Anal. Chem. 1995,67,2835-2841
Chromatographic Frequency Domain Fluorescence Modulation Lifetime Errors Caused by Photomultiplier Baseline Offsets Thomas. E. Johnston* Neptune and Co.,1505 15th Street Suite B, Los Alamos, New Mexico 87544
Using exponentially modified Gaussian functions, computer simulations of HPLC fluorescence signals are used to quantify the effects of previously unreported detector baseline offset errors on observed modulation lifetimes. The simulations reveal that electronic baseline offset errors less than 1%of peak maximum c8n translate to relative lifetime errors exceeding 60%in chromatographically signiscant regions of peaks. Experimental data are presented to substantiate and validate the simulations. The relationship of lifetime errors to baseline offsets is demonstrated to vary with true component lifetime and the modulation frequency used to probe the sample. This relationship is explored with a derivation of the relative modulation lifetime error equation subject to ac and dc signal offsets. Simulations and mathematical derivations reveal that dc intensity matching of chromatographic signals cannot correct for baseline offset errors except in unlikely circumstances. A plotting method useful for identifying baseline errors is introduced, and its use in making accurate determinationsof fluorescencelifetimes in the presence of baseline errors is explained. In 1989, a s i m c a n t emission intensitydependent modulation lifetime error was reported for a chromatographic system coupled to an SLM-48OOOS sequential multifrequency phase-modulation spectrofluorometer.' The origin of the error was not identified, and the simultaneously determined phase lifetimes appeared to be unaffected. The error is systematic and therefore cannot be the result of stochastic phenomena such as signal noise, nor can it be caused by scattered light because the symptom is increased lifetimes at low signal intensities. Application of dc intensity matching is reported to have corrected the modulation lifetime error, though without theoretical justification.' This paper shows why dc intensity matching of chromatographic fluorescence modulation signals is partially or wholly ineffective in correcting the intensity-dependentmodulation lifetime error and, at least, is unwarranted when other corrections are applied (vide infra). In 1990 and 1991, a previously unreported baseline offset artifact was identified which accounts for the origin of intensitydependent chromatographic modulation lifetime errors (unpub lished work, T. E. Johnston). A remarkable similarity was demonstrated in that work between the unexplained modulation lifetime errors reported in ref 1 and the errors caused by chromatographic baseline offsets. Recapitulated and expanded here are portions of the unpublished work which show the
following. First, when baseline offsets are corrected, intensitydependent modulation lifetime errors essentially vanish with no use of intensity matching. Second, the limited success of dc intensity matching to correct modulation lifetime errors in the presence of baseline artifacts is expected. Third, the modulation depth of a pure chromatographic component can be determined in the presence of detector offset errors by using a simple plotting technique. Furthermore, mathematical notation is introduced which this author believes is more appropriate than notation used previously1 to represent chromatographic fluorescence modulation signals. THEORY If a fluorophore subject to monoexponential photodecay is excited by light that is sinusoidally intensity modulated, the fluorescence emission is intensity modulated at the same frequency as the irradiating light. However, relative to the excitation beam wave form, the fluorescencewave form is phase shifted and the ratio of ac peak amplitude to dc amplitude (Le., modulation depth, M) is reduced. The degree of phase shift and demodulation depend on the lifetime of the fluorophore and the modulation frequency. Neglecting experimental artifacts, the single frequency modulation depth of the excitation beam, Me,, should be constant. The same is true of the observed modulation depth of a sample, M,, whose lifetime composition is fixed. Dividing M, by Me, yields the demodulation of the sample, m,,and from this quantity the observed modulation lifetime, Zm,& may be computed. For a single ground electronic state fluorophore in a homogeneous microenvironment, the observed lifetime is the true sample fluorescence lifetime, ts,me, and should be independent of modulation frequency. If multiple fluorescence lifetimes coexist in the sample, then Zm,& is a weighted combination of individual true lifetimes contributing to the total fluorescence signal, and the observed lifetime varies with modulation frequency.2 In chromatographic experiments, the fluorescence emission signal is sampled periodically, producing paired ac and dc amplitudes at each retention time. The ac/dc signal ratio at each retention time yields the modulation depth,
(wt:
where ac is the ac peak amplitude, dc is the dc amplitude, and t is the retention time. At a fixed modulation frequency, (M), for a pure chromatographic component should be constant across ~~~~~~~
(1) Cobb, W. T.; McGown, L. B. Appl. Spectrosc. 1989,43 (8),1363-1367.
