ANALYST, SEPTEMBER 1991, VOL. 116 909 Generalized Treatment of a Stray Radiant Energy Test Method in Absorption Spectrometry Paddy Fleming Sligo Regional Technical College, Ballinode, Sligo, Ireland The test method of Mielenz et a/. used t o determine the relative stray radiant energy (SRE) level in spectrophotometers is generalized for all sample cell t o reference cell thickness ratios greater than unity. It is extended further t o include situations where the required ‘cut-off solution is not transparent t o the SRE. The experimental SRE value which ensued by applying the above method t o a Shimadzu 260 ultraviolet/visible spectrophotometer is reconciled with the corresponding experimental values arising from two other SRE test methods. Keywords: Spectrophotometer; stray radiant energy; cell pathlength ratio In this paper a method for determining the relative stray radiant energy (SRE) in ultraviolet/visible (UVNIS) spectro- photometers’ is generalized to include all sample cell to reference cell thickness ratios greater than unity and instances where the transmittance of the ‘cut-off‘ solution to SRE is not necessarily unity.The modified test method was used to determine the relative SRE level in a Shimadzu 260 spectro- photometer at a Mielenz peak1 wavelength of 654 nm and with its spectral slit-width set at 1 nm. The exercise was repeated for the same instrumental conditions by using Fleming’s transmittance ratio spectrometry method’ and Fleming and O’Dea’s direct transmittance method.3 Fleming’s SRE test method’ is based on transmittance ratio spectrometry and it may be regarded as the opposite side of the same coin as the test method of Mielenz et al.1 Both test methods measure the differential absorbance of a solution placed in the sample beam relative to an identical solution placed in the reference beam while the sample cell is thicker than the reference cell.The Mielenz method gradually increases differential absorbance by wavelength scanning through the leading or trailing absorbance edge of a cut-off solution which has been placed in both the sample and reference beams, whereas the transmittance ratio method is carried out at a fixed wavelength while differential absorbance is gradually increased by advancing the concentration of the solution held in the sample and reference beams. The differential absorbance for both methods will not increase indefinitely but will peak at a value determined by the relative SRE level of the spectrophotometer, the cell pathlength ratio employed and the SRE transmittance of the test solution.The direct transmittance SRE test method involves determining the actual absorbances ( A ’ ) of a series of concentrated solutions the monochromatic transmittances of which are at least a factor of 50 lower than the relative SRE level to be determined. Although the Mielenz test method is presented here in a generalized form in order to accommodate the attenuation of the SRE by the sample, that attenuation must be determined independently. Fleming and O’Dea’s direct transmittance SRE test method3 yields accurate estimates of both the SRE and the attenuation of the SRE by the sample, and if the attenuation of the SRE by the sample is known then it may be used in the Mielenz method to give a further accurate estimate of the SRE, provided the same sample type is used under identical instrumental conditions in both the test methods.The terms relative transmittance and differential absor- bance are used synonymously in the text. Formulation of Experimental Quantities If the same cut-off solution is placed in the beams of a double beam, ratio recording spectrophotometer but the sample cell is a-times as thick as the reference cell (a = b,/b,, where the subscripts s and r refer to the sample and reference beams, respectively, and b refers to the pathlength of the cells