Graphene Origami Research Articles

Atomistic simulations of graphene origami: Dynamics and kinetics

Origami offers two-dimensional (2D) materials with great potential for applications in flexible electronics, sensors, and smart devices. However, the dynamic process, which is crucial to construct origami, is too fast to be characterized by using state-of-the-art experimental techniques. Here, to understand the dynamics and kinetics at the atomic level, we explore the edge effects, structural and energy evolution during the origami process of an elliptical graphene nano-island (GNI) on a highly ordered pyrolytic graphite (HOPG) substrate by employing steered molecular dynamics simulations. The results reveal that a sharper armchair edge is much easier to be lifted up and realize origami than a blunt zigzag edge. The potential energy of the GNI increases at the lifting-up stage, reaches the maximum at the beginning of the bending stage, decreases with the formation of van der Waals overlap, and finally reaches an energy minimum at a half-folded configuration. The unfolding barriers of elliptical GNIs with different lengths of major axis show that the major axis should be larger than 242 Å to achieve a stable single-folded structure at room temperature. These findings pave the way for pursuing other 2D material origami and preparing origami-based nanodevices.

Fracture resistance of graphene origami under nanoindentation

Graphene has received extensive research interest from both scientific and technological communities due to its excellent physical properties. However, owing to its two-dimensional structure, graphene experiences brittle fracture under external loading, which limits its application as reinforcing fillers in composites. In this study, we apply an origami technique to improve the flexibility of graphene under nanoindentation. Based on intensive molecular dynamics simulation, we found that graphene origami (GOri) can withstand loads and indentation depths up to 37% and 138% greater, respectively, than pristine graphene. The flexibility and strength of GOri can be further enhanced in the bilayer format by adding one pristine graphene or one identical GOri. The maximum indentation loads of the bilayer model are at least 60% higher than that of its single-layer counterpart. Though Young's modulus remains unchanged, the bending stiffness is improved remarkably due to the auxeticity of GOri. The study provides significant insights into the failure mechanisms and mechanical properties of GOri and offers practical design guidelines for graphene-based impact protection applications.

Vibrational characteristics of functionally graded graphene origami- enabled auxetic metamaterial beams with variable thickness in fluid

Within the framework of Timoshenko beam theory, this paper examines the effect of negative Poisson’s ratio (NPR) on the free vibration characteristics of functionally graded (FG) graphene origami (GOri)-enabled auxetic metamaterial (GOEAM) beams with variable thickness submerged in fluid. Poisson’s ratio and other elastic properties of the beam are graded in a layer-wise manner along the thickness direction and are predicted by genetic programming (GP)-assisted micromechanics models. With the hydrodynamic pressure effect on the beam being modelled as added mass, the equations of motion are derived from Hamilton’s principle then discretised and solved using the differential quadrature (DQ) method in conjunction with an iterative process to determine its natural frequencies and mode shapes. The effects of GOri folding degree, metamaterial distribution, graphene distribution pattern and content, fluid temperature and density on the free vibration behaviour of FG-GOEAM beams are discussed in detail. It is found that the FG-GOEAM beam outperforms its pristine metallic counterpart in terms of vibration performance.

Bandgaps in functionally graded phononic crystals containing graphene origami-enabled metamaterials

This paper investigates the dispersion characteristics of elastic waves propagating along the thickness direction in functionally graded laminated phononic crystals (FGLPCs) containing novel auxetic metamaterials enabled by graphene origami that is created with the aid of hydrogenation. Both graphene weight fraction and hydrogen coverage which are the key parameters governing the auxetic property are nonuniformly distributed in unit cells of FGLPCs whose material properties are determined by genetic programming-assisted micromechanical models. The dispersion relations of elastic waves in the structure are obtained based on the state space approach and the method of reverberation-ray matrix. A comprehensive parametric study is conducted to discuss the effects of graphene origami weight fraction and hydrogen coverage on bulk waves in elastic solids made of the metamaterial and elastic waves in FGLPCs. It is found that introducing auxetic metamaterials into FGLPCs can effectively manipulate elastic waves. The graded distribution of weight fraction in FGLPCs can lead to bandgaps for both transverse and longitudinal waves, while a through-thickness graded pattern in hydrogen coverage can trigger broad bandgaps for longitudinal waves only with transverse waves nearly unchanged.

