Luminescence Quantum Yields. An Analysis of Finite Excitation Bandpass Errors Sir: The measurement of luminescence quantum yields has recently been reviewed (1-3). As pointed out, one of the most frequently neglected sources of error in yield determinations is that produced by the finite bandpass of the excitation source (2). These errors are especially serious in optically dilute measurements, which are the techniques presently in widest use. With the exception of some cautionary notes and limited quantitative warnings (2, 4), no attempt seems to have been made to systematically analyze the magnitude of these errors and to provide reliable correction procedures. The purpose of this paper is to give very simple procedures for estimating these errors and for making semi-quantitative corrections. Only the special case of a xenon arc coupled to an excitation monochromator having a triangular transmission function will be considered; however, since most of the measurements are presently being carried out on such instrumentation, the limitation is not overly serious. The procedures given here can also be used to estimate the upper error bounds when a pressure-broadened line is the excitation source. In the subsequent discussion, it is assumed that the reader is familiar with the mechanics and theory of quantum yield determinations. In any optically dilute method of determining luminescence or photochemical yields, the effective sample absorbance, A , should be used for estimating the fraction of exciting light absorbed (2).
where A(X) is the wavelength dependence of the sample absorbance and I ( X ) is the spectral distribution (relative quanta sec-1 nm-1) of the excitation intensity. The integration is carried out over all wavelengths where A(X) I ( X ) is not zero. I t is customary for most workers to use A(X,) in place of A where X, is the center of the excitation band. This procedure is only acceptable if A(X) is essentially constant over the excitation band. As we shall show, however, very serious errors can result when this condition fails. When A ( X ) varies significantly across the excitation band, the exact evaluation of A can be an experimentally and computationally tedious task. Z(X) is measured by directing the exciting light into the emission monochromator either directly (if a straight through geometry can be established) or by reflection off a mirror or a solution or solid scatterer. The bandpass of the emission monochromator is adjusted so that distortions are negligible. If necessary, corrections are applied for the spectral response of the emission system. A(X) is determined on a good spectrophotometer operated with a bandpass small enough to prevent spectral distortions. Integrations are usually carried out numerically.
(1) F. R. Lipsett. Progr. Dielec. 7, 217 (1967). (2) J . N. D e m a s a n d G . A. Crosby, J . Phys Chem.. 75,991 (1971) (3) G. A. Crosby, J . N . Demas, and J . Callis, J. Res. Nat. Bur. Stand. ( U . S . ) ,76A, 561 (1972). ( 4 ) Notes on the Determination of Quantum Efficiency with the Model 210 "Spectro," G. K. Turner Associates, Palto Alto, Calif., Feb. 1966.
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The measurement of A( A) is normally straightforward. Errors can arise, however, with solutions of some rare earths and organics (e.g., anthracene) having unusually sharp spectra. For such samples, spectral bandpasses of 50.5 nm may be required to obtain an accurate A(X). In such cases, many inexpensive spectrophotometers are inadequate. For some gas phase work (e.g., benzene), even the very best photoelectric instruments may fail. Accurate evaluation of I ( X ) is not always easy either, especially if an excitation monochromator and complex optical system is used. The excitation beam is not spatially homogenous as to wavelength or intensity, and depending on the orientation of the reflector and the remaining optics, various portions (wavelengths) of this beam will be transmitted with different efficiencies to the detector. Errors in I ( X ) then result. In fact, it is possible for some excitation frequencies to never reach the detector. To detect errors from this source, I ( X ) should be measured a t several different positions of the optics, scatterer, or mirror. Consistency between all measurements establishes that the measured Z(X) is probably the true one. There is an experimental way of evaluating A . The same light source used for the yield determination is used to carry out a series of absorption measurements on different concentrations of sample. Then, ?cl = log(l/T) where T i s the sample transmittance, 1 is the path length, c is the concentration, and ? is the effective or operational extinction coefficient. The slope of the plot of log(l/T) us. cl is taken to yield Z, Alternatively, z may be evaluated from a single measurement. In the yield determination, one assumes A = ~ c l .The appealing simplicity of the procedure belies the pitfalls, however. Emission excitation systems, because of arc noise and stability, are not usually well designed for absorption measurements. As a result, high values of log(1/T) (20.3) are frequently used to get reasonable accuracy. l however, the plot of log(l/T) us. cl is For high ~ c values, not linear if finite bandpass errors are significant, that is ? is concentration dependent. Experimental scatter will frequently obscure this curvature, and a slope measured through these points may yield an Z which is quite inaccurate for calculation of A in optically dilute measurements. Before optically dilute A's calculated by this approach can be trusted, it should be confirmed by calculation using Equation 17 of Ref. (2), that the log(l/T) us. cl plots will be accurately linear over the concentration range experimentally used. The experimental procedure is, of course, rigorously correct if the yield and absorption solutions are identical.
