论文标题
应变诱导的聚合物结晶的几何热力学
Geometric Thermodynamics of Strain-Induced Crystallization in Polymers
论文作者
论文摘要
除了爱因斯坦波动理论的古典高斯近似值之外，鲁皮恩（Ruppeiner）为其提供了带有熵指标的黎曼几何结构。这产生了基本数量 - riemannian曲率，该曲率用于提取有关流体，理想气体和其他开放系统中分子之间相互作用的性质的信息。在本文中，我们研究了这种曲率在非平衡热力学系统中的含义，在非平衡热力学系统中，松弛足够慢，以免使局部平衡假设无效。非平衡系统包括经过应变诱导结晶的橡胶聚合物。发现曲率可以传达有关已经结晶段的构象拉伸引起的虚假等齿能的信息。由于结晶的歧管被认为是通过欧几里得公制定义的拉伸措施，因此可能会出现这种非物理成分。与曲率相关的热力学状态是确定等距拉伸并因此伪造能量的关键。我们确定了这一点，并提出了一个伪造自由能的形式，必须从总能量中删除，以便恢复正确的应力。
Going beyond the classical Gaussian approximation of Einstein's fluctuation theory, Ruppeiner gave it a Riemannian geometric structure with an entropic metric. This yielded a fundamental quantity - the Riemannian curvature, which was used to extract information on the nature of interactions between molecules in fluids, ideal gases and other open systems. In this article, we examine the implications of this curvature in a non-equilibrium thermodynamic system where relaxation is sufficiently slow so as not to invalidate the local equilibrium hypothesis. The non-equilibrium system comprises of a rubbery polymer undergoing strain induced crystallization. The curvature is found to impart information on a spurious isochoric energy arising from the conformational stretching of already crystallized segments. This unphysical component perhaps arises as the crystallized manifold is considered Euclidean with the stretch measures defined via the Euclidean metric. The thermodynamic state associated with curvature is the key to determine the isochoric stretch and hence the spurious energy. We determine this stretch and propose a form for the spurious free energy that must be removed from the total energy in order that the correct stresses are recovered.
