Theoretical and numerical study on adhesive interactions between graphene and substrate




Wang, Peng, Ph. D.

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This dissertation presents a set of theoretical and numerical studies on adhesive interactions between monolayer graphene membranes and their substrates. Both continuum mechanics models and molecular dynamics simulations are developed to investigate deformation of graphene membranes depending on the adhesive interactions with the substrates. First, a numerical study on snap transitions of gas-filled graphene blisters is presented, based on a continuum model combining a nonlinear plate theory with a nonlinear traction–separation relation. The numerical results may be used in conjunction with experiments for quantitative characterization of the interfacial properties of graphene and other two-dimensional (2D) membrane materials. Next, a statistical mechanics analysis on thermal rippling of monolayer graphene supported on a rigid substrate is presented and compared with molecular dynamics simulations to reveal the entropic effects of thermal rippling on van der Waals interactions between graphene and the substrate. While the amplitude of thermal rippling is reduced by the adhesive interactions, the entropic contribution of thermal rippling leads to an effective repulsion, thus reducing the effective adhesion. Moreover, the effect of a biaxial pre-strain in graphene is considered, and a buckling instability is predicted at a critical compressive strain that depends on both the temperature and the adhesive interactions. This motivates a systematic study on morphological transitions of monolayer graphene on a substrate under uniaxial compressive strain, from rippling to wrinkling/buckling and to folding. The presence of water at the interface has significant influence on the adhesive interactions between graphene and its substrate. Molecular dynamics simulations are performed to study the interactions between graphene and a wet substrate that is covered by a thin layer of water. Four stages of the traction-separation relations are identified and they are analyzed approximately by simple continuum models. When the thickness of water layer is below 1 nm, the water molecules form discrete monolayer or bilayer structures, leading to different traction-separation behaviors. Finally, with a finite number of water molecules trapped between a monolayer graphene and its substrate, water-filled graphene blisters form spontaneously. Based on molecular dynamics simulations and a simple theoretical model, the work of adhesion for the graphene/substrate interface may be estimated by measuring the aspect ratios of the graphene blisters. Unlike gas-filled graphene blisters in previous studies, the shape and size of the water-filled graphene blister depend on the wetting properties of graphene and the substrate. The results on wet adhesion and water-filled blisters can be readily extended to other 2D materials.


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