Influence of Structural Characteristics on Stretching-Driven Swelling of Polyrotaxane Gels with Movable Cross Links

Stretching-driven swelling of polyrotaxane (PR) gels whose cross-linked cyclic molecules can slide along the network strands in response to imposed strain is investigated as functions of cross-link concentration ( c x ), the length of network strands ( M s ) and the content of cyclic molecules threaded onto the network strands (ϕ CD ). For the PR gels with high c x, equilibrium Poisson’s ratio (μ ∞ ) which is a measure of stretching-driven swelling is independent of imposed stretch (λ) as in the case of classical gels with fixed cross-links. In contrast, μ ∞ for the PR gels with sufficiently low c x depends on λ: μ ∞ increases with λ in the regime of λ < λ c whereas μ ∞ levels off in the region of λ > λ c . The λ-dependent μ ∞ under moderate elongation is attributed to a function characteristic of movable cross-links (pulley effect) which can vary the network topology under imposed deformation so that the configurational entropy can be maximized. The level-off behavior of μ ∞ at high elongation is explained by the suppression of pulley effect caused by high stacking and/or localization of cross-linked cyclic molecules at the chain ends. The content ϕ CD influences the variation in the λ dependence of μ ∞ driven by a change in c x as well as the values of μ ∞ . These results indicate that (1) the cross-links in the PR gels move nonaffinely and (2) ϕ CD influences how the cross-links slide along the network strands in nonaffine manner in response to imposed deformation.