Vibrational characteristics of functionally graded graphene origami-enabled auxetic metamaterial beams based on machine learning assisted models

This paper studies the free vibration behavior and dynamic responses of functionally graded (FG) beams made of novel graphene origami (GOri)-enabled auxetic metal metamaterials (GOEAMs) under an impulsive load within the framework of the first-order shear deformation beam theory. The auxetic property of the beam is effectively controlled by graphene content and GOri folding degree that are graded across the thickness direction of the beams in a layer-wise manner such that Poisson's ratio and other material properties are position-dependent and are estimated by the genetic programming (GP)-assisted micromechanical models. The governing equations are derived by using Lagrange equation approach together with Ritz method. Newmark-β method is employed to solve the governing equations for obtaining dynamic responses of the beams subjected to three different impulsive loads. A comprehensive parametric study is performed to examine the effects of graphene content, GOri folding degree and distribution patterns as well as temperature on the natural frequencies and dynamic responses of the beams. Numerical results show that high tunability in structural vibration characteristics can be achieved via GOri, which offers important insight into the application of FG-GOEAM beams in aerospace engineering structure for significantly improved dynamic structural performance.

Tunable nonlinear bending behaviors of functionally graded graphene origami enabled auxetic metamaterial beams

This paper investigates tunable nonlinear bending behaviors of functionally graded composite beams made of graphene origami (GOri)-enabled auxetic metal metamaterials (GOEAMs) within the theoretical framework of the first-order shear deformation theory and von Kármán type nonlinearity. The beam is comprised of multiple GOEAM layers with GOri content and folding degree being variables to effectively control its auxetic property that is graded from layer to layer across its thickness direction. Our developed genetic programming (GP)-assisted micromechanical models are used to estimate the position- and temperature-dependent Poisson’s ratio and other material properties of each GOEAM layer in the beam. The nonlinear governing equations of the FG-GOEAM beam are derived by the principle of virtual work and numerically solved by the differential quadrature (DQ) method. A detailed parametric investigation is conducted to examine the effects of GOri content, folding degree, and temperature on the tunability of the nonlinear bending deflection and normal stress of the FG metamaterial beam. Numerical results offer significant insights into the design of FG-GOEAM beam structures with enhanced bending performances.

A functionally graded auxetic metamaterial beam with tunable nonlinear free vibration characteristics via graphene origami

Auxetic metamaterials with negative Poisson’s ratio (NPR) are attracting tremendous attention due to their unusual and intriguing mechanical properties. This paper proposes a novel functionally graded (FG) beam made of graphene origami (GOri)-enabled auxetic metamaterials (GOEAMs) and investigates its nonlinear free vibration characteristics tuned by GOri. The beam consists of multilayer GOEAMs with GOri content changed across the beam thickness in a layer-wise mode such that the auxetic property and other material properties are varied in a graded form and can be effectively estimated by genetic programming (GP)-assisted micromechanical models. The Timoshenko beam theory and von Kármán type nonlinearity are adopted herein to derive the nonlinear kinematic equations that are numerically solved by the differential quadrature (DQ) approach. Detailed parametric studies are performed to discuss the influences of GOri content, distribution pattern, GOri folding degree, and temperature on the nonlinear frequencies of FG-GOEAM beams. Numerical results indicate that the nonlinear free vibration behaviors of the beam can be effectively tuned via GOri parameter and distribution.

Functionally graded graphene origami-enabled auxetic metamaterial beams with tunable buckling and postbuckling resistance

Auxetic metamaterials have emerged as novel advanced materials with unique physical and mechanical properties that conventional materials do not possess. This paper examines the buckling and postbuckling properties of functionally graded (FG) graphene origami (GOri)-enabled auxetic metallic metamaterial (GOEAM) beams. The beam is comprised of multiple GOEAM layers with GOri content varying in layer-wise patterns to realize gradient-changing Poisson’s ratio and stiffness coefficient through the beam thickness. The material properties of each GOEAM layer are estimated by the genetic programming (GP)-assisted micromechanical models. The first-order shear deformation theory and von Kármán type nonlinearity are employed to derive the nonlinear governing equations that are numerically solved by the differential quadrature method (DQM). Numerical investigations are carried out with the main focus on the impacts of GOri content, distribution pattern, folding degree, and temperature on the buckling and postbuckling behaviors of FG metamaterial beams. The theoretical results show that GOri is capable of contributing to the formation of auxetic metal metamaterial, leading to the tunable bucking and postbuckling properties of FG beams, which sheds significant insights into the design of high-performance structures.