employed) then the transmittance of the sample beam solution relative to the reference beam solution, t’, in the presence of a relative SRE level of s is given by (1) tf + svff t’=- th + sv where th is the monochromatic transmittance of the reference beam solution and v, which may be weakly dependent on A, is its transmittance to SRE.When scanning through the absorbance edge of the cut-off solution a relative transmittance minimum, i.e., t’ (min) = t”, will be encountered1 at th = T . If the derivati used, i.e., setting dt’/dth equal to zero at = T , gives Tm + svm = ( T + S V ) ~ T ~ - ~ Solving for s in eqn. (2) gives (a - 1)Tm V“ - ( ~ v T f f - 1 S = However, the spectrophotometric observable ii e method is hen eqn. ( 1 ) ( 3 ) this experi- ment is not Tbut t”.Ifthe expression for s given by eqn. (3) is substituted into eqn. (l), simplified and rearranged, then the following ensues: T = (~“/a)1/(&-1) (4) Eqn. (4) may now be substituted into eqn. (3) to give (a - l)(T”/a)m’(ff-’) S = vff - vt” Eqn. (5) is an exact general expression which relates the relative SRE level (s) to the Mielenz relative transmittance minimum (t“), transmittance of the reference beam solution to SRE ( v ) , and sample cell to reference cell thickness ratio (a). The SRE transmittance was assumed to have remained constant over the spectral range covered by scanning through a Mielenz peak. The transmittance ratio ( r ) at wavelength h of a sample beam solution the cell pathlength of which is a-times greater than an identical reference beam solution is given by2 where p is the SRE transmittance of the reference sample the monochromatic transmittance (th) of which is 0.1 and Ah = -log th.This transmittance ratio function has a minimum, r(min) = p, at a certain monochromatic reference910 ANALYST, SEPTEMBER 1991, VOL. 116 transmittance, TL = t , which is determined by s, p and a. If p is taken to be unity, then, by using the derivative method, an expression may be derived2 which relates the relative SRE level to p and a (7) (a - 1) (p/a)a’(-l) 1 - P S = However, p is less than unity and its experimental value must be determined independently before eqn. (6) may be numeri- cally modelled for a selected value of a and trial relative SRE values. The trial relative SRE value which, when inserted into eqn.(6) for zh values in the range 1 d rk d O.lt, gives the best match with experimental transmittance ratio measurements may be taken as the best estimate for the said relative SRE level. The direct transmittance SRE test method3 allows for the direct determination of p and s through observing the actual transmittances (T’) of an arithmetic series of concentrated solutions the monochromatic transmittances (T~) of which are less than 0.02s. The relationship between T’, s, p and ‘ch is then given by (where Ah = -loglOth) (8) (9) T’ = spAk Taking the loglo of eqn. (8) gives log1oT’ = Iogl@ + Ah loglop At these very high monochromatic absorbances eqn. (8) is a linear relationship between logloT’ and Ah with a slope of loglop and an ordinate intercept of logl$. Experimental All the spectrophotometric measurements reported here were made with a Shimadzu 260 double-beam spectrophotometer at a spectral slit-width setting of 1 nm.Matched pairs of 1,2,5, 10, 20, 50 and 100 mm quartz-glass cells were at hand. Therefore, various nominal sample to reference cell pathlength ratios were possible and the following nominal values were used: 2 (= 10/5 and 20/10), 2.5 (= 50/20), 4 (= 20/5) and 5 (= 50/10). The working solutions were obtained from a 50 g 1-1 Orleans Blue food dye (E123) stock aqueous solution. The UVNIS absorption spectrum of 10 g 1-1 of the same solution in a 1 mm cell was given previously.2 An arithmetic concentration series of the parent solution was prepared. The most dilute and concentrated members had monochromatic absorbances