  Understanding the relationship between the microstructures and overall
properties is one of the basic concerns for the material design and
applications. As a ubiquitous structural configuration in nature, the folded
morphology is also widely observed in graphene-based nanomaterials, namely
grafold. Recently, a self-folded graphene film (SF-GF) material has been
successfully fabricated by the assembly of grafolds and exhibits promising
applications in thermal management. However, the dependence of thermal
properties of SF-GF on the structural features of grafold has still remained
unclear. We here develop an analytical model to describe the thermal transport
behavior in SF-GF. Our model demonstrates the relationship between the geometry
of grafolds and thermal properties of SF-GF. The predictions of temperature
profile and thermal conductivity are well validated by molecular dynamics
simulations. Using this model, we further study the evolution of thermal
conductivity of SF-GF with the unfolding deformation during stretch. Moreover,
the effect of geometrical irregularity of grafolds is uncovered. Interestingly,
the predicted transport behaviors of SF-GF under stretch fit some analogous
experimental observations reported in graphene-based strain sensor. Our results
not only reveal the mechanisms behind some physical phenomenon in the
applications of graphene-based devices, but also provide practical guidelines
for the property design of SF-GF and other graphene assemblies with folded
microstructure.
