In this paper, Paul’s model is advanced to forecast the tensile modulus of polymer nanocomposites reinforced by carbon nanotubes (CNT) above percolation onset. The developed model assumes the CNT network density by CNT aspect ratio (α), percolation onset and CNT density (n). The experimental results from several samples containing a filler network confirm the predictability of the advanced model. However, undesirable results are reported for the samples without the filler network. Also, both α and n directly manipulate the nanocomposite’s modulus above percolation onset, because they positively influence the polymer-CNT interfacial area and network size. The reasonable effects of α, n and percolation onset on the predicted moduli of nanocomposites validate the developed Paul model.

中文翻译：

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聚合物碳纳米管纳米复合材料在通过填料网络密度达到渗透阈值后拉伸模量的常规 Paul 模型的开发

在本文中，Paul 的模型用于预测由碳纳米管 (CNT) 增强的聚合物纳米复合材料在渗透开始时的拉伸模量。开发的模型通过 CNT 纵横比 (α)、渗透起始和 CNT 密度 (n) 假设 CNT 网络密度。来自包含填充网络的多个样本的实验结果证实了高级模型的可预测性。然而，对于没有填料网络的样品，报告了不希望的结果。此外，α 和 n 都直接操纵纳米复合材料在渗透开始以上的模量，因为它们对聚合物-CNT 界面面积和网络尺寸产生积极影响。α、n 和渗透开始对纳米复合材料的预测模量的合理影响验证了开发的 Paul 模型。