Anal. Chem. 1996,67,511-518
Simultaneous Measurement of the Fluorescence Spectrum and Lifetime of Rhodamine B in Solution to the Subpicomole per Liter Level Mitsuru Ishikawa,*gtg* Motoyuki Watanabe,@Tsuyoshi Hayakawa,* and Musubu Koishir Precursory Research for Embryonic Science and Technology (PRESTO), Light and Material, Research Development Corporation of Japan (JRDC), Hamamatsu Photonics K. K. Tsukuba Research Laboratory, Tokodai 5-9-2, Tsukuba, lbaraki 300-26, Japan, and Hamamatsu Photonics K. K. System Division, Joko 8 12, Hamamatsu, Shizuoka 43 1-91, Japan
The fluorescence spectrum and lifetime of rhodamine B (3.5 x 1OV9-3.5 x M in methanol) were simultaneously measured as two-dimensional images by means of a streak-camera technique. This study used an easy sample preparation involving simply loading the sample into a capillary tube and sealing the tube. Thus, this novel analytical procedure should find wide application. The average number of probed molecules was estimated to be 0.16 when the concentration was 3.5 x M. The number of fluorescence photons that were experimentally detected was consistent with the number of fluorescence photons that were computed with available experimental parameters.
One of the ultimate goals of analytical chemistry is to detect and identify individual molecules. Recently, a number of studies have appeared on the detection, spectroscopy, and lifetime measurements of single organic molecules based on laser-induced fluorescence Single-molecule detection (SMD) in +
PRESTO.
* Hamamatsu Photonics K. K Tsukuba Research Laboratory. Hamamatsu Photonics K. K. System Division. (1) Omt, M.; Bernard, J. Phys. Rev. Lett. 1990,65, 2716-9. (2) Ambrose, E. P.;Basche, Tn.;Moemer, W. E. J. Chem. Bys. 1991, 95,
7150-63. (3) Basche, Th.; Moemer, W. E.; Omt, M.; Talon, H. Phys. Reu. Lett. 1992, 69,1516-9. (4) Wild, U.P.;Giittler, F.; Pirotta, M.; Rem, A Chem. Phys. Lett. 1992,193, 451-5. (5) Pirotta, M.;Giittler, F.; G y g a , H.; Renn, A; Sepiol, J.; Wild, U. P. Chem. Php. Lett. 1993,208,379-&1. (6) Omt, M.; Bemard, J.; Personov, R 1.1. Phys. Chem. 1993,97,10256-68. (7) Moemer, W. E.; Basche, Th. Angew. Chem., Int. Ed. Engl. 1993,32,45776. (8) Moemer, W. E. Science 1994,265,46-53. (9) Betzig, E.;Chichester, R J. Science 1993,262,1422-5. (10) Giittler, F.;Imgartinger, T.; Plakhoinik, T.; Renn, A; Wild, U. P. Chem. Php. Lett. 1994,217,393-7. (11) Ishikawa, M.; H m o , K. Hayakawa, T.; Hosoi, S.; Brenner, S.Jpn. J. Appl. Php. 1994,33,1571-6. (12) Palm, V.;Rebane, K. IC;Suisalu, A J .Phys. Chem. 1994,98,2219-21. (13) Ambrose, W. P.; Goodwin, P. M.; Martin, J. C.; Keller, R A. Phys. Reu. Lett. 1994,72,160-3. (14) Trautman, J. K;Macklin, J. J.; Brus, L E.; Betzig, E.Nature (London) 1994, 369,40-2. (15) Xie, X.S.;Dunn, R C. Science 1994,265,361-4. (16) Ambrose, W. P.;Goodwin, P. M.; Martin, J. C.; Keller, R A Science 1994, 265.364-7. 0003-2700/95/0367-0511$9.00/0 Q 1995 American Chemical Society
solution was first achieved by the burst-detection technique”-23 using flowing sample streams. In this scheme, the volume of the sample being measured is smaller than 1pL (restricted by a laser beam waist size and a spatial filter) and contains less than 0.01 molecule on average. Thus, one can only observe the bursts from fluorescence photons when individual molecules pass through the probe volume. Recently, this technique has been extended to the lifetime measurements of single molecule^^^-^^ employing pulsed excitation and timegated detection. The second approach to fluorescence-detection SMD in solution utilizes a single-droplet trapping technique with an electrodynamic levitator.nq28 The number of dye molecules in the droplets was determined by Poisson’s formula. One can compute the mean number of the trapped molecules in a droplet from the droplet volume and the analytical concentration of the dye solutions. A significant advantage of the flow technique is its short measurement time, which is governed by the transit times (I 1ms). However, there is a trade-off between quick measurements and laser-dye interaction time to obtain a good signal-to-noise (S/N) ratio. The droplet technique has several advantages over the flow technique. For example, laser-analyte interaction time can be extended arbitrarily because all molecules remain in the interaction region until being photolyzed. This allows for the maximum number of fluorescence photons to be detected. Recently, a third SMD technique for use with solutions was reported.% Here a small Dovich, N. J.; Martin, J. C.; Jett, J. H.; Trkula, M.; Keller, R A Anal. Chem. 1984,56,348-54. Nguyen, D.C.;Keller, R A; Jett, J. H.; Martin, J. C. Anal. Chem. 1987, 59,2158-61. Peck, IC;Shyer, L;Glazer, A N.; Mathies, R A PYOC.NatLAcad. Sn‘. USA. 1989,86,4087-91. Mathies, R A;Peck, K Anal. Chem. 1990,62,1786-91. Shera, E. B.; Seitzinger, N. K.; Davis, L M.; Keller, R A; Soper, S. A Chem. P h p Lett. 1990, 174, 553-7. Soper, S. A; Shera, E. B.; Martin, J. C.; Jett, J. H.; Hahn, J. H.; Nutter, H. L.; Keller, R A Anal. Chem. 1991,63,432-7. Soper, S.A; Matlingly, Q. L;Vegunta, P.Anal. Chem. 1993,65, 740-7. Soper, S. A;Davis, L. M.; Shera, E. B. J. Opt. SOC.Am. B 1992,9,17619. Wilkerson, C. W., Jr.; Goodwin, P. M.; Ambrose,W. P.; Martin, J. C.; Keller, R A Appl. Phy. Lett. 1993,62,2030-2. Tellinghulsen, J.; Goodwin, P. M.; Ambrose, W. P.; Martin, J. C.; Keller, R A Anal. Chem. 1994,66,64-72. Ng, K C.; Whitten, W. B.; h o l d , S.; Ramsey, J. M. Anal. Chem. 1992, 64, 2914-9. Barnes, M. D.;Ng, K. C.;Whitten, W. B.; Ramsey, J. M.Anal. Chem. 1993, 65, 2360-5. Eigen, M.; Rigler, R Proc. Natl. Acad. Sci. U S A . 1994,91, 5740-7.
