RELAXATION OF ENTANGLED POLYMERS AT THE CLASSICAL GEL POINT

We examine the relaxation behaviour of an entangled cross-linked polymer gel as it approaches the gel point in mean field (Flory-Stockmayer) percolation. The calculation is based on a tube model for the topological interactions in which stress is lost via hierarchical fluctuation of the primitive paths between cross-links. The decay time of a segment is calculated via a recursion relation which has an analytic solution near the gel point. The startling conclusion is that all clusters relax in a finite time T∞ For timescales much shorter than T∞ this may resemble a weak power law. The unphysically rapid relaxation of the largest clusters is prevented by a transition to percolation statistics at long length scales. The timescale separating the two regimes is close to T∞.