Pronounced effects of the densities of threaded rings on the strain-dependent Poisson's ratio of polyrotaxane gels with movable cross-links.

The density of threaded ring molecules (fCD) in polyrotaxane (PR) chains has pronounced effects on the strain-induced swelling of PR gels where the cross-linked ring molecules are slidable along the network strands. The equilibrium Poisson's ratio (μ∞), which is a measure of the strain-induced volume change, for the PR gel increases with an increase in elongation (λ) at moderate λ but becomes a constant value () at sufficiently large λ. When the modulus exceeds a threshold value (Ec), the λ dependence of μ∞ disappears due to the loss of the slidability of the cross-links. The fraction fCD significantly influences the values of and Ec. When fCD is sufficiently small (<14%), (≈0.25) agrees with the values of μ∞ for the classical gels in good solvents. When fCD is high (>25%), varies over a wide range (0.22 < < 0.33) depending on fCD and the cross-link concentration in a complicated way. The modulus Ec at fCD = 25% is more than twice as high as that at fCD = 5% due to the finite contribution of the larger amount of uncross-linked ring molecules via combinatorial entropy in the axial polymers. The origin of the markedly small values of μ∞ (less than 0.1) at small λ is also considered on the basis of the magnitude of the accompanying force reduction caused by the slidable function of the cross-links.