Analytical Chemistry, Vol. 67, No. 3, February 1, 1995 511
volume is formed by using a diffraction-limited laser beam in combination with conforcally imaged pinholes or fiber optics in sample droplets. Individual molecules are detected as fluorescence bursts when the molecules pass across the probe volume due to self-diffusion. In many applications, however, one does not necessarily need to identify the exact number of molecules, although increasing the detection limits is always preferable. The procedures reported to date for SMD in solution have several inconveniences for those not experienced in sample preparation and the measurement. In a conventional chemical analysis, we need only sample concentration or the average number of molecules within a probe volume. In this study, we present a novel fluorometry which enables us to measure simultaneously a fluorescence spectrum and lifetime to subpicomole per liter level by simple sample preparation. A common way to improve analytical detection limits is to use time-resolved measurements, especially in combination with excitation pulses with high-repetition rates (e.g., from kilohertz to several tens of megahertz). Here, random noise is out of synchronization with the excitation pulses and is thus discriminated from the fluorescence from analytes. In this scheme, identification of a lifetime is not necessarily of primary importance: a great advantage is in the discrimination. Recently, a novel technique was reported based on timeresolved two-photonexcited fluorescence detection?O in which detection limits were expanded to -10 pM regime with S/N = 3. The merits of the two-photonexcited fluorescence scheme are in the significant reduction of interference due to Raman scattering from solvents and in avoiding direct excitation of impurities that share common spectral regions with analytes in absorption. A disadvantage is much smaller twophoton cross sections compared to that of one photon. A timeresolved measurement to improve analytical detection limits has already been published. The objective of this measurement was to discriminate between signals and noises based on one-photon absorption by means of time-gated detection.3l This study showed that the lower limit of detection (S/N = 2) was 1.8 x 10-13 M rubrene in benzene for a 1Ws counting period. This performance, however, came from extrapolation. Actual measurements were carried out to 5 x M. This measurement addresses only total fluorescence intensity. Almost all of the schemes described above use laser-induced fluorescence detection based on photoncounting techniques with conventional photomultiplier tubes, microchannel-plate photomultiplier or single-photon avalanche d i o d e ~ Thus, . ~ ~ one must observe time-resolved fluorescence spectra by tediously changing individual wavelength steps. In practice, fluorescence spectra1-4.6-8J2J4or decays5J5J6were separately measured by these methodologies. Here we demonstrate for the first time that simultaneous measurement of spectra and lifetimes are possible down to subpicomolar concentrations (3.5 x 10-13) of rhodamine B (RhB) in methanol (S/N = 2.8) by means of a two-dimensional photoncounting technique based on the streak-camera technologies. We not only obtained the calibration line for sample concentration versus total fluorescence photons but also observed the fluorescence spectra and lifetimes in the M regime. The (30) Lytle, F. E.; Dinkel, D. M.; Fisher, W. G.Appl. Spectrosc. 1993,47,20026. (31) Haugen, G.R; Lytle, F.E.Anal. Chem. 1981,53, 1554-9. (32) Yamazaki, I.; Tamai, N.; Kume, H.; Tsuchiya, H.; Oba, K Rev. Sei. Instnrm. 1985,56,1187-94. (33) Li, L.-Q.; Davis, L. M. Rev. Sci.Instrum. 1993,64,1524-9.
512 Analytical Chemistry, Vol. 67, No. 3, February 1, 7995
use of RhB is primarily due to its well-documentedphotophysical and photochemical properties. The present method can easily be extended to other fluorescent dyes used as tags for chemically or biologically important molecules if appropriate excitation wavelengths are available. The average number of dye molecules in a probe volume is estimated to be less than unity when the concentration is 3.5 x M. The application of this technique to chromatographical use could provide fundamental improvements in identifying a very small number of analyte molecules. EXPERIMENTAL SECTION
Materials and Sample Preparation. Rhodamine B chloride (Nacalai Tesque, CAlN203C1, M W 479.02) was used as supplied.
