Thermal Conductivity of Nanopaper Films: A Continuum Micromechanics Approach
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Nanopaper films made of cellulose nanofibrils are suitable candidates for heat management in several flexible electronics applications [1]. However, natural, as well as technical and technological variability, frequently results in cellulose nanofibrils and nanopaper films made thereof, exhibiting a wide range of thermal properties. Hence, it is important, from an application viewpoint, to develop theoretical models that can guide empirical activities related to such materials (such as their production, research and development, or use), and assist in reducing present uncertainties. With this purpose in mind, the mathematical analogy, in the context of continuum micromechanics and mean-field homogenization, between the conductivity and the elasticity problems [2], serves as the starting point for a straightforward adaptation of a continuum-micromechanics-based theoretical model for the elasticity of paper sheets, to the case of thermal conductivity of nanopaper films [1]. Thereby, large collections of experimental determinations enable estimation of volume fractions of crystalline cellulose Iα, crystalline cellulose Iβ, crystalline cellulose II, amorphous cellulose, and water in “mean” cellulose nanofibrils of various origins [3]; while a selection of thermal conductivity properties of the abovementioned constituents of cellulose nanofibrils, make estimate respective thermal conductivity tensors [1]. Moreover, recent findings on the elasticity of hydrated amorphous cellulose [3], strongly suggest that self-consistent, mean-field homogenization of amorphous cellulose and water thermal conductivities yields reliable results for the thermal conductivity of the corresponding mixture, as a function of water content. Theoretically predicted relationships between porosity and in- as well as out-of-plane thermal conductivity of corresponding nanopaper films, agree well with respective, experimentally determined relationships [1]. Similar agreement is found for cellulose fibrils [1]. The proposed theoretical model makes similar models (for instance, for water diffusivity or permeability) more accessible, and paves the way to a higher level of control in empirical activities related to such materials.