Non-linear Effects in Asymmetric Catalysis: Whys and Wherefores

Abstract

It is argued that the titled non-linear effects (NLE) may arise whenever the order of the reaction in the chiral catalyst in greater than 1. In a fundamental departure from previous approaches, this is mathematically elaborated for the second order case. (NLE may also be observed if the chiral catalyst forms non-reacting dimers in a competing equilibrium; practically, however, this implies the in situ resolution of the catalyst.) The amplification of enantiomeric excess by NLE implies a relative (although modest) reduction in the entropy of mixing. The consequent increase in free energy apparently indicates a non-equilibrium process. It is suggested, based on arguments involving the chemical potential, that kinetically-controlled reactions lead to a state of “quasi-equilibrium”: in this, although overall equilibrium is attained, the product-spread is far from equilibrium. Thus, both the linear and NLE cases of chiral catalysis represent departures from equilibrium (which requires that the product e.e. = 0). Interesting similarities exist with models of non-equilibrium systems, the NLE cases apparently being analogs of open systems just after the bifurcation point has been crossed.