High-grade methanol (Luminasol, Dojindo Laboratories) was used as a solvent to minimize the interference from impurities. A 3.5 x M RhB methanol solution, which was preserved in a refrigerator (277 K), was diluted to 3.5 x 10-13M. Rhodamine B is largely in the zwitterionic form in alcohols, for which the absorption and fluorescence maxima are 545 and 569.6 nm, respectively, in methanol at 298 K34 The fluorescence quantum yield (Q and the lifetime (t3 were reported to be 0.52 and 2.54 ns, respectively, in methanol at 298 Fluorescence measurements were completed within 3 h after the samples were prepared. Disposable glass cuvettes (500 pL) were used for the successive dilutions because repeated use of the same cuvettes sometimes led to poor reproducibility. The sample cuvettes used for the fluorescence measurements were quartz capillaries (100." length with a l.0-mm inside diameter and 3.0-mm outside diameter). The quality of data did not depend on the grade of the quartz used, either fluorescence-freegrade or ordinary grade, even though the ordinary grade quartz often emits blue fluorescence on ultraviolet excitation (1270 nm). This insensitivity to the quality of the quartz used is because the excitation light used in this study was in the visible region. The surface of the quartz capillary was polished to reduce the scattering of exciting light by surface irregularities. Both ends of the tubes were sealed with poly(tetrafluoroethy1ene) stoppers. AU measurements were carried out using airequilibrated solutions at 296 K. EZvcitation Source. The light used for excitation was picosecond pulses from a CW dye laser (Spectra-Physics, 375B), which was cavity-dumped (Spectra-Physics, 344s) and synchronously pumped by a CW mode-locked Art laser (Spectra-Physics,203018). The wavelength of the picosecond pulses was tuned to 540 nm. Disodium fluorescein (Exciton) was used as a gain medium. An average power of -100 mW was obtained at a 4MHz repetition rate with a 10-ps full width at half-maximum (fwhm) pulse width. A variable neutral density (ND) filter that changes light intensity by reflection was used to adjust the intensity of the laser beam. One should avoid ND tilers that change light intensity by absorption because the spatial profile of the laser beam is deformed due to a thermal-lens effect. The direction of the laser beam polarization was adjusted by means of a half-wave plate so that it was vertical to the capillary axis. This diminishes the Rayleigh scattering from the laser beam. To obtain enough stability in the pulse energy (within about f3%),the mode-locker driver and the cavity-dumper driver were warmed up at least overnight. For best reproducibility, it was important to carefully tune the frequency synthesizer for the mode-locker driver and to tune the t i m i i of the cavity-dumper driver. (34) Chang, T.-L.; Cheung, H. C. J. Php. Chem. 1992,96,4874-8
Mode-LockedCW Ar Ion Laser
Cavity Dumper
\
CW Dye Laser
Sample
1 Power Supply
?J2
ND
&@
LP Filter.
-1
w.
r-H outer
1
W
Lens(f=50)
The fundamental advantage of the streak scope is its twodimensional nature. Simultaneous measurements of lifetimes and spectra with picosecond time resolution are displayed on twodimensional images. This is particularly advantageous in measuring timeresolved fluorescence spectra. Recently, improved photoncounting capability was added. The images are composed of 640 x 480 pixels; where each pixel is equivalent to a 16-bit photon counter. The channel number (ch) of 640 was assigned to the spectral range, where M = 93.5 nm in this study. The channel number of 480 was allotted to the entire time range, 10 ns in this study. Thus, we denote the two-dimensional fluorescence intensity as Zr(,l,t) per ch2 (or per pixel) and often use for convenience the following onedimensional expressions.
I Figure 1. Diagram of the picosecondfluorometer used in this study (top view minus the computer). Laser pulses passing through a microscope objective were used to excite the dye solution: Obj(1) is x40 and NA is 0.40 after passing through a 1/2 plate and a ND filter. The emitted fluorescence photons were collected with a microscope objective: Obj(2) is x 10, NA is 0.21, and a conventional achromatic convex lens was used ( f = 50, 30 4). The collected photons were focused onto the incident slit after passing through a long-pass (LP) filter. The partially divided laser beam was introduced into a PIN photodiode (PD) and used for the trigger pulses. The trigger pulses were suitably delayed with a variable cable delay unit.
