To predict and understand the properties of polymer networks, it is necessary to quantify network defects. Of the various possible network defects, loops are perhaps the most pervasive and yet difficult to directly measure. Network disassembly spectrometry (NDS) has previously enabled counting of the simplest loops—primary loops—but higher-order loops, e.g., secondary loops, have remained elusive. Here, we report that the introduction of a nondegradable tracer within the NDS framework enables the simultaneous measurement of primary and secondary loops in end-linked polymer networks for the first time. With this new “NDS2.0” method, the concentration dependences of the primary and secondary loop fractions are measured; the results agree well with a purely topological theory for network formation from phantom chains. In addition, semibatch monomer addition is shown to decrease both primary and secondary loops, though the latter to a much smaller extent. Finally, using the measured primary and secondary loop fractions, we were able to predict the shear storage modulus of end-linked polymer gels via real elastic network theory (RENT).

中文翻译：

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准确预测末端连接的聚合物网络弹性需要计算二次回路

为了预测和理解聚合物网络的特性，有必要量化网络缺陷。在各种可能的网络缺陷中，环路可能是最普遍但难以直接测量的。网络反汇编光谱法 (NDS) 以前可以对最简单的循环（初级循环）进行计数，但高阶循环（例如二级循环）仍然难以捉摸。在这里，我们报告说，在 NDS 框架中引入不可降解的示踪剂，首次能够同时测量末端连接的聚合物网络中的初级和次级回路。使用这种新的“NDS2.0”方法，可以测量初级和次级回路馏分的浓度依赖性；结果与从幻象链形成网络的纯拓扑理论非常吻合。此外，半批量单体添加显示可减少一级和二级循环，尽管后者的程度要小得多。最后，使用测量的初级和次级环分数，我们能够通过真实弹性网络理论 (RENT) 预测末端连接的聚合物凝胶的剪切储能模量。