Competing irreversible cooperative reactions on polymer chains

We analyze model processes involving competition between several irreversible reactions at the sites of a 1D, infinite, uniform polymer chain. These reactionscan be cooperative, i.e., the corresponding rates depend on the state of the surrounding sites. An infinite hierarchy of rate equations is readily derived for the probabilities of various subconfigurations. By exploiting a shielding property of suitable blocks of unreacted sites, we show how exact hierarchy truncation and solution is sometimes possible. The behavior of solutions is illustrated in several cases by plotting families of ‘‘reaction trajectories’’ for varying ratios of reactant concentrations. As a specific application, we consider competition between coordination of ZnCl2 to pairs of oxygen atoms and to single oxygen atoms in poly(propylene oxide). The observed glass transition temperature behavior is eludicated. Disciplines Biological and Chemical Physics | Chemistry | Physics Comments This article is published as Evans, J. W., D. K. Hoffman, and D. R. Burgess. "Competing irreversible cooperative reactions on polymer chains." The Journal of chemical physics80, no. 2 (1984): 936-943, doi:10.1063/1.446751. Posted with permission. This article is available at Iowa State University Digital Repository: http://lib.dr.iastate.edu/physastro_pubs/437 Competing irreversible cooperative reactions on polymer chains J. W. Evans, D. K. Hoffman, and D. R. Burgess ) Ames Laboratoryl') and Department o/Chemistry, Iowa State University, Ames, Iowa 50010 (Received 29 August 1983; accepted 14 October 1983) We analyze model processes involving competition between several irreversible reactions at the sites of a ID, infinite, uniform polymer chain. These reactions can be cooperative, i.e., the corresponding rates depend on the state of the surrounding sites. An infinite hierarchy of rate equations is readily derived for the probabilities of various subconfigurations. By exploiting a shielding property of suitable blocks of unreacted sites, we show how exact hierarchy truncation and solution is sometimes possible. The behavior of solutions is illustrated in several cases by plotting families of "reaction trajectories" for varying ratios of reactant concentrations. As a specific application, we consider competition between coordination of ZnCl2 to pairs of oxygen atoms and to single oxygen atoms in poly(propylene oxide). The observed glass transition temperature behavior is eludicated.