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Anal. Chem. 1981, 53, 2103-2106
Data Reduction Methods for First-Order Kinetics of Phosphorescence Decay L. J. Cline Love" and Marie Skrllec DepartmenP of Chemistry, Seton Hall University, South Orange, New Jersey 07079
Data reductlon methods used to calculate triplet-state llfetlmes are evaluated with partlcular emphasis on the method of Guggenheim. Several instrumental and chemlcal sources of error are pointed out, and their effects on accuracy and preclslon of lifetime data are illustrated by use of three simulated curves. Experimental data for the decay of phenanthrene by the micelle-stabilized room temperature phosphorescence method and the conventional low-temperature method are evaluated by the Guggenhelm method. It Is shown to be useful for any exponential decay signal contalning an Interferlng background level.
The lifetime of the excited triplet state is a characteristic property of a molecule and its environment and can be used as a qualitative and quantitative descriptor of the species. The accurate measurement of the phosphorescence decay constant and subsequent calculation of the corresponding triplet-state lifetime are important in studies of kinetic processes associated with the triplet state as well as for analytical purposes. Researchers have developed many methods, varying in speed, accuracy, simplicity, and cost, to deconvolute phosphorescence decay data from interfering signals of varying functional forms. Blank substraction (1-3) and empirical background fitting (4) techniques which utilize a computer's speed, accuracy, and storage capabilities are ueed often. These techniques usually use the leaqt-squares method to obtain the best fit of the slope. The decay rate has also been estimated manually by observing the time needed for the phosphorescence intensity to decay by l / e of its initial value (5-7). In many of these cases only a portion af the decay curve is selected to estimate the triplet-state lifetime and no consideration is given to accurate background compensation. Some commercial instruments have built-in photomultiplier tube (PMT) delay or gating which can be use to facilitate measurements and some useful computer programs and instrumental attachments are available commercially (8, 9). Many of the simple techniques can lead to erroneous results. First, a nonexponential decay may not be detected if only a few data points are collected or only a small part of the curve is analyzed. Second, an improper background correction can make the decay appear nomexponentialleading to an erroneow interpretation of the data. We have applied the principles used by Guggenheim (10) in reduction of first-order kinetic data to deconvolute phosphorescence decay curves, and this paper brings into focus this simple, accurate, and fast method of calculating triplet-state lifetimes. This method is often used by researchers studying kinetics but has seldom been used by spectroscopists studying the excited triplet state processes. The alternate method of Mangelsdorf is faster to apply but it is not our method of choice because it gave worse correlation coefficients and it necessitated assuming a value for the anticipated lifetime. We are also aware of a method recently published in this journal which is very similar to Mangelsdorf's (11)and a method utilizing Laplace transformation of the decay function (12). 0003-2700181/0353-2 103$01.25/0
EXPERIMENTAL SECTION Purification of reagents, solvents, nitrogen, and phenanthrene and preparation of thallium lauryl sulfate (TILS) were described elsewhere (13, 14). The samples were prepared as described previously (13, 14). Sodium lauryl sulfate (NaLS) (BDHBiochemicals, Poole, England),specially purified for biochemical work, was used as received. The TlLS/NaLS mixed detergent concentration was 0.10 M with Tl/Na at a 30%/70% concentration ratio for the micelle stabilizedroom temperature phosphorescence (MS-RTP) investigations. Luminescence spectra and triplet state decay curves were ohtained by using instrumentation discussed previously (14-16). The phosphorescence decay of analyte in the micellar solutions was studied with several 1.5 X M phenanthrene samples. Only the data for five separate phosphorescence decay accumulationls on a single sample are given here. A Corning 7-54 filter was useld for the excitation wavelength selection and a Corning 3-72 was used for emission wavelength selection. The instrumental settings were as follows: PMT voltgate = 1000 V; amplifier gain = 106 and risetime = 0.03 ms; waveform eductor gain = 10, delay = 280 ps, sweep = 4 ms, and time constant = 10. The instument was pulsed at 8 ms with a pulse width of 270 ps. The data accumulation time was 15-20 s. Uranyl glass was used as a reference standard to check that the instrument functioned properly. The low-temperaturedecay data were obtained on 1 X lo4 14 phenanthrene sampleia excited at 300 nm. The decays were measured over at least 7 lifetimes with the emission monochromator set first at 500 nm and then at 461 nm. PRINCIPLES A brief description of the remedial kinetics involved will facilitate illustration of the sources of error in data reduction. In the absence of secondary processes, the decay of the triplet state follows fist-order kinetics. This decay may be expresseld mathematically as d[T]/dt = -k[T] (1) where k and [TI are the decay constant and the concentration of the species in the triplet state, respectively. Integration with respect to time, t , and rearrangement of eq 1 yields
[TI,= [TIoe", (2) For an absorbing system (analyte) assumed to be optically thin and in the absence of secondary processes such as self-ablsorption, the [TI is directly related to the relative intensitg of the phosphorescence signal, I . Substituting I for [TI in eq 2 and taking the natural logarithms yields the familar equatioin for a straight line hi It = -kt In Io (3) Ideally, a plot of In It vs. time should yield a straight line where the slope is the triplet state decay constant and In Io is
