Monomer decay

Kinetic gelation simulations seek to follow the reaction kinetics of monomers and growing chains in space and time using lattice models [43]. In one example, Bowen and Peppas [155] considered homopolymerization of tetrafunctional monomers, decay of initiator molecules, and motion of monomers in the lattice network. Extensive kinetic simulations such as this can provide information on how the structure of the gel and the conversion of monomer change during the course of gelation. Application of this type of model to polyacrylamide gels and comparison to experimental data has not been reported. 

For excimer-forming bichromophoric compounds in solution, the probability M of ultimate monomer decay in Eq. (1) is given by 37)... 

Table I. Pyrene Monomer Decay Time on Decanol-Covered Si02 as a Function of Temperature...

Nagle et al. have reviewed the kinetic scheme that underlies excimer formation, as it applies to Pt complexes [19]. A plot of Id/Im (integrated emission intensities of excimer and monomer bands, respectively) versus concentration of the complex should be linear. The slope is determined by all the rate constants of formation and decay of both excimer and monomer, but is approximately related to the equilibrium constant for excimer formation. Typically for Pt complexes that do show excimer emission, the rate constants for formation and subsequent decay of the excimer are substantially larger than monomer decay. The decay of both monomer and excimer are thus governed by the rate of excimer formation, leading to nearly identical decay kinetics for the two species. 

According to eqns. (105)—(107), the dependence of the decay of active centres on time is linear, exponential, and hyperbolic, respectively. The best approximation is obtained by a comparison of the observed course with the rate of monomer decay calculated for the assumed termination mode. This is, of course, a very rough method, which often does not reveal the effect of other components on termination, for example that of the monomer (its wrong addition etc.)... 

We therefore expect monomer decay curves to rfiow Aral exponentiality while excimer decays should show a rise followed by an expcmential decay. 

It is of interest to note that within the limit of acoiracy of these experiments, monomer decay curves (Fig. 22) were single exponential, whereas Sdieme 1 predicts dual exponentiality (Eq. 65). The results thus imply that in pdyslyrene reverse dissociation ( feedback ) of the excimer is not of importance. This point is amplified by time-resolved fluorescence spectra which show that late- ted >ecti a (see experimental section) are composed exclusively of excimer emission (Fig. 23). The same is true in poly(a-methylstyrene) In view of more recent work mi other vinyl aromatic ptdymers, it would be of interest to study pdy(styrene) further with more sophisticated techniques. 

In a prdiminary study on the time-resolution of fluorescence in pdy(l-vinyl naphthalaie) the kinetics were constrained to fit Scheme 1, yielding values of monomer decay times in methylene chloride sdutiMi ci 7.4 and 43.1 ns. Late-gated spectra indicated that reverse dissociaticm of the excimer occurred. With improvements in techniques, these studies have been greatly an lified recently. In particular, studies on copolymers have permitted more detailed analysis of the concentration dependence of excimer formation, and improved statistical analyses have permitted reEned modelling of the kinetics. We will discuss at some length one of these papers, and summarize rearlts on other sterns. 

Fig. 2. Effect of molecular weight of the aryl vinyl polymer on the probability that an absorbed photon leads to excimer decay (1-M) divided by the probability of monomer decay M, This is directly proportional to the observed ratio of integrated excimer to monomer intensities. Reproduced from Reference 2A.

Fig. 3. Dependence of the probability of eventual monomer decay M on the concentration of polystyrene in a PS/PVME blend. (Reproduced from Reference 9. Copyright 1982 American Chemical Society.

Rate constants are obtained from fluorescence decay analyses of the monomer decay profile I (t) and the excimer/exciplex profile Ig(t). These are fit to sums and differences of two exponential... 

As indicated in Figure 8, the limiting (at presently accessible temperatures) low-temperature excimer emission intensity is only about 20% lower than the room-temperature value and no rise-time consistent with the monomer decay can be discerned. The limiting low... 

STYRENE POLYMERS. In our earlier work on styrene (12,13,30). heterogeneity was emphasised as being the major cause of complex decay of fluorescence, leading to the adoption of a multiple component analysis. We have tested the simplest alternative model. Equation 15 against a multiple exponential model, where we have shown, (Figures 5 and 6) that a dual component fit is acceptable statistically for homopolymer monomer decay. Figures 7and 8 show that the simplified Equation 15 is certainly unacceptable. 

