Fabrication and characterization of cg-G
cg-G is produced through an alkaline-assisted hydrothermal synthesis using graphene oxide (GO) as precursor (see Methods for details, Supplementary Figs. 1 and 2). The graphene walls are aligned around the geometric axis, which concurrently serves as the axis of curvature of the obtained structure. Using laser processing technology, one can shape the materials with exceptional precision, achieving accuracy of ca. 10 micrometers when combined with an evaporate-casting process (Fig. 2a and Supplementary Fig. 3). The resultant superstructure is featured with a curvature gradient (Fig. 2b), where the curvature is smaller further from the curvature center and increases as one approaches the center. The scanning electron microscopy (SEM) investigations demonstrate that the structure at point a (farther from the curvature center) shows a nearly align parallel to the central axis of curvature (Fig. 2c), while the one at point b (near to the curvature center) exhibits neat remarkable curved arrays toward the concentric axis. The side view cross-section at point c (parallel to the curvature central axis) shows a similar parallel structure to the one at point a (Fig. 2d).Fig. 2: Morphology and structure characterizations of cg-G.a Photograph of a cuboid-shaped cg-G. b Schematic structure of cg-G. Three colorful points a (green), b (yellow), and c (purple) represent three different positions on the assembly. c SEM images of point a and point b in (b). The position close to the center of curvature shows obvious curvature gradient structure. d SEM image of point c and corresponding enlarged image. The structure of point c is composed of parallel graphene walls and gaps between them. e SEM images of graphene sheets in cg-G before and after evaporate-casting. f STEM images of point c in Fig. 2b after evaporate-casting. Yellow arrows represent the aligned direction of compact graphene walls. g Specific compressive strength comparison of various densified materials including normal graphene hydrogel after dehydration, graphite, kinds of metals, and cg-G after evaporate-casting (n = 3, error bar: standard deviation). Source data are provided as a source data file.In a swelling state, the gaps amidst the walls become saturated with water molecules. The evaporate-casting process generates capillary forces through water evaporation, drawing the flat graphene assembly and yielding the protruding structures (Fig. 2e, Supplementary Figs. 4 and 5). Analysis via X-ray photoelectron spectroscopy indicates an oxygen composition of approximately 20% within the cg-G, affirming the presence of hydrophilic oxygen functional groups (Supplementary Fig. 6a). This observation emphasizes a robust interaction between water and the internal surfaces, thereby ensuring the potency of the capillary forces. Both Fourier transform infrared spectroscopy and energy dispersive spectroscopy before and after water evaporation indicate that the casting process does not alter the composition or content of functional groups on graphene sheets (Supplementary Fig. 6b, d, e). Additionally, X-ray diffraction patterns demonstrate no discernible peak shift between the dehydrated and hydrated states (Supplementary Fig. 6c), signifying a consistent interlayer structure connecting the two graphene nanosheets within the assemblies. This suggests that the protruding structures retain the intrinsic mechanical attributes of the graphene assembly. Upon complete dehydration, an aligned microstructure is observed under scanning transmission electron microscopy (STEM), wherein the protrusions are mechanically interlocked in a serrated configuration (Fig. 2f, Supplementary Fig. 7). Due to this distinctive structure, cg-G after deformation demonstrates a density of ~1.5 g cm−3 and high compressive strength of up to 70 MPa/(g/cm3), surpassing that of various metals including stainless steel (SUS304) and doubling the strength of traditional graphene-based structural materials (Fig. 2g, Supplementary Fig. 8).Controllable shaping based on curvature gradientTo achieve precise control over curvature gradients, we utilized the distance (d) extending from the geometric center (O) of the samples to the curvature axis of the superstructure (O’) as a governing parameter (Fig. 3a, 3b-i). In situations where the curvature axis of the graphene superstructure is perpendicular to the plane of the cross-shaped samples, variations in the distribution of curvature gradients within the sample result in diverse bending behaviors during the evaporate-casting process (Fig. 3b-ii and 3b-iii, Supplementary Figs. 9 and 10, Supplementary Video 1). The deformation of samples with diverse curvature gradients can be anticipated via computational prediction (see Methods for details). While