Monomers decay constants

The decay of monomer emission is thus a sum of two exponentials. In contrast, the time evolution of the excimer emission is a difference of two exponentials, the pre-exponential factors being of opposite signs. The time constants are the same in the expressions of iM(t) and iE(t) (/ , and fl2 are the eigenvalues of the system). The negative term in iE (t) represents the increase in intensity corresponding to excimer formation the fluorescence intensity indeed starts from zero because excimers do not absorb light and can only be formed from the monomer (Figure 4.8A). 

Fytas et al. [18[ observed polymer dynamics associated with height fluctuations of PEO-PS copolymers attached to glass in toluene. Some of the measured normalized autocorrelation functions are shown in Fig. 8. The data was well represented by a single exponential function with a decay constant that exhibited minimal dependence on q. There is no calculation of the structure factor for such a system, but it is possible to rationalize the dependence of the decay constant on the 5/3 power of the chain density and the cube of the number of monomers in the PS segment. 

N-isopropylcaibazole (NIPC) was studied as a model for the monomer repeat unit of PVK by Mort et al. (1976). The concentration dependence was described by a wavefunction decay constant of 1.5 A, compared to 1.2 A for PVK (Gill, 1972). Composite plots of the logarithm of the photocurrent versus the logarithm of time were universal when normalized to the transit time. The activation energy was 0.1 eV smaller than for PVK. The results were described by the Scher-Montroll model (1975). 

Table I lists the decay constants, X, obtained for the different concentrations of the monomers studied. These Xs are the average of the left and right values obtained for each concentration (11). Though statistical errors range from 5% to 17%, experimental irreproducibilities in target geometry, field homogeneity, detector thresholds, muon beam asymmetry and background result in a more probable error of 25% ( ). This level of reproducibility is quite reasonable when compared to rate constants obtained by competitive rate techniques and direct physical methods.

The emission properties of some carbazole double molecules [l,n-bis(JV-carbazoyl)alkanes] have been examined and one compound in particular, 1,3-bis-(N-carbazoyl)propane (1,3-BCP), was found to be a useful model for poly-(/V-vinylcarbazole). Measurements of the temperature dependence of monomer and excimer decay constants have provided useful kinetic and thermodynamic information on this system. The binding energy for the intramolecular excimer of 1,3-BCP was shown to be 2.76 kcal mol-1, a rather low value. Measurements on other carbazole double molecules showed that Hirayama s n = 3 rule is obeyed and that the preferred geometry of the intramolecular excimer is sandwichlike.161... 

The temperature at which a dynamic equilibrium is reached between the formation and the decay of monomer macroradicals is called a ceiling temperature. For certain monomers, there are published ceihng temperatures, heats, and entropy of polymerization (28,29). Their values are, for example, 150°C for MAH, 200°C for methacrylate, 400°C for acrylate and styrene (28). It should be noted that these values are typical of reactions occurring at a constant (atmospheric) pressure and monomer concentration (usually 1 mol). The peak temperature rises with monomer concentration and pressure. That is why MAH was observed to homopolymerize at an extrusion temperature above 160°C (30). 

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... 

Despite deviations from the ideal kinetics at early and late conversion, rationalized by existing models, quasi-steady state approximation (QSSA) proved to be an appropriate approximation for analyzing the reactions and obtaining the associated rate constants. Several reaction features such as the dependence of and initiator decay rates on l/[/]o and respectively, and the first-order decay of monomer during the majority of the conversion allowed verification of the ideal kinetics applicability. 

Morishima et al. [75, 76] have shown a remarkable effect of the polyelectrolyte surface potential on photoinduced ET in the laser photolysis of APh-x (8) and QPh-x (12) with viologens as electron acceptors. Decay profiles for the SPV (14) radical anion (SPV- ) generated by the photoinduced ET following a 347.1-nm laser excitation were monitored at 602 nm (Fig. 13) [75], For APh-9, the SPV- transient absorption persisted for several hundred microseconds after the laser pulse. The second-order rate constant (kb) for the back ET from SPV- to the oxidized Phen residue (Phen+) was estimated to be 8.7 x 107 M 1 s-1 for the APh-9-SPV system. For the monomer model system (AM(15)-SPV), on the other hand, kb was 2.8 x 109 M-1 s-1. This marked retardation of the back ET in the APh-9-SPV system is attributed to the electrostatic repulsion of SPV- by the electric field on the molecular surface of APh-9. The addition of NaCl decreases the electrostatic interaction. In fact, it increased the back ET rate. For example, at NaCl concentrations of 0.025 and 0.2 M, the value of kb increased to 2.5 x 108 and... 

