278208 Modeling the Polymeric Microstructure of Ldpe with a Novel Hybrid Simulation Approach
A novel hybrid simulation approach is developed, which combines the advantages of deterministic and stochastic modeling for complex polymerization networks. The first field of application is the description of industrial LDPE tubular reactors with peroxide or oxygen initiation.
This hybrid concept is motivated by the fact that the well established modeling techniques such as deterministic simulation handles with respect to microstructural properties mean values (e.g. averaged long and short chain branch densities), but is not able to generate individual macromolecule samples with exact polymeric topology. This type of information can only be derived from the stochastic Monte-Carlo simulation. It plays an important role for the determination of characteristics the control the (application) behavior of the polymeric species. A parameter of interest is e.g. the contraction factor g, which is the ratio of the mean square radius of gyration of a branched and a linear molecule with same molar mass. Furthermore, the access of the exact topology of an exemplary macromolecule allows the description of the topological β-scission, which has a significant effect on the chain-length distribution. Unfortunately, a pure stochastic simulation with sufficient accuracy to microstructural properties, heat and pressure balances requires extreme large molecule ensembles and therefore enormous computational demand. Thus the hybrid concept is based on the idea to use the Monte-Carlo approach as an optional add-on for the computation of the polymeric microstructure based on deterministic simulation of complex reactor operation.
The combined simulation approach is implemented as follows:
The deterministic simulation tool Predici is used to compute the effective reaction rates for each elemental reaction connected to the polymerization of ethylene as a function of the position inside the tubular reactor. In this step also the speed of flow and the probability function for the formation of radicals with the chain-length one are determined. In a second step this data set is used in the stochastic algorithm to simulate a certain number of distinct macromolecules with completely known microstructure one after another. Thus there is no necessity to handle large molecule ensembles. The resulting topology array is used as input for a three dimensional random walker, which computes the contraction factor g of the individual molecule without any model assumption like for example Zimm-Stockmayer-Theory.
The results of this hybrid simulation technique show good agreement with experimental chain-length distributions and contraction factors. Furthermore, the topological correct description of the β-scission in the stochastic approach allows a back coupling and improvement of the deterministic simulation. Applying it without any modification to autoclave reactors tests the validity of the demonstrated concept.
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