Anal. Chem. 1984, 56, 1395-1400
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Transient Digitizer for the Determination of Microsecond Luminescence Lifetimes R. J. Woods, Stephen Scypinski, and L. J. Cline Love*
Department of Chemistry, Seton Hall University, South Orange, New Jersey 07079 H. A. Ashworth
Department of Physics, Seton Hall University, South Orange, New Jersey 07079
A mlcroprocessor-controlled hlgh-speed translent dlgitlzer capable of measuring experlmental lumlnescence llfetlmes In the 0.1-10 ms reglon Is descrlbed. Practical conslderatlons for measurement of klnetlc decay phenomena, In particular of micelle stablllzed room temperature phosphorescence lifetimes, are dlscussed. Callbratlon procedures are reported and a comparison Is made of the ltfetlme data obtalned wlth the dlgltlzer to results obtalned with a commerclally avallable Instrument. Acceptance and rejectlon crlterla for ltfetlme data using flve methods of determlnatlon of the rate constant of a first-order exponentlal decay are dlscussed.
Many important photochemical or photophysical processes occur on a microsecond scale. Our particular interest is in determining micelle stabilized room temperature phosphorescence (MSRTP) lifetimes. The potential analytical utility of MSRTP has been demonstrated in our laboratory (1-3). Briefly, the technique involves solubilizing an analyte molecule in an aqueous, deaerated heavy-atom micellar solution. External spin-orbit coupling occurs, resulting in a greater intersystem crossing rate and/or increased rate of triplet radiative deactivation to produce high intensities of phosphorescence for many compounds. An important aspect for understanding analyte-micelle interactions is an accurate determination of the experimental triplet-state lifetime. While phosphorescence lifetimes measured at 77 K are usually in the millisecond to second region, the sph-orbit coupling provided by the heavy atom along with the kinetics of the micelle and lumiphor interaction at room temperature result in typical MSRTP lifetimes on the 0.1-1 ms scale ( 4 , 5 ) . Such decay phenomena occur slowly enough to be followed by conventional electronics (photomultiplier tube (PMT),amplification, and data acquisition). In the past, MSRTP lifetimes have been determined in our laboratory by employing a nanosecond pulsed light source, gated PMT, and wave form eductor. The decay curve resulting from a summation of approximately 10000 decays in the eductor (a 100-channel analog integrator) was displayed on an oscilloscope, plotted on a strip chart recorder, and analyzed manually by the Guggenheim method (5-7). The Guggenheim method and four other data reduction methods are described below. Unweighted least-squares regression analysis of the natural logarithm of the phosphorescence signal vs. time (natural log or LN method) is used to determine the slope (or decay constant) and slope error, where the negative reciprocal of the slope is the experimental lifetime of the solute. The natural logarithm method assumes that as time approaches infinity the observed signal level decreases to zero. Experimentally, the observed signal level is not only a function of the phosphorescence signal intensity but also is a function of dark current, amplification offsets, emission from impurities, and other factors.
The Mangelsdorf method (8) is a modification of the LN method, where one substracts the known base-line signal level from the individual observed signal levels. Error occurs if the observed base line data are not sufficiently accurate because of noise, resolution, and/or the data have not approached t
-- a.
