2. Modeling and simulation
2.1. KMC simulation of ethylene/1-hexene coordination copolymerization
Generally, when the reaction scheme consists of N ABT-737 elementary reaction channels, the mth reaction can be selected in a given time interval from uniformly distributed random numbers in a unit interval, according to the following relationships:equation(1)∑i=1m-1Pi?r1<∑i=1mPidt=1∑i=1NRiln1r2where r1 and r2 are two random numbers, Pi and Ri are the reaction rate probability and rate of reaction i, respectively, and dt is the time interval between two successive reactions.
In the present study, Gillespie’s algorithm was hybridized with classical statistical copolymerization equations to precisely determine the optimal feeding policy to attempt synthesizing ethylene/1-hexene copolymer chains with predetermined molecular architecture ,  and .
To produce copolymer chains, semibatch coordination copolymerization process of ethylene (monomer E) and 1-hexene (comonomer or monomer H) was simulated. The KMC-based algorithm was constructed on the basis of the reaction scheme and copolymerization conditions suggested by Zhang et al. . In this copolymerization process, according to the proposed mechanism ( Scheme 1), the microstructural characteristics of the final product are significantly controlled by the activation of Et(Ind)2ZrCl2 catalyst, initiation of living chains, propagation of growing chains, chain transfer to 1-hexene, hydrogen abstraction, and the catalyst deactivation. Drawing on the fact that the KMC simulation approach is capable of analyzing and reporting all instantaneous and cumulative microstructural variations during the copolymerization of ethylene/1-hexene, the proposed reaction channel is expected to visualize a more comprehensive and reliable image of the process.