A thermal boundary resistance model via mean free path suppression functions and a Gibbs excess approach

The impact of interfaces and grain boundaries on heat transport is often quantified in terms of thermal boundary resistance. Numerous models have been proposed over the years to describe this resistance. Recent experimental results in thermal conductivity imaging have highlighted the possibility of a local suppression in conductivity around material grain boundaries. In this work, we propose a semi-empirical model to predict the thermal conductivity profile as a function of distance to a boundary, to help explain experimental observations. The model is based on a geometrical suppression in the phonon mean free path and accounts for phonon transmission at the boundary. Calculated excess thermal boundary resistances, extracted from spatially dependent thermal conductivities with a Gibbs excess approach, are well-matched with predictions from the Landauer formalism when considering heat flow normal to the boundary. This agreement holds for different material systems and over temperature. The excess thermal resistance is thus expected to represent well the theoretical boundary resistance. The model in this work provides novel insights on the expected spatial extension of interface thermal effects, aiding the interpretation of thermal conductivity images. Rationalizing the impact of specific defects on heat transport can significantly advance the design of materials and devices for applications in energy, heat management and electronics.