Instrumentation (1). Figure 1shows a schematic illustration of the experimental setup used in this study. The excitation laser beam was focused with a x40, 0.40 numerical aperture (NA) microscope objective (Nikon, CF M Plan SLWD). The emitted fluorescence was collected with a combination of a x 10,0.21-NA microscope objective (Nikon, CF M Plan SLWD) and a 50-mmfocal length achromatic lens and then focused onto the entrance slit of a polychromator (Chromex, 250IS, f/4) after passing through a long-pass filter (HOYA, 056) to reject the scattering from 540-nm excitation pulses. An astigmatismcorrected holographic grating (Chromex, 150 grooves/") was used in the polychromator. The efficiency of transparency of all of the optical components were measured with a power meter (UDT,2370) and a Xe lamp source coupled with a band-pass filter that transmitted light nearly matching the fluorescence maximum (-575 nm) or the CW Art laser. The dispersion of the 150-groovegrating covers a 93.5nm spectral range and was used in combination with a detector to be described later. One can of course choose lowdispersion gratings (e.g., 100 grooves/") to cover a wider spectral range. The astigmatism-free grating improves the efficiency of fluorescence collection, which is an important point in the present study. The reason for the improvement will be described later. Instrumentation (2)and Analysis. A key component of the fluorometer is the compact streak scope detector (Hamamatsu Photonics, C4334). Its operating principles and basic performance, as well as recent improvements in its dynamic range and sensitivity over the previous v e r ~ i o n s , have ~ ~ . ~already ~ been described elsewhere.37Here we only describe the specitications that are signscant to this study. (35) Tsuchiya, Y. IEEE J. Quantum Electron. 1984,QE-20, 1516-28. (36) Davis, L. M.; Parigger, C. Meas. Sci. Technol. 1992,3, 85-90. (37) Watanabe, M.; Koishi, M.; Roehrenbeck, P. W. Proc. SPIE Adv. Fluor. Sets.
Tech. 1993,1855, 155-64.
Here one can arbitrarily set an integration interval between 0 and 479 ch for time (0 ch 5 a 5 b 5 479 ch) and between 0 and 639 ch for wavelength (0 ch I c 5 d 5 639 ch). Incident fluorescence photons on the entrance slit of the polychromator are spatially dispersed and then focused onto the photocathode of the detector. The lateral size of the dispersed fluorescence image on the photocathode corresponds to the wavelength range, which is simultaneously observable. The vertical size of the fluorescence image restricts the time resolution because the fluorescence image, which is converted to photoelectrons on the photocathode, is swept in the vertical direction. The convolution of the vertical size of the fluorescence image, the laser pulse width, and triggering jitter in the time sweep determines the effective time resolution of the detector. The best time resolution was reported to be less than 20 ps fwhm on a 1 nd480 ch time range.37 Here we used a 10 ns/480 ch time range only because the fluorescence lifetime of RhB in methanol was reported to be 2.54 118.3~ For this time range, both the vertical size of the fluorescence image and the triggering jitter are the main factors in determining temporal response, because the pulse width (10 ps fwhm) of the laser was negligible compared with the time range. The temporal response is typically 5 150 ps fwhm. Using a grating with astigmatism and then focusing spectrally, we obtained a fluorescence image that was blurred in vertical direction, which corresponds to the time axis, thus degrading the time resolution of the detector. To improve the time resolution, a slit was positioned before the photocathode to restrict the vertical width of the fluorescence image. This results, however, in loss of fluorescence photons. For example, the vertical width of the fluorescence image is -2.5 mm in spectrographs with a 250." focal length. If we use a slit with a 50-pm width, which is a typical width in fluorescence measurements, the attenuation factor amounts to 1/50. On the other hand, the use of an astigmatismfree grating relieves the problems associated with the use of the incident slit. To avoid degradation of the wavelength and time resolutions, the fluorescence image is directly focused onto the photocathode. Other improvements in the photosensitivity were obtained by modfication in the streak scope detector.37 A timing chart showing the relation between triggering and excitation pulses is illustrated in Figure 2. Note that the streak scope was operated at 0.67 MHz in the 10 ns/480 ch range Ana!ytical Chemistry, Vol. 67, No. 3, February 1, 1995
513
T
E
E
4
1
1500 ns
.. : .. .
Trigger Pulses
.. . .. :
.. . .. :
.. . .. :
.. ... :
$ 2
n Trigger Delay t Variable Delay (60-90 ns)
7
Sweep Ramp voltage
1
0 0
Streak Sweep (10 ns)
Figure 2. Timing sequences of the laser pulses, trigger pulses, and streak sweep. The trigger pulses, which were synchronized with laser pulses, were decreased to 0.67 MHz inside the controller: pulses indicated by T triggered the streak sweep, whereas pulses indicated by E excited the sample solutions.
although the excitation pulses were emitted at 4 MHz. This is due to the intrinsic nature of the trigger circuits that are now used. The fluorescence lifetimes were computed with a nonlinear least-squares iterative convolution procedure based on the Marguardt alg~rithm.~~-~O The temporal response function (-130 ps fwhm in 10 ns/480 ch time range) of the instrument was obtained from the scattered laser light. Data analyses other than the lifetime calculations were carried out using commercially available software (Igor Pro version 2.0.1, WaveMetrics) on a personal computer (Macintosh, Apple Computer). RESULTS AND DISCUSSION
Dark Count Measurements. We first measured the dark current noise on a 640 ch x 480 ch x 16 bit image at the maximum sensitivity of the detector, which was the setting under which all the fluorescence measurements were carried out. The dark noise, which mainly comes from the photocathode, ultimately restricts the detection limits. Figure 3 shows the dark noise under time sweep with a time range of 10114480 ch: &dla,k(i,t) dt from a = 0 ch to b = 479 ch, where &&(A$) is dark counts per channel squared. The total amount of dark noise mobs)was 80 counts/ 100 s on the 640 ch x 480 ch image. The value was essentially constant under the various discrimination thresholds that were used in the photoncounting measurements. The dark noise density (&ens) from S20 photocathodes used in conventional photomultiplier tubes is known to be 6.25 x 1026.25 x lo3countss-1*cm-2at ambient temperatures. The area S, of the photocathode used in the streak scope is 0.007 cm x 0.48 cm = 3.36 x cm2. The small area of the photocathode is effective in reducing the dark noise. The amount of calculated dark noise per unit time @dC) under the time sweep is given by the following equation. (38) Marquardt, D.E.]. SOC.Ind. Appl. Math. 1963,11, 431-41. (39) Bevington, P.R Data Reduction and ErrorAnalysisfor the Physical Sciences; McGraw-Hill: New York, 1969. (40) O’Conner, D. V.; Philips, D. Time-Correlated Single Photon Counting; Academic: New York, 1984; Chapters 2 and 6.
