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Figure 4. Typical time-resolved ETM of 2-naphthoic acid and p-amino-benzoic acid Reprinted from Reference 31
tion time and data format. Since sev eral methods of determining the lumi nescence lifetime can be used, it is useful at this point to discuss briefly the theory of the two commonly used techniques (12). These methods are based on the use of two types of in strumentation: time resolved and phase resolved. In the time-resolved method, the sample is excited with a short-dura tion pulse of light, and the time-de pendent decay of the luminescence in tensity can be used to calculate the lifetime. In the phase-resolved meth od, the sample is excited with sinusoidally modulated light. The phase shift and demodulation of the emis sion, relative to the incident light, are parameters that can be used for calcu lation of the lifetime. Both methods require some calculations to obtain the luminescence lifetime of the lumi nophore. This is especially true for the second method if the sample contains more than one luminophore. In general, the excitation of a lumi nophore with an infinitely short pulse of light (δ function) provides the best approach to explaining the lumines cence decay. The luminescence inten sity as a function of time after the ex citation pulse is assumed to be an ex ponential decay curve since the lumi nescence decay process usually obeys first-rate kinetics IjM) (5) /χ,(Ο) where /χ,(ί) and / L ( 0 ) are the intensi ties of the luminescence at time t and time 0, respectively. The parameter k is the first-order rate constant for the decay process.
Equation 5 indicates that a timeluminescence decay curve can be ob tained if an ideal delta pulse excita tion is used. Unfortunately, any prac tical instrument is nonideal and can provide only an excitation pulse of fi nite duration. In addition, the associ ated electronics will have a response function of finite width. Consequent ly, the use of a nonideal lifetime in strument will produce data that are a convolution of several response char acteristics. A mathematical process is therefore needed to deconvolute the time decay curve. With an appropriate modulation frequency for the excitation beam, the luminescence will also have an associ ated modulation depending on the time delay. This property is used in phase-resolved luminescence measure ments. The phase-resolved method uses a continuous sinusoidally modu lated excitation beam. If the modula tion frequency (f) and degree of mod ulation of the excitation source are known, a simple derivation (12) of the phase difference, φ, between the exci tation source and the fluorescence gives the lifetime, τ, as
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τ = — - (tan φ) (6) 2π{ Similarly, the observation of the de modulation (M) is also suitable for calculation of the lifetime since 2TT/V M2
1
(7)
Equations 6 and 7 are valid if the emission of the luminophore is spec trally homogeneous. If the system is more complex, the calculation of the lifetimes is more complicated.
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ANALYTICAL CHEMISTRY, VOL. 57, NO. 3, MARCH 1985 · 471 A
