Thermal Resistance Network Model for Heat Conduction of Amorphous Polymers

Polymers are ubiquitous in a wide range of applications from structure materials to electronics due to their diverse functionality, lightweight, low cost, and chemical stability. The thermal conductivities of the vast majority of amorphous polymers are in a very narrow range, even though single polymer chains possess thermal conductivities of orders of magnitude higher. The low thermal conductivity of polymers is a major technological barrier for the reliability and performance of polymer-based electronics due to a limited heating spreading capability. The thermal conductivity of amorphous polymers is universally confined in a very narrow range of 0.1-0.5 W/(m*K). This feature indicates the possible existence of a universal thermal transport mechanism in amorphous polymers regardless of their distinct chemical structures. Researchers have developed and tested several minimum thermal conductivity models for amorphous polymers. All those models use bulk properties as inputs, which lack molecular chain details and thus are not able to describe the dependence of thermal conductivity on temperature, pressure, and orientation, simultaneously. An amorphous polymer is a three-dimensional van der Waals solid formed by entangled, long, one-dimensional molecular chains. Molecular dynamics simulations suggested that a single molecular chain may have a very high thermal conductivity of orders of magnitude higher than its amorphous counterpart. This difference is attributed to the fundamental distinction between the one-dimensional chain and three-dimensional network. A theoretical model for the thermal conductivity of an amorphous polymer considering the microscopic structure of a three-dimensional network is highly desirable. Both intrachain and interchain thermal transport should be incorporated, where the intrachain thermal transport through a covalent bond is more efficient than the interchain thermal transport via van der Waals interactions. We proposed a thermal resistance network model to describe the thermal conductivity in amorphous polymers. The chemical structure (entangled network) of molecular chains and the interplay of interchain and intrachain thermal transport are considered. Our model elucidates the physical origin of the low thermal conductivity universally observed in amorphous polymers with various chemical structures. The fundamental mechanism of a universally low thermal conductivity of polymers is attributed to the similar mean distance due to the van der Waals interaction. The empirical formulas of the pressure and temperature dependence of thermal conductivity can be successfully reproduced from our model not only in solid polymers but also in polymer melts in addition to the experimentally observed anisotropic thermal conductivity. We further quantitatively explain the anisotropic thermal conductivity in oriented polymers.