Genetic programming-assisted micromechanical models of graphene origami-enabled metal metamaterials

Graphene origami (GOri) enabled metallic metamaterials are novel nanomaterials simultaneously possessing negative Poisson's ratio (NPR) and enhanced mechanical properties that are independent of the topology/architecture of the structure. Predicting their material properties via existing micromechanical models, however, is a great challenge. In this paper, a highly efficient micromechanical modeling approach based on molecular dynamics (MD) simulation and genetic programming (GP) algorithm is developed to address this key issue. The GP-based Halpin-Tsai model is extensively trained from MD simulation data to accurately predict the Young's modulus of GOri/Cu metamaterials with various GOri folding degrees, graphene contents and temperatures with a high coefficient of determination (R2) of ∼0.95. Meanwhile, the well-trained GP-based rule of mixture can accurately predict the coefficient of thermal expansion (CTE), Poisson's ratio and density of metamaterials with R2 of ∼0.95, ∼0.93 and ∼0.99, respectively. The excellent agreement between our estimated results and experimental data shows that the models developed herein are highly efficient and accurate in predicting mechanical properties that are essential for the analysis and design of functionally graded metal metamaterial composite structures. The theoretical results demonstrate that the proposed functionally graded metamaterial beam achieves significantly improved bending performance.

Functionalized graphene origami metamaterials with tunable thermal conductivity

Graphene with tunable thermo-mechanical property is of great importance for next-generation thermal management devices. Distinct from previously reported porous graphene materials that tune the thermal conductivity at the cost of degrading their mechanical properties, non-porous hydrogenated graphene origami metamaterial exhibits a unique combination of tunable thermal conductivity, high strength, and enhanced stretchability. Through molecular dynamics simulation, a vast range of thermal conductivity can be found by tuning the geometrical parameters of the Miura-ori graphene origami, altering the adatom types and density, designing new origami patterns, and applying mechanical strains. By analyzing and comparing the numerical results from atomistic and continuum-based simulations, the effect of length scale on the thermal property of graphene origami metamaterials is explored. The temperature distribution, phonon density of states, phonon group velocity, and the atomic heat flux of the graphene origami are examined to illustrate the heat conduction mechanism. Finally, 3D graphene origami metamaterials are constructed by assembling the graphene origami strips, followed by evaluating their thermo-mechanical performance. Negative coefficients of thermal expansion are also observed in the functionalized graphene origami nanotubes. The introduced strategy for controlling the thermo-mechanical properties of graphene metamaterials can open up new avenues for developing thermoelectric devices, heat management systems, and flexible nanoelectronics.

Mechanically reconfigurable and electrically tunable active terahertz chiral metamaterials

Active and efficient control of polarization states of electromagnetic wave is highly desirable in broad optical and terahertz (THz) devices. Herein, we have proposed a type of mechanically reconfigurable and electrically tunable THz chiral metamaterials that are consisting of periodical U-shaped split ring resonators (USRRs) patterned on the graphene Miura-origami (G-Mori) structures. We demonstrate that their circular dichroism (CD) as high as 0.93 originate from the coupling effect between the proper arranged USRRs and the G-Mori structure, which can be tuned through continuous change of the folding angle and Fermi energy level of graphene origami via mechanical and electrical methods in reversible manner, respectively. Furthermore, the proposed chiral metamaterials possess ideal quarter-wave-plate behavior at the resonance which also can be controlled by combining mechanical and electrical methods. The mechanically reconfigurable and electrically tunable circular dichroism and polarization conversion properties of the chiral metamaterials will be suitable for development of various polarization-related THz devices, such as highly sensitive chiral sensors, active polarization modulators and converters.

