A Mathematical Model for the Longest Ethylene Sequence Distribution of Random Ethylene Copolymers

Abstract

AbstractSummary: In the first step to model Crystaf® curves, a mathematical expression ψ has been derived to describe the longest ethylene sequence (LES) distribution of random binary (e.g., ethylene/α‐olefin) copolymer chains. Based on this expression, a method Ψpolymer has been developed to describe the LES‐distribution of random copolymers. Comparisons of the LES‐distribution of a random copolymer with polydispersity of 2, as calculated by Ψpolymer, with Monte Carlo simulation and with a method previously described in literature show that the derived mathematical expression ψ is correct. This model allows for the description of the crystallizing temperature‐distribution of polymers using the reported relation between crystallizing temperature and LES. It will also hold if the crystallizing temperature of a chain would depend on other chain properties next to its LES. Exactly this latter prospect will favor the use of the mathematical expression derived in this report, above the ones from the literature.LES weight‐distribution of a random copolymer, calculated by Ψpolymer and by a Monte Carlo simulation.imageLES weight‐distribution of a random copolymer, calculated by Ψpolymer and by a Monte Carlo simulation.