0003-2700/95/0367-2835$9.00/0 0 1995 American Chemical Society
(2) Lakowicz,J. R Principles of Fluorescence Spectroscopy; Plenum Press: New York, 1983.
Analytical Chemistry, Vol. 67, No. 17, September 1, 1995 2835
the entire peak (Le., for all t). Furthermore, plotting act versus dct for a pure component should yield a straight line with slope equal to M,and a zero intercept. The sample demodulation at each retention time, (mdt, is computed from the ratio of fluorescence and excitation beam modulation depths:
(2) where (MJ, is the modulation depth for the sample emission at retention time, t, and Mexis the modulation depth of the excitation beam. Signal averaging, combined with an inherently high excitation beam S/N ratio, renders Me, constant over the sample measurement period and allows for omitting the subscript t in eq 2. To minimize photomultiplier illumination geometry and color errors, the emission from a pure fluorophore rather than the excitation beam may be used as the reference? In that case, Me, of eq 2 is replaced by Mr[l + ( ~ t r , ~ e ) ~ where ] ~ / ~ ,Mr is the timeindependent modulation depth of the reference fluorophore emission? o is the circular modulation frequency, and z ~ is , the true, independently determined lifetime of the reference compound. The 11 ( ~ t ~ , ~ term ~ ~ compensates ) ~ 1 ~ / ~for the demodulation of the reference fluorophore emission relative to excitation. The observed modulation lifetime is computed at each retention time by using the ac and dc information from both sample and reference fluorophores: (mJ t = (MJ t/Mex
+
values, respectively; dac and ddc are the ac and dc signal offsets, respectively. When the baseline is uncorrupted, dac and ddc equal zero, and eq 5 reduces to eq 1. If dac and ddc are relatively small, they exert little effect on (M)!at high signal intensities, but they can have a marked effect at low intensities. If dac and ddc are non-zero but constant over time, a plot of measured ac intensity, (ac dac)t, versus measured dc intensity, (dc ddc)!, for a pure component will exhibit the same slope as a plot of (ac), versus (dc),. Thus, the true modulation depth for a pure component, which is the slope of the plot, can be accurately determined in the presence of constant baseline errors. And, since signal intensity and retention time are correlated, if such a plot on either side of a peak maximum exhibits a changing slope, one may conclude that the baseline is drifting underneath the peak, or that the peak represents chromatographically unresolved fluorophores of measurably different lifetimes. Setting M e , , and Me,,equal and making the appropriate substitutions in eq 4,the complete modulation lifetime equation may be written to account for sample and reference fluorophore ~ ac ~and dc signal offsets:
+
+
(Zm,obs)t
=
‘li w
[l
+ ( w ~ , , ~ ~ ) ~+] 6acJ2(dcS (ac~ + 6dcJ; (ac, + 6acJ;(dc, + 6dcr)2
-
1 (6)
where subscripts r and s represent reference and sample and Me,, is assumed to equal Reference values are assumed to be measured under static conditions, rendering them independent of retention time.
