Comparison of topological properties between end-linked and statistically cross-linked polymer networks

Abstract

This paper compares topological properties of computer-generated unimodal end-lined and statistically cross-linked polymer networks. The bond-fluctuation algorithm was used to obtain the different networks. The networks were analyzed by using knot theory. The results show that the average number of trapped entanglements increases linearly with the length of the subchains. The slope is about 2 times higher in the case of end-linked networks. Although the overall number of entanglements is higher in the end-linked case, swelling experiments reveal that the distribution of subchain lengths of statistically cross-linked networks produces inhomogeneities in the structure which lead to a stronger contribution than for the end-linked networks. A homogeneous mean-field ansatz for the influence of entanglements to the deformation modulus used by most theories therefore appears to be not applicable to statistically cross-linked networks.