J. Phys. France 51, 2829-2842 (1990)
DOI: 10.1051/jphys:0199000510240282900

Critical properties of crosslinked polymer melts

Gary S. Grest^{1, 2} et Kurt Kremer<sup>1

1</sup>  Institut für Festkörperforschung, Forschungszentrum Jülich, D-5170 Jülich, F.R.G.
²  Corporate Research Science Laboratories, Exxon Research and Engineering Company, Annandale NJ 08801, U.S.A.

Abstract
The critical behavior at the percolation threshold for a randomly crosslinked polymer melt of linear chains is studied by computer simulations. We show that the fraction of crosslinks per chain pc at the vulcanization/percolation threshold is independent of chain length N for large N. Thus for long chains, the volume fraction of crosslinks at the transition decreases as 1/N in agreement with Flory. If we allow linkages only between different chains and no self-linkages, we find that pc ˜ 0.6 in the limit of large N. This value in 20 % larger than Flory's mean field result, pc = 1/2, as some of the crosslinks do not increase the number of chains in a cluster. When we allow intra-chain linkages as they occur experimentally, the scaling with N remains unchanged but pc increases by an addition 20 % for the present model. We also find in agreement with de Gennes that the critical exponents are well described by their mean field values and that the size of the critical region where fluctuations are important is small for long polymer chains. The fractal dimension of the percolating cluster at pc was found to be 3.

PACS
6460A - Renormalization-group, fractal, and percolation studies of phase transitions.
8105L - Polymers and plastics; rubber; synthetic and natural fibers; organometallic and organic materials.
0570J - Critical point phenomena.
6125H - Macromolecular and polymer solutions; polymer melts; swelling.

Key words
critical fluctuations -- digital simulation -- fractals -- percolation -- polymer melts -- vulcanisation