Origin of Nonlinear Effects Some Models

It is difficult to give general rules predicting the possibility of NLE in a given chemical system. One statement that we proposed is the following  

If several molecules of the chiral auxiliary are involved in autoassociation or in any type of molecular species, then the passage from enantiopure auxiliary to nonenantiopure auxiliary may produce new diastereomeric entities. Consequently, the enantioimpure system may have new stereochemical properties. 

An easy kinetic treatment has been done by taking as parameters the relative rate constants and the relative amounts of the meso versus homochiral complexes  

Equation (7.2) has been established, which is equal to Eq. (7.1) multiphed by a fraction where g and p are involved. If p = 0 (no meso complex) or g = 1 (same reactivities of meso and homochiral complexes), then Eq. (7.2) gives back to Eq. (7.1). When g 1 (meso complex slower than homochiral catalyst) the fraction will be a number 1, meaning that eep od will be higher than the value predicted by Eq. (7.1)  

Blackmond pointed out that asymmetric amplification always has, as a consequence, a decrease in reactivity when compared to the enantiopure catalyst. This can be calculated on the various models proposed for the interpretation of nonlinear effects. It is qualitatively visible in the reservoir model above as well as in the ML2 model, where the asymmetric amplification given by g 1 (low reactivity of the meso catalyst) has as consequence the overall slowdown in reaction rate. The generalized model ML has been discussed (for n = 2,3,4) when the various species are in equilibrium. The complexity of the curve can increase sharply as soon as n 2. 

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