A conditional Monte Carlo method to predict branched architectures from molecular weight and degree of branching distribution of polyethylene for single and mixed systems with a constrained geometry metallocene catalyst in continuous reactors

Any two polymer molecules of the same length (n) and the same number of branch points (N) can have different properties, since they may possess distinct architectures. In this paper we present conditional Monte Carlo algorithms for the virtual synthesis of polyethylene (PE) catalyzed by one branch forming constrained geometry metallocene catalyst (CGC, 1C-system) or by a mixture of CGC and linear metallocene catalyst (2C-system) in a continuous stirred tank reactor. The condition for the Monte Carlo method consists of a fixed chain length distribution and degree of branching distribution. To calculate these distributions explicit algebraic relations are available Macromolecules 36 (2003) 10037. The synthesis method is a recursive algorithm that subsequently creates insertions of sub-structures containing numbers of monomer units and branch points according to one- or two-dimensional probability density functions. We developed a general 2C-algorithm and a simplified 1C-algorithm applicable for 1C-systems only. They provide an adjacency matrix describing the connectivity between the branch points, while separately (1C-method Macromol Theor Simul 12 (2003) 484) or simultaneously (2C-method) a vector containing the length of segments between branch points and terminal segments is generated Macromol Theor Simul 10 (2001) 855. Characterization of the architectures proceeds by calculating the topological variables seniority and priority as well as the radius of gyration Macromol Theor Simul 10 (2001) 870. As regards seniority and priority good agreement is found with results from the analytical approach Macromolecules 36 (2003) 10037 is found. 2C-architectures turn out to possess more comb-like structures than 1C-architectures. Concerning molecular sizes an interesting effect of the segment length distribution in 2C-molecules is observed.