The Guggenheim method (7) uses data point pairs separated by a constant time interval and the natural log of the difference in intensity between the pairs of data points is plotted against time. The base line level must be greater than or equal to zero. The constant time interval should be at least 1 lifetime, preferably 2 to 3 lifetimes (6),and the decay curve should be followed over a minimum of 3 to 4 lifetimes. A recent adaptation of the phase plane method for determination of first-order decay constants has been reported (9). The phase plane method allows calculation of the base line, lifetime, and the signal amplitude at zero time through digital integration. The most recent method, the rapid lifetime determination (RLD) method (10) assumes the availability of digital data, that the data are observed at equal time intervals, and that all data points from the experimental start-to-stop time must be used. When a fixed time interval, to,exists between all data points, N , as shown in Figure 1,three sums are determined over an equal time interval, Stp S is equal to the number of data points, N , divided by 3. One need not start the summation process at zero time as long as one knows how far from zero time one starts and the use of zero in Figure 1 and eq 1 is arbitrary. The sums are taken as follows:
s-1 Do = CIi 0
2s-1
D1 = C Ii S
3s-1
D, =
2s
Ii
(1)
where Ii is an individual intensity reading. One solves three equations for three unknowns, the amplitude ( A ) ,base line ( B ) ,and a term from which one can calculate the lifetime
Y
(Dl - Dz)/(Do - 01)
(2)
The lifetime, T , can be calculated by T
= - Sto/ln (Y)
(3)
Similarly one can calculate the base line and amplitude through A ' = (Do - 0 J 2 / ( D o - 2 0 1 + D J
(44
B = (Do - A')/S
(4b)
A = A'(l - Yl/')/(l
- Y)
(4c)
Performing these calculations by hand is tedious and time consuming, regardless of the method employed. It was our intention to construct an automated system for acquiring lifetime data by using a microcomputer to control data acquisition, manipulation, and calculation using the optimum
0003-2700/84/0356-1395501.50/0 0 1984 Amerlcan Chemical Soclety
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ANALYTICAL CHEMISTRY, VOL. 56, NO. 8, JULY 1984
Table I. ComDonents of Transient Digitizer Lifetime InstGment component
(I)
S
I I I
I I I
T i me Figure 1. Graphical representation of the RLD method.
data reduction method. Advantages over manual methods include reduction of operator error, increased speed of calculation, and the capability of more complex data handling. Such manipulations allow for a ready determination of whether the data contains the decay curve of one or two components ( I O ) . The transient digitizer is designed to obtain the lifetime of a solute from a single flash of a pulsed xenon flashlamp. Some reactive phenomena, such as deactivating mechanisms and solute/matrix light sensitivity, which occur in this time region cannot be properly studied by use of an averaging method but can be probed with this approach. This paper reports the design and application of such an instrument as well as the evaluation of the RLD method ( I O ) as compared with four other computational methods.
EXPERIMENTAL SECTION Reagents and Procedures. Preparation of micellar solutions for the MSRTP technique have been reported previously ( I , 2). Solutions of europium(II1) chloride hexahydrate and terbium(II1) chloride hexahydrate (prepared from reagents provided by Spex Industries, Metuchen, NJ) were used as calibration standards for the lifetime instrument. Preparations are as follows: Distilled deionized water was adjusted to pH 1.8 with concentrated HC1 (Fisher ACS Reagent grade) and 0.01 M Eu(II1) and 0.1 M Tb(II1) solutions were prepared with this solvent. Instrumentation. All phosphorescence spectra were measured on a Fluorolog 2+2 spectrofluorometer with double excitation and emission monochromators (reciprocal linear dispersion 1.8 nm/mm), a Peltier-cooled Hammamatsu R928P PMT, and photon counting detection (SPEX Industries, Inc., Metuchen, NJ). A pulsed 150-W (peak power) xenon source (SPEX Industries digital phosphorimeter, Model 1934) was used for excitation. Decay curves were obtained in the real-time mode with the monochromators set at the wavelengths of phosphorescence excitation and emission signal maxima using 14.4-nm spectral band-passes. A decay curve was obtained by manually varying the delay period on the digital phosphorimeter between time of lamp flash and time that data are accepted. Delay steps, typically on the order of 10-120 bs, were changed to allow sampling over 3 or more lifetimes. The signal was averaged over a fixed data acquisition period, typically 1 to 2 s (this averaging mode is identified as integration by SPEX Industries, Inc.) with a summation of 10 of these data points being used to represent one point of the 30 or more points used in the construction of a decay curve. The components of the transient digitizer lifetime instrument are listed in Table I and are shown in Figure 2. The Commodore 4032 microcomputer (Commodore Business Machines, Conshohocken, PA) together with an external control box triggers the lamp, provides an external trigger for the oscilloscope, and gates the PMT. The purpose of the external control trigger box was to provide the neccesary signal for each of the electronic events, a 1 A active low for the external trigger of the lamp and +5 V for turning off the PMT with the EM1 Gencom gating circuit (Plainview, NY). The +5 V triggered the oscilloscope to allow a momentary display of the decay curve. The external trigger
model and manufacturer
