Exact Mean-Field Theory for the Amorphous Solid State of Vulcanised Macromolecular Matter.
Abstract
At a certain critical crosslink concentration, systems of randomly crosslinked macromolecules undergo an equilibrium phase transition from a liquid to an amorphous solid state.(See, e.g., H. Castillo et al., Europhys. Lett. 28), 519 (1994) and references therein. For a review, see P. Goldbart et al. (UIUC P-95-09-062-i). We present a mean-field description of this vulcanisation transition, in which the emergent state is diagnosed by a novel order parameter that is capable of detecting the random localisation of the macromolecules. The state is characterised by the fraction of localised monomers and the distribution of their localisation lengths. There are two striking aspects to this approach. First, it contains the percolative description of the statistical architecture of crosslinked networks in terms of the fraction of localised monomers. Second, it goes beyond the percolative description in the sense that it also yields statistical-mechanical information concerning the (random) degree to which monomers are localised. We conclude with a discussion of the elastic properties that result from the random localisation of the macromolecules.
- Publication:
-
APS March Meeting Abstracts
- Pub Date:
- March 1996
- Bibcode:
- 1996APS..MAR.N2515C