Sample and reference fluorophore emissions must be monitored in separate chromatographic runs. During each.of those runs, the modulation depth of the fluorophore emission is normalized against the excitation beam modulation depth:
EXPERIMENTAL SECTION Simulations. An exponentially modified Gaussian dc basis function was generated using Maple V3 software (Mathsoft). The basis function, (Id&, representing the dc signal intensity of a tailing Chromatographic peak was
where Ma,, and Me,, are the modulation depths of the excitation beam during sample and reference measurements, respectively. Inclusion of (Mex,J and (MeXJ in eq 4 compensates for changes in the excitation beam modulation depth that may occur between sample and reference measurements since those data are collected at different times. Ideally, Mex,, and Mex,r will be equal, rendering eqs 3 and 4 identical. At a given modulation frequency,Y (= o/2~r),Zm,obs should be constant across the entire peak profile of a pure chromatographic component. If components of different lifetimes are incompletely resolved, Zm,& varies in the peak overlap region as a function of the relative contributions of each component to the total signal. Prior to data collection, the photomultiplier dark current is nulled. If the detector null point drifts away from zero, the ac or dc signals become corrupted by an electronic offset. Equation 1 can be modified to account for such offsets:
where t represents retention time, a = 15, w = 0.6, p = 0.9, q = 7 and z = [ ( t - q)/wl - tu/$. Using 35digit precision to avoid rounding errors, (Id&was evaluated over the “retention time” range of 0-18 s at intervals of 0.1 s. Those data, representing a digitized chromatographic dc fluorescence signal probed at a single modulation frequency, were transferred to MS Excel 5.0 for further manipulation and plotting. A second basis function, (Iac)( = 0.6(Zd3tl was generated to simulate the corresponding digitized ac signal of a pure chromatographic component with a modulation depth of 0.6. From those data, additional ac and dc chromatographic signals were generated as the basis functions plus varying degrees of baseline offset:
where ac and dc are the theoretically correct ac and dc signal (3) If gradient elution were used in place of isocratic elution, one would expect the modulation depths of fluorophore emissions to change with eluent polarity and, hence, with retention time.
2836 Analytical Chemistry, Vol. 67, No. 17, September 1 , 1995
It’ = It+ b,
(8) where Zt‘ is the corrupted ac or dc signal, It is the uncorrupted ac or dc signal basis function, and br is the ac or dc baseline offset at every t. For these simulations, bt was set equal to a constant, c, to yield It‘ = It + c. primarily negative offsets of sample ac signals are considered here. Modulation depths and demodulation envelopes across simulated peak profiles were computed for several combinations of ac signal offsets, fluorescence lifetimes, and modulation frequencies. Those signals were used with eq 6 to generate modulation lifetime
envelopes. The reference lifetime was fixed at 12.4 ns, representing the approximate lifetime of 4anthracenecarbonitrile in an 80/ 20 acetonitrile/water matrix. No offsets were applied to the reference ac or dc signals; negative offsets were applied to the sample ac signals. In some computations, modulation frequency was changed while keeping true sample fluorescence lifetime k e d and varying the sample ac signal offset. In other computations, lifetime envelopes were generated for various true sample lifetimes and sample signal ac offsets at a fixed modulation frequency. For non-zero ac and dc offsets of sample signals only, the equation relating percent modulation lifetime error to experimental variables was derived (Appendix A, supporting information):
-&s,true
Using eq 9 and MathCad 5.0 Plus (Mathsoft) with Me,, = 1,error surfaces were generated for various experimental conditions. Experiments. A Waters Model 501 high-performance liquid chromatograph with a U6K injector, a 100 mm x 3.0 mm Vydac 201-T€-B-5(2-18 separator column, and a 10 mm x 3.0 mm (2-18 cartridge guard column (Chrompak) was coupled to an SLM48000s phase-modulation spectrofluorometerequipped with a 450 W xenon arc lamp and Hamamatsu R928 photomultiplier tubes (SLM Inc., Urbana, IL). Filtered (0.45 pm Teflon or nylon membrane, Millipore) and degassed 93/7 acetonitrile/water (Burdick &Jackson) was the mobile phase flowing at 0.25 mL/ min. Polycyclic aromatic hydrocarbon standards prepared in spectroscopic grade acetonitrile using as-received, high-purity (298%) powders (AccuStandard, Inc., New Haven, CT and Ultra Scientific, Hope, RI) were injected in 20 pL volumes. The reference fluorophore was Santhracenecarbonitrile (SAC?. The spectrofluorometer was used in the slow time-based acquisition mode with an average of two signal samples per data point; the modulation frequency was 30.0 MHz. A 20 pL low-fluorescence, black quartz chromatographic flow cell (Hellma, Jamaica, NY) with 1.5 mm optical path length was used in the sample chamber. The excitation monochromator bandpass was 2 nm; a 345-600 nm emission bandpass was achieved by combining short- and longpass low-fluorescence filters (Oriel Corp., Stratford, c??. The sample channel photomultiplier voltage and gain were 900 V and 100, respectively; on the excitation reference channel, the corresponding values were 540 V and 1. The high voltage and gain settings on the sample channel required repeated nulling of that detector before the zero set point would stay reasonably close to zero and the experiment could begin. Intensity matching was performed on some data as described in Appendix B (supporting information). The computerized intensity matching routine applied here is identical to that used in ref 1. All dc signals were shifted to compensate for the relative ac-dc signal time lag reported previously for the SLM-48000S.1 RESULTS AND DISCUSSION
Simulations. Ideal instrument responses (dac, = ddcr = dac, = 6dc, = 0) for pure chromatographic components would reveal
constant modulation lifetimes and demodulationsfrom peak center to baseline regions. In practice, measured signals suffer from
LI
’I 10.0 a
’**O
8.0
r1
dc lnbnrily
n
I\
I
tl
“ 2.0
0.0
-2.0
2.0
4.0
6.0
8.0
10.0 12.0 14.0
16.0 I .O
Retention Time, seconds Flgure I.Simulation: overlay of observed modulation lifetime, noisy ac peak and ideal dc peak profiles for pure chromatographic peak. Assumes modulation lifetime = 1.333 ns, modulation frequency = 212.2 MHz, excitation is the reference, offsets for ac and dc signals are zero, and modulation depth of excitation beam is unity. Imaginary lifetime values are set equal to zero.
