Diffusional Effects on Reactions

Some rapid homogeneous reactions are controlled by the rate of diffusion of reagents towards each other. In some cases, as pressure increases in an SCF, a reaction may pass from activation control to diffusion control [10]. In the simplest analysis of diffusion control, the second-order rate coefficient in terms of mole fractions, kx, is given by the Smoluschowski equation. 

The Stokes-Einstein equation, relating the diffusion coefficient to the fluid viscosity, is used to rewrite eq (1.3-1) in terms of viscosity as 

Diffusion is also important for unimolecular fission. Thus, radical initiators under SCF conditions are able to escape more readily from solvent cages, and the rate coefficient for the initiation process is markedly increased. Pro- 

In a complex reaction scheme, where only some of the steps are diffusion controlled, the course of the reaction can be changed by controlling the diffusion coefficients. The archetypal example here is polymerization. The effect of diffusion control on overall rate and the rates of the different steps is first discussed. A simplified equation, sufficient for a qualitative discussion, for the instantaneous rate of polymer formation is 

When the molecule concerned is a radical initiator this has implications for the efficiency of radical production, related to cage escape. Under supercritical conditions, geminate recombination can be controlled by density, as described earlier. 

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