the level of shrinkage is notably high, the overall form of the cross-shaped samples is upheld when d = 0. This phenomenon arises due to the counteraction of configurational forces in these sections, which is a consequence of the symmetric microstructures aligning along the in-plane direction. In contrast, the prominence of the differential distribution of the shrinkage coefficient amplifies as d increases (Supplementary Fig. 11). In this context, the degree of shrinkage escalates alongside a more substantial curvature gradient. As a result, these cross-shaped cg-Gs exhibit in-plane deformations toward the curvature center direction following the process of evaporate-casting.Fig. 3: In-plane and out-plane evaporate-casting processing of cg-G.a–c In-plane processing. a Schematic diagrams of cross-shaped cg-G with an axis-center distance (d) perpendicular to centric axis of curvature. b Demonstrations of cross-shaped cg-Gs with different microstructures before and after deformation: (i) Schematic diagrams of three cross-shaped cg-G with different d values (d = 0, 3, 7 mm) on in-plane direction. (ii) Gradient distribution of the curvatures and theoretical predictions of the deformation of the three cg-Gs based on finite element analysis (FEA). (iii) SEM images of the three deformed cg-Gs. The colors in FEA from yellow to dark blue indicate an increase of the radius of curvature (ρ). The degree of deformation can be represented by the included angle (αe). Scale bar: 500 μm. c αe and lateral length of final graphene architectures as a function of d (n = 3, error bar: standard deviation). d–f Out-plane processing. d Schematic diagrams of cg-Gs with different d values along the centric axis of curvature. e Demonstrations of cross-shaped cg-Gs with different microstructures before and after deformation: (i) Schematic diagrams of three cross-shaped cg-Gs with different d values (d = 0, 3, 7 mm) on out-plane direction. (ii) Corresponding gradient distribution of the curvatures and theoretical predictions of the deformation of the three cg-Gs based on FEA. (iii) SEM images of the three deformed cg-Gs. The degree of out-plane deformation can be represented by αe. Scale bar: 500 μm. f αe and lateral length of final graphene architectures as a function of d (n = 3, error bar: standard deviation). Source data are provided as a source data file.The microscopic observation via SEM (Fig. 3b-iii) experimentally validated the correlation between deflection and curvature gradient. Samples with a carefully designed curvature gradient exhibited corresponding bending angles (αe) along the longer sides (the long side of the initial cross-shaped cg-G) that aligned with the values derived from computational predictions (αc) (Fig. 3b-ii, Supplementary Fig. 9b). This alignment suggests a high level of uniformity in the self-deformation facilitated by the curvature gradient. The lateral dimension, which signifies the extent of the long side of the initial cross-shaped cg-G after deformation, is utilized to exemplify the pronounced regularity of self-deformation. Notably, despite the progressive augmentation in the curvature gradient, the lateral length remains invariant (Fig. 3c). The alterations in shape along the horizontal direction are relies on the decreasing gap width of the wall structures. As a result, the constant lateral dimension not only denotes a consistent curvature gradient but also a contraction that closely approximates the characteristics of an ideal coaxial circular arc model (see Supplementary Fig. 12 for details), which concurs with the structural characterization elucidated in Fig. 2. More examples of the in-plane deformation are shown in Supplementary Figs. 13 and 14.We also examined a scenario where the axis of curvature is parallel to the plane of the cross-shape specimen, and we denoted the distance between the geometric center point and the curvature axis as d (Fig. 3d, 3e-i). The deformation induced by the evaporate-casting process was simulated computationally (Fig. 3e-ii, Supplementary Fig. 15a). Despite the significant contraction (high shrinkage coefficient level), the fundamental configuration of the cross-shaped samples remains unaltered when d = 0. This phenomenon can be ascribed to the equilibrium between internal stresses within symmetric microstructures. The distribution of the shrinkage coefficient becomes more pronounced as the curvature gradient increases (Fig. 3e-iii), signifying that the relationship between the degree of out-plane bending and curvature gradient mirrors that of in-plane deformation. Additionally, a distinct out-plane deformation becomes evident, aligning with the computational predictions. The independence of the lateral length on the curvature gradient underscores the nearly ideal arrangement of