Excimer kinetics

Since the modelling of excimer kinetics is very relevant to the discussion of excimer formation in synthetic polymers, detailed examination and analysis of the kinetics of fluorescence decay in these systems is deferred until section C of this review. Suffice it to say here that the time dependence of the fluorescence of the monomer unit M is the sum of two exponentially decaying terms, that of the excimer the difference between the same two exponentials. 

The scheme usually adopted to explain excimer kinetics between free aromatic moieties in dilute solution and based upon the notation of Birks is own in Fig. 18. 

The exciraer decay at 475 nm was not adequately matched by dual exponential fits would be expected according to the conventional monomer/excimer scheme 1. Due to uncertainties with the method in correction for photomultiplier response as a function of wavelength, analysis of excimer kinetics in terms of three exponential terms, although indicated by the data, is not justifiable in any quantitative sense. Decay parameters obtained are given in Table 4. 

A recent study on poly(2-vinyl naphthalene) P2VN has also concluded that the simple scheme 1 is inappropriate for the description of excimer kinetics in this polymer, and on the basis of comparison with isomers of 1, l -di-2-naphthyldiethyl ether (III), explanations of behaviour which emphasize conformational aspects (see ) have been proposed. In the polymer, monomer fluorescence decays... 

In synthetic polymers, the interpretation is necessarily more difficult The form of Equation 4 and Equation 5 requires that the kinetics of formation and decay of complexes are modelled adequately by rate-constants and that they take place in a homogeneous medium. If, as in synthetic polymers, the population of excimer trap sites, may occur through energy migration or rotational diffusion, a rate-constant may not be an adequate representation of the process, some time-dependent parameter being required (see below.) Heterogeneity may also play an important role. Thus in earlier work the fluorescence decay of excimer-forming polymers was modelled adequately by a scheme based upon simple excimer kinetics to which had been added terms to account for the occurrence in co-polymers of monomer sites which, by their isolation, could not form excimers (4-10). For polymers which contain isotactic and syndiotactic sequences, or rather, are made up of meso and racemic triads (14), the kinetics may be similarly a superimposition of simple schemes appropriate for the different sequences. 

Analysis of the fluorescence decay profiles indicates that a two exponential fit, which would be expected for conventional monomer/ excimer kinetics (2-4), is inadequate to describe the decay at any wavelength of observation throughout the emission band. A fit to a sum of three exponentials leads to significant improv ents in the fitting criteria and examples of the results obtained at wavelengths in the monomer and excimer regions of the spectrum are presented in Table I. 

The application of time-resolved fluorescence spectroscopy to studies of excimer formation and energy transfer in PACE and P2NMA provides an overview of the emitting species present and the dynamics of energy relaxation in these polymers. The results of fluorescence decay analyses suggest that kinetic models which have been proposed to explain monomer/excimer kinetics may require further refinanent. 

A stimulating paper deals with a revision of the familiar, and widely used, monomer-excimer kinetics by treating such systems as examples of reactions with time dependent rate constants. The simple mathematical formulations usually employed in systems where excimers are involved are shown to be inadequate. No doubt future efforts will be directed to rectifying the situation. Strong transient effects arising from nonstationary diffusion which occur during excimer formation through reactions with time dependent rate coefficients have been used as a scheme to test different models used in convolution kinetics . Time dependent excimer... 

Pyrene excimer formation still continues to be of interest and importance as a model compound for various types of study. Recent re-examinations of the kinetics have been referred to in the previous section. A non a priori analysis of experimentally determined fluorescence decay surfaces has been applied to the examination of intermolecular pyrene excimer formation O. The Kramers equation has been successfully applied to the formation of intermolecular excimer states of 1,3-di(l-pyrenyl) propane . Measured fluorescence lifetimes fit the predictions of the Kramer equation very well. The concentration dependence of transient effects in monomer-excimer kinetics of pyrene and methyl 4-(l-pyrenebutyrate) in toluene and cyclohexane have also been studied . Pyrene excimer formation in polypeptides carrying 2-pyrenyl groups in a-helices has been observed by means of circular polarized fluorescence" . Another probe study of pyrene excimer has been employed in the investigation of multicomponent recombination of germinate pairs and the effect on the form of Stern-Volmer plots ". 

Szabo, A. Theoretical approaches to reversible diffusion-influenced reactions—Monomer excimer kinetics. J. Chem. Phys. 1991, 95,2481. 

The effect of excimer kinetics on fluorescence decays of monomers and excimers upon excitation with a short pulse was studied first by Birks et al. [119]. They took into account all the relevant processes that proceed after the excitation of a low fraction of monomers by an ultrashort pulse and derived the rate equations describing the monomer and excimer decays. Most processes involved in the Birks scheme are monomolecular and depend only on the concentration of the excited species and on the first-order rate constant one of them is a bimolecular process and depends on the concentrations of both the excited and ground-state molecules. They include (1) monomer fluorescence, (rate constant fM), (2) internal monomer quenching, M —>M, ( iM). (3) excimer formation, M - -M D (bimolecular reaction, i.e., the rate depends on the product of the rate constant and concentration of the ground-state... 

Measurements of excimer kinetics are widely used fluorescence methods for studying the dynamics of multiply labeled polymer chains. For probes attached to the chain, the kinetic scheme is more complex and the resulting decays are also substantially more complicated. Because the chapter on hydrophobically modified polymers treats this topic very thoroughly, we will not go into more detail here. 

The second approach to the study of excimer kinetics has been more theoretical In experiments on dilute solutions of unlinked chromophores, there has been some success in considering the process of excimer formation as a difiusive process [25]. Nemzek and Ware [26] used an extension of the Smoluchowski equation [27] devised by Collins and Kimball [28], which gives for k(t)j ... 

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