514 Analytical Chemistry, Vol. 67,No. 3, February 1, 1995
100
200
300 400 Channel Number
500
600
Figure 3. Dark counts (80 counts) observed at the maximum sensitivity of the streak scope with a time sweep of 10 ns/480 ch. The accumulationtime was 100 s with off-laser excitation and a 0-pm slit width. Dcalc
=s p d e n p
(3)
Here& the frequency of the excitation pulses (0.67 MHz in the present study) and T is the entire time range (10 ns). If we use the maximum value of &ens of 6.25 x 103 countss-Lcm-2, we obtain a D d c value of 21 countsjs x 0.67 x 106/s x 10 x s or 0.14 counts/s and total calculated dark count CTDdc) of 0.14 counts/s x 100 s or 14 counts. The larger value of m o b s (80 counts/100 s) than that of TDd, is due in part to the enhnaced red sensitivity (2600 nm) of the S20 photocathode used in streak scopes. Excitation Energy Dependence of FluorescenceIntensity. We then evaluated the optimum excitation energy to avoid saturation in the photon-counting measurements. The saturation occurs when a large number of photons impinge on a photocathode. The excess photons increase the probability of mistakenly counting a signal due to the overlapping of two or more photoelectrons as a signal coming from one photoelectron. We measured the excitation power dependence of the fluorescence spectra and decays from 0.005 to 5.00 mW using a 3.5 x M solution of the sample. The background was observed with 0.00 mW excitation power. The accumulation time was 300 s with a 5@,mslit width. The saturation is not easily noticeable in the spectral shape in Figure 4a, but it appears explicitly on fluorescence decay curves above 2.5 mW in Figure 4b. That is, one can identify unusual deviations from single-exponential behavior in two of the decay curves, (1) and (a), in Figure 4b. We therefore used l.@mW laser pulses in the following experiments. The spectra in Figure 4a were defined by Zf(i) = Spf(A,t)dt, where the integration interval ranged from a = 0 ch to b = 479 ch. Also the fluorescence decays defined by I&) = &(i,t) dA in Figure 4b were obtained by integration of ifrom c = 0 ch to d = 639 ch. Both m r e s are displayed without background subtraction. The criteria for avoiding saturation have already been discussed for the time-correlated singlephotoncounting technique using photomultiplier tubesa We showed that saturation occurs above If (t) x 2000 counts/ch from curves 1 and 2 in Figure 4b. This means that we should restrict the average counting rate (CR, count*s-1*ch-2)to less than 0.01 at the maximum of the decay curves because 300 s x 640 ch x CRis less than or equal to 2000 counts/ch. The probability of counting a signal due to two or
4 \--r
f3
......... .
.._c--
. I . . ..
....
....
...
...I
1 o3
1000
B C
s80 lo2 E 1 0'
83
100
E
10
s0
1
1 oo
560
580
600 620 Wavelength(nm)
560
640
580
600 620 Wavelength(nm)
640
1 o4 1000
B C
z s
1 o3
0-2 c. C
83
1 o2
0
E
100
0 0
c.
2
10
10'
1
1 oo
0
2
4
6 Time(s)
8
10x109
Flgure 4. Fluorescence spectra (a) and decay curves (b) of RhB in methanol (3.5 x M) with various excitation powers: (1) 5.0, (2) 2.5, (3) 1.0, (4) 0.5, (5) 0.25, (6), 0.05, (7) 0.005, and (8) 0.000 mW. The data indicated by (8) in (a) and (b) show the background. The fluorescence lifetimes were identified to be 2.3 ns. The accumulationtime was 300 s,and the slit width was 50pm. Deformation of decay curves appeared in (1) and (2) in (b) as a departure from the straight lines: the early parts of the decay curves were saturated above intensities of 2000 counts. Table 1. Fluorescence Lifetimes (rf),Reduced2,and Total Fluorescence Photons ( after Background Subtraction at Selected Concentratlons of RhB in Methanol at 296 K
conc (M) (1) 3.5 10-9 (2) 3.5 x (3) 3.5 x lo-" (4) 3.5 x
tf
(ns)
2.350 2.253 2.314 2.241
x2
Texp(counts/300 s)
1.174 0.995 0.901 1.659
327307 34357 3668 1094
The number of background counts was 1447, and the slit width was 50 pm. The curvefitting calculations were carried out from 110 to 480 ch for (1) and (2) and from 110 to 300 ch and 110 to 180 ch for (3) and (4), respectively.
