Peculiar elasticity and strain hardening attributable to counteracting entropy of chain and ring in slide-ring gels

A systematic study on the elasticity of slide-ring gels in which polymer chains can slide through cross-links and ring components slide on the chains reveals the contributions of entropy of both the chains and rings to the elasticity. The equilibrium modulus exhibits a significantly weak power dependence on the cross-linking density (estimated from the modulus at the rubbery plateau and determined by dynamic viscoelastic measurements). This suggests the considerably smaller contribution of chain entropy to the equilibrium elasticity in comparison to chemically cross-linked gels. Increasing stress with temperature indicates entropic origins of the elasticity. The stress-compression curve exhibits a strong non-linearity with a strain hardening: the modulus at the linear regime, within 1% strain, increases drastically (one full order of magnitude) and becomes constant at the intermediate regime strains from 2 to 6%. The modulus of the intermediate strain is in close agreement with that of the rubbery plateau observed by dynamic viscoelastic measurements at the high frequency limit. This suggests that the stress at the intermediate strain originates mainly from the chain entropy in a way similar to that of conventional chemical gels. The fact that chain entropy that contributes hardly to the stress at the linear regime conversely dominates the elasticity at the intermediate regime indicates the counteraction of the entropy of rings, which decreases with the degree of chain sliding.