co-axial circular arc-shaped graphene assemblies, reinforcing the concordance between observations and expectations (Fig. 3f, Supplementary Fig. 15b). The consistency of these phenomena with the results of in-plane deformation experiments highlights satisfactory controllability facilitated by the curvature gradient in self-shaping processes.Mechanism of self-shapingThe evaporate-casting enabled self-shaping relies on the hierarchical deformation of graphene walls. Water molecules serve as plasticizers, enabling relative sliding of graphene nanosheets within the walls. In this context, as water within surface wrinkles evaporates, capillary forces prompt each graphene nanosheet to crumple (Fig. 4a). Consequently, protrusions emerge on the dehydrated wall surfaces (Fig. 2e, f), causing shrinkage along the plane of the wall. It’s worth noting that due to robust π-π interaction forces between graphene sheets, the crumpled walls retain their form even when in contact with water. On an assembly scale, capillary forces exert a tautening effect on the wall structures, diminishing gap sizes and hence yielding a compact arrangement (Fig. 4b). The emergence of protrusions and the constriction of wall structures collectively bring about macroscopic shape contraction in orthogonal directions. This behavior can be reflected on a cuboid sample comprising a centrosymmetric curvature gradient microstructure (Fig. 4c, Supplementary Figs. 16 and 17). The ratio of contraction along the wall plane (l’) compared to that perpendicular to the wall plane (w’) was measured at 1.4, indicating the anisotropic contraction behavior that could significantly bolster the efficacy of the curvature gradient induced deformation. This casting method demonstrates high stability. The ratio of l’/w’ is determined by the microstructure of cg-G (Supplementary Fig. 18), and remains unaffected by the surrounding environment during water evaporation (Supplementary Fig. 19).Fig. 4: Mechanism of evaporate-casting of cg-G.a Schematic of capillary force (Pc) of water in the groove of a monolayer graphene sheet, and the deformation of graphene groove after dehydration. The capillary force acts perpendicular to the water surface and can be divided into two force modes: one is normal to the graphene sheet (Fx) and the other is along the sheet (Fy). b Schematic of the dehydration process of graphene walls arrayed in parallel during evaporate-casting. c Photographs of cuboid-shaped cg-G comprising a centrosymmetric curvature gradient structure after dehydration of 0 h and 5 h, and the corresponding SEM image of dehydration for 5 h. Scale bar: 500 μm. Initial size: 8 mm × 8 mm × 2 mm. The ratios of the two sides along and perpendicular to the wall plane before (l, w) and after (l’, w’) dehydration are different, specifically, w/w’ > l/l’. d Digital images of top and side views for dumbbell-shaped cg-G. e Gradient distribution of the curvatures and theoretical predictions of the deformation of the dumbbell-shaped cg-G. f SEM images of the dumbbell-shaped cg-G after evaporate-casting. The colors in FEA from yellow to dark blue indicate an increase of the radius of curvature (ρ). Scale bar for the two images on the left: 500 μm. g Schematic diagrams of the microstructure of (i) arc-shaped cg-G, and corresponding schematic diagrams of the assembly after being twisted to different angles (small angle of 10° (ii) and large angle of 30° (iii)). F and F’ represent two forces with equal magnitude but in opposite directions. After being twisted, the direction towards the curvature center (blue arrow) shifts from in-plane to out-plane. h Digital photos and SEM images of three cg-G assemblies with a twisted angle of 0o (i), 10o (ii), and 30o (iii) before and after evaporate-casting.Then we delve into how the self-tightening effect of cg-Gs during the evaporate-casting process is harnessed to programmatically transform simple profiles into intricate structures. According to the Kelvin curvature effect22, water molecules are more likely to escape from curved surfaces. This observation aligns with our experimental findings that water evaporates more rapidly from the side with larger curvature. With water evaporating, moisture near highly curved graphene sheets becomes depleted first, leading to more pronounced deformations compared to regions with lower curvature. Considering these mechanisms, we can postulate the following relationship between radial strain (εr, strain towards the center of the curvature) and curvature radius (ρ) of cg-G during evaporate-casting:$${\varepsilon }_{r}={\varepsilon }_{0}+{bf}(\rho )({\varepsilon }_{r}\, < \, 0)$$
(1)
