Mathematical analysis of intra-stack dimerizations in reactive crystalline solids

Abstract

Photodimerization in many crystalline solids, such as β-phase trans-cinnamic acids, can be treated as a one-dimensional phenomenon. Those monomers which become flanked by a pair of dimers during the course of the dimerization reaction are themselves unable to form a dimer molecule and remain as ‘isolated’, unreacted monomers. As a result, the monomer-to-dimer conversion at the end of reaction is usually substantially less than 100%. In this paper, we assess theoretically the mean final conversion in systems undergoing irreversible linear dimerization. Two mathematical models (the so-called monomer excitation and bond insertion models) have been developed to describe this process, and information relating to dimerizations conforming to the dictates of these models has been determined by computer simulation and by exact mathematical analysis. For each model, the results obtained from these contrasting approaches agree well. The mean conversion at the end of reaction (which differs for the two models considered) does not correspond, in either case, to the conversion in the final state of maximum entropy.