more photoelectrons as one count is -1% based on Poisson's formula, where the expectation value is 0.01. MeasurementofZdA,t)to 1.0 pM. Here we measured I@$) using a laser power of 1.0 mW, a 50-pm slit width, and a 300-s accumulation time. We summarize the relation between the observed photocounts and the analytical concentration of RhB in methanol in Table 1. The data were obtained after background subtraction. The background, which was obtained using neat methanol, amounted to 1447 counts on a 640 ch x 480 ch image. The background includes Raman scattering from the methanol (0-H stretching, 0-H bending, C-0 stretching, and C-H bending modes). The intrinsic dark noise from the photocathode
0
2
4
6 Time(s)
8x10-'
Figure 5. Fluorescence spectra (a) and decay curves (b) of RhB in methanol at various concentrations: (1) 3.5 x (2) 3.5 x 10-lo, (3) 3.5 x and (4) 3.5 x lo-'' M. The excitation laser power was 1.OmW, and the slit width was a 50pm. The accumulation time was 300 s. The spectra are shown after background subtraction, whereas the decay curves are shown without background subtraction. The background is displayed as a baseline.
is calculated to be 240 counts from the dark count measurements. Agood linear relation was obtained from 3.5 x 10-9 to 3.5 x 10-11 M. The extrapolation of the results to lower concentrations indicates that we must measure 300-350 or 30-35 counts above the 1447 background counts to obtain 3.5 x 10-l2 or 3.5 x 10-13 M detection, respectively. The departure from a linear relation, especially in the 10-l2 regime, was possibly due to contamination from the ambient air or other factors associated with the sample preparations. The fluorescence spectra and lifetimes were barely identiiiable at 3.5 x 10-l2 M as shown in Figure 5a,b, where &(A) = @&t) dt from a = 0 ch to b = 479 ch and I&) = JfZf(A,t) ct3. from c = 0 ch to d = 639 ch are displayed. It should be noted that the background, which was obtained from neat methanol, was subtracted in Figure 5a, whereas the background was displayed in Figure 5b as a baseline. The rapidly declining response at the early part of the fluorescence decays that appeared in curves 3 and 4 arises from the Raman scattering from the methanol. In Table 1, we summarize rf and the reduced x2 at each concentration. It has been suggested that acceptable x 2 values range from 0.8 to 1.2.& Thus, the value for the 3.5 x 10-12 M concentration (1.66) is unsatisfactory based on this criterion. Measurements of to the Subpicomolar Level. To further extend the linearity of the measurements into the 10-1210-13 M regime, more fluorescence photons are needed, together with careful sample preparations to reduce contamination. Thus, we expanded the slit width from 50 to 100 pm and extended the accumulation time from 300 to 600 s with an excitation power of 1.0 mW. Here, the background amounted to 5781 counts, of Analytical Chemisfry, Vol. 67, No. 3, February 1, 1995
515
Table 2. Fluorescence Lifetimes (GO, Reduced2,and Total Fluorescence Photons (T.-) after Background Subtraction at Selected Conoentratlons of RhB in Methanol at 296 K
conc (M)
zr (ns)
X2
T .(counts/600 s)
(1) 3.5 x (2) 3.5 x lo-" (3) 3.5 x (4) 3.5 x
2.277 2.338 2.326 2.314
1.119 1.101 1.234 1.217
248914 18889 2218 71
Y
24
I\
I
2
0
4
6
a The number of background counts was 5781, y d the slit width was 100 pm. The curvefitting calculabons were camed out from 110 to 480 ch for (1) and (2) and from 110 to 300 ch and 110 to 250 ch for (3) and (4), respectively.
1000
B
24
0 10
I\
I
2
6 Time(s)
4
8x10'
1000
U
0
f
8X1O9
Time(@
I
Y
o
8
5
-10
560
580
600
620
E
640
Wavelength(nm)
10 1 Time(@
Flgure 7. Fluorescence decay curves of RhB in methanol at (a) and (b) 3.5 x M without background subtraction. The background (c) is shown as a baseline. The accumulation time was 600 s, the slit width was 100 pm, and the laser power was 1.O mW.
3.5 x
8
10
E
-10
560
580
600
620
640
Wavelength(nm)
Flgure 6. Fluorescence spectra of RhB in methanol at (a) 3.5 x lo-" and (b) 3.5 x M after background subtraction. The accumulation time was 600 s, the slit width was 100 pm, and the laser power was 1.O mW.