noise, and signals withii a ce@n tolerance of baseline are rounded to zero. The noise and rounding to zero can lead to undehed and imaginary modulation lifetimeswith significant data scatter. Figure 1displays the modulation lifetime of an ideal pure peak with random noise incorporated into the ac signal. The noise maximum is 0.05 arbitrary units, which is < 1%of either the ac or dc signal maximum and is essentially “invisible.” In the peak wings, this seemingly insignificant noise causes significant lifetime errors. Nevertheless, the average lifetime across chromatographically signiiicant portions of the peak is constant, with no apparent systematic deviations except where imaginary lifetimes are intentionally plotted as zeros. Figure 2 manifests the effects of negative sample ac signal offset and modulation frequency on ‘rm,obs (non-zero offset applied to ac signals only). The horizontal dotted line in each panel identifies rs,me(i.e., Bac, = ddc, = 0). The computed modulation lifetime envelopes curve upward and away from peak center, and at a given modulation frequency (i.e., within a panel), increasingly negative ac offsets cause the upward curvature to become more pronounced in chromatographicallysignificant regions of the peak. If modulation frequency is fixed and true lifetime is varied, similar effects are observed. Each corrupted lifetime envelope in Figure 2 is undefined at two points between t = 0 and 18 s, where the negative offset causes the corresponding ac signal (not shown) to pass through zero. This occurs in the front and tail of a peak, where (ac, 6acJ approaches a finite offset and the uncorrupted dc, signal approaches zero. When the radicand of eq 6 is negative, the computed modulation lifetime is an imaginary number. For plotting purposes, the imaginary lifetime values are set equal to exactly 0 ns. There are nine ways to combine positive, negative, and zero ac and dc offsets for a sample signal, and both positive and negative lifetime biases are possible, depending on the algebraic sign of the ac and dc signal offsets. Assuming z , , = ~ 10.0 ~ ns, a maximum dc intensity of 10.2 units, a modulation frequency of 2.0 MHz (= w/2n), and various ac and dc offset values, relative lifetime errors ranging from f0.35%to approximately f67%were computed at 10% of the dc peak maximum. Under similar conditions, but for a true lifetime of 40 ns, the relative lifetime
+
Analytical Chemistty, Vo/. 67,No. 17,September 1, 1995
2837
10.0
50
(m3,=
i
(ac,
'0
$ 6.0 -1 .g 2.0
305
5
[ (acr + dacr)for (dc,+ddcJ
s log 3
-2.0
6
8
12
15
50
e
.-d
6.0
30
4
-.g
2.0
I Og
(ZIn,Obs)f
=
y
5 2 0
-2.0
3
6
9
12
15
lb-lo
4
Retention lime, second8
Figure 2. Simulations: effect of ac signal offset and modulation frequency on modulation lifetime error. Offsets are -0.05 (A), -0.007 (U),and -0.0005 (-) arbitrary units ( a u ) in each panel. Modulation frequencies are 80.0 (A) and 2.00 MHz (B). Sample lifetime = 15.0 ns (both panels); reference lifetime = 12.4 ns. Horizontal dotted lines depict true fluorescence lifetimes; dashed line is chromatographic dc intensity in arbitrary units.
