A differential model for coupled heat conduction in highly porous polymer networks

Abstract Highly porous polymer networks combine a continuous solid skeleton with a gas-filled pore space and may exhibit effective thermal conductivities close to, or below, that of the unconfined gas. Predicting this conductivity from independently measurable material properties remains difficult because heat is transported through the polymer skeleton, the confined gas, and thermal radiation, while each contribution depends differently on density and microstructure. A differential framework is developed in which the nonporous polymer or multicomponent solid is taken as the initial material and gas-filled pores are introduced incrementally. This construction preserves the connected character of the solid skeleton and couples solid and gas conduction within a single effective-medium equation. Unlike conventional decompositions that add separately estimated solid and gas contributions, the confined gas is homogenized directly into the evolving connected skeleton. In addition, the commonly fitted density exponent is predicted from the pore depolarization factors and can be evaluated from a measured pore-shape distribution. The conductivity of the pore gas is allowed to depend on temperature, pressure, and pore size through Knudsen suppression, while pore shape is represented by the depolarization factors of randomly oriented spheroids. Thermal radiation is added through an independently measurable infrared extinction coefficient. For spherical nonconducting pores, the model recovers the density scaling with exponent 3/2 associated with the classical differential effective-medium result; for nonspherical pores, the corresponding exponent follows directly from pore geometry. Multicomponent polymer, cross-linker, and particulate skeletons are incorporated through a fixed-composition differential homogenization at the solid-skeleton scale. The resulting model requires bulk constituent conductivities, skeletal and apparent densities, gas properties, an effective pore size or pore-size distribution, and at most a small number of microstructural parameters. It therefore provides a practical basis for comparing different polymer aerogels and for predicting the effects of composition, porosity, pore geometry, gas pressure, and temperature.