Graphene Foam: Uniaxial Tension Behavior and Fracture Mode Based on a Mesoscopic Model

Mechanical Properties of Graphene Networks under Compression: A Molecular Dynamics Simulation

Molecular dynamics simulation is used to study and compare the mechanical properties obtained from compression and tension numerical tests of multilayered graphene with an increased interlayer distance. The multilayer graphene with an interlayer distance two-times larger than in graphite is studied first under biaxial compression and then under uniaxial tension along three different axes. The mechanical properties, e.g., the tensile strength and ductility as well as the deformation characteristics due to graphene layer stacking, are studied. The results show that the mechanical properties along different directions are significantly distinguished. Two competitive mechanisms are found both for the compression and tension of multilayer graphene—the crumpling of graphene layers increases the stresses, while the sliding of graphene layers through the surface-to-surface connection lowers it. Multilayer graphene after biaxial compression can sustain high tensile stresses combined with high plasticity. The main outcome of the study of such complex architecture is an important step towards the design of advanced carbon nanomaterials with improved mechanical properties.

Study of Viscoelastic Properties of Graphene Foams Using Dynamic Mechanical Analysis and Coarse-Grained Molecular Dynamics Simulations

As a promising nano-porous material for energy dissipation, the viscoelastic properties of three-dimensional (3D) graphene foams (GrFs) are investigated by combining a dynamic mechanical analysis (DMA) and coarse-grained molecular dynamic (CGMD) simulations. The effects of the different factors, such as the density of the GrFs, temperature, loading frequency, oscillatory amplitude, the pre-strain on the storage and loss modulus of the GrFs as well as the micro-mechanical mechanisms are mainly focused upon. Not only the storage modulus but also the loss modulus are found to be independent of the temperature and the frequency. The storage modulus can be weakened slightly by bond-breaking with an increasing loading amplitude. Furthermore, the tensile/compressive pre-strain and density of the GrFs can be used to effectively tune the viscoelastic properties of the GrFs. These results should be helpful not only for understanding the mechanical mechanism of GrFs but also for optimal designs of advanced damping materials.

A Review of the Mechanical Properties of Graphene Aerogel Materials: Experimental Measurements and Computer Simulations

Graphene aerogels (GAs) combine the unique properties of two-dimensional graphene with the structural characteristics of microscale porous materials, exhibiting ultralight, ultra-strength, and ultra-tough properties. GAs are a type of promising carbon-based metamaterials suitable for harsh environments in aerospace, military, and energy-related fields. However, there are still some challenges in the application of graphene aerogel (GA) materials, which requires an in-depth understanding of the mechanical properties of GAs and the associated enhancement mechanisms. This review first presents experimental research works related to the mechanical properties of GAs in recent years and identifies the key parameters that dominate the mechanical properties of GAs in different situations. Then, simulation works on the mechanical properties of GAs are reviewed, the deformation mechanisms are discussed, and the advantages and limitations are summarized. Finally, an outlook on the potential directions and main challenges is provided for future studies in the mechanical properties of GA materials.

Functionally gradient three-dimensional graphene foam-based polymeric scaffolds for multilayered tissue regeneration

Physiological bioengineering of multilayered tissues requires an optimized geometric organization with comparable biomechanics. Currently, polymer-reinforced three-dimensional (3D) graphene foams (GFs) are gaining interest in tissue engineering due to their unique morphology, biocompatibility, and similarity to extracellular matrixes. However, the homogeneous reinforcement of single polymers throughout a GF matrix does not provide tissue-level organization. Therefore, a triple-layered structure is developed in a GF matrix to closely mimic native tissue structures of the periodontium of the teeth. The scaffold aims to overcome the issue of layer separation, which generally occurs in multilayered structures due to the poor integration of various layers. The 3D GF matrix was reinforced with a polycaprolactone (PCL), polyvinyl alcohol (PVA), and PCL-hydroxyapatite (HA) mixture, added sequentially, via spin coating, vacuum, and hot air drying. Later, PVA was dissolved to create a middle layer, mimicking the periodontal fibers, while the layers present on either side resembled cementum and alveolar bone, respectively. Scanning electron microscopy and micro-computed tomography revealed the structure of the scaffold with internal differential porosities. The nanoindentation and tensile testing demonstrated the closeness of mechanical properties to that of native tissues. The biocompatibility was assessed by the MTT assay with MG63 cells (human osteosarcoma cells) exhibiting high adhesion and proliferation rate inside the 3D architecture. Summing up, this scaffold has the potential for enhancing the regeneration of various multilayered tissues.

