A study of the entanglement in polymer melts
Seminar Room 1, Newton Institute
Polymer melts are dense systems of macromolecules. In such dense systems the conformational freedom and motion of a chain is significantly affected by entanglement with other chains which generates obstacles of topological origin to its movement. In this talk we will discuss methods by which one may quantify and extract entanglement information from a polymer melt configuration using tools from knot theory. A classical measure of entanglement is the Gauss linking integral which is an integer topological invariant in the case of pairs of disjoint oriented closed chains in 3-space. For pairs of open chains, we will see that the Gauss linking integral can be applied to calculate an average linking number. In order to measure the entanglement between two oriented closed or open chains in a system with three-dimensional periodic boundary conditions (PBC) we use the Gauss linking number to define the periodic linking number. Using this measure of linking to assess the extend of entanglement in a polymer melt we study the effect of CReTA (Contour Reduction Topological Analysis) algorithm on the entanglement of polyethylene chains. Our results show that the new linking measure is consistent for the original and reduced systems.
For a collection of open or closed chains in 3-space or in PBC, we define the linking matrix. The eigenvalues of this matrix provide insight into the character of the entanglement.