1882
Anal.
Chem. 1988, 6 0 , 1882-1886
Nicholson, R. S. Anal. Chem. 1965,3 7 , 667. Wightman, R. M. Anal. Chem. 1981,5 3 , 1125A. Howeii, J. 0.; Wightman, R. M. Anal. Chem. 1984, 56, 524. Scharifker, B.; Hills, G. J . Nectroanal. Chem. 1981, 130, 81. Fitch, A.; Evans, D. H. J . Nectroanal. Chem. 1986,202, 83. Bond, A. M.; Fleishmann, M.; Robinson, J. J . Nectroanal. Chem. 1984, 168, 299. Baer, C. D.; Stone, N. J.; Sweigart, D. A. Anal. Chem. l988*6 0 , 188. Howell, J. 0.; Wightman, R. M. J . Phys. Chem. 1984,88, 3915. Saito. Y. Rev. Polarogr. 1968. 15, 177. Dayton, M. A.; Brown, J. C.; Stutts, K. J.; Wightman, R. M. Anal. Chem. 1960,5 2 , 946. Bond, A. M.; Oldham, K. B.; Zoski, C. G. J . Nectroanal. Chem. 1988, 2 4 5 , 71. Bond, A. M.; Luscombe, D.; Oldham. K. B.; Zoski, C. G. J . Electroa nal. Chem., in press. Bewick, A.; Meilor, J. M.; Pons, B. S. Nectrochim. Acta 1980, 2 5 ,
-
931. Fleischmann, M.; Lasserre, F.;Robinson, J.; Swan, D. J . Nectroanal. Chem. 1985, 177, 115. Bond, A. M.; Fleischmann, M.; Robinson, J. J . Nectroanal. Chem. 1984. 180. 257. - . , _. Bixier, J. w.; Bond, A. M.; Lay, P. A.; Thormann, w.; Pons, B. s.; Fleischmann, M. Anal. Chim. Acta 1986, 187, 67. Fieischmann, M.; Lasserre, F.; Robinson, J.; Swan, D.J . Necfroanal. Chem. 1984. 177. 97. Anderson, J.'E.; Bagchi, R. N.; Bond, A. M.; Greenhill, H. B.; Hender-
.
son, T. L. E.; Waiter, F. L. Am. Lab. (FairfieM, Conn.) 1981,Feb. 21. Bard, A. J.; Faulkner, L. R. Electrochemical Msthods: Fundamentals and Applications; Wiley: New York, 1981; Chapter 13. Gennett, T.; Milner, D. F.; Weaver, M. J. J . Phys. Chem. 1985, 89, 2787. Fleischmann, M.; Pons, S.; Rollson, D.R.; Schmidt, P. P. Ultramicroelectrodes ; Datatech Systems, Inc., Science Publishers: 1987; pp 276-268. Bruckenstein, S.Anal. Chem. W87, 59, 2098. Oidham, K. B. J . Hectroanal. Chem. 1987,237, 303. Daschbach, J.; Biackwood. D.; Pons, J. W.; Pons, S. J . Nectroanal. Chem. 1987,237, 269. Myiand, J. C.; Oldham, K. B. J . Nectroanal. Chem. 1985, 185, 29. Myiand, J. C.; Oldham. K. B.; Zoski, C. G. J . Electroanal. Chem. 1986,206, 1. He, P.; Faulkner, L. R. Anal. Chem. 1986,58,517. Brown, E. R.; Smith, D. E.; Booman, G. L. Anal. Chem. 1968, 4 0 , 1411. Brown, E. R.; Hung, H. L.; McCord, T. G.; Smith, D. E.; Booman, G. L. Anal. Chem. 1968,4 0 , 1424.
RECEIVED for review December 15, 1986. Resubmitted July 9, 1987. Accepted April 18, 1988. The authors gratefully acknowledge the Australian Research Grants Scheme for its financial support of this work.
Comparison of Time and Frequency Domain Methods for Rejecting Fluorescence from Raman Spectra M. J. Wirth* and Shiow-Hwa Chou Department of Chemistry & Biochemistry, University of Delaware, Newark, Delaware 19716
Analytic expresslons are derived for the enhancement of Raman signals over fluorescence signals for time-resolved, frequency domaln demoduiatlon and frequency domain phase-nulllng methods. Very high enhancements are predicted for the phase-nulllng method when hlgh-frequency modulatlon is used. Experimental results for the phase-nulling method, using a conventlonal photomultiplier tube and a modulation frequency of 329 MHr, show an enhancement of 200 for Raman signals In the presence of a fluorophor having a 3.9-11s Ilfetime. The signal-to-noise ratlo in the Raman spectrum Is limited by phase jitter in the instrument.