High-Throughput Generation of 3D Graphene Metamaterials and Property Quantification Using Machine Learning

3D graphene assemblies are proposed as solutions to meet the goal toward efficient utilization of 2D graphene sheets, showing excellent performances in applications such as mechanical support, energy storage, and electrochemical catalysis. However, given the diversity and complexity of possible graphene 3D structures, there does not yet exist a systematic approach that can generate target 3D shapes and also, evaluate their performance. Here high-throughput data generation is combined with artificial intelligence approaches to realize rapid structure formation and property quantification of 3D graphene foams with mathematically controlled topologies, driven by molecular dynamics simulations. More than 4000 different foam structures are created, which feature diverse topologies that contain potential pathways for small molecules and auxetic structures with negative Poisson's ratio. Empowered by machine learning (ML) algorithms including graph neural networks, not only global properties such as elastic moduli, but also local behaviors such as atomic stress can be predicted and optimized based on their atomic structure, bypassing expensive atomistic simulations. The key findings of the research reported in this paper include a high-throughput virtual framework of generating diverse 3D graphene assemblies with mechanical performances quantification, and highly efficient methods of evaluating physical properties based on ML.

Mechanical Properties and Deformation Mechanisms of Graphene Foams with Bi-Modal Sheet Thickness by Coarse-Grained Molecular Dynamics Simulations

Graphene foams (GrFs) have been widely used as structural and/or functional materials in many practical applications. They are always assembled by thin and thick graphene sheets with multiple thicknesses; however, the effect of this basic structural feature has been poorly understood by existing theoretical models. Here, we propose a coarse-grained bi-modal GrF model composed of a mixture of 1-layer flexible and 8-layer stiff sheets to study the mechanical properties and deformation mechanisms based on the mesoscopic model of graphene sheets (Model. Simul. Mater. Sci. Eng. 2011, 19, 54003). It is found that the modulus increases almost linearly with an increased proportion of 8-layer sheets, which is well explained by the mixture rule; the strength decreases first and reaches the minimum value at a critical proportion of stiff sheets ~30%, which is well explained by the analysis of structural connectivity and deformation energy of bi-modal GrFs. Furthermore, high-stress regions are mainly dispersed in thick sheets, while large-strain areas mainly locate in thin ones. Both of them have a highly uneven distribution in GrFs due to the intrinsic heterogeneity in both structures and the mechanical properties of sheets. Moreover, the elastic recovery ability of GrFs can be enhanced by adding more thick sheets. These results should be helpful for us to understand and further guide the design of advanced GrF-based materials.

Compressive modulus and deformation mechanisms of 3DG foams: experimental investigation and multiscale modeling

Due to the wide applications of three-dimensional graphene (3DG) foam in bio-sensors, stretchable electronics, and conductive polymer composites, predicting its mechanical behavior is of paramount importance. In this paper, a novel multiscale finite element model is proposed to predict the compressive modulus of 3DG foams with various densities. It considers the effects of pore size and structure and the thickness of graphene walls on 3DG foams' overall behavior. According to the scanning electron microscope images, a unit cell is selected in the microscale step to represent the incidental arrangement of graphene sheets in 3DG foams. After derivation of equivalent elastic constants of the unit cell by six individual load cases, the whole unit cell is considered an equivalent element. The macroscale model is prepared by defining a representative volume element (RVE), containing a sufficient number of the equivalent elements. Assigning a stochastic local coordinate system for each equivalent element in the macro RVE provides a model that could be utilized for elastic modulus estimation of 3DG foams in macroscale. To investigate the correspondence between the theoretical results and experimental data, 3DG foams were synthesized with four densities, and their compressive behavior were evaluated. The mass densities of the prepared foams were 5.36, 8.50, 9.37, and 11.5 mg cm^-3, and the corresponding measured elastic modulus for each were 6.4, 10.7, 16.9, and 29.1 kPa, respectively. The predicted modulus by the proposed model for the synthesized foams were 6.1, 13.1, 15.6 and 21.7 kPa, respectively. The results show that the maximum divergence between estimated values and experimental data is less than 25%, confirming the high capability of the model in the estimation of 3DG foams' properties.

