Relaxation of entangled polymers at the classical gel point

2014 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~ giving a relaxation modulus G (t ) = Go 03B3-2[03B1-1 ln (T~/t)]4, where 03B1 counts the number of entanglements between cross-links and 03B3 is a constant of order unity. 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~. J. Phys. France 51 (1990) 757-775 15 AVRIL 1990, Classification Physics Abstracts 47.50 61.25 46.30