Statistical patterns of geometric features of mechanically exfoliated two-dimensional (2D) materials : mechanics-based interpretation and application

Abstract

Two-dimensional (2D) materials refer to layered crystalline materials with one or a few atoms along the thickness direction. Recent years have witnessed surging research interest and major breakthroughs in the fabrication, characterization and application of 2D materials. Owing to their phenomenal physical properties (electrical and thermal conductivity, optical transmittance, photoresponsivity, mechanical properties, impermeability, etc.), 2D materials exhibit enormous application potential in various fields, including new generation electronics, novel nanocomposites, photodetectors, energy storage devices, etc. In these applications, the mechanical properties and behaviors of 2D materials largely dominate the shape, size, edge chirality and surface topography of the 2D material samples, thus influencing the structural integrity and reliability of the fabricated products. These mechanical properties and behaviors can also couple with other physical mechanisms, which can be easily exploited to tune and tailor the performance of 2D materials-based devices. Comparing to the intensively investigated electrical properties of 2D materials, their mechanical behaviors and properties have yet to be fully understood. This calls for investigation and exploration of 2D materials from a mechanical perspective, which should be beneficial to both scientific research and industrial application. In this dissertation, attention is primarily focused on the mechanics of 2D materials, specifically, the fracture behaviors of 2D materials and their coupling and interaction with other mechanical behaviors. Geometric features and the corresponding statistical patterns of the resulting fragments are also analyzed. Typical 2D materials, like graphene, TMDs (dichalcogenides of transition metal) and phosphorene (black phosphorus (BP)) are specifically investigated. Results and techniques to be developed could also be broadly applicable to other 2D materials. Chapter 1 briefly introduces the basic knowledge about 2D materials, including typical members of the 2D material family, common fabrication methods, crystal structures, physical properties and application potential of 2D materials. Subsequently, literature regarding the mechanics of 2D materials in recent years is reviewed in Chapter 2, especially on the mechanical property characterization and fracture behaviors of 2D materials. Statistical patterns of the geometric features of the fractured fragments of 2D materials are also discussed. In Chapter 3, main research methods for theoretical analysis are presented, followed by a brief introduction of the experimental techniques for sample preparation and characterization. In Chapter 4, crystal orientations of edges of mechanically exfoliated 2D materials are systematically studied. A theoretical tearing model is developed to investigate the mechanics during the exfoliation process. The theoretical investigation reveals that the cracking direction of 2D materials during mechanical exfoliation is synergistically determined by the specific tearing angle and the anisotropy of the fracture energy of the material. For a given 2D material, the theory facilitates us to predict the possible crystal orientations of the as exfoliated flakes' edges, together with their occurring probabilities. Combining the symmetry and periodicity of the crystal structure of the specific 2D material, we can further predict the distribution patterns of the inter-edge angles (IEAs) of the exfoliated flakes, which are defined as acute angles formed by any two edges. Experimental results of the IEAs of the exfoliated flakes for 4 representative 2D materials (black phosphorus (BP), graphene, PtS2, and MoS2) show good agreement with the theoretical ones. The finding casts light on the understanding of the mechanics of 2D materials under out-of-plane tearing. It also implies potential on the controlling of edge chirality during the fabrication of highly anisotropic 2D materials. Subsequently, the size of mechanically exfoliated 2D material fragments is studied in Chapter 5. Mechanics accounting for the delamination and in-plane fracture of 2D material is analyzed using a peeling model. Using this model, the stress distribution in the 2D material layer is obtained. According to the statistical strength theory of brittle materials, the sequential probabilistic fracture of 2D material is analyzed. The correlation between the size of the exfoliated 2D material fragments and their mechanical properties is revealed. This enables us to deduce the mechanical property of 2D materials using their statistical size distributions. The subsequent experimental tests on graphene and MoS2 both yield results that agree well with those reported by the literature. These findings indicate a facile approach to estimating the mechanical properties of 2D materials. Moreover, they also suggest methods to obtain 2D material flakes with controllable lateral size using mechanical exfoliation. In Chapter 6, a facile method for rapid identification of 2D material flakes and simultaneous characterization of their thickness and size using optical microscope images is developed. This is achieved by a supervised machine learning-based image processing model, which is trained to identify and classify 2D materials with different thickness from the substrate using the color information of the image. The size of 2D material flakes can be then obtained by analyzing the geometric feature of the identified 2D material regions. Tests on graphene manifest that our proposed method, compared with the manual visual inspection, can greatly enhance the processing efficiency without sacrificing the measurement accuracy. Combined with the theoretical model described in Chapter 5, the mechanical property of graphene is further characterized using the size statistics obtained by the proposed method. The corresponding results are consistent with those recorded in the relevant literature, which affirms the validity of the proposed approach. Our approach also offers valuable references for the high-throughput characterization of 2D materials. Through comprehensive and systematic investigation, the underlying mechanisms of the distinctive novel mechanical behaviors and properties of 2D materials are enlightened. Findings in this thesis could provide useful guidance towards shape/size-controllable fabrication and strain engineering of 2D materials. The investigations here shed light on the understanding of novel mechanics of 2D materials. They also imply facile methods towards the mechanical property characterization of 2D materials, which can be easily automated by artificial intelligence-based processing.