errors ranged from 0.4%to 7.4%at 10%of the dc peak maximum. This emphasizes the impact of true fluorescence lifetime on observed lifetime error for a given modulation frequency and signal offset. Error surfaces for Zm,obs as a function of modulation frequency, true component lietime, and ac signal offset are presented in Figure 3. That figure accounts for nonzero ac sample signal offsets only. The plots depict the nonlinear relationships among lifetime error, true lifetime, and modulation frequency, and they reveal a sharp sensitivity of modulation lifetime error to ac signal offset under certain experimental conditions. The condition of dacs = 0 results in no liietime error (ddc, = 0 is assumed), and for a given ac offset value and true lifetime, each error surface passes through a minimum near the optimum modulation frequency for the selected lifetime (vopt= l/zmmJ. These theoretical computations show that chromatographicbaseline corrections can be essential to accurate lifetime determinations. Though modulation lifetime envelopes similar to those depicted in Figure 2 are reported to have been corrected through the use of dc intensity matching,' the problem with using dc intensity matching to correct modulation lifetime errors caused by baseline offsets is evident from the following discussion. The sample demodulation, (mJt,using intensity matching, may be represented as
(mJ, = (ac, rof): :
equal to (dc,+ddcJ,
f
?
I
+ dacJ,
Under this special condition of perfect dc intensity matching, substituting eq 11 into eq 6 yields
B lb-lo
-
10.0
e
would reduce to
e
+ dacJt/(dcs + ddcJ,
(dc,+ddcJ
-4
(lo)
closest to (dc,+ddcJ,
Note that reference data at each chromatographic time slice are not selected on the basis of retention time but of dc signal intensity relative to that of the sample. The ideal situation would permit perfect matching of sample and reference dc signal intensities. Then (dc, + ddc3t would be identical to (dc, + ddcJ, and eq 10 2838 Analytical Chemistry, Vol. 67, No. 17,September I, 1995
r
o
I(acr + dacr)for (dc,+ddcJ equal to (dc,+ddc,), Thus, even with perfect dc intensity matching throughout a chromatogram, the computed lifetimes will be corrupted except (1) when the ac offsets are zero or (2) when the offsets are equal and the sample and reference lifetimes (and hence ac signals) are equal. By inspection of eq 12, it is clear that modulation lifetime errors will be greatest when offsets are large relative to the corresponding signals. In a chromatographic system with a k e d baseline offset, this occurs at the peak peripheries, where chromatographic signals approach baseline. At best, a constant modulation lifetime envelope should only be expected for a pure chromatographic component (1) when all offsets are zero with sample and reference lifetimes not necessarily equal or (2) when sample and reference are isochronal, the ac offsets for sample and reference are identical, and the dc offsets for the two components are also identical. While condition 1 is plausible if the detector zero point is stable, condition 2 is virtually untenable because of the requirement that three separate conditions be satisfied simultaneously over the entire peak profile. Experiments. Figure 4 shows various treatments of 1.13 pM anthracene data collected against a 9-AC reference in a 93/7 acetonitrile/water eluent. The high gain and ampliication on the sample detector resulted in noisy signals, especially for the ac signal. The reference modulation depth was determined by plotting the stopped flow ac values (Le., ac + dac) against the corresponding dc values (i.e., dc + ddc). The slope of the plot (Le., 9-AC modulation depth) was 0.285, with a linear correlation coefficient of 0.975. Panel A of Figure 4 shows the modulation lifetime computed from ac and dc signals without baseline correction. A negative ac signal baseline offset and a positive dc signal offset are easily identified. Visible in the peak tail beyond 200 s is a lifetime curving upward toward 20 ns. Based on the simulations of Figure 2, such curvature is expected at both front and tail ends of the peak and is typically observed experimentally. In this case, such curvature at the peak front is not clear, possibly due to small signal distortions. From t = 193 to 203 s in panel A, where the lifetime envelope is fairly flat, the average lifetime is 5.2 f 0.8 ns (tm,av i 1 SD). Across most of the peak (185 s It I220 s), the average liietime is 8.3 ns. In both cases, the agreement with the expected lifetime of 3.2 ns is poor. Panel A typifies experimental modulation lifetime errors caused by baseline offsets. Panel B of Figure 4 is a plot of rm computed using dc signal intensity matching. The computationsgenerallyyielded a negative radicand in eq 12. The negative radicands translate to imaginary modulation lifetimes over most of the peak profile, those lifetimes
am.
am.
