We present a theory of anisotropic thermal interface (Kapitza) resistance for rough interfaces in nanocomposite materials. This is based on an extension  of a modified effective medium theory [2,3] that includes anisotropically resistive interface regions in a model of the lattice thermal conductivity of anisotropic nano insertions in anisotropically conductive hosts. The thermal conductivities of the host and nanodot insertions have been evaluated using a semi ab-initio theory  based on the solution of the linearised phonon Boltzmann transport equation within a generalized  Callaway effective relaxation time scheme . Phonon boundary scattering and the Kapitza resistance at the insertion-host interface have been treated by taking into account both specular and diffuse contributions [7,8]. The theory has been applied to a transition metal dichalcogenide (TMD) nanocomposite consisting of 2H WS2 inserts in a 2H MoS2 host. In general, it is found that the effect of specular scattering due to interface roughness is more pronounced for inserts smaller than 100 nm. Analysis of the results allows us to identify key physical parameters that should prove effective in controlling (i.e. obtaining minimum) lattice thermal conductivity of TMD nanocomposites.
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