4 . 0 83 0 8 2 . 3 81 0 84 3 83 2 periods interaction mean square was significant ( V , = 0.795 for S e w standarde 8 4 . 0 82 0 8 2 . 4 81 0 83 8 83 8 which P = 5.75* with 2 and 6 degwes of freedom). Thus, oae may conclude that in the, case of the red-sensitive tubc the values decreased by 2.00% in a more or less parallel fadiion, in the case of the ultraviolet-senuitive tube there wytli: no and dark current balance, this difference should increase as the sensichange in mean value orei, this &month period, but thcre tivity setting is changed toward the counterclockwise limit. was a significant change in the linearity of the instrumental r e Table X shows the results obtained when this was tried. The xponse which manifested itself as an apparent failure of the soluchange in Bensitivity setting tov ard the counterclockwise limit t.ions to obey Beer’s law. This can r d i l y be seen by inspectiou made the lack of agreement progressivelr le-, instead of more of the data. This change in linearit). amounted to an error of pronounced, u = 0.63%. Two factors have been suggested (12) as causes of the effect. I t has been reported (18) that concentrated cupric solutiolis noted in Table X: ( a ) “. . , effective wavelength displacement do not obey Beer’s law. Table X and the data from the redis an inevitable accompaniment of the cmployment of finite slit sensitive phototube as reported in Tables V and VI would tend widths and continuous sources . . . , I ’ and ( b ) “another significant to confirm this; however, the rest of the data i n Tables V and \’I cause for the discrepancies seen is variatious in the sensitivity must be taken as evidence to the contrary. Before one can claim of the photo cathodes from one area to another.” The suggestion that a chemical system shows (or does not show) a deviation from that to correct for these factors the results should he extrapolated Beer’s law, he niust be ready to prow that the observed nonliticarto zero slit width is considered below. ity does not arise from within the instrument used. A further example of the nonlinearity of response in the H i ~ k CHANGES WITH TIME inan spc.ctrophotometer has been reported by Vandenbelt ri al. ( 2 3 ) . In their data the same tj-pe of rionlincarity is found ill the -4 comparison of the values in Table X with those in Table VI case of five very different chemical compound..: two organic wnifurther raises the question of changes in instrumental response pounds in ethyl alcohol, tivo inorganic. salts in water, and onr n:itwith respect to time. The readings were all made with the same ural product,. Again, this nonliiiearit~~would appear ti) i)e solutions, but 8 months had intervened between the readings in characteristic of their instruincnt rather than of the compounds. Table VI and those in Table X. The solutions had been careIn all five cases this error amounts to a 4 to 5% deviation from fully kept in glass-stoppered bottles during this time. It would linearity for readings taken at 0.1 to 0.4 on the optical delisit\appear as though a change in instrumental response had taken scale. and runs as high as 10 to 15c:, error for values below 0. I place which resulted in a 2 to 47, change in extinction coefficient. To check the constancy of these standards another set of copper DISCUSSION sulfate solutions was made up. A comparison of the old and new standards is ahown in Table XI. Table S I 1 summarizes the Bources of variation that have lrcrn On one occasion, when the old copper sulfate solutions were discussed. It is recognized that each of these values is an cstiallowed to stand in the instrument for several hours between two mate, and that many more measurements of this type carried out sets of readings, slightly lower values were obtained in the second on a large series of instruments may be required before it call be set of readings. This suggested that a settleable turbidity might stated with certainty how representative these values are. LIany have developed in these solutions during the 8 months of standthings that have been found true of the Beckman quartz spectroing in contact with glass. Both the new and the old solutions photometer may hold true t o an ?qual or greater extent iii the were centrif‘uged for 20 minutes in a clinical centrifuge and the case of other instruments. readings were repeated. Though initially the newly prepared There is fairly good agreement between the different estiiiiates solutions gave slightly lower readings than the older solutions, of replicate variation in Table XII. \\-ith care, the variation between duplicate readings made under ideal conditions is u = this difference disappeared when the solutions were centrifuged before comparison. The turbidity present in the older solu0.1 to 0.270 when the optical density reading is around 0.4 to tions was too slight to be noticed easily, but resulted in an error 0.5. In most analytical work this variation may be somewhat of u = 0.90%. In practice, this interference due to turbidity higher. To take this value, the smallest source of variation may be of considerably more importance than such items as listed in Table XII, as representing “the error of the instrument” small cell corrections. Though generally ignored in past dismay be very misleading. The sizable difference between preI
V O L U M E 23, NO. 9, S E P T E M B E R 1 9 5 1 cision and accuracy in photoelectric colorimetry has long been recognized (22). Such a representation, however, is all too com~ errors. mon in reporting method errors as well a . instrumental The largest sources of instrumental variation were found to be a-Ysociated with the phototube circuit. The variation between red- and ultraviolet-sensitive phototubes (u = 3.23%), the variation between a series of different ultraviolet-sensitive phototubes (u = 1.09 and 5.37%), the difference between results obtained from the same phototube a t two different times ( u = 2.00 and 0.63oJ,),and perhaps also the terms associated with changes in light intensity, slit width, and wave length are examples of this. It must be remembered, when attributing errors to the phototube, that each component of the instrument has been studied in the presence of all the other components. The performance of a phototube is dependent upon circuit potential ( I @ , size of phototube coupling resistor (18), slit width (12). the level of scattered light (8), and perhaps other in4mmental factors. Such variables as differences in spectral distribution of lamp energy with age, battery voltage, lamp focus, or changes in stray light within the instrument due to aging of the optical surfaces, may be responsible for changes In “phototube response.” Thus, the variations attributed to a comporient may, in certain rases, be better explained in t e r m of the may that component ii uqed within the instrument. The actual physical mechanisms involved are left to further work The primary interest, here, is in evaluating the over-all inqtruniental response, and it, effcct upon analytical error
Table XII.
Summary of Error Terms
(Valuea are standard deviations expressed in per cent relative error) yo Error Variation between Red- and ultraviolet-aensitive ultraviolet-sensitive phototubes 3 . 2233 fioiirrm 1 . 32 Lieht Light sources 32 Slit widths (for Slzw
