Polymer length distributions for catalytic polymerization within mesoporous materials: Non-Markovian behavior associated with partial extrusion

TitlePolymer length distributions for catalytic polymerization within mesoporous materials: Non-Markovian behavior associated with partial extrusion
Publication TypeJournal Article
Year of Publication2010
AuthorsLiu DJ, Chen HT, Lin VSY, Evans JW
Journal TitleJournal of Chemical Physics
Volume132
Pages154102
Date Published04/21
ISBN Number0021-9606
Accession NumberISI:000276971500003
Keywordscatalysis, diffusion, equations, extrusion, kinetics, lattice theory, mesoporous materials, molecule-molecule reactions, monte carlo methods, polymerisation, POLYMERS, random-walks, reaction kinetics theory, reaction-diffusion systems
Abstract

We analyze a model for polymerization at catalytic sites distributed within parallel linear pores of a mesoporous material. Polymerization occurs primarily by reaction of monomers diffusing into the pores with the ends of polymers near the pore openings. Monomers and polymers undergo single-file diffusion within the pores. Model behavior, including the polymer length distribution, is determined by kinetic Monte Carlo simulation of a suitable atomistic-level lattice model. While the polymers remain within the pore, their length distribution during growth can be described qualitatively by a Markovian rate equation treatment. However, once they become partially extruded, the distribution is shown to exhibit non-Markovian scaling behavior. This feature is attributed to the long-tail in the "return-time distribution" for the protruding end of the partially extruded polymer to return to the pore, such return being necessary for further reaction and growth. The detailed form of the scaled length distribution is elucidated by application of continuous-time random walk theory.

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