lamp power supply Model 457A Micropulser, Xenon Corp., Wilmington, MA lamp Model N722 pulsed xenon flash tube, Xenon Corp.; specifications: typically 5 ps pulse duration, peak power 5-10 Jlpulse sample laboratory constructed (90" compartment geometry) filters Corning No. 7-54 (excitation), Corning No. 3-69 and 3-72 (emission), F. H. Grey, Inc. (Queens, NY). PMT power supply Model Eu-42A, Heath Co. (Benton Harbor, MI), operated between -500 and -1000 V PMT Hammamatsu R928 photomultiplier tube (Middlesex, N J ) PMT housing Model Eu-701-93,GCA McPherson (Chicago, IL); modified for electronic gating circuitry as follows: addition of 1N5271, 100-V Zener diode between photocathode and second dynode resistor; two 0.01 pF 3-kV capacitors from second dynode to ground; 1.2 K load resistor from anode to ground PMT gating circuit Model GBlOOlA, EM1 Gencom, Inc. (Planview, NY); + 5 V 0.5 p s minimum variable width gate input amplifier Model 427 current to voltage amplifier, Keithley Instruments, Inc. (Cleveland, OH) oscilloscope Type 7704 with 7A22 differential amplifier, 7A12 dual trace amplifier, and 7B70 time base modules, Tektronix (Portland, OR)
trigger box interface
microcomputer
laboratory constructed from TTL components with BNC connectors laboratory constructed: accepts 0 to 5 V input; contains 7-bit 500-ns flash A/D converter, 4 MHz; oscillator, and 2K external buffer memory; internal board interface with BNC connectors Pet Model 4032, 32K byte, 8 bit, 6502 CPU chip, Commodore Business Machines (Conshohocken, PA)
microcomputer
m
1 :: I
1trigger
u
transient
Figure 2. Block
diagram of transient digitizer lifetime instrument.
box also contained a variable time delay (30 ws to >500 gs) that allowed for the turn-on time of the PMT. This delay was 120 p s for typical operation. The turning off and on of the PMT as well as other switching operations made the first 150 ws or more of acquired signal unusable due to switch ringing.
ANALYTICAL CHEMISTRY, VOL. 56, NO. 8, JULY 1984
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Table 11. Luminescence Lifetimes of Europium Ion in Aqueous Solution Using Two Instruments and Four Calculation Methodsa method of determination
L
_ _ _ _ _ _ _ _ _
RLD Guggenheim phase plane natural log
i
Flgure 3. Transient digitizer interface.
The analog signal output from the PMT is amplified by the preamplifier (Keithley Model 427 current-to-voltage amplifier, Cleveland, OH) and differential amplifer of the oscilloscope, which allows real time observation of the signal. If the observed signal is between 0 V and 5 V it is transmitted to the transient digitizer interface, from which the data can be read directly into the computer. The transient digitizer divides the incoming data into 1024 channels with a time base which varies from 0.5 to 8 ps per channel and stores the data in 2K of external memory. The 7-bit "flash" AID converter of the transient digitizer divides the 5 V dynamic range into 128 steps of 39.1 mV, such that a 1V input signal is rounded up to 26 counts. Manual adjustments of amplification, offsets, and PMT power supply voltage were used to provide a signal height which would be close to the full dynamic range of the instrument (90-127 counts) and to obtain a low (1-5 counts) base line level. A simple calculation shows that the 7-bit AID converter of the transient digitizer is incapable of following a solute lifetime for more than 4.5 lifetimes. This temporal limit can be increased by taking multiple decay curve data sets, varying the amplification settings and the time window involved. Figure 3 shows a block diagram of the interface which forms the core of the lifetime instrument. The microcomputer controls and triggers the counters which keep track of the time base of the experiment. The microcomputer also receives and stores the data from the external 2K of memory. This external memory is needed to accept the data because the PET microcomputer cannot acquire data on the time scale associated with the microsecond lifetime measurements. The interface board containing the counters and memory were incorporated inside the microcomputer chassis for freedom from radio frequency noise problems. The high power pulsed (3 ps pulse width at one-third height) xenon source induced high phosphorescence signal intensity so that typical amplification factors were no more than 2 X lo5 V A-l and the PMT power supply voltage was generally kept under -700 V. The Commodore 4000 series computers used for the off-line calculation of phosphorescence lifetimes were found to be free of computational artifacts. Additionally, the algorithm programs written for the Commodore computers were checked with simulated noise-free decay curves for computational accuracy. A comparison was made by using the difference between the simulated lifetime and the calculated lifetime, divided by the simulated lifetime, and was converted to a percentage value, the relative error (RE). With a simulated 1200 ps lifetime, and 7-bit nontruncated data, all of the methods were accurate to better than 0.06% RE (except the natural log which was accurate to 5% RE, because of a round-off-induced base line error). The amplitude and base line calculationsfor the RLD and phase plane methods were also performed with truncated simulated data and found to be accurate within 0.5% RE. Similar results were obtained for other lifetime values by using 7 bit data. Results from the SPEX Datamate system and software were compared with those from a Burroughs 6800 computer with MINITAB 80 software (Penn State University, University Park, PA) using real data and no variation from the SPEX Industries Datamate results were observed to four decimal places for the RLD, Guggenheim, and LN methods.
