Chemical kinetics in entangled media

Let us imagine a reagent to be attached to a chain, and a different reagent Y to be attached to another chain (which is chemically identical to the first one). We wish to study the kinetics of a reaction of the type  

Deactivations (XV1 ) are particularly interesting at a fundamental level, since the final product (X + y) is still formed by two independent chains the medium is not altered by the reaction. 

In the following, we shall limit ourselves for the sake of simplicity to optical deactivation reagents X and Y are attached to two flexible chains and immersed in a liquid of the same chains. We shall also assume that the reaction occurs whenever the distance between the two centers X and Y becomes smaller than a given trapping radius b. 

When X and Y are not attached to any chain, but are small molecules (with concentrations n, and n,) in a dilute solution, the kinetics is simple  

How could we transfer these results to our entangled molecules It is initially tempting simply to introduce into equation (24) the macroscopic diffusion coefficients defined by (21) and (22). The constant k should then be proportional to iV . We can, however, show that this idea is wrong. The reaction occurs at spatial distances between reagents of the order of b, which are smaller than the statistical size Rq of the chains an analysis solely based on macroscopic concepts is not sufficient. 

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