Unusually low and density-insensitive thermal conductivity of three-dimensional gyroid graphene

Graphene has excellent mechanical, thermal and electrical properties. However, there are limitations in utilizing monolayers of graphene for mechanical engineering applications due to its atomic thickness and lack of bending rigidity. Synthesizing graphene aerogels or foams is one approach to utilize graphene in three-dimensional bulk forms. Recently, graphene with a gyroidal geometry has been proposed. A gyroid is a triply periodic minimal surface that allows graphene sheets to form a three-dimensional structure. Its light weight and high mechanical strength suggests that the graphene that constitutes this geometry can synergistically contribute to the mechanics of the bulk material. However, it is not clear whether gyroid graphene can preserve the high thermal conductivity of pristine graphene sheets. Here, we investigate the thermal conductivities of gyroid graphene with different porosities by using full-atom molecular dynamics simulations. In contrast to its excellent mechanical properties, we find that the thermal conductivity of gyroid graphene is more than 300 times lower than that of pristine graphene, with a bulk density of only about one-third of that of graphene. We derive a scaling law showing that the thermal conductivity does not vary much with different bulk densities, which contrasts the behavior of conventional porous materials. Our analysis shows that the poor thermal conductivity of gyroid graphene can be attributed to defects and curvatures of graphene, which increase with the density, resulting in the reduction of a phonon mean free path by phonon scattering. Our study shows that three-dimensional porous graphene has potential that may be utilized in designing new lightweight structural materials with low and density-insensitive thermal properties and superior mechanical strength.