where \({\varepsilon }_{0}\) (<0) represents the uniform shrinkage strain (the curvature radius equals zero). \(b\) (>0) is the curvature deformation coefficient, indicating the sensitivity of deformation to changes in curvature radius. f(ρ) is a function of ρ, signifying that as the curvature radius increases, the shrinkage deformation decreases. In this study, when analyzing cg-G slices consists of graphene walls positioned at co-axial curvature centers (Supplementary Fig. 20), we assumed a relationship between εr and ρ, i.e., εr = ε0 + bρ2 (see Supplementary text for details). Specifically, the curvature microstructures of cg-G slices can be described by their d and θ values. Based on above relationship, we investigated the deformation of cg-G with different d and θ, and provided corresponding analytical expressions (see Supplementary text for details). Theoretical results not only effectively accord with the deformation states discussed in Fig. 3, but also accurately predict deformations of dumbbell-shaped cg-Gs (see Figs. 21–23 for a detailed discussion). For example, the FEA results and SEM images reveal that the dumbbell architecture (Fig. 4d, with a θ value of 45°) presents twists around the long center axis after deformation (Fig. 4e, f), resulting in a stereo and centrosymmetric final geometry, and bilateral cuboids transformed to be approximate trapezoidal cube due to the in-plane deformation. These results validate the mechanism of curvature gradient-induced bending deformation.Apart from the self-shaping cg-G structures that can be predicted and understood through having defined the relevant θ and d parameters, this behavior can be further programmed through external force which allows the assembly to exhibit self-plastic capability like metals. To demonstrate this point, we applied two forces of equal magnitude and opposite direction on both ends of an arc-shaped cg-G (Fig. 4g), resulting in the initial twist deformations with different bending angles, such as a small angle of 10° (Fig. 4g-ii) and a large angle of 30° (Fig. 4g-iii), respectively. After deformation, the direction towards the curvature center (blue arrow) shifts from in-plane to out-plane. The coarse-grained molecular dynamics (CG-MD) calculation model show that the energy of the system initially increases and then decreases as raise of twist angles because of inter-adhered graphene walls driven by strong π–π interactions (Supplementary Fig. 24). As the degree of deformation intensifies, the quantity of adhering walls escalates, causing a continual reduction in the system’s energy. When the energy drops below zero, the system achieves stability, and the structure displays plasticity, enabling it to preserve the shape shaped by external forces (Fig. 4g-ii, iii).The cg-G slices can be shaped due to their distinctive curvature gradient structures through evaporate-casting. As water evaporates, all arc-shaped cg-G architectures are expected to undergo alterations in their initial profiles (Fig. 4h). The one with symmetrical curvature center structure transformed into a closed-loop structure during the evaporate-casting process (Fig. 4h-i), aligning with the previously mentioned self-shaping principles. When subjected to additional forces with initial twist angles of 10° (Fig. 4h-ii) and 30° (Fig. 4h-iii), the direction pointing towards the center of curvature changed, signifying the existence of out-of-plane components of the asymmetry within the curvature structure. The changes directly resulted further structural deformations out of plane. In SEM images, two helix-shaped cg-G architectures with the same deformation mode but different pitches can be observed, and the twist angle is larger than it before deformation. These deformations resulted from the configurational forces generated by the combined effects of the initial curvature gradient and the additional twist angle during dehydration. These results confirm the previously established deformation mechanism.Enhanced mechanical strength through hierarchical self-tighteningWe constructed a gasket structure (Fig. 5a), aligning the curvature center axis with the geometric center axis, to investigate the self-tightening effect induced by evaporate-casting across a highly symmetric curvature gradient. Impressively, when five micro-fixators were placed between two thick stainless steel plates (Fig. 5b), the assembly could withstand nearly one ton of weight as exemplified by a car (weighing ~1200 kg) running over on the top (Fig. 5c). Throughout the compression process, the gasket structure remained unchanged (Supplementary Fig. 25), while distinct indentations appeared on the stainless steel plate (Fig. 5d), underscoring the superior strength of the gasket structure in comparison to stainless steel. By taking virtue from self-deformation behaviors induced by curvature gradient structures, we showed that various preset architectures could be accurately