As a limiting situation, the monomer decay becomes single-exponential, with a reciprocal decay time 1/x = + 1/x, when... 

Section 2.2.3), excimer formation of Py in the hydrocarbon layer on Si-C g is dynamic, not originating from ground state dimers. This conclusion is supported by the observation that the excitation spectra at the monomer and excimer wavelength are identical (see Section 3.2.2) and that the excimer emission is completely frozen out at 77 K (21). The corresponding monomer decay, having a value similar to the excimer decay time, was represented as a single-exponential. 

Interestingly, the monomer decay is practically double-exponential (Table 4), the triple-exponential fit having only a relatively small amplitude for the decay time tg corresponding to the growing-in of the excimer. It is seen that the two longer monomer times Tg and represent important fractions of the total decay. 

For Scheme (IV), one obtains a double-exponential monomer decay (ijj(t)) and a triple-exponential excimer decay (ip(t)) ... 

Silica/i-Octanol. The monomer and excimer fluorescence decays of 1Py(3)1Py in the system silica/octanol were fitted with three exponentials (38), double-exponential fits giving unacceptable results. The decay times at 25°C (38) for the monomer (20, 43 and 146 ns), have values in the same range as those of the excimer (27, 51 and 106 ns). As was noted in studies with 1Py(3)1Py and related compounds in homogeneous solution (20,62), the monomer decay often contains a contribution from an impurity with a lifetime similar to that of e.g. 1-methylpyrene (x ), becoming more important with increasing fluorescence quenching. This then leads to the difference observed in the longest decay times of excimer and monomer. 

Alkylpyrenylsilanes Chemically Bound to Silica. Loch-miiller et al. reported on time-dependent fluorescence studies with the alkylpyrenylsilanes PPS and PDS chemically bound to microparticulate silica (41-43). These compounds undergo intermolecular excimer formation in contact with a number of solvents such as tetrahydrofuran and methanol. For all solvents, at different surface concentrations of PPS and PDS, the monomer fluorescence decays ij (t) could be fitted with three exponentials. The excimer decays were also found to be triple-exponential, although only the excimer rise times, having values comparable with the shortest monomer decay times Tg, were reported. 

It was concluded that the observation of these three exponentials indicated the presence of three kinetically non-interacting, each in itself apparently completely isotropic, monomer populations of PPS or PDS. Lochmuller et al. based-their discussions on the values of the (normalized) amplitudes A. in the triple-exponential monomer decays, and stated that these amplitudes were a direct measure of the three fractions of monomers. 

In the derivation (42) of the physical meaning of the monomer amplitudes in [14], the concept of molecular fluorescence quantum yield is used, as if the decay times in the triple-exponential monomer decay were in fact the lifetimes x (i) of three molecules that do not interact in any way, i.c. do not form excimers. Therefore, valid information from these normalized amplitudes can only be obtained for such a mixture of completely noninteracting molecules. The ratio A x (i)/(E A T (i)), see [9], then is the fraction of each molecular species, provided any difference in excitation cross-section has been taken into account. 

Figure 6 Fluorescence decay curves for undegassed poly (acenaphthylene solution (THF, 298 K) (a) excitation pulse, (b) monomer decay (analysed at 325 nm), (c) excimer decay (analysed at 450 nm)...

As seen, the concentration of the monomer decays more significantly on the PFR reactor. 

This limitation leaves us with only five pieces of information from the fluorescence decays (three decay times and two ratios of pre-exponential coefficients from the monomer decay), for the six unknowns. 

The time-resolved fluorescence intensities, Fm(0 and Fd(0, are proportional to the instantaneous concentrations of the excited monomers and excimers, respectively. The monomer decay is a sum of two exponentials, which means that it decreases faster than the unquenched monomer decay. The excimer is not present immediately after excitation and is formed by a diffusion-controlled process, i.e., the emission increases at early times, passes maximum, and at later times decays more slowly than the monomer fluorescence. The realistic (experimental) decays, F,(0exp> are schematically shown in Fig. 11. 

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