which 480 counts came from the photocathode itself. We obtained, as tabulated in Table 2, an improved linear relation between the observed fluorescence photons and the analytical to 3.5 x concentration of the dye solutions from 3.5 x M. The data in Table 2 were obtained after background subtraction. We identified both the spectra and the lifetimes to 3.5 x 10-12 M. Although the identification of the spectrum at 3.5 x M is somewhat difficult to do compared with that at 3.5 x 10-l2 M, as shown in Figure 6a,b, the lifetime at 3.5 x M is recognizable in Figure 7b. tfand x2 are also summarized in Table 2. All of the fittings were satisfactory in terms of the x2 criterion. The S/N ratio of the total fluorescence photocounts at 3.5 x M based on the dark counts (5781) and the extrapolated fluorescence photons (-220) is computed to be as follows: S/N = 220/(5781 220)1/2= 2.8. From Tables 1 and 2 we identify the fluorescence lifetime of RhB in methanol as tf= 2.3 ns. Estimation of Probe Volume and the Average Number of Dye Molecules in the Volume. The probe volume was prescribed as a cylindrical shape in the sample solution and was
+
516 Analytical Chemistry, Vol. 67, No. 3, February 1, 1995
calculated from the Gaussian beam-waist area and the length of the cylinder. The length of the cylinder was determined by the slit width (50 or 100 pm) of the polychromator. The dimensions of the beam waist were measured to be 6 and 7 pm (l/e2> by moving a razor blade across the laser beam at the focal point. The fluorescence-collecting lenses imaged the fluorescent cylindrical volume (1 mm in length) formed within the sample capillary onto the slit, where the fluorescent image arrived at a magnification of 4.4. Thus, the slit width of 50 pm corresponds to the cylinder length of 11.4 pm at the sample tube. The measured beam-waist dimensions (6 pm x 7 pm) were essentially constant within the cylinder length of 11.4 pm. The photon density of the excitation laser beam was evaluated by use of the two beam-waist dimensions, which are approximated as the two axes u = 3.5 pm and b = 3.0 pm of an oval. The area of the beam waist is S, = nub = 33.0 pm2. Furthermore, we assumed for simplicity that the beam-waist size is constant within the cylinder length of 22.8 pm. The length of 22.8 pm corresponds to a 100-pm slit width. This assumption does not influence the conclusions of this study, which are directed at the topic of how to do simultaneous fluorescence spectrum-lifetime measurements to the M regime. Any deviation from the above assumption that the beam-waist area is constant can be evaluated on the basis of the ratio of counted fluorescence photons using 50- and 10O-pm slit widths. The fluorescence photocounts in a 3 W s accumulation time with a 50-pm slit width and a 600-s accumulation time with a 100-pm slit width (3.5 x 10-10 M sample) were 34 357 and 248 914,
because of the small triplet yield of RhB (0.0024),4l a(Zd is related to the difference between the ground state population, NI, and the lowest singlet excited state population, Nz, as follows.
20x10~j
Here, a, is the absorption cross section, which is independent of The relation describing the populations of this simple twolevel system is N1 NZ= N. Thus, when there is no excitation (Nz = 0), NI must equal N. These results are consistent with our common understanding of such systems. On the other hand, from eq 5 we can obtain a(&&= 0.85 x a(0) using I, = 5.6 mW and I, = 1.0 mW, the latter of which is the excitation laser power used in this study. Next, we can obtain Nz/(NI + Nz) = 0.075 from N1+ NZ= Nand Nl - Nz = 0.85N. This ratio means that the transition of one molecule from the ground state to the excited state occurs with a probability of 0.075 when one excitation pulse irradiates one molecule. We can then obtain the excitation rate as = 4.0 x 106 x 0.075 = 3.0 x 105 photons*s-lmolecule-l using a pulse repetition rate of 4 MHz. Estimation of the Detectable Fluorescence Photons and Comparision with Those Detected Experimentally. Here we calculate the number of fluorescence photons based on the photophysical and photochemical parameters of RhB, fluorescence collection efficiency, transmittance of the optical components, and photon-counting efficiency of the detector. The comparison between the calculated fluorescence photons and the observed photons will allow us to understand the reliability of the analytical measurements based on the two-dimensional photon-counting techniques. The total number of fluorescence photons (TcdJ emitted by molecules within the probe volume during the accumulation times were as follows: TCdc= Jabs x @f x 0.167 x 1.585 x 600 s = 2.48 x lo7photons. Note that the factor 0.167 comes from the discrete use of the 4MHz pulses for the triggering and sweeping as shown in Figure 2. The factor 1.585 is the average number of RhB molecules in the probe volume at a sample concentration of 3.5 x M. The gross efficiency of the fluorescence collection and the transparency of the two lenses, the longpass filter, and the polychromator is -0.31%. The efficiency of the photon counting of the detector is -3%. The calculated detectable fluorescence photons are Tcdcdet= 2.30 x lo3 photons from TCalc x 3% x 0.31%,which is, considering the approximate nature of the calculation, in good agreement with the experimentally detected total fluorescence photons (Tap) from a 3.5 x M solution as shown in Table 2 (Tew = 2.22 x 103 photons). In the above calculation,the contribution from photobleaching to the detected fluorescence photons is neglected. We can also compute the probability for dye molecules to survive bleaching. First, the average transit time rt of a molecule passing across the probe volume should be calculated, and then the photobleaching rate constant can be computed. It is appropriate to estimate zt based on the following equation.
Zep
0 0
I
I
I
I
1
5
10
15
20
25
Average Laser Power(mW)
Figure 8. Saturation characteristics of RhB fluorescence in methaM. A limiting fluorescence intensity (Fmm)of 22 062 nol at 3.5 x counts and a saturation power (l,) of 5.76 mW were obtained using the relation F = FmJ(l Idle,),where I, is the excitation power and Fis the fluorescence intensity. The curve was depicted using I, and Fmm. The error bars indicated &3% of each intensity. Accumulation time was 20 s; the slit width was 50 pm. The average laser power 1 mW (540 nm, 4 MHz, 10 ps fwhm) used for the experiments is converted into other useful parameters: 250 pJ/pulse, 6.77 x lo8 photons/pulse, or 7.58 x 10' W/cm2 using the beam-waist area (33.0 pm2).
