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

Abstract

The density of threaded ring molecules (f_CD) 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 (E_c), the λ dependence of μ_∞ disappears due to the loss of the slidability of the cross-links. The fraction f_CD significantly influences the values of and E_c. When f_CD is sufficiently small (<14%), (≈0.25) agrees with the values of μ_∞ for the classical gels in good solvents. When f_CD is high (>25%), varies over a wide range (0.22 < < 0.33) depending on f_CD and the cross-link concentration in a complicated way. The modulus E_c at f_CD = 25% is more than twice as high as that at f_CD = 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.