A Novel Stochastic Approach for the Prediction of the Exact Topological Characteristics and Rheological Properties of Highly-Branched Polymer Chains

A novel stochastic algorithm is described for the accurate prediction of the detailed molecular topology of highly branched polymer chains. Stochastic topological polymer chain simulations are carried out in conjunction with a polymerization kinetic MC simulator. Contrary to previous efforts on the stochastic simulation of topological features of branched polymer chains, the present approach does not apply any simplifying assumptions regarding the distributional form of “live” and “dead” polymer chain populations. The proposed stochastic approach takes explicitly into account the effects of various diffusional limitations in the termination and propagation rate constants (i.e., gel- and glass-effect) as well as the effect of branching density on the kinetics of various reactions (i.e., transfer to polymer and chain scission reactions). To demonstrate the predictive capabilities of the proposed stochastic approach, the free-radical polymerization of ethylene in an industrial high-pressure tubular reactor is investigated. It is shown that the present stochastic kinetic/topology algorithm can provide detailed information on the topological features of highly branched polymer chains (i.e, long- and short-chain branching distributions, segment seniority and priority distributions, etc.). The topological information, obtained by the application of the stochastic kinetic/topology algorithm, is then used together with a 3-D molecular random-walk simulator to predict the 3-D random spatial configurations of branched polymer chains as well as some important rheological parameters (i.e., the mean radius of gyration, Rg, the mean hydrodynamic radius, Rh, and the average branching factor, g) of low-density polyethylene.