Quenching rate model

FIGURE 7.17 Fluorescence lifetime temperature measurements for gas-phase biomolecular ions of (a) Trp-cage protein charge states (b) Dye-(Pro) -Arg-Trp peptide sequences, [M -H H] (c) Vancomycin-peptide non-covalent complexes, [M H- H] +. Best-fits for the quenching rate model are shown by lines through each set of data points. 

Hamiltonian does not give rise to any crystalline order in the system. By employing models hke this, the quench-rate and chain-length dependence of the glass transition temperature, as well as time-temperature superposition, similar to experiments [23], were investigated in detail. 

Other groups may cause shortening of the lifetime. The phosphorescence of parvalbumin is quenched by free tryptophan with a quenching rate constant of about 10s M i s l (D. Calhoun, unpublished results). A more extensive survey of proteins or model compounds with known distances between tryptophans is needed to study how adjacent tryptophans affect the lifetime. It should be noted that at low temperature the phosphorescence lifetime of poly-L-tryptophan is about the same as that of die monomer.(12) This does not necessarily mean that in a fluid solution tryptophan-tryptophan interaction could not take place. Thermal fluctuations in the polypeptide chain may transiently produce overlap in the n orbitals between neighboring tryptophans, thus resulting in quenching. 

The observed quenching rate constant, kq, according to this model will be a function of the internal diffusion of the quencher, fcrf(int), and is given by... 

Fig. 3.14 Simulated ALIS-based dissociation rate measurements. See text for details. (A) Quench experiments modeled at varying inhibitor association rates. Even with a very slow-binding inhibitor, the decay curve resembles pure first-order dissociation kinetics. (B) Data in (A), shown on a log axis. (C) Simulated ALIS quench experiment with varying protein-ligand dissociation rates,...

Rather than discuss the estimation of the density of the diffusing species around other species, it is perhaps of more interest to estimate the rate coefficient for a reaction, and certainly rather less complex than estimating the density. One of the first such studies was by Reck and Prager [507]. They considered the diffusion of the fluorophor in solution amongst an array of stationary quenchers. The fluorophor was excited at a constant rate F s-1 and the deactivation occurred by natural decay (lifetime r) and by contact quenching. This model is very similar to that chosen by Felderhof and Deutch [25] in their study of competitive effects. 

Since any quenching action is a bimolecular process, it is essential that the molecules M and Q should be in relatively close contact, but not necessarily in hard sphere (van der Waals) contact. Theoretical models lead to the distance dependence of the quenching rate constants as exponentials or sixth powers of r, the centre-to-centre distance of M and Q. Since these distance dependences are very steep, it is convenient to define a critical interaction distance r at which the quenching efficiency is, this being the distance at which 50% of the molecules M decay with emission of light (or undergo a chemical reaction) and 50% are quenched by some nearby molecule Q. 

At 2000 K and 1 atm, Hollander s state-specific rate constant becomes k. = 1.46 x 1010 exp(-AE/kT) s-1, where AE is the energy required for ionization. For each n-manifold state the fraction ionized by collisions is determined, as well as the fraction transferred to nearby n-manifold states in steps of An = 1. Then the fractions ionized from these nearby n-manifold states are calculated. In this way a total overall ionization rate is evaluated for each photo-excited d state. The total ionization rate always exceeds the state-specific rate, since some of the Na atoms transferred by collisions to the nearby n-manifold states are subsequently ionized. Table I summarizes the values used for the state-specific cross sections and the derived overall ionization and quenching rate constants for each n-manifold state. The required optical transition, ionization, and quenching rates can now be incorporated in the rate equation model. Figure 2 compares the results of the model calculation with the experimental values. 

The anionic and cationic ends of the NC s TICT state were found to be quenched by electron donors and acceptors respectively. The quenching rate constants were analyzed with the help of the Marcus model and found consistent with the expected value for electron transfer mechanism. This was confirmed by photochemical reactions running through a radical cation or a radical anion intermediate. The isomerization of quadricyclane to norborna-diene was used as a check for the reactivity of the radical-cation end of the NC s... 

Figure 3. Scheme of the PL quenching model (A) and and the comparison (B) of experimental quenching rate A, constants (left axis) with calculated probability density functions i/(r) of a Is electron at the outer interface. 

The term "disruptive quencher" is applied to the case in which all exciton contacts with the quencher results in completely effective quenchingIt is not at all clear that this property is applicable to Cu quenching. The case of a non-dlsruptive quencher is much harder to analyze and does not lead to a convenient expression for the excitation decay, analogous to eqn. (18). Based on classical diffusion equations it seems plausible that the disruptive quencher model is applicable so long as the quenching rate at the quenched site is of the same order of magnitude as the transfer rate from that lattice site to neighboring sites. ... 

Fitzgibbon, P.D. Frank, C.W. Macromolecules 1982, 15, 733. Specifically if Nk /W 1 where k and W are the quenching rate and hopping rite respectively (S.E. Webber, unpublished calculations, based on the classical "surface evaporation" model (J. Crank, Mathematics of Diffusion, (Oxford Press, 1983), section 4.3.6). 

The structure of amorphous metals, quasicrystals, and crystalline inter-metallic compounds can be modelled by atom clusters with icosahedral arrangement [3.113-117]. The differences between the various phases result from a different arrangement of the individual atom clusters. Therefore, it is evident that there exists a close relation between the different states of matter, and that the different phases corresponding to minima of the free enthalpy can be quite easily transformed into each other. For example, rapid cooling from the melt results in an amorphous alloy for high quenching rates, and a quasicrystalline... 

The three rate constants, kq, kr, kd, and one coefficient a, theoretically can be solved by the slopes and intercepts in eqs. 83 and 88. However, the intercept of Eq. 88 is a virtual intercept, which was physically meaningless since the y-intercept did not exist in the case of high humic concentration, (i.e. humic concentration cannot be zero in this model). Therefore, another equation is needed to solve the four constants. Practically, it is normally assumed that the rate for exothermic quenching is diffusion-controlled. The quenching rate, kq, can therefore be evaluated from the modified Debye expression (William M., 1976). 

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