constructed, such as a blooming flower-like configuration (Supplementary Fig. 26a–c). Additionally, the macroscopic-scale self-tightening is demonstrated by the mortise and tenon structure. We employed asymmetric shrinkage to craft samples featuring mortise structures (Fig. 5e). For the tenon structure, we positioned the curvature center axis at the center of the mortise circle. This arrangement enabled the tenon structure to display an inward deformation tendency during the coupling process with evaporate-casting, ultimately achieving a macroscopic self-tightening effect. Upon examining the microscopic morphology of the joint, we observed slight deformation in the shoulder part of the mortise structure (Supplementary Fig. 26d), indicating the centripetal deformation inherent in the tenon structure. A tight juncture of the mortise and tenon structures revealed by the SEM investigation further confirmed the self-locking behavior (Fig. 5f, Supplementary Fig. 26e). Remarkably, a self-tightening mortise and tenon configuration, measuring merely 1 cubic millimeter in volume, demonstrated the capacity to lift a weight weighing 300,000 times its own mass (Fig. 5g, Supplementary Video 2). Its specific tensile strength reached up to 143 MPa cm3 g−1 (Fig. 5h, Supplementary Figs. 27 and 28), comparable to welded metals23,24, and far superior to various types of connectors including self-healing polymer25,26,27, and 3D printed structures28,29,30 (Supplementary Table 1). Energy utilization can also be calculated through the thermal transfer power during the material preparation process, and the mechanically interlocked structure exhibits values that are 1 to 4 orders of magnitude higher than those of the aforementioned contrast materials (the calculation of energy utilization is detailed in Supplementary Information). Concurrently, its substantial materials and size expandability, and adaptability serve to position it as a promising, innovative, and eco-friendly technology for structural connections (Supplementary Figs. 29 and 30).Fig. 5: Mechanical strength and demonstrations of cg-Gs after evaporate-casting.a Schematic and optical images of cuboid-shaped cg-G with circular void in the middle after evaporate-casting. Scale bar: 1 mm. b Optical images of five cuboid-shaped cg-Gs with circular void in the middle after evaporate-casting. Those cuboids are put on a stainless steel plate and sandwiched by two pieces of stainless steel plates without binder (thickness: 1 mm). c Optical images of a car upon the five graphene architectures sandwiched by two pieces of stainless steel plates and the enlarged image. d Five obvious pits impressed on steel plate after being run over by car. e Schematic and corresponding optical photos of cg-G blocks with mechanical interlocking structure. f Optical and SEM images of the clasped structure after evaporate-casting process. g Mechanical performance display of clasped structure. A single interlocking structure could pull up a laptop (~1.28 kg). h An Ashby diagram showing the energy utilization versus specific connection strength of graphene assemblies with mortise and tenon structure, as well as various 3D printing structures, self-healing polymers, and some typical welded same and dissimilar metals. Source data are provided as a source data file.The evaporate-casting of curvature gradient graphene superstructures presented herein allow for the controllable fabrication of graphene micro-architectures with diverse designed functional shapes and high mechanical strength. With the controllable design of uniform arc-shaped assembly of graphene nanosheets positioned at co-axial curvature centers, configurational force pointed to the center of curvature generated during dehydration. As a result, the assembly is tightened during the dehydration-based evaporate-casting process via capillary force, inducing local bending. Through precisely tuning the axis-center distance and tilt angle, we realized accurate control over the shape of obtained evaporate-casting structure. In addition, mortise and tenon structure is induced to this work and the internal stress can be leveraged to reinforce the formation, leading to a high-strength connection (~200 MPa), surpassing that of multiple materials with connection structures, and even welded metals. Compared with traditional welding technology, the proposed evaporate-casting processing can occur spontaneously at room temperature, greatly reduced the threshold and energy consumption of the combination reaction. The entire process is characterized by its high level of controllability, feasibility, cost-effectiveness, versatility, and environmentally friendly attributes.
Evaporate-casting of curvature gradient graphene superstructures for ultra-high strength structural materials