EXPERIMENTAL F o r t h e i d e a l i z e d case of a q u a n t u m f l a t l i g h t source a n d a m o n o c h r o m a t o r w i t h a t r i a n g u l a r transmission f u n c t i o n , I( A) is given by
I ( h ) = 0,
X I A 0 - Ah and h 2 Xo
+ AX
(2c)
AX is the bandpass of the monochromator (ie., the full bandwidth at 50% of peak transmission points). Three trial procedures were adopted for evaluating A : (a) A(X) was fit to a parabola passing through A(X,), A(X, - AX), and A(X, + AX). The integrals of Equation 1 were then evaluated exactly; (b) the integrand of the numerator of Equation 1 was evaluated at X, - Ah, X - AX/2, A, A, + AX/2, and A, + AX. The integration of the numerator was then carried out numerically using Simpson’s rule. For purposes of visualization of the quality of the fit, it should be recognized that this procedure is equivalent to first fitting two parabolas, one through A(X, - AX), A(X, - AX/ 2), and Xo and the second through A ( X , ) , A(X, + Ah/2), and A(X, + AX), then carrying out the integrations of Equation 1 exactly; (c) the same procedure as (b) was employed except that the trapezoidal rule was used for carrying out the integration of the numerator. These procedures resulted in the following expressions:
-
A = A(XJ
-
A
=
+
‘I,{A(Xo)
+ ‘/,[A(Xo + A,X/2) + A(ho - AA/2)I\
(3c) The letter in the equation number represents the procedure used. To test the reliability of these equations, the approximate values for A obtained from Equations 3a, 3b, and 3c were compared with the “exact” values (obtained using a trapezoidal rule integration of Equation 1 with ten evenly spaced intervals across the excitation band) for several compounds using i o ’ s corresponding to minima, maxima, and shoulders which were both close t o and well-removed from absorption maxima and minima.
RESULTS AND DISCUSSION All three procedures yielded estimates of A which were significantly better than if A(A,) had been used. Method ( a ) usually gave very good results, but because of undue weight to the less important end points, large errors occasionally occurred. Method (c) was in general somewhat less accurate than Method ( a ) , but it was not so prone to the large errors in Method (a). Large errors did arise a t times, however. In addition to being computationally the simplest, Method ( b ) was, on the average, equivalent or superior to either of the other two procedures tried. We recommend Equation 3b for approximate evaluations of A. From our experience we can formulate the following approximate rule: A t the level of approximation of Equations l and 2. the accuracy of A calculated from Equation 3b will be -2% for A within 10-15% of A(A,), -1% for A within -3-10% of A(A,), and -0.5% for A within -3% of A( A,). Several comments are in order. Equation 3b can be expected to yield realistic results only if the conditions of Equation 2 hold. In fact, the xenon arc only approximates a quantum-flat light source. In the further ultraviolet ( A < 300 nm), the intensity decreases rapidly with decreasing wavelength; the xenon continuum also has some line structure, especially in the 450-500 n m region. These factors will tend to decrease somewhat the accuracy of the A’s calculated by the approximate equations. To fully assess these errors, the detailed calculation of A described earlier would be required; however, normally the effect on the accuracy should not be too large. Results obtained by using the approximate formulas should still be better than if A(h,) were used, but not so good as if an exact procedure were carried out. A further problem may arise, since some monochromators can have transmission functions which are more nearly trapezoidal. This property can be checked experimentally or verified from the manufacturer’s specifications.
