UNIVERSALITY OF GELATION - END-LINKING VERSUS CROSS-LINKING AND STIFFRODS VERSUS FLEXIBLE CHAINS

End-linking is the process in which junctions that permanently connect l ends of polymers are introduced at random. Sufficient end-linking c auses a system of polymers to undergo a continuous equilibrium phase t ransition from a liquid to an amorphous solid state, i.e., to gel. Thi s gelation transition is explored for a variety of end-linked polymer systems, focusing on universal aspects, and is contrasted with that ca used by cross-linking. The dependency of this phase transition on the single-chain statistics and on the functionality l of the junctions is investigated. As an example of a single-chain statistics, stiff rods with a finite bending energy are considered. The shear modulus and the distribution of localization lengths are calculated, and found to be universal near the transition.