The results are summarized in Fig. 9 giving the relative abundance of the various ions at the end of the flow-tube as functions of the initial concentration of the monomer. From the decay of the signal of e/m = 69 (CF3 ) the rate constant of the bimolecular reaction... 

Observed monomer concentrations are presented by Figure 2 as a function of cure time and temperature (see Equation 20). At high monomer conversions, the data appear to approach an asymptote. As the extent of network development within the resin advances, the rate of reaction diminishes. Molecular diffusion of macromolecules, initially, and of monomeric molecules, ultimately, becomes severely restricted, resulting in diffusion-controlled reactions (20). The material ultimately becomes a glass. Monomer concentration dynamics are no longer exponential decays. The rate constants become time dependent. For the cure at 60°C, monomer concentration can be described by an exponential function. 

By numerically fitting the decay curves of [Ti(III)] with the simulation program Gepasi [52], it was established that the dimer opens the epoxide with a rate constant of k = 1.4 M 1 s, whereas the monomer reacts more slowly (k = 0.5 M 1 s 1). At the usual initial Cp2TiCl2 concentration of 10 mM, this means that 84% of 25 molecules are opened by the dimer. 

Class (3) reactions include proton-transfer reactions of solvent holes in cyclohexane and methylcyclohexane [71,74,75]. The corresponding rate constants are 10-30% of the fastest class (1) reactions. Class (4) reactions include proton-transfer reactions in trans-decalin and cis-trans decalin mixtures [77]. Proton transfer from the decalin hole to aliphatic alcohol results in the formation of a C-centered decalyl radical. The proton affinity of this radical is comparable to that of a single alcohol molecule. However, it is less than the proton affinity of an alcohol dimer. Consequently, a complex of the radical cation and alcohol monomer is relatively stable toward proton transfer when such a complex encounters a second alcohol molecule, the radical cation rapidly deprotonates. Metastable complexes with natural lifetimes between 24 nsec (2-propanol) and 90 nsec (tert-butanol) were observed in liquid cis- and tra 5-decalins at 25°C [77]. The rate of the complexation is one-half of that for class (1) reactions the overall decay rate is limited by slow proton transfer in the 1 1 complex. The rate constant of unimolecular decay is (5-10) x 10 sec for primary alcohols, bimolecular decay via proton transfer to the alcohol dimer prevails. Only for secondary and ternary alcohols is the equilibrium reached sufficiently slowly that it can be observed at 25 °C on a time scale of > 10 nsec. There is a striking similarity between the formation of alcohol complexes with the solvent holes (in decalins) and solvent anions (in sc CO2). 

Excitation of the coupled A2, Bi states results in the decay rate designated X3 which appears to be nearly independent of cluster size. A small increase in the value of x3 appears to occur for (S02)m clusters from the monomer (0.6 ps) to the dimer (0.9 ps), but remains constant at about 1 ps for larger cluster sizes. A likely interpretation of the observed decay process can be found in a detailed computational study [6] which reports that following the initial vertical excitation of the 1 B state, the excited state wave packet travels from the Bi state into the double wells that result from the crossing of the 1A2 and Bi states. The transition of the excited state population into the double wells of the A2 and B states is believed to lead to the decay observed in the pump-probe experiment because the potential energy well minima of both of these states are outside of Franck-Condon region for the absorption of the probe laser pulse. Therefore, ion signal is not observed once the transition has occurred. The primary discrepancy between the computational results of Ref. [6] and the... 

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. 

If h > 0, then helical assemblies do not form. There is an isodesmic polymerization from monomers to "disordered" supramolecular polymers that takes place around X l. The theory of Section 1 applies and the equivalent equilibrium constant obeys K = exp [. jy. Its value can be probed by means of radiation scattering, fluorescence decay, and UV absorption spectroscopy (Brunsveld et al., 2001 Jonkheijm et al., 2006). 

In spite of the presence of Nd-clusters, partial alkylation and micro heterogeneities the number of active Nd-species seems to be fairly constant during the course of a polymerization. Otherwise neither consistent polymerization kinetics (particularly lst-order monomer consumption up to high monomer conversion) nor linear increases of molar mass during the whole course of the polymerization would be observed in so many studies. It therefore can be concluded that the fraction of active Nd as well as the number of active catalyst species are fixed either at an early stage of the polymerization or even prior to initiation of the polymerization. It can be speculated whether the fixation of the number of active species occurs during catalyst prefor-mation/activation or even during the preparation of the Nd compound. In contrast to this consideration Jun et al. report on the decay of active cen-... 

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