Several recent experiments have shown that the glass-transition temperature and temperature-dependent storage modulus of graphene-polymer nanocomposites are dependent on the graphene loading, but at present no theory exists to explain these observations. In this paper, we take the view that both issues are closely tied to the principle of irreversible thermodynamics, and that, by considering the phase transition from the glassy to the rubbery state in the polymer, and the temperature-affected degradation of the interphase, two independent state variables can be chosen and implemented into a two-scale homogenization scheme. In this approach, we also adopt the temperature-dependent complex modulus in the reduced frequency scale as the homogenization parameter. The developed theory is highlighted with a direct comparison with experiments. It is demonstrated that, with the addition of graphene fillers, both theory and experiments show an increase of glass-transition temperature and effective storage and loss moduli, but that, within the glass-transition range, the storage and loss moduli decrease drastically. The present research could provide the directions to tune the glass-transition temperature and storage modulus of graphene-polymer nanocomposite through graphene loading and temperature.

最近的一些实验表明，石墨烯-聚合物纳米复合材料的玻璃化转变温度和与温度相关的储能模量取决于石墨烯的负载量，但目前尚无理论来解释这些观察结果。在本文中，我们认为这两个问题都与不可逆热力学原理密切相关，并且考虑到聚合物中从玻璃态到橡胶态的相变以及受温度影响的中间相降解，可以选择两个独立的状态变量，并将其实现为两尺度均化方案。在这种方法中，我们还采用降频范围内温度相关的复数模量作为均化参数。通过与实验直接比较突出了已发展的理论。结果表明，通过添加石墨烯填料，理论和实验均显示出玻璃化转变温度的升高和有效的储能模量和损耗模量，但是在玻璃化转变范围内，储能模量和损耗模量急剧下降。本研究可为通过石墨烯负载和温度调节石墨烯-聚合物纳米复合材料的玻璃化转变温度和储能模量提供指导。