Diffusion-controlled, bimolecular elementary

Diffusion-Controlled Encounter. Elementary bimolecular reaction mechanisms require diffiisional encovmter before the reaction. If the intrinsic kinetics are fast, and/or the viscosity of the solution is high, diffusion-controlled encounter may occur. In a homogeneous medium, a rate constant /jdiff can be evaluated which reflects the effective bulk-averaged rate constant associated with bimolecular encounters (45). Diffusional bimolecular encounter should be considered in the appropriate context. If Areact is the intrinsic bimolecular rate constant and djff is the differential rate constant defined above, then the observed rate constant for the bimolecular reaction is given by equation (11) (46). The limiting cases of this equation can be readily identified that is when the rate constant is very large, the observed rate constant corresponds to the diffusional rate constant. 

The experimental and simulation results presented here indicate that the system viscosity has an important effect on the overall rate of the photosensitization of diary liodonium salts by anthracene. These studies reveal that as the viscosity of the solvent is increased from 1 to 1000 cP, the overall rate of the photosensitization reaction decreases by an order of magnitude. This decrease in reaction rate is qualitatively explained using the Smoluchowski-Stokes-Einstein model for the rate constants of the bimolecular, diffusion-controlled elementary reactions in the numerical solution of the kinetic photophysical equations. A more quantitative fit between the experimental data and the simulation results was obtained by scaling the bimolecular rate constants by rj"07 rather than the rf1 as suggested by the Smoluchowski-Stokes-Einstein analysis. These simulation results provide a semi-empirical correlation which may be used to estimate the effective photosensitization rate constant for viscosities ranging from 1 to 1000 cP. 

Another unsolved fundamental problem of this theory concerns the correct description of copolymerization kinetics which obviously requires a well-grounded expression, from the physicochemical viewpoint, for the rate constant of the bimolecular chain termination reaction. This elementary reaction of interaction of two macroradicals proves to be diffusion-controlled beginning from the very initial conversions, and therefore, its rate in the course of the entire process is controlled by physical, rather than chemical factors. Naturally, the consideration of the kinetics of bulk copolymerization requires different approaches ... 

There are several variants of the DCR theory differing from one another by the way in which account is taken of the physical factors influenced by the diffusion control on the description of elementary reactions rate. As a rule, the main factor influenced is the bimolecular chain termination process. The constant rate of chain termination is considered as a fnnction of the macroradical s mobility, their length [9-14], free volume [12,15-17] or characteristic viscosity of monomer-polymeric system. However, with the aim of explaining the auto deacceleration stage, the efficiency of initiation and constants of rate chain propagation are also considered to be functions of the macroradical s mobility [12,15,18]. 

There are different variants of the DCR conception, differing one from another by the set of physical parameters, which are taken into account, and by the details of the analytical description of diffusion control on the rate of an elementary reaction. As a rule, the main attention focuses on bimolecular chain termination, the constant rate of which is considered as a function of macroradicals mobility, depending on their length [34-46], free volume [47-53] or characteristic viscosity [54-57] of the monomer/polymeric solution. In a range of studies [58-61] the initiation efficiency and the constant rate of the chain propagation are also used as a function of macroradicals mobility. 

Another challenge is the conversion number within the observation volume of 1 fl. Assuming an elementary bimolecular reaction where both molecules are fluorescing, their concentration should not exceed 1 nM. Even if diffusion-controlled conditions are assumed, that is, > 10 s , only one reactive collision... 

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