of 0.025 and 0.5, respectively, in a cell of pathlength 1 mm at 654 nm and the arithmetic series had an absorbance increment of 0.025.This yielded a set of 20 solutions the monochromatic absorbances of which, at 654 nm, ranged from Amin to A,,, [incremented in steps (AA)] in various cell pathlengths (b) as follows: Amin + (AA x 19 steps) = A,,, in a b mm pathlength cell 0.025 + (0.025 x 19 steps) = 0.5 in a 1 mm pathlength cell 0.050 + (0.050 x 19 steps) = 1.0 in a 2 mm pathlength cell 0.125 + (0.125 x 19 steps) = 2.5 in a 5 mm pathlength cell 0.250 + (0.250 x 19 steps) = 5.0 in a 10 mm pathlength cell 0.500 + (0.500 x 19 steps) = 10.0 in a 20 mm pathlength cell 1.250 + (1.250 X 19 steps) = 25.0 in a 50 mm pathlength cell The experimental cell pathlength ratios were determined by measuring the absorbance at 630 nm of a dilute Orleans Blue food dye (E123) solution in all the available cells and this yielded the following relative pathlengths: 1.00 & 0.008; 2.00 k 0.013; 5.00 -t 0.017; 10.00 k 0.013; 20.01 k 0.013; and 50.00 k 0.039.The Mielenz test method was applied repeatedly to the Shimadzu 260 spectrophotometer by scanning slowly in the range 750 3 h(nm) 3 625, the spectral slit-width having been 3 2 1 0 625 650 675 700 725 ( b) 2 Sample concentration increasing 4 625 645 665 685 705 725 625 645 665 685 705 725 Wavelengthlnm Fig. l(a) Four Mielenz differential absorbance spectra in the wavelength range 725 3 h(nm) 3 625 for nominal cell pathlength ratios ((Yb) of A, 2; B. 2.5; C, 4; and D, 5. The Orleans Blue food dye concentration IS gradually increased with decreasing (Y values so as to maintain the Mielenz peak at 654 nm.( b ) Six Mielenz differential absorbance spectra in the range 725 3 h(nm) 3 625 for a nominal cell pathlength ratio ((Yb) of 2. (c) Four Mielenz differential absorbance spectra in the wavelength range 725 3 h(nm) 3 625 for nominal cell pathlength ratios ((Yb) of A , 2; B, 2.5; C, 4; and D, 5 , and for a fixed concentration of Orleans Blue food dye set at 1 nm. A food dye test solution had been placed in a pair of matched quartz cuvettes the nominal pathlength ratio of which was 2 (a = 10 mm : 5 mm). The ensuing differential absorbance spectra displayed the expected SRE Mielenz peaks at 654 nm. The monochromatic absorbance of the test solution at 654 nm in the 5 mm reference cuvette was 2.0 and the Mielenz peaks had an average absorbance of A” = 1.680 k 0.005.Eqn. (4) predicts that if the absorbance of the reference sample in the Mielenz SRE test method (-log T ) is 2 and a is 2, then the absorbance of the Ivlielenz peak should be 1.699 (-log t”). If a more concentrated member of the prepared Orleans Blue food dye test solutions had been used in the above experiment then the Mielenz peak would have occurred at a longer wavelength. The Mielenz analysis, s = 0.25 x 10-2A”, which is only applicable for a = 2, yields a relative SRE level of 0.000113 for the above experiment while eqn. (5); for v = 1 and a = 2, yields s = 0.000116. If the MielenzANALYST. SEPTEMBER 1991. VOL. 116 91 1 peak is to occur at 654 nm for all a values, then a priori knowledge of the absorbance of the test solution in the reference cell at 654 nm (-log 7) is necessary for each a value. A value for T" for a given a may be calculated using trial values for T" in eqn.