Complex fluorescence decays. Lifetime distributions

When the fit with a single exponential is unsatisfactory, a second exponential is often added, ff the quality of the fit is still unsatisfactory, a third exponential term is added. In most cases, a fourth component does not improve the quality of the fit. A satisfactory fit with a sum of two (or three, or four) exponential terms with more or 

In some circumstances, it can be anticipated that continuous lifetime distributions would best account for the observed phenomena. Examples can be found in biological systems such as proteins, micellar systems and vesicles or membranes. If an a priori choice of the shape of the distribution (i.e. Gaussian, sum of two Gaussians, Lorentzian, sum of two Lorentzians, etc.) is made, a satisfactory fit of the experimental data will only indicate that the assumed distribution is compatible with the experimental data, but it will not demonstrate that this distribution is the only possible one, and that a sum of a few distinct exponentials should be rejected. 

To answer the question as to whether the fluorescence decay consists of a few distinct exponentials or should be interpreted in terms of a continuous distribution, it is advantageous to use an approach without a priori assumption of the shape of the distribution. In particular, the maximum entropy method (MEM) is capable of handling both continuous and discrete lifetime distributions in a single analysis of data obtained from pulse fluorometry or phase-modulation fluorometry (Brochon, 1994) (see Box 6.1). 

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In other media like micelles, cyclodextrin, binary solvent mixtures, and proteins (47-55), lifetime distributions are routinely used to model the decay kinetics. In all of these cases the distribution is a result of the (intrinsic or extrinsic) fluorescent probe distributing simultaneously in an ensemble of different local environments. For example, in the case of the cyclodextrin work from our laboratory (53-55), the observed lifetime distribution is a result of an ensemble of 1 1 inclusion complexes forming and coexisting. These complexes are such that the fluorescent probe is located simultaneously in an array of environments (polarities, etc.) in, near, and within the cyclodextrin cavity, which manifest themselves in a distribution of excited-state lifetimes (53-55). In the present study our experimental results argue for a unimodal lifetime distribution for PRODAN in pure CF3H. The question then becomes, how can a lifetime distribution be manifest in a pure solvent ... 

As far as the excimer decay kinetics of PAA in aqueous media is concerned, de Melo and coworkers [122,130,131] have investigated the time-resolved fluorescence from a series of samples modified with various amounts of pyrene and naphthalene, respectively. Even when the aromatic content was as low as 2mol%, excimer formation was evident in the steady-state spectra. The fluorescence decays were complex irrespective of the label and were best modeled by a triple-exponential function (as in Eq. 2.8) both when emission was sampled in the monomer and excimer regions. In contrast to the distribution of rate constants in the blob model [133,134], the authors favored a scheme that describes the decay kinetics in terms of discrete rate constants. The data were also consistent with previous schemes [124-127] that account for the presence of two distinct types of monomer in addition to that of excimer in macromolecular systems one monomer enjoys kinetic isolation and is unable to form excimers, whereas the second is able to participate in excimer formation within its fluorescence lifetime. The authors [130] concluded from both steady-state and time-resolved data that PAA undergoes a conformational change from a compact form in acidic solution to an open coil at high pH. Furthermore, as the... 

Fluorescence lifetime data of 1, 4, 5, and 6 in presence of 10 M -CD were collected with frequency-domain fluorometry. These probes gave only 1 1 complexes with P-CD [58] and, given the association constant values, the complex molar fraction was >0.95 for 4 and 5 and 0.1 for 6. The fluorescence decay of all the probes was best described by unimodal Lorentzian lifetime distribution [51,59] rather than by a mono- or biexponential function corresponding to the emission of the complexed and the free probe. This distribution was attributed to the coexistence of molecules included in the cavity to different extents. It was proposed that, in the case of 4, the apolar benzene ring enters the cavity first and penetrates until the whole naphthalene is included. This is the most stable and, hence, the most populated conformation of the complex. The distribution of the lifetimes suggests that at any time there is an ensemble of molecules in different stages of complexation which have slightly different lifetimes. 

The complexes of 2,3 (sodium salt) and 4 (potassium salt) with P-CD and (2,3,6- tri-0-methyl)-/ -CD were studi using steady-state fluorescence and time-correlated, single-photon counting techniques [52]. The formation of both 1 1 and 2 1 complexes between p-CD and 2,3 was confirmed. Trimethyl- -CD gave evidence only of 1 1 complexes. The fluorescence decay of systems giving exclusively 1 1 complexes was collected at CD concentrations that ensure more than 90% complexation. The analysis performed using a continuous lifetime distribution model... 

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