Fluorescence is well known to interfere in Raman spectroscopy. With visible excitation there is usually spectral overlap between the two emission processes, with the cross section for fluorescence spectra larger than that for Raman spectra. Methods for reducing the fluorescence interference in Raman measurements include the use of far-UV excitation ( I , 2) and near-IR excitation ( 3 , 4 ) ,minimizing the spectral overlap between the two processes. UV or IR excitation is not a universal solution to the problem, as UV excitation can damage the sample, and near-IR excitation gives low sensitivity. Time-resolved spectroscopy has been employed to reject fluorescence from Raman emission based upon the difference in emission decays times between the two processes. The time scale of Raman emission is determined by the dephasing time, T,, of the transition. For a homogeneously broadened band, T , is given by the relation fwhm T2 = l / ~
(1)
where fwhm is the full-width at half-maximum of the Lorentzian b a n band. For liquids, the homogeneous dephasing times are typically on the picosecond time scale. For inhomogeneous broadening, the Raman lifetimes are shorter yet. By contrast, the intrinsic fluorescence lifetime, 7 O , is related to the Einstein coefficient, A , of the emission transition, resulting in lifetimes on the nanosecond time scale even for very strong emitters. The observed fluorescence lifetime, 7, is 7
= [A
+ k,, + k , [ Q ] ) - l
(2)
where k , is radiationless decay rate, k , is the quenching rate constant, and [Q] is the quencher concentration. Radiationless and quenching processes shorten the lifetime at the expense of quantum yield rather than by redistributing intensity into the early part of the emission decay. The inherent factor of 100 difference in time scales of fluorescence and Raman emission for liquids allows fluorescence to be rejected from Raman by time resolution. Experimentally, time-resolved fluorescence rejection is accomplished by exciting the sample with a short optical pulse. A fast detector then monitors the early part of the time-dependent emission. Yaney (5) was the first to implement this idea and, using a pulsed Nd:YAG laser, enhanced the contribution of Raman relative to fluorescence by a factor of 63 when the fluorescence lifetime was 125 ps and the detection window was 1 ps. With the advent of mode-locked lasers and the parallel developments in detection speed, enhancements greater than 100 have been achieved for Raman emission in the presence of short-lived fluorescence. A fast photomultiplier coupled with dual-level discrimination allowed an enhancement of 115 for the Raman emission of benzene in the presence of rubrene fluorescence having a lifetime of 15.6 ns (6). A microchannel-plate photomultiplier with a 31-ps gating
0003-2700/88/0360-1882$01.50/00 1988 American Chemical Society
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aperture gave an enhancement of 129 for ethanol Raman emission in the presence of rhodamine 6G fluorescence having a lifetime of 3.9 ns (7). Rejection of fluorescence from Raman can equivalently be accomplished by frequency domain techniques. These techniques involve monitoring the phases and amplitudes of the individual frequency components that comprise the timedomain response. The phase shift and demodulation are related to the lifetime by Fourier transformation. For a single exponential decay time, T , the demodulation, m, of the frequency component, o,is m = [1/(1 ( W T ) ~ ) ] ~ / ~ (3)
+
For the same conditions the phase shift is described by tan 4 = WT (4) The value of m ranges from unity to zero for modulation frequencies ranging from 0 to 03. Fluorescence signals can be rejected from Raman signals by using high-frequency modulation, where the long-lived fluorescence is demodulated while the Raman modulation remains strong. The fluorescence from a 3.6-ns fluorophor was reduced by a factor of 7 from Raman emission by using a modulation frequency of 328 MHz (8). The phase shift also has been used for fluorescence rejection from Raman emission. At frequencies greater than 100 MHz, Raman emission is phase-shifted negligibly, while the phase shift is large for fluorescence. The fluorescence is also demodulated, and the ac component is reduced further by a method called phase-nulling. In phase-nulling, a phase-sensitive detector, such as a lock-in amplifier, is used to detect the modulated Raman emission. With the phase of the lock-in amplifier set to 90' from the phase of the fluorescence, the fluorescence signal is nulled. Phase-nulling thus combines the effects of demodulation and phase-shifting to reduce the fluorescence contribution to the Raman signal. For a long fluorescence lifetime, the Raman contribution to the in-phase signal remains strong, dowing a large enhancement of Raman over fluorescence. Phase-nulling has previously been applied to the analysis of mixtures of fluorophors ( s 1 3 ) . For rejection of fluorescence from Raman,phase-nullinghas been used thus far at a low modulation frequency, 40 MHz, to reject the contribution of a fluorophor having a 3-ns lifetime (14). Although no number was explicitly stated, a rejection of 35 is estimated from the graphical data. These three techniques for rejecting fluorescence from Raman emission-time resolution, frequency domain demodulation, and frequency domain phase-nulling-cannot be readily compared because each reported result depends upon the specific choice of detector speed and fluorescence lifetime, as well as experimental parameters such as time window of observation or modulation frequency. The purpose of this paper is 2-fold. First, unifying analytical expressions are derived for the three fluorescence rejection methods. The detector speed and fluorescence lifetimes are parameters in the equations to allow pedagogical comparisons of the techniques. Second, new experimental results are presented for the phase-nulling technique to provide experimental data at a high modulation frequency. This allows for a complete set of experiments to be compared with the analytical expressions derived.