(5) and assuming s = 0.000116 and v = 1. Eqn. (4) may then be employed to predict the appropriate approximate absorbance of the test solution which, when placed in the sample and reference cells, will give a Mielenz peak at 654 nm, e.g., if s = 0.000116 and a = 2.5, then t" = 0.0085 satisfies eqn. ( 5 ) for v = 1, and eqn. (4) yields T = 0.0226 or -log T = 1.646. This calculation procedure was executed in turn for a = 2.5, 4 and 5 and was facilitated by having prior knowledge of the absorbance of the Mielenz peak (A") at 654 nm which ensued from scanning the differential absorption of a selected food dye sample for CY = 2.The Mielenz test method was replicated for a = 2.5, 4 and 5 by using the food dye sample of appropriate concentration for each a and then eqn. (5) (with v = 1) was used to calculate the relative SRE level. The resulting Mielenz differential absorbance spectra are given in Fig. l(a). The Mielenz peaks occur at approximately the same wavelength (654 k 0.5 nm) for all cell pathlength ratios used but increase in amplitude as Q/ increases. Fig. 1 (b) displays six Mielenz differential absorbance spectra which were obtained for a constant nominal cell pathlength ratio of 2 (= 10/5) and by changing the sample concentration in the cuvettes for each scan. Note the red shift of the Mielenz peaks which occurs with increasing sample concentration.Fig. 1 ( c ) displays four Mielenz differential absorbance spectra which were scanned for constant sample concentration 0 1 .o 2.0 3.0 Monochromatic reference absorbance Fig. 2 Four plots of the differential absorbance versus the monochromatic reference absorbance of an arithmetic concentration series of Orleans Blue food dye (E123) solutions placed in pairs of cells the pathlength ratios (ab) of which were: A. 2.001; B, 2.499; C, 4.00; and D, 5.00. The measurements were made at 654 nm and with a spectral slit-width of 1 nm in the cuvettes and by changing the cell pathlength ratio between the following nominal values: 2 (= 10/5), 2.5 (= 50/20), 4 (= 20/5) and 5 (= 50/10). Note the red shift of the Mielenz peaks which occurs with increasing a values.Fleming's transmittance ratio2 and Fleming and O'Dea's direct transmittance3 SRE test methods were also applied to the Shimadzu 260 spectrophotometer set at 654 nm and a spectral slit-width of 1 nm. The ensuing experimental determinations are plotted in Figs. 2 and 3. The above mentioned food-dye concentration series was appropriately employed in both tests. Fig. 2 displays differential absorbance versus monochromatic reference absorbance plots for four cell pathlength ratios, a = b,/b,. The experimental cell pathlength ratios are as follows: 20.01/10.00 = 2.001 f. 0.005; 50.00/20.01 = 2.499 k 0.004; 20.01/5.00 = 4.00 k 0.016; and 50.00/10.00 = 5.00 f. 0.01. Fig. 3 is a plot on semi-log axes of the observed average transmittance (in 20 mm pathlength cells) of solutions ( T ' ) at 654 nm versus the respective monochromatic absorbance ( A ) in the range 0 d A d 10.0.The exponential regression equation of fit to the linear part of the plot in the upper absorbance range is given by T' = 0.000140 x lO-0.029A. Results Eqns. ( 5 ) and (6) cannot be applied to the differential absorbance maxima in Fig. l(a) and (b), respectively, without a priori knowledge of the transmittances of the samples to SRE at the wavelength of interest. The quantity 'v' in eqn. ( 5 ) is given by PA, where A (= -loglo7) is the monochromatic 100 L - a, 10-1 0 c m c .- E 10-2 2 10-3 2 8 10-4 10-5 m t 4- Q, m 0 2 4 6 8 10 Monochromatic absorbance (A) Fig. 3 Plot on semi-log axes of the observed transmittance (T) versus the monochromatic absorbance ( A ) at 654 nm and with a spectral slit-width of 1 nm.The measurements were made in a pair of matched 20 mm quartz cells with a Shimadzu 260 spectrophotometer. The analyte samples were dilutions of a 50 g I- Orleans Blue food dye in distilled water. The monochromatic absorbance range, 7 d A d 10, yielded s = 0.000140 and p = 0.935 Table 1 Relative SRE level in a Shimadzu 260 spectrophotometer set at 654 nm and a spectral slit-width of 1 nm using a revised Mielenz er af.' and the transmittance ratio spectrometry2 test methods Cell pathlength ratio. a(= b,lb,) 2.001 f 0.005 2.499 -t 0.004 4.00 k 0.016 5.00 k 0.01 Mielenz's peak absorbance at 654 nm (- log,oT") 1.68 2.08 2.73 2.94 Monochromatic reference absorbance at 654 nm (-logloT) from eqn.