Diffusive encounters

When (DEB), is much smaller than unity, the polymer relaxation is relatively rapid compared to diffusion. In this case, conformational changes take place instantaneously and equilibrium is attained after each diffusional jump. This is the type of diffusion encountered ordinarily and is called viscous diffusion. Therefore, the transport will obey classical theories of diffusion. When (DEB), is much larger than unity, the molecular relaxation is very slow compared to diffusion and there are no conformational changes of the medium within the diffusion time scale. In this case, Fick s law is generally valid, but no concentration dependence of the diffusion coefficient is expected. This is termed elastic diffusion. When (DEB), is in the neighborhood of unity, molecular rearrangment... 

It is important to notice that a change in lifetime is not a necessary result of a change in fluorescence intensity. For instance, the Ca2+ probe Fluo-3 displays a large increase in intensity on binding Ca2+, but there is no change in lifetime. This is because the Ca-free form of the probe is effectively nonfluorescent, and its emission does not contribute to the lifetime measurement. In order to obtain a change in lifetime, the probe must display detectable emission from both the free and cation-bound forms. Then the lifetime reflects the fraction of the probe complexed with cations. Of course, this consideration does not apply to collisional quenching, when the intensity decay of the entire ensemble of fluorophores is decreased by diffusive encounters with the quencher. 

At present it is universally acknowledged that TTA as triplet-triplet energy transfer is caused by exchange interaction of electrons in bimolecular complexes which takes place during molecular diffusion encounters in solution (in gas phase -molecular collisions are examined in crystals - triplet exciton diffusion is the responsible annihilation process (8-10)). No doubt, interaction of molecular partners in a diffusion complex may lead to the change of probabilities of fluorescent state radiative and nonradiative deactivation. Nevertheless, it is normally considered that as a result of TTA the energy of two triplet partners is accumulated in one molecule which emits the ADF (11). Interaction with the second deactivated partner is not taken into account, i.e. it is assumed that the ADF is of monomer nature and its spectrum coincides with the PF spectrum. Apparently the latter may be true when the ADF takes place from Si state the lifetime of which ( Tst 10-8 - 10-9 s) is much longer than the lifetime of diffusion encounter complex ( 10-10 - lO-H s in liquid solutions). As a matter of fact we have not observed considerable ADF and PF spectral difference when Sj metal lo-... 

Analysis of kinetic equations for the scheme (4) taking into account steady-state concentrations leads to the following relation between the TTA rate constant kj and constant k[Pg.125]

Condensed monolayer films of pure 6 polymerized rapidly, as did mixed 6/DSPE films of up to 75% DSPE, provided the monolayers were in the condensed state [33], In the liquid-expanded state, polymerization did not occur. In the condensed state, lateral diffusion of individual lipids within the monolayer is severely restricted compared to the liquid-like state. This precludes initiation of polymerization by diffusive encounter between excited-state and ground-state diacetylene lipids. In order for polymerization to occur in the condensed state, the film must be separated into domains consisting of either pure 6 or pure DSPE. A demonstration that the rates of photopolymerization for pure 6 and mixed 6/DSPE monolayers are equal would be a more stringent test for separate domains of the lipids, but no kinetic data have been reported for this system. 

The primary effect of micelles on light-induced electron transfer involves the intervention of an interfacial region which can significantly influence the radical ion association and dissociation equilibria by a combination of electrostatic and hydro-phobic interactions. Diffusive encounters of reaction partners are controlled within a micelle by the diffusion of one reactant to the highly polar surface, by collision of two reactants confined within the hydrophobic region in the interior of the micelle, and by the reaction of two reactants whose motions are confined to diffusion along the micellar surface. 

The key idea in [140] is that, even though the binding energy of structures such as loops or hairpins are smaller than the interparticle association energies, a fast temperature quench can favor the formation of the loops and hairpins inside the DNA coatings. This is possible if such structures form over times that are smaller than the typical time of diffusive encounter of the particles. Of course, this is easier for smaller particle concentrations as shown in Fig. 34. 

R2-R2 was 25%, 50%, and 25%, respectively, and did not vary with pressure. The fact that a statistical 1 2 1 ratio of bibenzyls is produced, at all pressures examined including near the critical pressure, suggests that these products are produced by diffusive encounters of (Ri.)free and (R2.)free rather than by in-cage coupling (which would yield solely Ri R2). Thus, these authors found no evidence for an enhanced cage-effect that might be attributable to solute solvent clustering. 

When the solvent itself is the nucleophile X, then the transition state map has to be modified since there is now no diffusive encounter of the solvent and the species RY the solvent is already there. The diagram for a solvolysis reaction is shown in Fig. 3. The great difference between Fig. 1 and Fig. 3 is that in the former there can be no merging between the geometry of the SN1... 

For an ensemble of two different radicals undergoing diffusive encounters, the enhancement factor can be further expressed as... 

The presence of a quencher molecule decreases the intensity of photoluminescence since the fluorophore is often returned to the ground state during a diffusive encounter with the quencher. In this process the fluorophore is not chemically modified. For collisional quenching the decrease in intensity is described by the Stern-Volmer equation ... 

Scheme 24 summarizes the possible processes that can occur during a free-radical polymerization induced via an intermolecular electron transfer process (PET) in the presence of aromatic amines kdii is the rate constant of diffusive encounters be-... 

Spin labels undergoing translational diffusion encounter each other at a frequency given by the Smoluchowski equation... 

The simplest treatment of diffusive encounters considers two noninteracting hard spheres that have radii r, and r2, diffusion constants D and Di, and isotropic reactivities such that any collision (i.e., when the distance between the two spheres is equal to the sum of their radii) leads to the reaction. This model requires solution of the Smoluchowski equation215 with a perfectly absorbing condition at R = r, + r2. The resulting rate constant k(R) has the simple form... 

Figure 14.7 Refined model for proton transfer between acids and bases with a three-stage mechanism consisting of diffusion, encounter and reaction stages. In this model the Eigen-Weller on-contact reaction rate k, is to be...

This reformulation in terms of diffusive propagation and microscopic dynamics in the boundary layer is reminiscent of Noyes s encounter formulation that we briefly described earlier. Now each diffusive encounter is interrupted by sequences of collisions and very short excursions into the fluid. The analysis of nonhydrodynamic effects on the rate kernel can, therefore, be discussed naturally in terms of the encounter formalism. 

Polarization obtained by RTPM is related to the RPM in that diffuse encounters are still required, but differs... 

Models of pathways exist in many forms but most of these are static representations, not dynamic models of metabolism. They show the network topology of interconnected pathways of enzymes or signalling molecules, but they contain no dynamic information on reaction rates of diffusive encounters. The JWS-online database (http //jjj.biochem.sun.ac.za/database/index.html) on the other hand, is a web-based database containing over 90 dynamics models. Of these however, only a few are approaching what is desired. 

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