The problem of stray light far removed from the excitation band is also ignored [see Refs. (2) or (5) for details]; this experimental difficulty can usually be eliminated by careful design of the measurement. Additionally, reasonable prudence should be used in applying these formulas. Clearly, they will fail badly if the excitation bandpass spans several minima, maxima, or inflection points. Data which cannot be fit well to one or two parabolas will-be prone to large errors; the only recourse in such cases is to resort to a refined treatment of Equation 1 or to reduce the slit width and/or change the excitation wavelength to a more favorable region. We shall now consider the magnitude of such errors for some of the more common standards. The results quoted here are for the “exact” integrations, but virtually identical results are obtained using Equation 2b. Quinine sulfate, the most popular standard, is usually excited a t the absorption maxima a t 347 nm. At this wavelength, using a 10-nm bandpass, A = 0.98 A/347), and A = 0.93 A(347) when a 20-nm bandpass is used. Since bandpasses this large are certainly used by some workers, the problem is clearly not trivial even with the very broad quinine absorption. A 6-nm or less bandpass virtually eliminates this error source for quinine. Dyestuffs such as fluorescein and rhodamine B are even worse. Fluorescein when excited with a 20 nm bandpass a t the visible absorption maximum at 490 nm yields A = 0.85 A(490). Even the relatively narrow 10-nm bandpass 0.96 A(490), an unacceptable error in accurate yields A work. Bandpasses of 4 nm or less must be used to eliminate significant error when A(490) is used in place of A . Anthracene, a typical highly structured aromatic, presents dire problems. For an ethanol solution, excitation a t the 376-nm absorption maximum using AA = 5 nm results in A being -20% lower than A(376). For PA = 2 nm, A is still -6% lower than A(376). To bring A within 1% of A(376), the bandpass must be reduced to less than -0.5 nm; this narrow a bandpass is rarely feasible and correction would be necessary. Excitation a t the minimum a t 366 nm results in some improvement; AA = 3-4 nm produces an -6% difference between A and A(366). Similar results prevail for excitation over the entire first electronic transition. These results are especially unfortunate in view of the rather wide use of anthracene as a standard, and they again e-mphasize the great care which must be exercised in carrying out yield experiments if the results are to be of lasting significance. As a final point, transition metal complexes such as tris(2,2’-bipyridine)ruthenium(II)have been suggested as potential standards (2, 3). This particular compound, when excited a t the absorption maximum a t 453 nm, has in fact a slightly smaller bandpass error associated with its use than even quinine. This feature is one of the compelling reasons for studying this type of system in greater detail. When excitation is with a monochromatized pressurebroadened line (e.g., high pressure mercury arcs), Equation 3b clearly fails because the resultant excitation is much more sharply peaked than given by Equation 2. Equation 3b does, however, yield an upper limit on the uncertainty of A if A, corresponds t o t h e center of t h e excitation line.
CONCLUSIONS In addition to the recommendations made earlier for reporting quantum yield results (2, 6), the following points (5) C. A. Parker, “Photoluminescence of Solutions,’’Elsevier. N e w York, N . Y . . 1968.
(6) J . H. C h a p m a n , Th. Forster, G. Kortum, E. Lippert. W. H. M e l h u i s h . G . Nebbia. and C. A . P a r k e r , Z. A n a l . C h e m . . 197, 431 (1963). A N A L Y T I C A L C H E M I S T R Y , VOL. 45, NO. 6, M A Y 1973
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should also be discussed in any paper using optically dilute measurements: First, the yield data should be calculated using A values estimated from Equation 3b or by a more exact procedure; second, since detailed absorption spectra are not always available for others to assess the magnitude of the errors, the percentage differences between A andA(X,) should be given. In summary, Equation 3b for calculating A is so simple to use and so accurate that there is no longer any excuse for failing to make a first order correction for the finite bandpass error in the usual yield determinations. Only three absorbance values, rather than the usual one, are required, and the arithmetic work involved is trivial even when carried out by hand. It should be stressed that Equation 3b is at best approximate for real systems. Rea-
sonable accuracy can be expected only when it is applied critically and the experimental conditions are such that Equation 2 is nearly satisfied. When significant deviations are expected, when doubt exists concerning the reliability of Equation 3b, or when the greatest accuracy is desired, the exact procedure should always be employed. J a m e s N. Demas Chemistry Department University of Virginia Charlottesville, Va. 22901 Received for review September 25, 1972. Accepted January 5, 1973.