THEORY The detected fluorescence and Raman signals in the absence of any rejection are defined as Foand Ro, respectively. With a chosen rejection technique, the fluorescence and Raman signals are modified to F and R , respectively. The enhancement of Raman to fluorescence, E , is defined as R / F = ERo/Fo (5) In this section, the values of the enhancement are predicted
'
I
-.do0
4d.O
I
TIME
sd.0
'
I
I
120.
I
I
16'0.
'
(nsl
Synthetic time-resolved curves to illustrate the effect of window position on fluorescence rejection from Raman signals: (a) a normalized Gaussian, u = 5 ns, represents the excitation pulse; (b) the corresponding fluorescence decay curve is for T = 20 ns. The dashed line shows the enhancement of Raman to fluorescence intensity detected, for a window opened from -03 to t . This illustrates the advantage in using just the first half of the excitation pulse for fluorescence rejection. Figure 1.
for time-resolvedspectroscopy,amplitude demodulation, and phase nulling. A. Time-Resolved Rejection of Fluorescence from Raman. The theoretical aspects for time-resolved rejection of fluorescence signals from Raman signals are discussed thoroughly in the experimental papers (6, 7). Synthetic time-resolved response curves are illustrated in Figure 1for a Gaussian excitation pulse and a single exponential fluorescence decay. In time-resolvedexperiments the Raman emission approximately coincides with the excitation pulse, while the longer-lived fluorescing population builds during the excitation pulse and emits well after the excitation is zero. To detect Raman selectively over fluorescence, emission is monitored during the excitation pulse. A trade-off is made in setting the position of the detector window. The detection window must be set wide enough to overlap as much of the excitation pulse as possible, maximizing the Raman contribution, but the window must also be set narrow enough to avoid significant fluorescence emission. A good compromise position is to set the time window to overlap just the first half of the excitation pulse. For derivation of the enhancement, the leading half of the excitation pulse is assumed to be a Gaussian with standard deviation u, and the time window is adjusted to collect exactly the integral of the first half of the excitation pulse. The fluorescence decay is treated as a single exponential. Under these conditions, the enhancement factor for time-resolved spectroscopy, Et,, is
E, =
[I - exp(u2/2Tz2)(1- erf(u/Tzfi))l
[I - e x p ( a 2 / 2 ~ ) ( 1 -erf(u/&)]
(6)
Equation 6 is rigorous for the stated conditions. The Raman lifetime is usually considered negligibly short, but with increasing detector speeds, the full representation in eq 6 may be applicable. Otherwise, assuming Tz< u,the numerator simplifies to unity. The relation adopts a very linear form for lifetimes longer than the half-width of the impulse re-
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sponse. As the fluorescence lifetime shortens to be comparable to the Raman lifetime, E approaches unity, as expected. For 7 L 3HW, where HW is the half-width at half-height of the detector response on the leading side, eq 6 becomes highly linear, with a slope of 1.47. The relation in eq 7 is a generally
1.5r/HW
E,,
+1
(7)
useful one, as it gives only a 10% error for a lifetime as short as the detector HW itself. In the application of this model to experiments where the emission is sampled at earlier times in the decay curve, Figure 1 reveals that the enhancement increases approximately linearly as the detection window decreases. The predicted enhancement factor agrees well with the results obtained previously. Watanabe et al. (7)chose a detection window to be the leading half of the impulse response, represented well by the model. For rhodamine 6G fluorescence of 3.9 ns and a detection window of 31 ps, the observed enhancement was 129, while that predicted by eq 7 is 190. The minor disagreement is possibly due to the high repetition rate of the laser, which causes fluorescence from the previous pulse to interfere. In the same work, a Hamamatsu R928 tube was used to gate over a 220-ps aperture to reject fluorescence having a decay time of 600 ps. The observed enhancement was 7.0 and the enhancement predicted from eq 7 is 9.2. Harris et al. (6) obtained enhancements of 34 and 115 experimentally (6),compared to 35 and 107 predicted from the model. The fluorophors were acridine orange and rubrene, having lifetimes of 4.5 and 15.6. These workers use a photomultiplier having a leading-edgehalf-width of 1.1 ns and an time window that accepted 10% of the Raman photons, rather than the 50% used for eq 7. The predicted enhancements of 35 and 107 were calculated by using the linearity of the enhancement with respect to the width of the time window. The theoretical predictions are robust, with less than a factor of 2 error for both the Watanabe and Harris experimental results. The relation provides a reasonable estimate of the enhancement that can be expected from time-resolved spectroscopy. B. Frequency Domain Demodulation of Fluorescence. Using eq 3, the enhancement of Raman to fluorescence for the frequency demodulation technique, Efd, is determined rigorously to be
+ (wT2)2]-'/2 [l + (wr)2]-'/2
[l Efd
=
for a single exponential decay. As with time-resolved spectroscopy, a useful mathematical prediction of the enhancement relies on choosing measurement conditions that resemble actual experiments. The trade-off in frequency domain demodulation is the modulation frequency must be made high to reduce fluorescence, but not so high as to exceed the detector roll-off. Analogous to observing half of the excitation window in time-resolved spectroscopy, the frequency at which the detector response drops in half is chosen for modeling this experiment. This is termed the fab frequency. Under the conditions of T2