241
Mod. Freq., MHz
am.
241
Mod. Freq.,
MHz
a.u. Mod. Freq., 241 Mod. Freq., MHz MHz Fisun 3. Simulations: modulation lifetimepercant relative a r m as function of acsignal oflset and modulation frequency lor two different tnre fluorescencelifetimes,and two differentdc intensities. T N fluorescence ~ lifetimes= 3.00(A, C ) and 60.0 n s (6. D); dc intensities = 0.574 (A. 6 ) and 3.00 arbitrary units (a.u.) (C. D); dc maximum intensily = 10.18 am.; &,* = M,,, = unity; z , , = ~ 12.4 ns. 241
b e i i set equal to zero for plotting purposes. The result is a r,
envelope that is grossly in error over the entire peak The average (2.0i 0.5 ns) of the 6ve non-zero lifetimes near the center of the peak in panel B is signscantly less than the expeeted 3.2 ns. ?his apparent tendency of intensity matching to overcorrect the modulation lifetime envelope is also evident in ref 1. In that reference, Figures 4b-d and 5d reveal modulation lifetimes that are systematically less than z4 values across most, if not all, of each peak profile. Yet, a condition of phase lifetimes systematically exceeding modulation lifetimes is theoretically impassible for fluomphores exhibiting monwxponential decay. F i r e 4, panel C is a plot of the modulation lifetime computed &er ac and dc signals were adjusted for baseline offsets. The ac signal had a constant offset, which was corrected by adding 0.323 intensity units to each ac value. The de signal exhibited a positive sloping linear baseline drift (b, = O.OO0 34% + 0.0935), and the signal was corrected by subbacting the drift. The overlaid ac and dc signals show that the corrections returned the ac and dc peaks to hue baseline. The computed lifetime in panel C is clearly flatter than that in panel A The lifetime envelope appears to sweep slightly upward and away from the peak center, but this is an illusion caused by the signal noise and the fact that imaginary lifetime values are plotted as m e s (see panel D discussion below). The average modulation lifetime for 193 s 5 f 5 203 s is 3.2 i 0.8 ns, which agrees well with the expecled value. The average lifetime from f = 185 to 220 s. with the exclusion of the zero values, is 3.7 f 1.3 ns, also in agreement with the expected value. Panel D of F i r e 4 is an overlay of dc intensity with the hue demodulationenvelopes (i.e., demodulationsrelative to excitation)
corresponding to the lifetime envelopes of panels A-C. The demodulation envelope corresponding to uncorrected signals is in error at low dc intensities but approaches the correct demodulation value near peak center. This agrees with the simulations and is typical of demodulation values computed from uncorrected ac and dc signals An algebraic sign reversal in the demodulation envelope is also evident on each side of the peak. These sign reversals OEN in any region where the sample modulation depth changes sign but the reference modulation depth does not. The intensity-matched demodulation envelope of panel D generally falls outside the range of il.OO0. and this translates to a negative radicand in eq 12. which explains the appearance of the modulation lifetime envelope in panel B. Except for a slight rise near t = 215 s in panel D, the demodulation envelope corresponding to the baselinecorreeted ac and dc signals is essentially flat across the peak, even at very low intensities. This is the most accurate of the three demodulation signals over the greatest retention time range. It shows how a combination of increased noise in the demodulation envelope and plotting imaginary lifetime values as zemes causes the lifetime envelope of panel C to appear to increase at low dc intensities when in reality it does not ?his conbasts with panel A, where the r, envelope clearly curves upward at low dc intensities in the peak tail,indicative of systematic errors.
cowcLusloNs Photomultiplier baseline offsets cause chromatographicmodulation lifetime envelopes to sweep upward and away from the center of a peak. Intensity matching should not be expected to correct such lifetime errors, though unusual circumstances can Analyiical Chemistry, Vol. 67, No. 17, September 1. 1995
2839
$
/
4f
\
I
\
I
0
\
Retention Time, seconds
a
4.