RESULTS AND DISCUSSION Calibration Standards. In order to establish the accuracy of lifetimes, it is neccesary to duplicate values for which a number of current literature values exist (11-17). Two of the
transient digitizer T , ps % RSD 107 105 98
1.9 2.5 4.4
SPEX T,
ps
%
113 114
2.6 1.7
C
2.6
111
d
RSD
EuCl, 0.01 M in pH 1.8 water, HC1 0.015 M ; literature values: 104 t 5 ps, ref 12; 104 ? 5 ps, ref 11;119 ps, ref 15. &I h e x 397 nm, hem 600 nm, spectral band-pass 14.4 nm, photon counting, Peltier-cooled PMT, Fluorolog 2+ 2, digital phosphorimeter no. 1934. Not calculated. Inaccurate due to high base line. a
Table 111. Luminescence Lifetimes of Terbium Ion in Aqueous Solution Using Two Instruments and Four Calculation Methodsa method of determination RLD Guggenheim phase plane natural log
transient digitizer T , ps % RSD 427 428 432 d
1.6
2.3 6.6
SPEX T ,ps
% RSD
444 444
1.5 1.1
C
440
0.6
a TbCI, 0.1 M in pH 1.8 water, HCl 0.015 M; literature values: 400 p s , ref 13; 0.43 ms, ref 16; 444 p s , ref 15. hex 264 nm, hem 542 nm, spectral band-pass 14.4 nm, photon counting, Peltier-cooled PMT, Fluorolog 2+ 2, digital phosphorimeter no. 1934. Not calculated. Inaccurate due to high base line.
standards used were solutions of europium(II1) and terbium(111) ion. Lifetimes were measured on the transient digitizer instrument and the SPEX Industries system, and the calculated lifetimes using four methods were compared with those reported in the literature. Table I1 contains lifetime data for the europium ion. The initial data appeared to contain two components upon examination of residuals from the reconstructed decay curve, and one of the components could have been due to the gating of the PMT. This switching produces an approximately 30-ps lifetime artifact using the transient digitizer instrument when a low intensity, short-lived sample was observed. This artifact is easily reduced by using higher concentrations of material for very short lived species or by looking at a time interval away from the zero time (250-500 p s starting times). This lifetimes found in our laboratory for europium ion ranged from 100 to 115 ps and vary, depending on the instrument used as well as the algorithm used for calculation. This range of values compares favorably with literature values (11-13). When the two-component RLD algorithm was used (IO),no second component was observed. The unusable, initial 150 p s region does not limit calculation of 100 ps lifetimes if one examines the second or higher radiative half lives. The SPEX Industries instrument data show that in the presence of a very small base line, the natural log method gives results similar to the more elegant calculation methods. When one implements the transient digitizer analog detection, the natural log method fails and one must use other means of calculating the lifetime from the exponential decay data. The terbium ion data displayed single component characteristics and was useful in comparing the two instruments (Table 111) on a different time scale. Some of the micelle solutes were also compared between instruments and were found to be in agreement.