Strain Hardening in Graphene Foams under Shear

Strain hardening is an important issue for the design and application of materials. The strain hardening of graphene foams has been widely observed but poorly understood. Here, by adopting the coarse-grained molecular dynamics method, we systematically investigated the microscopic mechanism and influencing factors of strain hardening and related mechanical properties of graphene foams under shear loading. We found that the strain hardening is induced by cumulative nonlocalized bond-breakings and rearrangements of microstructures. Furthermore, it can be effectively tuned by the number of graphene layers and cross-link densities, i.e., the strain hardening would emerge at a smaller shear strain for the graphene foams with thicker sheets and/or more cross-links. In addition, the shear stiffness G of graphene foams increases linearly with the cross-link density and exponentially with the number of graphene layers n by G ∼ n 1.95. These findings not only improve our understanding of the promising bulk materials but also pave the way for optimizing structural design in wide applications based on their mechanical properties.

Microscopic deformation mechanism and main influencing factors of carbon nanotube coated graphene foams under uniaxial compression

Many experiments have shown that carbon nanotube-coated (CNT-coated) graphene foam (CCGF) has specific mechanical properties, which further expand the application of graphene foam materials in many advanced fields. To reveal the microscopic deformation mechanism of CCGF under uniaxial compression and the main factors affecting their mechanical properties, numerical experiments based on the coarse-grained molecular dynamics method are systematically carried out in this paper. It is found that the relative stiffness of CNTs and graphene flakes seriously affects the microscopic deformation mechanism and strain distribution in CCGFs. The bar reinforcing mechanism will dominate the microstructural deformation in CCGFs composed of relatively soft graphene flakes, while the microstructural deformation in those composed of stiff graphene flakes will be dominated by the mechanical locking mechanism. The effects of CNT fraction, distribution of CNTs on graphene flakes, the thickness of graphene flakes, and the adhesion strength between CNTs and graphene flakes on the initial and intermediate moduli of foam materials are further studied in detail. The results of this paper should be helpful for a deep understanding of the mechanical properties of CCGF materials and the optimization design of microstructures in advanced graphene-based composites.

The mechanical property and microscopic deformation mechanism of nanoparticle-contained graphene foam materials under uniaxial compression

Nanoparticle-contained graphene foams have found more and more practical applications in recent years, which desperately requires a deep understanding on basic mechanics of this hybrid material. In this paper, the microscopic deformation mechanism and mechanical properties of such a hybrid material under uniaxial compression, that are inevitably encountered in applications and further affect its functions, are systematically studied by the coarse-grained molecular dynamics simulation method. Two major factors of the size and volume fraction of nanoparticles are considered. It is found that the constitutive relation of nanoparticle filled graphene foam materials consists of three parts: the elastic deformation stage, deformation with inner re-organization and the final compaction stage, which is much similar to the experimental measurement of pristine graphene foam materials. Interestingly, both the initial and intermediate modulus of such a hybrid material is significantly affected by the size and volume fraction of nanoparticles, due to their influences on the microstructural evolution. The experimentally observed 'spacer effect' of such a hybrid material is well re-produced and further found to be particle-size sensitive. With the increase of nanoparticle size, the micro deformation mechanism will change from nanoparticles trapped in the graphene sheet, slipping on the graphene sheet, to aggregation outside the graphene sheet. Beyond a critical relative particle size 0.26, the graphene-sheet-dominated deformation mode changes to be a nanoparticle-dominated one. The final microstructure after compression of the hybrid system converges to two stable configurations of the 'sandwiched' and 'randomly-stacked' one. The results should be helpful not only to understand the micro mechanism of such a hybrid material in different applications, but also to the design of advanced composites and devices based on porous materials mixed with particles.

