Analysis of trapped entanglements in polymer networks

This work reviews different standard methods to analyze trapped entanglements of polymer networks and discusses their advantages and drawbacks with respect to simplicity, computing time and accuracy of the results. Since this standard analysis is based on the pairwise test of closed cycles, two algorithms for the determination of these cycles are introduced and compared. The decomposition into meshes creates unsolved problems regarding the non-ambiguity and the completeness of the received results. Examples are given in order to show their effects and to start further discussion to receive more convenient methods. As one possible solution Vassiliev's invariants are discussed and an approximation method is introduced to correct the possible multiple counting of entanglements