Wrong expectation of superinsulation behavior from largely-expanded nanocellular foams

This work aims to predict the thermal conductivity of microcellular and nanocellular thermal insulation foams to explore the correlation between the cellular structure and the thermal insulating properties. Closed-cell foam consisting of cell walls and struts was used as the base geometry for modeling. The mathematical correlations to calculate the thickness of cell walls and the diameter of struts for a given cell size, the void fraction and the volume fraction of polymer located in struts were investigated. Then, a mathematical model for the conductive thermal conductivity including the dependency on the void fraction, the strut fraction and the Knudsen effect for gas was introduced. The radiative thermal conductivity was determined by analyzing the attenuation of radiative energy by absorption and scattering based on Mie's theory together with electromagnetic wave interference, as well as interference of propagating waves and tunneling of the radiative energy by evanescent waves in the cells. The thermal conductivity model was validated by experimental data and used to predict the thermal conductivity of polystyrene (PS) and poly(methyl methacrylate) (PMMA) foams at various cell sizes and volume expansion ratios. It was found that the radiative thermal conductivity plays a crucial role in nanocellular foam. The trade-off between the cell size and cell wall thickness when cell walls become thinner and highly transparent to thermal radiation was demonstrated, leading to the optimal volume expansion ratio at which the thermal conductivities were minimized. Perspectives for the manufacture of high-performance thermal insulation foams are also discussed.