Modeling the heat transfer by conduction of nanocellular polymers with bimodal cellular structures

Nanocellular polymers are a new generation of materials with the potential of being used as very efficient thermal insulators. It has been proved experimentally that these materials present the Knudsen effect, which strongly reduces the conductivity of the gas phase. There are theoretical equations to predict the thermal conductivity due to this Knudsen effect, but all the models consider an average cell size. In this work, we propose a model to predict the thermal conductivity due to the conduction mechanisms of nanocellular materials with bimodal cellular structures, that is, with two populations of cells, micro and nanocellular. The novelty of our work is to consider not only the average cell size, but the cell size distribution. The predictions of the model are compared with the experimental conductivity of two real bimodal systems based on poly(methyl methacrylate) (PMMA), and it is proved that this new model provides more accurate estimations of the conductivity than the models that do not consider the bimodality. Furthermore, this model could be applied to monomodal nanocellular polymers. In particular, for monomodal materials presenting a wide cell size distribution and at low densities, the model predicts important variations in comparison with the current models in the literature. This result indicates that the cell size distribution must be included in the estimations of the thermal conductivity of nanocellular polymer