Monte Carlo Approach to the Simulation of Ethylene Oxide and Propylene Oxide Polymerization and Copolymerization

The simulation of block or random ethylene oxide (EO) and propylene oxide (PO) copolymerization with a deterministic model requires the solution of many thousands of differential and algebraic equations. This approach, therefore, is not practicable, requiring too long computer calculation time. The use of a stochastic model allows overcoming this drawback. In this work, a Monte Carlo based model has been developed considering, for a given substrate such as ethylene glycol, only the reaction of the overall consumption of the alkoxides. The addition of new units of EO or PO, respectively, to the hydroxyls of the substrate or the terminal hydroxyls of the growing chains is ruled by the stochastic probability of the two mentioned events. The developed model considers also the effect of the side reaction of PO conversion to allyl alcohol with the formation of new growing polymeric chains. To do the calculations a microscopic volume, assumed to be a well-mixed system, is considered containing about 5000 or a few more molecules, which is a number significant for statistical validity. Kinetic laws and related parameters have been estimated from data published in the literature. Examples of simulations of high-molecular-weight EO and PO homopolymers, of an EO-PO random copolymer, and a triblocks copolymer of the type (EO)a-(PO)b-(EO)a will be presented.