The special mechanical properties of natural rubber originate from the stretching of the network chains (i.e., cis-1,4-polyisoprene chains) in the rubber network. The chains with various lengths exhibit various relative extensions, leading to various normalized energy contributions to the mechanical properties of rubber. However, the stretching behaviors of cis-1,4-polyisoprene chains with different lengths are not studied clearly. Here, the stretching behavior, which is the basis for analyzing the normalized energy contribution, is obtained by the modified freely jointed chain model. Next, using a new statistical model, i.e., the two-component quantum-mechanics Gaussian (TCQMG) model, the relative extension–length relationship of network chains is determined. Combining the above results, the energy contributions of network chains with different lengths are analyzed. The results show that long and short chains show different stretching states. The following can be explained by these results: short chains play an important role in the mechanical properties of rubber. As the network chain density increases, the average length of the chains decreases, leading to the variation of the normalized extensions. It is found that the variation of the normalized extensions is responsible for both the effects of the network chain density and network chain length on the mechanical properties of rubber.

中文翻译：

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通过二元量子力学高斯模型揭示链长对橡胶力学性能的影响

天然橡胶的特殊机械性能源于橡胶网络中网络链（即顺式-1,4-聚异戊二烯链）的伸缩。不同长度的链表现出不同的相对延伸，导致对橡胶机械性能的标准化能量贡献不同。然而，不同长度的顺式-1,4-聚异戊二烯链的拉伸行为尚未得到明确研究。这里，拉伸行为是分析归一化能量贡献的基础，是通过修改的自由连接链模型获得的。接下来，使用新的统计模型，即二分量量子力学高斯（TCQMG）模型，确定网络链的相对延伸-长度关系。结合上述结果，分析了不同长度网络链的能量贡献。结果表明，长链和短链表现出不同的拉伸状态。这些结果可以解释以下内容：短链对橡胶的机械性能起着重要作用。随着网络链密度的增加，链的平均长度减小，导致归一化扩展的变化。研究发现，归一化伸长率的变化是网络链密度和网络链长度对橡胶机械性能影响的原因。