Department of Macromolecular Science and Engineering, Kyoto Institute of Technology, Sakyo-ku, Kyoto 606-8585, Japan.
Department of Advanced Materials Science, School of Frontier Sciences, The University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8561, Japan.
Soft Matter. 2018 Apr 18;14(15):2808-2815. doi: 10.1039/C8SM00257F.
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.
螺旋环分子（fCD）在聚轮烷（PR）链中的密度对 PR 凝胶的应变诱导溶胀有显著影响，其中交联的环分子可沿网络链滑动。平衡泊松比（μ∞）是衡量应变诱导体积变化的指标，对于 PR 凝胶，在中等伸长率（λ）下，μ∞随伸长率的增加而增加，但在足够大的 λ 下，μ∞变为常数（）。当模量超过阈值（Ec）时，由于交联的滑动性丧失，μ∞对 λ 的依赖性消失。fCD 分数显著影响和 Ec 的值。当 fCD 足够小时（<14%），（≈0.25）与良好溶剂中经典凝胶的 μ∞值一致。当 fCD 较高时（>25%），μ∞值在较宽范围内变化（0.22 < < 0.33），这取决于 fCD 和交联浓度，且以复杂的方式相关。由于轴向聚合物中未交联环分子的数量较多，通过组合熵产生的有限贡献，fCD 为 25%时的 Ec 比 fCD 为 5%时高两倍以上。还根据交联的滑动功能引起的伴随力减小的幅度，考虑了小 λ 时 μ∞（小于 0.1）明显较小的原因。
