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.

中文翻译：

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三维螺状石墨烯的导热率异常低且对密度不敏感

石墨烯具有出色的机械，热和电性能。然而，由于石墨烯的原子厚度和缺乏弯曲刚度，在机械工程应用中利用石墨烯单层存在局限性。合成石墨烯气凝胶或泡沫是利用三维本体形式的石墨烯的一种方法。最近，已经提出了具有回旋几何形状的石墨烯。陀螺仪是允许石墨烯片形成三维结构的三次周期性最小表面。它的轻量级和高机械强度表明，构成这种几何形状的石墨烯可协同作用于块状材料的力学。然而，尚不清楚陀螺石墨烯是否可以保持原始石墨烯片的高导热率。这里，我们通过使用全原子分子动力学模拟研究了不同孔隙度的回旋石墨烯的热导率。与优异的机械性能相比，我们发现，螺旋状石墨烯的导热系数比原始石墨烯的导热系数低300倍以上，堆积密度仅为石墨烯的三分之一。我们得出了一个定律，表明热导率在不同的堆积密度下变化不大，这与常规多孔材料的行为形成了对比。我们的分析表明，回旋石墨烯的导热系数差可归因于石墨烯的缺陷和曲率，这些缺陷和曲率随密度增加而增加，导致声子平均自由程因声子散射而减小。