RUBBER ELASTICITY - A CONTACT-PROBABILITY MODEL WITH HARMONIC ENTANGLEMENT CONSTRAINTS

This paper is devoted to the theoretical analysis of nonideality effec ts in stretched rubber samples. The joint effect of packing forces and topological constraints is accounted for by adopting harmonic potenti als between all pairs of network atoms, in addition to fixing a suitab le set of junctions at the macroscopic sample surface according to the James-Guth theory. The potential minima are set at the average, affin ely deformed interatomic distances. The force constant of each interac tion is proportional to the probability of interatomic contact in the undeformed state and is inversely proportional to the square strain ra tio along any space direction, thus accounting for the variation of th e entanglement concentration with sample stretching. The proportionali ty factor of the pair potential is an adjustable parameter of the theo ry. A periodic coarse-grained model is used and the sample free energy is evaluated through normal-mode self-consistent analysis. Both the M ooney effect and the observed radius of gyration of the chain strands projected along different directions are properly accounted for. The r esults are similar to those of the Ronca-Allegra theory, which is base d on direct application of constraints to the junction fluctuations. H owever, the present approach also embodies features of the theories wh ich adopt the tube model. Finally, the variation of the Mooney constan t C-2 With sample swelling is accounted for in a semiquantitative way. (C) 1996 American Institute of-Physics.