-1 J
I
I
I
\
\
t?
t
,I
4f
0
140 -1 J
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190
140
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200
210
220
-230
1
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Retentlon Time, seconds
--a E (D
\
Retention Time, seconds
L -10
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Retention Time, seconds
Figure 4. Experimental data. (A-C) Overlay of ac (A)and dc (- - -) signals with computed modulation lifetime envelope (0)for 1.13 pM anthracene; rr,true = 3.2 ns. (A) Neither intensity matching nor baseline corrections used; (6)only intensity matching used; (C) only ac and dc baseline corrections used. (D) Overlay of baseline-corrected dc intensity with demodulation envelopes corresponding to panels A (A), B (0)and
c ". exist in which it might appear to be effective. Instead, lifetimes should be corrected by compensating directly for the electronic offsets. Intensity matching can fail completely to yield acceptable lifetime values at all signal intensities, and it may overcorrect corrupted modulation lifetime envelopes. Another drawback to intensity matching is that stopped-flow collection of reference data takes about 30 min. This has an adverse impact on analysis times, especially when a common sample analysis can take less than 30 min. Detector baseline fluctuations within a chromatogram could render accurate baseline corrections impossible. Consequently, the ideal approach to obtaining accurate lifetimes should be to stabilize the instrumentation and prevent significant electronic baseline excursions from occurring. At least one commercial instrument, the SLM-MHF 4850 (SLM-Aminco), does incorporate a dynamic baseline offset correctionduring timedependent signal acquisitions. One of the most significant applications of chromatographic fluorescence lietime detection is in the use of multifrequency lifetime heterogeneity analysis to resolve overlapping components. The component relative lifetimes and the experimental modulation frequenciesinfluence the ability to ignore offset errors. Lifetimes and modulation frequencies aside, the greater the total signal intensity, the less effect a given offset will have. For overlapping chromatographic components, the between-peak signal may be great enough that relatively large errors are tolerable. However, when attempting to resolve, for example, a small peak on the tail of another, even small offset errors can cause complications. Though two fluorophores with a 1:l lifetime ratio cannot be resolved using lietime spectroscopy alone, it remains to be seen 2840 Analytical Chemisty, Vol. 67, No. 17, September 1, 1995
whether lifetime ratios approaching 1:l will be resolvable in a chromatographic system using this technique. The conclusion from previous unpublished work (T. E. Johnston) was that, to adequately resolve overlapping components, the lifetime ratio of overlapping components should be at least 1:2. More recently, similar experiments4with an SLM-MHF 4850 yielded resolution of a 1:3 lifetime ratio, corroborating the earlier findings. In a nonchromatographicsystem, good resolution of a minor fluorophore from a twocomponent mixture (lifetime ratio FZ 1:3) has been achieved using phase and modulation data with no prior knowledge of fluorophore spectra or lifetime^.^ Correcting or preventing chromatographic baseline offsets should become increasingly necessary as attempts are made to resolve increasingly minor components and fluorophore lifetimes approaching 1:l ratios. Using computer simulations to mimic, predict, and evaluate these types of experimental systems has proved invaluable. Simulations offer a significant advantage over experiments because many simulations can be performed in the time required to perform the equivalent spectroscopic experiment. ACKNOWLEDGMENT
Experimental work was supported financially by the Office of Exploratory Research, US. Environmental Protection Agency, and by Duke University. The experimental work was conducted at Duke University. (4) Smalley, M.B.;Shaver, J. M.; McGown, L. B. Anal. Chem. 1993,65,3466-
3472. (5) Lacowicz, J. R: Jayaweera, R: Smacinski, H.; Wiczk, W. Anal. Chem. 1 9 9 0 , 62. 2005-2012.
SUPPORTING INFORMATION AVAILABLE
Mathematical derivation of eq 9 and a detailed description of the dc intensity matching procedure (5 pages). Ordering informa tion is given on any current masthead page.
Received for review February 15,1995. Accepted May 25,
1995.m AC9501699 s.
Abstract published in Advance ACS Abstracts, July 1, 1995.
Analytical Chemistry, Vol. 67, No. 17, September 1, 1995
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