Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.
J Chem Phys. 2011 Aug 7;135(5):054902. doi: 10.1063/1.3622487.
Based on recent molecular dynamics and ab initio simulations of small isoprene molecules, we propose a new ansatz for rubber elasticity. We envision a network chain as a series of independent molecular kinks, each comprised of a small number of backbone units, and the strain as being imposed along the contour of the chain. We treat chain extension in three distinct force regimes: (Ia) near zero strain, where we assume that the chain is extended within a well defined tube, with all of the kinks participating simultaneously as entropic elastic springs, (II) when the chain becomes sensibly straight, giving rise to a purely enthalpic stretching force (until bond rupture occurs) and, (Ib) a linear entropic regime, between regimes Ia and II, in which a force limit is imposed by tube deformation. In this intermediate regime, the molecular kinks are assumed to be gradually straightened until the chain becomes a series of straight segments between entanglements. We assume that there exists a tube deformation tension limit that is inversely proportional to the chain path tortuosity. Here we report the results of numerical simulations of explicit three-dimensional, periodic, polyisoprene networks, using these extension-only force models. At low strain, crosslink nodes are moved affinely, up to an arbitrary node force limit. Above this limit, non-affine motion of the nodes is allowed to relax unbalanced chain forces. Our simulation results are in good agreement with tensile stress vs. strain experiments.
基于最近对小异戊二烯分子的分子动力学和从头算模拟，我们提出了一种新的橡胶弹性模型。我们设想链作为一系列独立的分子扭结，每个扭结由少数几个骨架单元组成，应变沿着链的轮廓施加。我们在三个不同的力区处理链的延伸：（Ia）在接近零应变的情况下，我们假设链在一个明确定义的管中延伸，所有扭结同时作为熵弹性弹簧参与，（II）当链变得相当直时，产生纯粹的焓拉伸力（直到键断裂发生），以及（Ib）在 Ia 和 II 之间的线性熵区，其中管变形施加力限制。在这个中间区，假设分子扭结逐渐变直，直到链在缠结之间变成一系列直段。我们假设存在一个管变形张力极限，它与链路径曲折度成反比。在这里，我们报告了使用这些仅延伸力模型的显式三维周期性聚异戊二烯网络的数值模拟结果。在低应变下，交联节点以仿射方式移动，直到达到任意节点力极限。在这个极限之上，允许节点的非仿射运动来松弛不平衡的链力。我们的模拟结果与拉伸应力与应变实验吻合良好。
