Numerous studies have been reported on thermal interface materials based on synergistic hybrid effects, however, most of them contain only fragmentary experimental results and the related model has been rarely proposed to explain the effects exactly. Herein, the thermal conductivities of the composites were systematically evaluated according to various filler contents and ratios. It was found that the fraction of the secondary filler inducing the maximum synergistic effect decreased as the total filler content increased. In addition, when the fraction was higher than the optimum fraction, the anti-synergistic effect occurred. At the optimum fraction, effective phonon transfer was induced due to the improved filler network formation of graphene nanoplatelet (GNP)-carbon nanotube (CNT), thereby achieving high thermal conductivity of 7.69 W/m·K at f_GNP = 27.69 vol% and f_CNT = 0.57 vol%. Moreover, the Kim-Jang-Lee (KJL) model for the synergistic effect was proposed by introducing filler-ratio variables into the critical percolation equation reported previously, and the KJL model for the anti-synergistic effect was proposed based on the rule of mixture of composites filled with the optimal connected filler network and filled with the excessive secondary filler.

基于协同混合效应的热界面材料已有大量研究报道，但其中大部分仅包含零碎的实验结果，并且很少提出相关模型来准确解释这些效应。在此，根据不同的填料含量和比例系统地评估了复合材料的导热性。发现当总填料含量增加时，引起最大协同效应的辅助填料的分数降低。此外，当分数高于最佳分数时，会出现抗协同作用。在最佳分数下，由于石墨烯纳米片 (GNP)-碳纳米管 (CNT) 的填料网络形成的改善，诱导了有效的声子转移，从而在 f 下实现了 7.69 W/m·K 的高热导率_GNP  = 27.69 vol% 和 f _CNT  = 0.57 vol%。此外，通过在先前报道的临界渗流方程中引入填料比变量，提出了协同效应的 Kim-Jang-Lee (KJL) 模型，并根据混合规则提出了反协同效应的 KJL 模型。填充了最佳连接填料网络并填充了过量二次填料的复合材料。