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ANALYTICAL CHEMISTRY, VOL. 56, NO. 8, JULY 1984
Table IV. Micelle Stabilized Phosphorescence Lifetimes of Selected Polynuclear Aromatic Compounds Determined Using Selected Algorithms with Data Acquired from the Transient Digitizer Instrumenta method of determinationC RLD
RLD-M %
solute
Nb
2,3-benzofl~orene~ 4 fluoranthene 8 fluorene 4 phenathrene 6 chrysene 5 5 pyrene (day 1) pyrene (day 2) 5 benzo[e]pyrene 5
rd
RSDe
1530 2330 423 885 1370 1150 1260 712
6.3 3.0 3.8 2.1 4.4 6.3 6.8 1.2
Guggenheim %
% T
RSD
T
RSD
1520 2330
6.4 3.1
1480 2290 410 878 1350 1120 1270 713
6.5 3.1 4.0 3.5 4.4 3.6 6.8
g
878 1350 1170 1250 708
2.0 4.5 7.6 7.2 1.2
LN
1.o
PP %
RSD
T
g
2480
4.6
g
1050 1660 1320 1420 804
4.0 14 1.9 1.5 2.2
PP-M %
% T
1400 2280 360 897 1260 1130 1280 711
RSD
T
RSD
9.1 5.0 8.4 5.0 6.8 5.3 8.2 2.9
1380 2270 g
895 1200 1130 1280 708
10
5.7 6.1 9.4 5.7 8.5 3.3
a All solutes 5 x M or less in 0.1 M 70:30 Na:TlDS, deaerated 30 min; PMT voltage typically -900 V, amplification 5 x l o 5 ,lamp discharge 7 kV, filters Corning 7-54 (excitation) and Corning 3-72 (emission). Number of replicates. Abbreviations: rapid lifetime determination (RLD), ra id lifetime determination-Mangelsdorf (RLD-M), natural log (LN), phase plane (PP),and phase plane-Mangelsdorf (PP-M). i is lifetime in microseconds. e RSD is relative standard deviation. f Some photodecomposition noted. P Not determined.
'
LIFETIME= 700 U S CHRNNEL YIDTH= 2
US
CHRNNEL Figure 4. Decay curve and deviations from RLD fit for benzo[e]pyrene (5 X M) in 0.1 M 70:30 Na:TIDS deaerated micellar solution using transient digitizer. Instrument settings are listed in Tables I V and V (run 4).
Micelle Stabilized Phosphorescence Lifetimes. Important factors in obtaining reproducible MSRTP lifetimes have been discussed (1, 3-6). In addition, the solute concentration should not exceed its solubility limit in the micellar solution to prevent solid-state phosphorescence or delayed fluorescence which can occur from microcrystals suspended in an aqueous environment (17). A typical MSRTP decay curve obtained by using the transient digitizer is shown in Figure 4. Micelle stabilized room temperature phosphorescence lifetimes of various solutes in 0.1 M 70:30 Na:TlDS micellar solution obtained with the transient digitizer instrument are listed in Table IV. The lifetime values obtained for phenanthrene and pyrene are consistent with earlier reported lifetimes for these solutes in heavy atom micellar solution (18). With the exception of fluorene, the RSDs reported for the RLD and Guggenheim methods are better than those previously obtained in our laboratories with the wave form eductor and manual calculation. In addition, the transient digitizer instrument is much faster in acquiring data and calculating a lifetime using the RLD method. Noise and Base Line Considerations. When a noise-free, single-component decay curve is obtained in the absence of
a base line (conditions which are approached when using the Spex Fluorolog 2+2), one can use the natural logarithm method for the determination of the first-order rate constant. This method fails in the presence of a significant base line component, which can result if the sample matrix produces a background signal, and/or high instrument noise is present. The base line may be caused by instrumental effects such as dc offsets and dark current, may be due to the solute or emission from impurities (6) and/or the noise may be a consequence of the amplification neccesary to obtain the 0-5 V signal range from weakly emitting species. The phosphorescence signal can be masked by fluorescence and scattering of the excitation light, so selective observation of the various signals by time discrimination, i.e., gating of the PMT, is frequently used to observe the phosphorescence signal. Temporal resolution techniques cannot remove the dc offset due to either white noise or the inability to follow the decay curve to t = m. The use of one of the algorithms discussed here is imperative if an instrumental technique is not used to decrease the white noise. Some lifetime instruments, such as the SPEX Industries instrument, minimize the dc background by photon counting detection utilizing a Peltier-cooled PMT. Cooling the PMT decreases shot noise and dark current, thus lowering the base line levels. Typical signal and base line levels using this instrument give a base line of 1part in 10000 parts signal. The Mangebdorf decay correction of subtracting a base line value is very useful when a known or calculated base line level is available. In the case of a 7-bit A/D converter interface, the base line level cannot be observed with sufficient accuracy to permit use of the Mangelsdorf method. For example 0.5% of full scale signal