Conditional Monte Carlo sampling to find branching architectures of polymers from radical polymerizations with transfer to polymer and recombination termination

A model is developed that predicts branching architectures of polymers from radical polymerization with transfer to polymer and termination by disproportionation and recombination, in a continuously stirred tank reactor (CSTR). It is a so-called conditional Monte Carlo (MC) method generating architectures of molecules of specified dimensions. The relevant dimensions in the present case are the number of branch points, np, and the number of combined parts a molecule consists of, nc. These branch points and combination points together are decisive for the connectivity inside molecules. The modeling strategy is based on backtracking of the molecular growth history in terms of the chemical events determining connectivity, transfer to polymer and recombination termination. The recombination termination mechanism requires the model to develop parts of the architecture following several paths back to the initial primary polymers that form the starting points for the molecules. The algorithm requires the construction of probability density functions being evaluated using a fast Galerkin-FEM method. The architectures generated by the conditional Monte Carlo method are compared to those from a full MC method using several qualifiers. One of these is the number of initial primary polymers in a molecule as well as their lengths, another is the radius of gyration contraction factor. Perfect agreement is found between the architectures found by the conditional and full MC methods.