Functionalized Graphene Origami Metamaterials with Tunable Thermal Conductivity

Graphene with tunable thermo-mechanical property is of great importance for next-generation thermal management devices. Distinct from previously reported porous graphene materials that tune the thermal conductivity at the cost of degrading their mechanical properties, non-porous hydrogenated graphene origami metamaterial exhibits a unique combination of tunable thermal conductivity, high strength, and enhanced stretchability. Through molecular dynamics simulation, an extremely broad range of thermal conductivity can be obtained by tuning the geometrical parameters of the Miura-ori nanoarchitecture of graphene origami, altering the adatom types and density, designing new origami patterns, and applying mechanical strains. By analyzing and comparing the results from atomistic and continuum-based simulations, the effect of length scale on the thermal property of graphene origami metamaterials is explored. The temperature distribution and the phonon density of states of the proposed graphene origami are examined to illustrate the heat conduction mechanism. Finally, 3D graphene origami metamaterials are constructed based on the coupling and assembling of graphene origami strips, and their thermo-mechanical performance is elucidated. Negative coefficients of thermal expansion are obtained in graphene origami nanotubes. The introduced strategy for controlling the thermo-mechanical properties of graphene metamaterials can open up new avenues for developing thermoelectric devices, heat management systems, and flexible nanoelectronics.

Graphene Origami-Enabled Auxetic Metallic Metamaterials: An Atomistic Insight

Auxetic metamaterials with programable negative Poisson's ratio (NPR) are of great significance in engineering applications. These materials, however, are either mechanically weak or heavily reliant on their specially designed architecture/topology to be auxetic. Consequently, their auxetic performance may be deteriorated or even lost due to local structural deformation or failure under excessive external loading. Developing materials simultaneously possessing auxetic characteristics and excellent mechanical properties still remains a great challenge. Herein, we report a class of graphene origami (GOri)-enabled metallic metamaterials with a highly tunable NPR as well as improved mechanical properties using molecular dynamics study. Simulation results reveal that embedding more GOri into Cu matrix can not only lead to a bigger NPR but also an increased elastic modulus of the nanocomposite. The NPR of the nanocomposite with 3.35 wt % Miura-patterned GOri can reach –0.2796 at room temperature. The application of pressure and temperature can further enhance the auxetic behavior of the nanocomposite. It is also found that GOri/Cu nanocomposite significantly outperforms its counterpart reinforced with pristine graphene in terms of NPR.

Designing graphene origami structures with a giant isotropic negative coefficient of thermal expansion

Materials with an isotropic negative coefficient of thermal expansion (CTE) of the order of −10−3 K−1 are rare, and almost all of them are porous. Using molecular dynamics simulations, we show that graphene origami structures obtained by pattern-based hydrogenation can exhibit a negative CTE. The magnitude and anisotropy of the CTE can be controlled by parameters of the pattern-based hydrogenation that determine the stiffness and Poisson ratio, respectively. We achieve an isotropic CTE of −20.7×10−3 K−1, which is an enhancement by three orders of magnitude as compared to reports for other graphene-based structures and comes close to the record of all known materials.

Carbon-nanotube Nanomotor Driven by Graphene Origami

Experiments have shown that graphene origami (GORI) can be formed by compressing a folio graphene ribbon. In this study, the GORI is introduced to a rotary nanomotor built from a double-walled carbon nanotube. By placing several cantilevered GORI around the long inner tube (rotor) of the nanomotor with their tips toward the rotor, the nonbonding interaction between the tips and the rotor becomes strong when their distance is less than 1 nm. Rotationally symmetrical layout of the GORI tends to induce nonzero unidirectional torque on the rotor. Thereout, the rotor is accelerated to rotate until a stable rotational frequency (SRF) is reached on the condition that the stators (short outer tubes) applying equal but opposite torque on the rotor. The molecular-dynamics simulation approach is adopted to verify the procedure of the proposed rotary nanomotor. Conclusions are drawn for fabrication of the present rotary nanomotor.

Dehydration of polymer chains initiates graphene folding in water

The popularity of graphene origami - eyed for applications in electronics, energy harvesting, molecular storage and membrane development - has been on the rise for the last few years. Experimental studies have demonstrated that graphene grafted with thermo-sensitive polymers such as poly(N-isopropylacrylamide) (PNIPAM) folds into three-dimensional (3D) structures in response to change in the surrounding temperature. This process, attributed to the coil-to-globule transition of PNIPAM, is however, poorly understood, making the creation and control of these self-folded 3D structures difficult. Here, for the first time, we employ coarse-grained (CG) molecular dynamics (MD) simulations to develop an accurate molecular-level mechanism for the self-folding of PNIPAM-grafted graphene in presence of an explicit solvent. Our analyses of contacts, energetics and structure of PNIPAM-solvent interface indicate that the process is actually initiated by the weakening of PNIPAM-water interactions at higher temperatures, resulting in strong hydrophobic graphene-PNIPAM interactions. By further varying system parameters like graphene width and polymer coverage, we also provide energy criteria for graphene-folding. The molecular-level insights obtained through this study can be essential for controlling and tuning the process of graphene self-folding via temperature control.