base line levels are sufficient to cause 7 % RE in lifetimes, and observable base line levels on a single reading are fl count on a range of 128 counts. The Mangelsdorf method, employing base line levels from the PP and RLD methods, was used to evaluate the calculated base line levels obtained from the phase plane and RLD methods by comparison of lifetime values. The Guggenheim method is not sensitive to base line levels until the base line is a large fraction of the observed signal due to its removal of any base line by subtraction across a fixed time interval of successive point pairs. The Guggenheim method was applied at less-than-optimum fixed time intervals, frequently 1 lifetime in this study. The fixed time interval was always half the time interval used to acquire the data used in the calculation. The base line and noise rejection capability of the Guggenheim method has recently been compared unfavorably to the phase plane method (9). However, in our
ANALYTICAL CHEMISTRY, VOL. 56, NO. 8, JULY 1984
comparison the data did not contain levels of noise and/or base line which would cause the Guggenheim method to fail. Although the Guggenheim method is better than the natural log or Mangelsdorf methods for determining lifetimes in the presence of an unknown positive base line level, it does not allow for the calculation of base line or amplitude for a reconstruction of the decay curve and estimate of the variance between the original and reconstructed curves (fit error). For these reasons and for better noise and base line rejection, the phase plane and RLD methods are superior. The phase plane method of Demas and Bacon (9) is a reliable and accurate method for determining phosphorescence lifetimes and allows the calculation of amplitude and base line. The method excells for lifetime determinations in a very high base line and noise environment. The one limitation of this technique when compared to the RLD method is the execution time for calculation which is generally an order of magnitude larger than that of the RLD method. The accuracy of the RLD method is comparable to the phase plane method in a high noise environment and better in a low noise environment where the number of data points is limited (10). The program i s given in Chart I. This is the entire program necessary to calculate the lifetime, amplitude, and base line for intensity values I(J) over an interval of 3s points with a channel width of TO between points. The RLD and the phase plane methods are well suited to small computers and for data of limited dynamic range because of the data point summation. The RLD algorithm is the method of choice for determining phosphorescence lifetimes because of ease of programming and swift execution time. The algorithm is adaptable to two emitting components (IO)while the phase plane method in its present form is not. The RLD method calculates the base line and amplitude factors for ready reconstruction of a decay curve and calculation of fit error. The fit error, amplitude, base line, and lifetime for a single component are comparable to that of the phase plane method using simulated noise and base line data (IO), with the phase plane method having a marginal advantage in certain situations. Fit Testing. Once the RLD and the phase plane methods have calculated their respective lifetime values, amplitudes, and base line levels, a decay curve can be simulated
+
I ( t ) = Ae(-t/r) B (5) where I ( t ) is the intensity at time, t , and T is the lifetime. Different intensity values are calculated for each algorithm using the respective lifetime, base line, and amplitude values over the same time interval as the data used to determine the lifetime. The intensity values are then truncated to integer values to simulate real data. The simulated data are then subtracted from the real data and the residual is squared. The sums of squares listed in Table V are those calculated on a per point basis. If nontruncated or rounded-up intensity values had been used, the sum of squares per point would have been decreased. Typical sum of squares for simulated, noise-free, truncated 7-bit data were 0.085 counts2 (or a standard deviation of 0.3 counts). Typical calculated base lines were -0.44 counts; the negative base line results from the truncation. Real data fits for benzo[e]pyrene in deaerated 0.1 M 70:30 Na:TlDS micellar solution are reported in Table V. Several trends can be noted. When simulated data are used, the phase plane method generally gives a better fit, i.e., a lower sum of squares per point, than does the RLD method. When using real data for these two methods, the RLD method does give a marginally lower sum of squares. Simulation runs adding Poisson noise, truncating the data, using limited dynamic range data, and base line variations were unable to explain this. The slightly poorer fit may explain the generally higher
