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 (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 (mu(infinity)), which is a measure of the strain-induced volume change, for the PR gel increases with an increase in elongation (lambda) at moderate lambda but becomes a constant value (mu(infinity)*) at sufficiently large lambda. When the modulus exceeds a threshold value (E-c), the lambda dependence of mu infinity disappears due to the loss of the slidability of the cross-links. The fraction f(CD) significantly influences the values of mu(infinity)* and E-c. When f(CD) is sufficiently small (<14%), mu(infinity)* (approximate to 0.25) agrees with the values of mu infinity for the classical gels in good solvents. When f(CD) is high (>25%), mu(infinity)* varies over a wide range (0.22 < mu(infinity)* < 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 mu infinity (less than 0.1) at small lambda is also considered on the basis of the magnitude of the accompanying force reduction caused by the slidable function of the cross-links.