(4) 2.00 1.65 1.10 0.90 Relative SRE level [s( x ? 0.101 from eqn. ( 5 ) ( a ) for v = 1 1.12 1.12 I .08 1.14 ( h ) for v = 0.9354 1.53 1.51 1.46 1.55 from eqn. (7) and Fig. 2 maxima 1.04 1.01 1.14 1.13 from eqn. (6) for p = 0.935 in Fig. 2 1.35 1.25 1.45 1.40 Relative SRE level [s ( x 10-4) k 0.101 Relative SRE level [s ( x 10-4) f 0.101912 ANALYST, SEPTEMBER 1991, VOL. 116 transmittance of the samples employed was assumed to be unity. The direct transmittance SRE test method of Fleming and O’Dea,3 which allows for the non-transparency of the samples towards SRE, yielded an SRE value of 0.000140 -t- 0.000015 for the Shimadzu 260 spectrophotometer at 654 nm and a spectral slit-width of 1 nm. This was significantly greater than the average SRE values of 0.000112 -t 0.000010 and 0.000108 Ifr 0.000010 which were obtained by the two other test methods mentioned, based on calculations using eqns.( 5 ) and (7), respectively, for v = p = 1 and using four distinct cell pathlength ratios. These results may be reconciled with the direct transmittance SRE test method result if the SRE transmittance value yielded by the last test method, i.e., p = 0.935, is employed in eqns. (5) and (6). Eqn. (5) with p = 0.935 gave s = 0.000151 k 0.000010 and eqn. (6) with p = 0.935 gave s = 0.000136 k 0.000010 from the curves of best fit to the experimental points in Fig. 2. The three test methods gave relative SRE levels which agree within the experimental error, provided allowance is made for the absorption of the SRE by the test solution being used.However, only the direct transmittance SRE test method is self-contained in that it yields all the information required to specify the true relative SRE level in a spectrophotometer without having recourse to any other test method. absorbance at 654 nm of the reference beam sample used in the method of Mielenz et al. and p has been defined in eqn. (6). However, eqn. (8), applied to the linear portion of the upper absorbance range of Fig. 3, yields the following experimental values for p and s: p = 0.935 k 0.015 and s = 0.000140 k 0.000015. If the monochromatic absorbances at 654 nm of the reference beam samples are known, then eqn. (5) can be applied to the maxima in Fig. l ( a ) to yield the relative SRE levels recorded in Table 1.Eqn. (6) can then be used to generate four sets of data points, i.e., a matching set of data points for each set of experimental differential absorbance points in Fig. 2, through using trial s values for the relative SRE level and a setting p = 0.935. The ensuing simulated curves are traced in Fig. 2 and the optimum trial relative SRE values are listed in the bottom row of Table 1. Conclusion The original purpose of this paper was to generalize the theoretical basis of the SRE test method developed by Mielenz et al.1 so as to embrace all cell pathlength ratios greater than unity. The generalized theory was tested experimentally in this paper for four disparate cell pathlength ratios to yield relative SRE levels for a Shimadzu 260 spectrophotometer which agreed within the limits allowed by the experimental errors involved [see Table 1 for eqn. (5) and v = 11. However, the test method, being sample based, would underestimate the relative SRE levels in spectrophotometers if the test solutions absorbed the SRE. This postulate was tested in this paper by comparing the relative SRE levels in a Shimadzu 260 spectrophotometer determined in three semi-independent ways under identical instrumental conditions. The SRE test methods of Mielenz et al.1 and Fleming2 yielded compatible SRE results if the SRE References 1 Mielenz, K. D., Weidner, V. R., and Burke, R. W.,Appl. Opt., 1982, 21, 3354. 2 Fleming, P., Analyst, 1990, 115, 375. 3 Fleming, P., and O’Dea, J., Analyst, 1991, 116, 195. Paper IlOO489A Received February 4th, 1991 Accepted April 29th, 1991