+
respectively. The ratio of these two values, including correction for the larger slit width (factor of 2) and longer accumulationtime (factor of 2), is 248914/(34357 x 2 x 2) = 1.81. This indicates that the assumption is accurate within a factor of -2. The probe volume v based on the above assumption is v = S, x 22.8 ym = 754 ym3 when the slit width is 100 ym. Thus, we obtain 1.585 molecules as the average number of molecules within the probe volume when the concentration of the sample solution is 3.5 x M. Evaluation of Excitation Rate. We first evaluated the saturation energy of RhB in methanol using a 3.5 x M solution according to the following equation.
Here, F is the fluorescence intensity, I, is the excitation laser power, and I, is the saturation power. F,, is the limiting fluorescence intensity when I,, approaches infinity. We obtained a value for F,, of 22 062 counts and for I, of 5.76 mW by doing a curve-fitting analysis of the data in Figure 8 using eq 4. We were careful to avoid trivial saturation, which can occur due to an excess incident fluorescence photons on the photocathode, as was discussed in a previous part of this paper. A 10%ND filter was placed before the entrance slit. The origin of the saturation intensity should be due to the depletion of ground state population if the photobleaching of the dye solution is negligible. Thus, I, has the following relation.
+
"x
Here, a(Ie3is the amplitude absorption coefficient under saturation and a(0) is the amplitude absorption coefficient without saturation. Furthermore, by assuming a simple two-level system
(7)
Here, x is the root-mean-square distance of displacement of a (41) Dunne, A;Quinn, M.F.J. Chem. SOC.,Faradny Trans. 1 1977,73,110410.
Analytical Chemistry, Vol. 67, No. 3, February 1, 1995
517
diffusing particle during time tt and the self-diffusion constant of the particle is D. The value of D that is acceptable for rhodamine dyes is 5 x 102 pm2/s.42 If, for simplicity, a rectangular probe volume (6 pm x 7 pm x 22.8 pm) is assumed,20the value of x is the average of the three dimensions: (6 pm 7 pm + 22.8 pm)/3 = 11.9 pm, because the probability for diffusion of a molecule through any of the three directions is the same. By substituting x = 11.9 pm and D = 5 x 102 pm2/s, we obtain tt = 0.142 s. The photobleaching rate kd is evaluated43 according to the following equation.
+
If we assume the photobleaching quantum yield @d = 5 x lo-', which is probably acceptable because the @d of rhodamine derivatives in ethanol is -5 x then we obtain kd = 0.16 s-l (Td = l/kd = 6.25 s). The survival probabilityp for a dye molecule is thus exp(-zJtd) = 0.978, which shows that the bleaching is negligible. Using p = 0.978, we can finally obtain the detectable fluorescence photons, corrected for the bleaching and according to the present experimental conditions, as follows: 0.978Zdfit = 2.25 x 103 photons. This again is in good agreement with the experimental value obtained. In conclusion, the ability to do the simultaneous measurement of the fluorescence spectra and lifetimes to the 10-13M regime is evident from the results described above. The detection limit in the present scheme was mainly limited by the contaminants in the solvent and fluctuations associated with the excitation laser ~~~
(42) Pratt, L. R; Keller, R A]. Phys. Chem. 1993,97, 10254-5. (43) Soper,S. A; Nutter,H. L;Keller, R A; Davis, L. M.; Shera, E. B. Photochem. Photobiol. 1993,57, 972-7. (44) Fodor, S. P. A; Rava, R P.;Huang, X C.; Pease,A C.; Holmes,C. P.;Adams, C . L. Nature (London) 1993,364, 555-6. (45) Takahashi, S.; Murakami, IC;Anazawa,T.;Kambara,H.Anal. Chem. 1994, 66,1021-6.
518 Analytical Chemistry, Vol. 67, No. 3, February 1, 1995
stability. All of these factors are inevitable for measurements involving samples in solution. We have not arrived yet at the ultimate detection level, where the dark-count noise will be responsible for mainly restrictingthe detection limit. One possible extension of our two-dimensional technique is to use positionsensitive multichannel lifetime measurements, in which the photocathode should be directly coupled to an array of optical fibers, of which their ends are pointed toward samples instead of a polychromator. This technique could be further developed to meet the needs of recently proposed DNA-sequencing schemes, where DNA chipsM or multiple capillarie~~~ could be used. In general, position-sensitive techniques should prove to be quite effective in such demanding analytical procedures. Another requirement to use this technique for observing not averaged but inhomogeneous fluorescence at the singlemolecule level would be fulfilled in samples particularly free from photobleaching. Not only the improvement of the efficiency of the detector and the fluorescence collection but also the protection of fluorescent dyes from photobleaching should be done to meet the requirement at the singlemolecule level in biological applications, in which fluorescence quenching often occurs and the photobleaching of dyes used for probes is accelerated by the combination of water and oxygen. ACKNOWLEDGMENT
We thank Dr. Shigeru Hosoi (Laboratory of Molecular Biophotonics, Hamakita) and Professor Hiroyuki Ohtani (Tokyo Institute of Technology, Yokohama) for their critical reading of the manuscript. Thanks are also due to Dr. L. M. Lewis (Tsukuba Research Consortium, Tsukuba) for his critical reading of the manuscript and advice on English usage. Received for review October 7, 1994. Accepted November 28, 1994.@ AC940993H
@Abstractpublished in Advance ACS Abstracts, January 1, 1995.