Versatile Technique for Signal Enhancement as Applied to High Resolution Mass Spectrometry Sir: When a mass spectrum is measured using an electron multiplier and a high-speed electrometer coupled to a fast sample-and-hold amplifier with an analog-to-digital converter, the peak profiles will be quite irregular and may drop below base line on smaller peaks. This is due to noise in the electron multiplier and unfavorable ion statistics on small peaks. Thus, small peaks may be so irregular that they will not be recognized and the mathematical deconvolution of partially resolved peaks will be uncertain. Several solutions to this problem have been proposed. One is pulse counting over fixed equal time increments using a pulse amplifier and discriminator coupled to a pulse counter in a small computer (1). The technique essentially integrates the signal over equal time increments and reduces the effect of adverse ion statistics and noise. One such system is commercially available. Use of a time averaging technique to average many scans has been described (2, 3). An elegant method has been proposed using on-line computer control to scan each peak many times during an overall scan of the spectrum and to average these peak profiles (4). In our data acquisition system, we use a sample-andhold amplifier and analog-to-digital converter with a conversion time of 6.3 psec for 14 bits (5). An additional 6.5 psec are required for an IBM 1800 computer to read this output. System logic allows 13.5.isec to complete this process. If, for example, we sample at 10 thousand points per second we have 100 psec between points. Since only 13.5 psec are used for measurements, information in the remaining 86.5 psec is not utilized. More information could be obtained if the signal were integrated during this time. A review of currently available electronic hardware showed that integration for signal-to-noise improvement over this short interval is feasiBulletin 21-094, DuPont Instrument Products Division, Monrovia, Calif. F. J. Biros, Anal. Chem., 42, 537 (1970). S. P. Markey, K . B. Hamond, and J. R. Plattner, Eighteenth Annuai Conference on Mass Spectrometry and Allied Topics, San Francisco, Calif., June 1970, p 870 F. W. Mciafferty, R. Venkataraghaven, J. E. Coutant, and B. G. Giessner, Anal. Chem., 43,967 (1971) R. P. Page, and A. V. Nowak, Nineteenth Annual Conference on Mass Spectrometry and Allied Topics, Atlanta, Ga., May 1971, p 84 Burr-Brown Electronic Switches Cataiog, PDS-222, Burr-Brown Research Corp., Tucson, Ariz., Sept. 1969.
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I
I I I
I
11
SWITCH AND r3MPLIFIER CURRENT I
A/D CONVERTER
I
-
OPT0 ELECTRONIC
I
CONVERTER LOGIC
Figure 1. Block diagram of analog incremental integration syst em
ble (6). We call this technique “analog incremental integration” and a block diagram is shown in Figure 1. It includes a high-speed operational amplifier integrator circuit reset by a switch with current gain to minimize reset time. This reset is initiated by an opto-electronic isolator operated by a pulse from the analog-to-digital conversion logic. Reset is accomplished during the same 6.5 psec used by the IBM 1800 computer to read the analog-to-digital converter output. Thus, we have peak profiles consisting of the integrals over 86.5-psec increments rather than more random discrete voltage values measured by a sample-and-hold amplifier. This kind of averaging, unlike analog filtering, produces no distortion of the peak envelope so that mathematical deconvolution can be used. This technique can also be used at high pulse rates where pulse counting techniques are not applicable. While this technique has been discussed as a way to improve high resolution mass spectral data, it can be applied to any system using an analog-to-digital converter. R. P.Page A. V. Nowak R. Wertzler Atlantic Richfield Company Harvey Technical Center Harvey, Ill. 60426 Received for review September 14, 1972. Accepted December 26, 1972.