v1
P
-c Y
.-Q a,
9
3
a
0
4a
P
c3
.-E
zE
U
1399
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ANALYTICAL CHEMISTRY, VOL. 56, NO. 8, JULY 1984
Chart I I(J),J=Oto3S-l ForJ=Oto3S-l DO=DO+ I ( J ) D1= Dl + I (S + J ) D 2 = D2 + I ( 2 S + J ) NEXT J Y (D2 - D l ) / ( D l - DO) TAU = S * TO / LOG (Y)
A 1 = (DO - D l ) ? 2 / (DO- 2 * D 1 + D2) B = (DO - A l ) / S A = AI. * (1- ( Y ) ? ( l / SI) / (1- Y )
for intensity data points I ( J ) over all points, 3s set loop for summation determine three sums
calculate lifetime, TAU, where TO is the time between points I (J) and LOG is the natural log calculate base line B calculate amplitude A
RSD values shown for the phase plane method as compared to the RLD or Guggenheim method in Table IV. The phase plane method attempts to fit a different region of the decay curve for some runs of some solutes. A possible reason for different regions of fit would be the presence of two emitting components in the decay curve; however upon examination of the residuals, no second component could be observed. The presence of a second component would cause a nonrandom variation of the residuals and this can be very useful in determining whether or not a single component is present (IO). Figure 4 includes a plot of the single-component solute residuals. If more than one component is observed, a twocomponent algorithm (10) can be used to determine the lifetime, or additional purification of the solute/solvent system can be done prior to further determinations of the lifetime. Referring to the RLD method and the RLD-Mangelsdorf (RLD-M) method lifetimes and s u m of squares values in Table V, one observes that the calculation of the base line for the RLD method using real data is accurate since the deviation of the lifetime calculated by the RLD-Mangelsdorf method is, at worst, 3.6% different from the RLD method values. Averaged over five runs, the deviation in lifetime from the RLD to the RLD-Mangelsdorf for benz[e]pyrene is 0.6%. If the calculated base line value was in error, then the observed variation between the two lifetimes would be much worse. As a second comparison, the variation for the natural log method as compared to the RLD method in Table IV for benz[e]pyrene is 12.9%. The fits between the phase plane (PP) and the phase plane-Mengelsdorf (PP-M) methods for benz[e]pyrene are similar. There is, at worst, a 1.0% deviation in lifetimes and the average over five runs, as seen in Table IV, is 0.6% deviation. Both methods appear to calculate good base line values.
CONCLUSIONS The transient digitizer is the fast and accurate instrument for the determination of microsecond lifetimes. In its present 7-bit configuration, the RLD, Guggenheim, and phase plane methods are the most accurate in determining the lifetimes
from the raw data. The RLD method, considering it determines the base line and amplitude which the Guggenheim method does not and is faster in execution time than either the Guggenheim method or the phase plane method, appears to be the method of choice. The limited dynamic range of the data values and the limited temporal capability of this instrument do not appear to substantially affect the ability of the RLD, phase plane, or Guggenheim methods to calculate accurate lifetimes or reaction rates. Future improvements which can be made in this instrument include the use of a narrow pulse width laser as an excitation source, a Peltiercooled PMT to decrease the white noise, and a larger dynamic range interface (12 bit) capable of following the data over a longer temporal region.
ACKNOWLEDGMENT The authors thank Raymond Kaminski and Frank Purcell of SPEX Industries for help in programming the SPEX Datamate. The authors also thank Amir Dabiran and Harry Brittain for help in calibrating the transient digitizer instrument and choice of calibration standards.
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RECEIVED for review October 7,1983. Accepted February 13, 1984. This work was supported in part by National Institutes of Health Grant No. GM-27350, National Science Foundation Grants No. PRM-8111335 and CHE-8216878, and the Environmental Protection Agency. Although the research described in this article has been funded, in part, by the United States Environmental Protection Agency under assistance agreement number R809474 to L. J. Cline Love, it has not been subjected to the Agency's required peer and administrative review and, therefore, does not neccesarily reflect the view of the Agency and no official endorsement can be inferred. This work was presented, in part, at the Pittsburgh Conference on Analytical Chemistry and Applied Spectroscopy, March 8, 1983, Atlantic City, NJ, Abstract No. 378.
