The theory of rubber elasticity



It is argued that one can envisage two extreme regimes in rubber. The first is a dilute regime, where crosslinks are the only significant interaction between chains, and is the conventional model. The other extreme is one in which a very entangled situation exists where the chain statistics under deformation are remote from free Gaussian statistics. This latter case is studied and it is argued that the entropy per crosslink takes the form

equation image

where α and β are independent of deformation but depend on temperature and density, and J2 is the usual first invariant. The dilute regime is α = β = 0.