Theoretical study on the wrinkle formation in two-dimensional materials

Abstract

Two-dimensional (2D) materials have remarkable properties such as higher strength and stiffness, electrical and thermal conductivity, allowing for a wide range of applications in electronic, mechanical and photonic devices. Nowadays, chemical vapor deposition (CVD) methods are commonly used to produce 2D materials such as graphene and hexagonal boron nitride (hBN) in large areas with high quality, and at a low cost. However, when the CVD growth system is cooled from high (~ 1000℃) to room temperature, wrinkles in 2D materials appear because of the compressive strain induced by the thermal expansion coefficient (TEC). The mechanical strength, carrier mobility and thermal conductivity of 2D materials in applications are degraded by the wrinkles. As a result, a systematic theoretical study of wrinkle formation mechanisms in 2D materials is highly important for their controllable synthesis. To date, many researchers have studied wrinkling behavior in 2D materials, including the experimental studies on the release mechanism of compressive strain, the effect of cooling rate, adhesion and friction on the graphene wrinkles and wrinkles elimination. Theoretical studies on the wrinkle conformation and fold collapse have also been done. However, atomic level exploration of the wrinkle formation mechanism remains poorly understood. (ⅰ) Friction is one of the most important factors in the formation of graphene wrinkles, for which an accurate method is essential. (ⅱ) The nucleation barrier of graphene wrinkles under compressive strain is crucial, but has never been investigated; (ⅲ) The formation of wrinkles in graphene depends on many factors, such as adhesion, friction, defects in both graphene and substrate, loading conditions. However, there is no systematic theoretical model that takes all these factors into account; (ⅳ) The distance between two adjacent graphene folds at different growth temperatures has been reported experimentally, but a theoretical model is still lacking. (ⅴ) The effect of temperature on graphene wrinkle formation is theoretically poorly understood; (ⅵ) Wrinkle formation in other 2D materials remains unknown. Therefore, we developed METCAR, an in-house molecular dynamics (MD) simulation package that allows us to explore these questions and to handle systems containing millions of atoms. First, dynamics frictional forces (DFFs) of graphene sliding on transition metal substrates (Cu(111), Ni(111) and Ru(0001)) were obtained by Ab initio molecular dynamics (AIMD) simulations. Supplying an initial velocity to the graphene layer, the DFFs can be estimated by simply using the energy and/or momentum conversions and Newton’s laws. We first revealed that the DFF of graphene sliding on Ni(111) surface is an order of magnitude greater than that on Cu(111) surface due to its high adhesion. Then, we demonstrated two types of energy dissipation channels, namely angle-dependent and angle-insensitive ones, based on the rotated graphene on Cu(111) and Ni(111) surfaces, respectively. Furthermore, we discovered two types of friction modes of graphene on the Ru(0001) surface: (ⅰ) the ultra-high frictional force of graphene sliding on the Ru(0001) surface (~1.3 nN/nm2) with the rotation angles (RAs) less than 20º, and (ⅱ) the superlubricity or ultra-low frictional force (~0.0063 nN/nm2) between the graphene and Ru(0001) surface with RAs greater than 20º. These sections are covered in Chapters 4 & 5. Second, we investigated the wrinkle nucleation barrier of single-layer graphene on a Cu substrate. We found that the wrinkle nucleation barrier decreases with increasing the applied compressive strain and can even be lowered under biaxial compressive loading. We further discovered that as the adhesion decreased, the wrinkle nucleation barrier dropped. We found that the energy nucleation barrier of wrinkle formation can be greatly degraded in the presence of imperfections in graphene or the substrate. Besides that, we studied the detailed kinetics of wrinkle formation on a Cu surface under compressive strain, from wrinkle nucleation to one-dimensional wrinkle propagation as well as the splitting of a large wrinkle into several smaller ones. This phenomenon has also been obtained experimentally. Moreover, we found that wrinkles can be easily formed under a smaller adhesion and/or a lower frictional force. We also found that the impurities in graphene or substrates and biaxial compressive loading can significantly decrease the nucleation of wrinkles. We finally proposed a theoretical model that considers the force equilibrium of friction and external compressive loading to construct the relationship between friction and temperature. These three sections are presented in Chapters 6-8. The temperature in our MD simulation package was implemented to mimic the cooling process of CVD growth. The wrinkle in the graphene layer atop a monolayer Cu substrate was first discovered when the system was cooled down from 1300 K to 630 K. However, a higher initiation temperature of 1080 K was achieved when graphene wrinkles were formed on multi-layers Cu substrate. That happens because a huge number of hill-shaped atomic structures form on the Cu surface at high temperatures, and then the wrinkles rose up at one of the hill-shaped nanoparticles. We further investigated how the interactions between graphene and Cu substrate influence the initiation temperature. The wrinkle formation in other 2D materials (hBN and VO2) on the corresponding substrates (CuNi(111) and mica) was also explored. Due to the higher adhesion and friction between hBN and substrate, the wrinkle-free single-crystal hBN on CuNi(111) thin-film was reported, and an analytical model was proposed to determine the critical thickness of the VO2 thin film for wrinkle formation. All these findings are discussed in detail in Chapters 9-11. Finally, several theoretical works related to solid-state batteries (SSB) are presented in Chapter 12. (ⅰ) FEM analysis was performed to explore the lithium deposition-induced fracture of carbon nanotubes (CNTs); (ⅱ) An analytical model is proposed, combining the FEM and density functional theory (DFT) calculations to study the size-dependent chemomechanical pulverization of sulfide solid electrolyte particles during the lithium deposition; (ⅲ) DFT calculations suggest that the deposition and stripping in Na crystallography is controlled by the Wulff’s law, which requires a higher mass flux to distribute the newly deposited Na.