Excitation, Birks’ scheme

Figure 4.2 Birks scheme [1] of excitation and deactivation by bimolecular processes k M nd the rate constants of excimer association and dissociation,...

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... 

Fig. 11 The time-resolved monomer, FmW. and excimer, Fd(0, fluorescence decays calculated according to Birks scheme, taking into account the convolution of decay curves with the excitation profile, P t). Reproduced from Proceedings of the Royal Society of London Series A, Mathematical and Physical Sciences 275, 1963, 575-588, figure 1, [119]. Copyright 1963. With kind permission from The Royal Society...

De Schryver et al [20] have undertaken a painstaking study of the comparison of the photophysics of pol3nner systems with those of low molar mass bichromophoric analogues. In an early report the inapplicability of the Birks scheme [2] to the description of excimer formation in poly(2-vinyl naphthalene) (P2VN) was expressed [19]. Comparison of the emission behaviour of P2VN with that of 1,3-di(2-naphthyl)propane combined with an observed dependence of the emission characteristics of P2VN upon excitation wavelength led to the formulation of scheme 4 [19]. 

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. 

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 ... 

Several years ago, Braun, Kato, and Lipsky (142) showed that in the vapor solution and bulk liquids, benzene and its methylated derivatives appeared not to undergo efficient internal conversion or intersystem crossing from higher excited singlet states to form either Sj or Tj states. This was confirmed by Birks, Conte, and Walker (143) who postulated a scheme involving excimers of higher excited states, to explain their data and noted that benzene proved to be the exception amongst similar compounds in that the effect decreased on dilution. 

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-... 

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. 

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