Tension-compression asymmetry of the stress-strain behavior of the stacked graphene assembly: Experimental measurement and theoretical interpretation

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Abstract

Two-dimensional (2D) materials as exemplified by graphene have received a bunch of attention for their outstanding properties and enormous application potential. Recently, a macroscopic graphene-based material was fabricated simply by stacking the few-layer graphene flakes. The resulting film, called SGA, exhibits unusual mechanical behavior, which implies the existence of tension-compression asymmetry in its mechanical property. However, direct experimental verification of such unique mechanical property of the SGA remains deficient because of the difficulty in fixturing and applying load on the samples. In this work, we tackle these problems by transferring the SGA film onto a polyethylene (PE) substrate which can elongate and contract in response to the variation of the ambient temperature. Tensile and compressive loads thus can be controllably applied to the SGA samples through the SGA/PE interface by tuning the temperature variation. The stress-strain curves of the SGA, including tensile and compressive, are deduced based on the Stoney equation for thin film-substrate systems, showing the tension-compression asymmetry as expected. Theoretical modeling is carried out and reveals the structural basis of such unique mechanical behavior. This work not only provides a facile yet effective approach to measuring the stress-strain behavior of less-cohesive materials like SGA but also is of great value to the design and applications of SGA and other stacked assemblies of 2D materials in flexible sensors and actuators.

Introduction

Two-dimensional (2D) materials refer to crystalline materials consisting of one or a few layers of atoms along the thickness direction. Recent years have witnessed the surging research interest in 2D materials and breakthroughs in this field. So far, a large family of 2D materials has been reported, including graphene, h-BN, 2D oxides, transition metal chalcogenides, 2D van der Waals heterostructures, β-Silicene, black phosphorus nanosheets, etc. Due to the ultrathin thickness and ultrahigh specific surface area, 2D materials exhibit a range of fascinating electronic, optical, and mechanical properties that are normally absent in their bulk counterparts (Bhimanapati et al., 2015; Geim, 2009; Nakada et al., 1996; Sorkin et al., 2017), implying great potentials in diverse applications including flexible electronics (Fiori et al., 2014; Kim et al., 2015), nanocomposites (Kim et al., 2010; Potts et al., 2011), photodetectors (Huo and Konstantatos, 2018; Long et al., 2019), energy storage devices (Pomerantseva and Gogotsi, 2017; Zhang et al., 2016), etc. To acquire high-quality 2D materials, a variety of physical and chemical methods have been developed, including mechanical exfoliation (Huang et al., 2015; Novoselov et al., 2004), liquid exfoliation (Coleman et al., 2011; Hanlon et al., 2015), thermal reduction (Chen et al., 2010) and chemical vapor deposition (Gupta et al., 2015; Jeon et al., 2015). However, the fabrication process of large-area high-quality 2D materials is generally complicated and involves costly equipment for achieving the required ultravacuum and high-temperature conditions. In contrast, small-area few-layer 2D materials, such as few-layer graphene flakes, can be produced by liquid exfoliation in large quantities at a low cost. One of the promising applications of such small-area flakes is to assemble them into macroscopic thin films via techniques such as vacuum filtration method (Hernandez et al., 2008) and Langmuir-Blodgett (L-B) method (He et al., 2019). Although the assembled graphene flakes cohere with each other through the weak van der Waals forces, excellent electrical conductivity was observed in the SGA film, making it an excellent candidate for soft conductive materials in sensors (He et al., 2019; Li and Yang, 2020). In addition, the mechanical behavior of the SGA film was also found unique. In our earlier study, the SGA was found to exhibit asymmetric elastoplasticity under tension and compression. Specifically, it exhibits apparent plasticity under tension while pure elasticity under compression, which endows the SGA-based soft actuators with great configurational programmability (Wang et al., 2020). However, this property of the SGA was inferred from the thermal-induced curling behavior of the SGA-based bilayer films and was testified merely by molecular dynamics (MD) simulation. The direct measurement of the mechanical behaviors of SGA under tension and compression remains deficient, not to mention the revelation of the underlying structure-property relations. The technical difficulty of experimentation mainly lies in the less-cohesive and fragile nature of the SGA films, which can be hardly clamped using the traditional fixturing method. Another challenge is the possible buckling of the freestanding SGA film under compression, which deters the possibility to measure the property of SGA under compression with the traditional testing method. To tackle these problems, in this paper, we transfer the SGA film on a polyethylene (PE) substrate, a thermal-responsive film, to form a thin film/substrate bilayer system. By increasing or decreasing the ambient temperature, the PE substrate tends to extend or contract while the SGA is relatively inert to the temperature variation, resulting in the tensile or compressive load applied on the SGA film through the interface with the PE substrate. By using the Stoney relation for thin film and substrate system, the stress and strain of the SGA can be deduced from the measured bending curvature of the bilayer structure, giving rise to the stress-strain curves under tensile and compressive loadings. To gain an insightful understanding of the experimental results, theoretical modeling is carried out to explore the structural dependences of the characteristic mechanical properties of the SGA including the elastic moduli under tension and compression as well as the tensile strength. The whole paper is concluded by discussing the potential applications of the results and the limitation of the present work.

Section snippets

Theoretical basis of the testing approach

Due to the weak cohesion between graphene flakes as well as the small thickness of SGA film, preparing a free-standing SGA sample remains challenging, not to mention fixturing and applying loads on it. To tackle these problems, we constructed a bilayer structure by transferring an SGA film on a PE substrate which can expand or contract in response to the variation of temperature (ΔT). As the thermal expansion of graphene is negligibly low, the strain misfit between the SGA film and PE substrate

Theoretical interpretation of the measured results

The experimental measurements above reconfirm the asymmetric elastoplastic behavior of the SGA film, which can be fully depicted by three characteristic parameters: tensile modulus (ESGAt), tensile strength (SSGAt), and compressive modulus (ESGAc). To disclose the dependence of these parameters on the microscopic structure of the SGA and the mechanical properties of the building graphene flakes, theoretical modeling was carried out.

Conclusion and discussion

In this paper, we experimentally investigated the mechanical behaviors of the SGA films under tensile and compressive loadings by taking advantage of the curling behavior of the SGA-based bilayers in response to temperature variation. It was shown that the SGA film exhibits elastic-perfectly plastic behavior under tension while purely elastic behavior under compression. This result verified our previous prediction based on the molecular dynamics simulations (Wang et al., 2020). Theoretical

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgment

Support for this work from the National Natural Science Foundation of China (Grant no. 11772283) is acknowledged.

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    These authors contributed equally to this work.

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