Trapped Entanglements in Polymer Networks

This work focuses on density, complexity, and experimentally observable effects of trapped entanglements in polymer networks. Using the bond-fluctuation method we crosslinked and end-linked systems with a random initial distribution of polymer and crosslinker. The structure of the generated networks has been analyzed by knot theory and graph theory concerning defects, ring structures, and trapped entanglements, resulting in a detailed description of network topology and connectivity. The knowledge on network structure is used to analyze computer simulations of swelling and solfraction experiments. The simulated swelling experiments show that the size of the fully swollen network depends strongly on the presence of trapped entanglements although the zero second Money-Rivlin term upon deformation indicates the absence of a tube like environment for individual network chains. Permanently trapped rings and the formation of network defects affect the weight of the measured gel component as function of the degree of crosslinking. The experimentally observed shift in size of the gel can be estimated based on the data of this study and is typically smaller than the shift due to ineffective reactions that lead to the formation of dangling rings and network defects.