Thermal-fluctuation gradient induced tangential entropic forces in layered two-dimensional materials

Recent studies on nanomechanical devices based on low-dimensional nanomaterials have revealed several different types of thermal fluctuation gradient induced tangential entropic forces (TEFs), including expulsion force, edge force, thermophoretic force, nanodurotaxis force, etc. While all these forces originate from thermal fluctuation gradients, they can take different forms for different problems and have been treated case-by-case in the literature. Here, we develop a unified theoretical framework for TEFs in layered low-dimensional materials. In particular, we derive explicit analytical solutions for TEFs in layered two-dimensional materials and validate them with molecular dynamics simulations for various bilayers composed of graphene, graphyne, hexagonal-boron nitride (h-BN), boron-carbon-nitride (BCN), and double walled nanotubes. We present also approximate solutions to TEFs in hetero- or substrate-supported-bilayers based on a solution-guided machine learning (SGML) technique. The developed concept for TEFs is unique to nanomechanical systems and may serve as one of the founding pillars of nanomechanics.