Molecular hierarchical release using hydrogenated graphene origami under electric field

In recent years, drug delivery has progressively become one of the main research areas in the field of biomedicine. However, the graded drug release remains a serious challenge at the nano-scales. Herein, we successfully simulated the graded release of C60 and C180 from the graphene box inspired by the origami technique under the control of an external electric field via molecular dynamics (MD) simulations. Our results provide a feasible scheme for hierarchical drug delivery at the nano-scales. The graphene origami was generated through the folding of graphene guided by its creases which were created by combining carbon atoms with hydrogen atoms and transforming sp2 to sp3 bonds at the combination line. We can construct complex graphene origami by designing reasonable hydrogen atoms distribution on graphene. This provides a simple and practicable program for designing complex graphene-based nanodevices for drug delivery.

The morphology of doubly-clamped graphene nanoribbons

Understanding the response of micro/nano-patterned graphene to mechanical forces is instrumental for applications such as advanced graphene origami and kirigami. Here, we analyze free-standing nanoribbons milled into single-layer graphene by focused ion beam processing. Using transmission electron microscopy, we show that the length L of the structures determines their morphology. Nanoribbons with L below 300 nm remain mainly flat, whereas longer ribbons exhibit uni-axial crumpling or spontaneous scrolling, a trend that is well reproduced by molecular dynamics simulations. We measure the strain of the ribbons as well as their crystallinity by recording nanometer-resolved convergent beam electron diffraction maps, and show that the beam tails of the focused ion beam cause significant amorphization of the structures adjacent to the cuts. The expansive or compressive strain in the structures remains below 4%. Our measurements provide experimental constraints for the stability of free-standing graphene structures with respect to their geometry, providing guidelines for future applications of patterned graphene.

Spontaneous Folding Growth of Graphene on h-BN.

Graphene has been the subject of much research, with structural engineering frequently used to harness its various properties. In particular, the concepts of graphene origami and kirigami have inspired the design of quasi-three-dimensional graphene structures, which possess intriguing mechanical, electronic, and optical properties. However, accurate controlling the folding process remains a big challenge. Here, we report the discovery of spontaneous folding growth of graphene on the h-BN substrate via adopting a simple chemical vapor deposition method. Folded edges are formed when two stacked graphene layers share a joint edge at a growth temperature up to 1300 °C. Using first-principles density functional theory calculations, the bilayer graphene with folded edges is demonstrated to be more stable than that with open edges. Utilizing this novel growth mode, hexagram bilayer graphene containing entirely sealed edges is eventually realized. Our findings provide a route for designing graphene devices with a new folding dimension.

Energetics of graphene origami and their “spatial resolution”

The extreme thinness of graphene combined with its tensile strength made it a material appealing for discussing and even making complex cut-kirigami or folded-only origami. In the case of origami, its stability is mainly defined by the positive energy of the single- or double-fold curvature deformation counterbalanced by the energy reduction due to favorable van der Waals contacts. These opposite sign contributions also have notably different scaling with the size L of the construction, the contacts contributing in proportion to area ~ L2, single folds as ~ L, and highly strained double-fold corners as only ~ L0 = const. Computational analysis with realistic atomistic-elastic representation of graphene allows one to quantify these energy contributions and to establish the length scale, where a single fold is favored (7 nm 21 nm), defining the size of the smallest possible complex origami designs as L ≫ 21 nm. The flexibility and foldability of graphene are some of its attractive properties inspiring the designs of origami structures with potential use in flexible electronics and electromechanical nanodevices. The aesthetics, precision, and ease of folding and stability, however, have limitations at the nanoscale. Here, by means of large-scale atomistic calculations and continuum models, it is quantified how the dimensions determine the relative robustness of the elementary folds of graphene (a single fold and a double-folded graphene forming a single order-four vertex), thereby mapping the spatial resolution limits and providing important guidance for graphene nano-origami realizations.