(342az) Chain Topology Structure Simulation of Linear Low-Density Polyethylene Based on Graph Theory and Monte Carlo Algorithm

Wang Jie, Yao Yang^*, Jingyuan Sun, Xiaoqiang Fan, Zhengliang Huang, Jingdai Wang, and Yongrong Yang

State Key Laboratory of Chemical Engineering, College of Chemical and Biological Engineering, Zhejiang University, Hangzhou, 310027, China

*Correspondence author, e-mail: yao_yang@zju.edu.cn

The highly branched topology structure of linear low-density polyethylene (LDPE) is directly relevant to its product properties, such as melt index, rheological, etc. In order to obtain a better description of the radical polymerization process, a topology structure simulation of linear low-density polyethylene chain based on graph theory and Monte Carlo algorithm is proposed in our study.

By converting reaction speed to the random sampling probability problem, Kinetic Monte Carlo algorithm is capable to predict accurate molecular weight distribution (MWD), copolymer composition distribution (CCD), short-chain branching distribution (SCBD), and long-chain branching distribution (LCBD). As simulation of chain full topology structure of linear low-density polyethylene could be the basement of many other applications or research, it can set our imagination about high pressure polyethylene polymerization free. The first problem researchers encountered is how to symbolize the chain topology structure, as the chain structure is not a digit number but a kind of connection graph. Some specially designed methods are developed for this problem, but they are dedicated to certain problem or based on some temporary trick, rather than elegant theory method via mathematics and graph theory. To solve this problem, we studied chain topology structure simulation of LDPE using graph theory and Monte Carlo algorithm, which could provide better accuracy and speed.

The algorithm we proposed could obtain more accurate simulation result comparing with traditional ones. For demonstrating the difference, we take an industry LDPE tubular reactor as example, and establish new Monte Carlo model and old method for the same simulation input data. Both methods could provide the molecular weight distribution, which is consistent with experiment data. But Monte model with graph theory show better accuracy of molecular chain length distribution, short-chain branching distribution, and long-chain branching distribution. Comparing with traditional method, our algorithm obtains bigger main carbon chain length, the difference is more significant with molecular weight growing. Because of the difference of main carbon chain length distribution, the SCBD and LCBD also show great difference in two method, long chain branch is shorted in our simulation method.

The combination of computer theory and chemical technology knowledge inspire us a lot and give new life to old simulation method.

Key words: Polymer chain structure, Graph theory, Polymers, Algorithms

Reference

[1] Meimaroglou, Dimitrios, and Costas Kiparissides. "A novel stochastic approach for the prediction of the exact topological characteristics and rheological properties of highly-branched polymer chains." Macromolecules 43.13 (2010): 5820-5832.