Ta. Vilgis et M. Otto, ELASTICITY OF ENTANGLED POLYMER LOOPS - OLYMPIC GELS, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 56(2), 1997, pp. 1314-1317
In this Rapid Communication we present a scaling theory for the elasti
city of olympic gels, i.e., gels wherp the elasticity is a consequence
of topology only. It is shown that two deformation regimes exist, The
first is the nonaffine deformation regime where the free energy scale
s linear with the deformation. In the large (affine) deformation regim
e the free energy is shown to scale as F chi lambda(5/2) where lambda
is the deformation ratio. Thus a highly non-Hookian stress-strain rela
tion is predicted.