Computational design of isotropic and anisotropic ultralow thermal conductivity polymer foams

Current state-of-the-art commercial polymer thermal insulation foam exhibits a thermal conductivity of 24 mW⸳m⁻¹⸳K⁻¹ (equivalently thermal resistivity of R-6/in.), similar to that of static air. To further optimize building energy efficiency, achieving even lower thermal conductivity is needed, which is, however, highly challenging. This paper presents computational evidence that demonstrates the feasibility of achieving an ultra-low thermal conductivity of less than 14.4 mW⸳m⁻¹⸳K⁻¹ (equivalently R-10/in.) using isotropic and anisotropic foam cell designs. For the isotropic design, we have identified analytical effective medium approximation (EMA) models within the accuracy of ±5% as finite element analysis (FEA) in predicting the effective thermal conductivity of foams with various porosities and filler gases. For the anisotropic design, we have developed and validated new EMA models against FEA in predicting the effective thermal conductivity of general anisotropic cuboids and Voronoi foams. For both isotropic and anisotropic designs, the design spaces for 18, 16, and 14.4 mW⸳m⁻¹⸳K⁻¹ (equivalently R-8, R-9 and R-10/in.) using various filler gases are obtained. It is found that polymer foams can be improved to achieve ultralow thermal conductivity by reducing CO₂ concentration, reducing radiation, increasing porosity, and using anisotropic pore geometry. These findings contribute to the development of highly efficient thermal insulation materials, enhancing building energy efficiency and promoting sustainable construction practices.