Birks kinetic scheme

It can be seen from Equations (1) and (2) that the monomer and excimer decays are both the sum of exactly two exponential decay terms, with the same lifetimes Ai and Aj appearing in both monomer and excimer decays. In addition, the two pre-exponential factors in the excimer decay are of equal magnitude but opposite sign. However, except to a first approximation, neither of these characteristics is usually seen experimentally in polymers [12-14] where, typically, the monomer and excimer decays will give different values of A, and A2 and the excimer decay will not have pre-exponential factors of equal magnitude. As real polymer decays do not follow the Birks kinetic scheme, the scheme evidently does not take account of all the photophysical processes which occur in polymers, and efforts to improve the models have been made in two main directions. The first approach... 

The Birks kinetic scheme can then be adjusted to include kfrloM- Because of the complexity involved, the rate constant k D usually neglected at this stage. The population of the monomer excited state then has the time dependence of Equation (7) ... 

In the Birks kinetic scheme, back-transfer is considered simply by the rate constant Icmd- Weixelbaumer et al. [40] used an approximate method to approach this, whereas Sienicki and Winnick [41] derived an exact result, and posed the question, what happens if monomers formed by back dissociation behave differently from those excited directly The question was answered by Berberan-Santos and Martinho [42], who showed that does not necessar-... 

The picture which evolved from stationary state experiments complemented by a few early time-resolved measurements invoked a modified Birks kinetic scheme. This notion was accepted virtually without question in studies prior to 1980. Further, the majority of authors cited the occurrence of singlet energy migration and subsequent sampling of potential excimer sites in the absence of concrete evidence for migration except for that afforded by emission depolarization [66,67]... 

In our early work, it became clear that simple Birks kinetic schemes representing excimer formation and decay were inadequate for modelling fluorescence in excimer forming polymers [17-22]. The empirical observation that multiple (dual and triple) exponential terms could model successfully the decay of monomer and excimer fluorescence in poly(vinyl naphthalenes) led us to propose simple models which... 

Numerous studies of the photophysics of aryl vinyl polymers have shown that the monomer emission intensity can be empirically fit to a triple exponential [15-17]. The immediate conclusion that may be drawn from this observation is that the Birks kinetic scheme [1], which was developed for a collision-induced intermolecular process between small molecules in solution, is inapplicable to intramolecular excimer formation in macromolecules. 

Polymers usually exhibit fluorescence and phosphorescence emission similar to that of low molecular weight model compounds. A general kinetic scheme can be used to describe the absorption and dissipation of energy in polymer films and solutions (the notation of Birks [3] has been used throughout this section) namely,... 

First observed in concentrated solutions of pyrene Cl], excimers are now known to be formed by the majority of aromatic molecules. Kinetic scheme 1, suggested by Forster and the kinetic derivations developed by Birks [2] et al have been validated in a host of systems involving intermolecular interactions between low molecular weight species. 

Since most of the experiments cited in Table I were performed when the vast majority of the work on macromolecular luminescence was confined to steady state excitation the aspirations of the investigators seems reasonable. However, the validity of the data in representation of the functions E and -AH is open to considerable doubt not only in view of the assumptions discussed above in derivation of the low and high temperature relationships from the Birks [2] scheme but also as a result of doubts recently expressed [16,20] regarding the applicability of the basic kinetic scheme itself to macromolecules. 

The decay kinetics of P2VN are temperature dependent and complex (compared, for example, to the predictions of the Birks [2] scheme). Comparison with the kinetic behaviour of meso D2NEE led to the proposal that isotactic sequences in the polymer were responsible for two exponential decay terms as contribution to the total excimer emission in P2VN. 

It will be assumed that Q does not absorb the excitation light and does not react with the ground-state M. The decay rate of M in the absence of Q will be denoted m- Such a chemical scheme is independent of any effective mechanism for the interaction between M and Q (Birks, 1970). It only states that, in the presence of Q, an additional deactivation pathway is present, through the creation of Z, which may be non-luminescent. By use of classical kinetic laws, one derives ... 

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. 

Fig. 18. Birks scheme for exdmer kinetics in simple (small molecule) systems...

The parameters that describe the properties of the excimer state may be extracted from kinetic analysis of transient and steady state luminescence data. The scheme due to Birks,... 

The formation of intreunolecular excimers in polymer systems has aroused much interest in recent years (1). Perhaps most notable is the general observation that the reaction kinetics do not obey the accepted Birks scheme for low molecular weight systems (2)- In this scheme the fluorescence decay kinetics of the monomer (M) eind excimer (D) species Ccui be separated spectrally with fluorescence response functions of the form... 

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... 

Fluorescence in such polymers is dominated by excimer formation, the simplest kinetics for which were described by Birks and co-workers [10,11] (Scheme 1). In... 

A quantitative explanation of this behavior has been somewhat difficult to obtain, however. There have been several proposals to identify the experimentally resolved exponentials with physical entities, such as multiple monomer states [17-20] or multiple excimer states [15,21]. It is quite probable that the kinetics of the aryl vinyl pol)nners are indeed more complex than the simple Birks scheme would allow. However, recent theoretical studies on electronic excitation transport in random systems of donors and traps have shown that the fluorescence decays are in general, nonexponential [4,5, 22-26]. A key feature of these analyses is that the trapping dynamics in one dimensional and quasi one dimensional polymeric systems require that a trapping rate function k(t) rather than a trapping rate constant be used. In Section 2.1 we give the relationship of k(t) to the observables in a trapping experiment and provide the connection with G (t), which is obtained from theory. 

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