The use of modern multiple-quantum proton NMR experiments for the determination of cross-link density requires precise knowledge of several model-dependent physical and structural quantities, like the dipolar static frequency or the definition of vector segmental order. In this paper, different models for describing segmental order of the polymer backbone, based on different assumptions about the contribution of cross-links and entanglements, are critically reviewed and applied for the analysis of unfilled natural rubber samples with average mass between cross-links and entanglements determined from network tube model fittings of stress–strain data. A recent theoretical model developed by Lang and Sommer, which allows for the consideration of junction fluctuations, is adapted for the analysis of NMR experimental results. After having verified the correlation between the calculations with this enhanced theoretical treatment and the residual dipolar coupling from multiple-quantum NMR experiments carried out in a low-field spectrometer, a new simplified approach to determine the segmental order parameter is proposed for sulfur-cured rubbers.

中文翻译：

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重新讨论分段顺序：考虑结点波动和缠结的硫磺硫化橡胶的简化方法

使用现代多量子质子NMR实验确定交联密度需要精确了解几种与模型有关的物理和结构量，例如偶极静态频率或矢量分段顺序的定义。在本文中，基于有关交联和缠结贡献的不同假设，对用于描述聚合物主链分段顺序的不同模型进行了严格审查，并将其用于分析平均质量介于交联和交联之间的未填充天然橡胶样品。根据应力-应变数据的网络管模型拟合确定缠结。Lang和Sommer开发的最新理论模型适用于分析结点波动，适用于NMR实验结果的分析。