Abstract Functionalized graphene/polymer composites are currently under extensive investigation due to their excellent mechanical and functional properties. Within the framework of electrical properties, many experiments have shown that their electrical conductivity and dielectric permittivity are strongly dependent on the frequency of the applied electric field and the volume concentration of graphene fillers. In this paper we first apply Dyre's hopping function and Debye's relaxation function to build the constitutive equations for the graphene fillers, polymer matrix, and the interface regions. In addition, Cauchy's cumulative probabilistic function is also introduced to account for the drastic increase of electron tunneling and the rapid build-up of Maxwell-Wagner-Sillars polarization at the interface. These functions are then integrated into an effective-medium framework in the complex domain to establish a complete theory for the frequency dependence of these two effective properties as a function of graphene loading. The developed theory is highlighted by a direct comparison with the experimental data of reduced graphene oxide/polypropylene (rGO/PP) nanocomposites. The results show that both the theory and experiment display a general increase of conductivity but a decrease of permittivity as frequency increases, and that, with the graphene loading of 0.2 vol%, there is a sustained, high level of dielectric constant beyond 1,000 covering the frequency range up to 104 Hz. This remarkable feature can be of particular significance to energy storage and conversion.

中文翻译：

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功能化石墨烯-聚合物纳米复合材料中频率依赖性和持续高介电常数的理论

摘要 功能化石墨烯/聚合物复合材料由于其优异的机械和功能特性，目前正受到广泛研究。在电性能的框架内，许多实验表明它们的电导率和介电常数强烈依赖于施加的电场频率和石墨烯填料的体积浓度。在本文中，我们首先应用 Dyre 的跳跃函数和 Debye 的松弛函数来构建石墨烯填料、聚合物基体和界面区域的本构方程。此外，还引入了柯西累积概率函数来解释电子隧穿的急剧增加和界面处 Maxwell-Wagner-Sillars 极化的快速建立。然后将这些函数集成到复杂域中的有效介质框架中，为这两个有效特性的频率依赖性作为石墨烯负载的函数建立完整的理论。通过与还原氧化石墨烯/聚丙烯 (rGO/PP) 纳米复合材料的实验数据的直接比较，突出了所发展的理论。结果表明，理论和实验均显示电导率普遍增加，但介电常数随着频率的增加而降低，并且随着石墨烯负载量为 0.2 vol%，介电常数持续超过 1,000，覆盖了频率范围高达 104 Hz。这一显着特征对能量存储和转换具有特别重要的意义。