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.

中文翻译：

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螺纹环密度对带有可移动交联的聚轮烷凝胶的应变依赖性泊松比的显着影响

聚轮烷（PR）链中带环分子（f _CD）的密度对应变诱导的PR凝胶溶胀具有显着影响，其中交联的环分子可沿网络链滑动。平衡泊松比（μ _∞），这是应变诱导体积变化的量度，对于具有在伸长率（增加了PR凝胶增加λ在中度）λ但变为恒定值（）在足够大的λ。当弹性模量超过阈值（ê _Ç），则λ的依赖性μ _∞由于交联的滑动性丧失而消失。f _CD分数显着影响和E _c的值。当˚F _CD是足够小（<14％），（≈0.25）同意的值μ _∞为在良好溶剂中的经典凝胶。当f _CD高（> 25％）时，取决于f _CD和交联浓度，会以复杂的方式在较大范围（0.22 <<0.33）内变化。模量ë _Ç在˚F _CD = 25％大于两倍高，在˚F_CD = 5％，这是由于轴向聚合物中大量未交联的环分子通过组合熵的有限贡献。的显着小的值的原点μ _∞在小（小于0.1） λ也被认为是引起交联的可滑动功能伴随力减小的幅度的基础上。