In silico design, building and gas adsorption of nano-porous graphene scaffolds

Graphene-based nano-porous materials (GNM) are potentially useful for all those applications needing a large specific surface area (SSA), typical of the bidimensional graphene, yet realized in the bulk dimensionality. Such applications include for instance gas storage and sorting, catalysis and electrochemical energy storage. While a reasonable control of the structure is achieved in micro-porous materials by using nano-micro particles as templates, the controlled production or even characterization of GNMs with porosity strictly at the nano-scale still raises issues. These are usually produced using dispersion of nano-flakes as precursors resulting in little control on the final structure, which in turn reflects in problems in the structural model building for computer simulations. In this work, we describe a strategy to build models for these materials with predetermined structural properties (SSA, density, porosity), which exploits molecular dynamics simulations, Monte Carlo methods and machine learning algorithms. Our strategy is inspired by the real synthesis process: starting from randomly distributed flakes, we include defects, perforation, structure deformation and edge saturation on the fly, and, after structural refinement, we obtain realistic models, with given structural features. We find relationships between the structural characteristics and size distributions of the starting flake suspension and the final structure, which can give indications for more efficient synthesis routes. We subsequently give a full characterization of the models versus H₂ adsorption, from which we extract quantitative relationship between the structural parameters and the gravimetric density. Our results quantitatively clarify the role of surfaces and edges relative amount in determining the H₂ adsorption, and suggest strategies to overcome the inherent physical limitations of these materials as adsorbers. We implemented the model building and analysis procedures in software tools, freely available upon request.

Graphene Foam: Hole-Flake Network for Uniaxial Supercompression and Recovery Behavior

We employed the coarse-grained molecular dynamics simulation method to systematically study the uniaxial supercompression and recovery behavior of multiporous graphene foam, in which a mesoscopic three-dimensional network with hole-graphene flakes was proposed. The network model not only considers the physical cross-links and interlayer van der Waals interactions, but also introduces a hole in the flake to approach the imperfection of pristine graphene and the hierarchical porous configuration of real foam material. We first recreated a typical two-stage supercompression stress-strain relationship and the corresponding time-dependent recovery as well as a U-type nominal Poisson ratio. Then the recovery unloading at different strains and multicycle compression-uncompression were both conducted; the initial elastic moduli in the multicycles were found to be the same, and a multilevel residual strain was disclosed. Importantly, the residual strain is not exactly the plastic one, part of which can resurrect in the subsequent loading-unloading-holding. The mesoscopic mechanism of viscoelastic and residual deformation for the recovery can be attributed to the van der Waals repulsion and mechanical interlocking among the hole-flakes; interestingly, the local tensile stress was observed in the virial stress distribution. Particularly, an abnormal turning point in the length-time curve for the mean bead-bond length was captured during the supercompression. After the point, the length abnormally increases for different size ratios of the hole to the flake, which is in line with the mesostructure evolution. The finding may provide a mesoscopic criterion for the supercompression of graphene foam related materials.

A Cut-Resistant and Highly Restorable Graphene Foam

High-pressure resistant and multidirectional compressible materials enable various applications but are often hindered by structure-derived collapse and weak elasticity. Here, a super-robust graphene foam with ladder shape microstructure capable of withstanding high pressure is presented. The multioriented ladder arrays architecture of the foam, consisting of thousands of identically sized square spaces, endow it with a great deal of elastic units. It can easily bear an iterative and multidirectional pressure of 44.5 MPa produced by a sharp blade, and may completely recover to its initial state by a load of 180 000 times their own weight even under 95% strain. More importantly, the foam can also maintain structural integrity after experiencing a pressure of 2.8 GPa through siphoning. Computational modeling of the "buckling of shells" mechanism reveals the unique ladder-shaped graphene foam contributes to the superior cut resistance and good resilience. Based on this finding, it can be widely used in cutting resistance sensors, monitoring of sea level, and the detection of oily contaminants in water delivery pipelines.

