Simulations on the number of entanglements of a polymer network using knot theory

Polymer networks, created on the computer using the Bond-Fluctuation-Algorithm, offer the possibility to count the number of entanglements. We generated networks consisting of 5000 chains that were cross linked at their end groups via tetra-functional cross linkers. The analysis of the topology was performed by computing the Homfly polynomial of the entanglements offering a much more precise determination of the knot and entanglement type than the Gaussian linking number. It also allows us to determine the influence of Brunnian links. Results concerning the connection between the chain length and the number of entanglements are shown.