An approach to rubber elasticity with internal constraints

The effect of configurational hindrances in unswollen rubberlike networks is taken into account by assuming the existence of a proper correlation between the macroscopic deformation and the rms fluctuations of the network junctions along the various directions of space. Following James and Guth’s approach, some junctions have been fixed at the surface of a proper parallelepiped in order to avoid collapse of the network, and the above correlation is expressed through the introduction of appropriate δ functions into the configurational partition function. Results identical with those previously arrived at by Flory–Hoeve–Ciferri are obtained by assuming that the rms fluctuation components transform as the macroscopic stretch ratios. This assumption cannot hold under high deformations because it implies that the junction fluctuations increase without limit with the deformation. Therefore an intermediate model is proposed where (i) the average ms fluctuations of the junctions are independent of strain, as in James–Guth theory, and (ii) the ratios between the rms (mean square) fluctuations are equal to those between the corresponding stretch ratios as in Flory–Hoeve–Ciferri theory. The intermediate model can explain, at least to some extent, the so-called Mooney effect. It is also shown that the relation −∂ln(σ/T)/∂TL,V=dln〈r2〉0/dT is valid for James–Guth theory only.