Structure and Dynamics of a Graphene Melt

We explore the structural and dynamic properties of bulk materials composed of graphene nanosheets using coarse-grained molecular dynamics simulations. Remarkably, our results show clear evidence that bulk graphene materials exhibit a fluid-like behavior similar to linear polymer melts at elevated temperatures and that these materials transform into a glassy-like "foam" state at temperatures below the glass-transition temperature ( T_g) of these materials. Distinct from an isolated graphene sheet, which exhibits a relatively flat shape with fluctuations, we find that graphene sheets in a melt state structurally adopt more "crumpled" configurations and correspondingly smaller sizes, as normally found for ordinary polymers in the melt. Upon approaching the glass transition, these two-dimensional polymeric materials exhibit a dramatic slowing down of their dynamics that is likewise similar to ordinary linear polymer glass-forming liquids. Bulk graphene materials in their glassy foam state have an exceptionally large free-volume and high thermal stability due to their high T_g (≈ 1600 K) as compared to conventional polymer materials. Our findings show that graphene melts have interesting lubricating and "plastic" flow properties at elevated temperatures, and suggest that graphene foams are highly promising as high surface filtration materials and fire suppression additives for improving the thermal conductivities and mechanical reinforcement of polymer materials.

Mimicking a Dog's Nose: Scrolling Graphene Nanosheets

Inspired by the densely covered capillary structure inside a dog's nose, we report an artificial nanostructure, i. e., poly(sodium p-styrenesulfonate)-functionalized reduced graphene oxide nanoscrolls (PGNS), with high structural perfection and efficient gas sensing applications. A facile supramolecular assembly is introduced to functionalize graphene with the functional polymer, combined with the lyophilization technique to massively transform the planar graphene-based nanosheets to nanoscrolls. Detailed characterizations reveal that the bioinspired nanoscrolls exhibit a wide-open tubular morphology with uniform dimensions that is structurally distinct from the previously reported ones. The detailed morphologies of the graphene-based nanosheets in each scrolling stage during lyophilization are monitored by cryo-SEM. This unravels an asymmetric polymer-induced graphene scrolling mechanism including the corresponding scrolling process, which is directly presented by molecular dynamics simulations. The fabricated PGNS sensors exhibit superior gas sensing performance with reliable repeatability, excellent linear sensibility, and, especially, an ultrahigh response ( R_a/ R_g = 5.39, 10 ppm) toward NO₂. The supramolecular assembly combined with the lyophilization technique to fabricate PGNS provides a strategy to design biomimetic materials for gas sensors and chemical trace detectors.

Size of graphene sheets determines the structural and mechanical properties of 3D graphene foams

Graphene is recognized as an emerging 2D nanomaterial for many applications. Assembly of graphene sheets into 3D structures is an attractive way to enable their macroscopic applications and to preserve the exceptional mechanical and physical properties of their constituents. In this study, we develop a coarse-grained (CG) model for 3D graphene foams (GFs) based on the CG model for a 2D graphene sheet by Ruiz et al (2015 Carbon 82 103-15). We find that the size of graphene sheets plays an important role in both the structural and mechanical properties of 3D GFs. When their size is smaller than 10 nm, the graphene sheets can easily stack together under the influence of van der Waals interactions (vdW). These stacks behave like building blocks and are tightly packed together within 3D GFs, leading to high density, small pore radii, and a large Young's modulus. However, if the sheet sizes exceed 10 nm, they are staggered together with a significant amount of deformation (bending). Therefore, the density of 3D GFs has been dramatically reduced due to the loosely packed graphene sheets, accompanied by large pore radii and a small Young's modulus. Under uniaxial compression, rubber-like stress-strain curves are observed for all 3D GFs. This material characteristic is dominated by the vdW interactions between different graphene layers and slightly affected by the out-of-plane deformation of the graphene sheets. We find a simple scaling law [Formula: see text] between the density ρ and Young's modulus E for a model of 3D GFs. The simulation results reveal structure-property relations of 3D GFs, which can be applied to guide the design of 3D graphene assemblies with exceptional properties.