The characterization of protein interactions has become essential in many fields of life science, especially drug discovery. Microscale thermophoresis (MST) is a powerful new method for the quantitative analysis of protein-protein interactions (PPIs) with low sample consumption. In addition, one of the major advantages of this technique is that no tedious purification step is necessary to access the protein of interest. Here, we describe a protocol using MST to determine the binding affinity of the PD-1/PD-L1 couple, which is involved in tumour escape processes, without purification of the target protein from cell lysates. The method requires the overexpression of fluorescent proteins in CHO-K1 cells and describes the optimal conditions for determining the dissociation constant. The protocol has a variety of potential applications in studying the interactions of these proteins with small molecules and demonstrates that MST is a valuable method for studying the PD-1/PD-L1 pathway. While the immune system attempts to neutralize malignant cells, some of the cells persist in a state of equilibrium between their elimination by the immune system and their proliferation. Indeed, tumour cells have developed immuno-evasion mechanisms that allow them to remain in equilibrium with the host by overexpressing immunoregulatory molecules such as PD-L1 and B7-12.The implications of the immune system for tumour control are well known3. Blocking the interaction between PD-1 and its ligand using an anti-PD-1 antibody enables restoration of this loss of immune function in cancers of the oropharynx4. Thus, some patients may benefit from a more targeted therapeutic approach that blocks the interaction of PD-1 with its ligands4. These observations have led to various clinical trials aiming to block the interaction between PD-1 and PD-L1 using the monoclonal antibodies anti-PD-1 or anti-PD-L1 in several types of cancers 5. Several therapeutic approaches that target the PD-1/PD-L1 blocking pathway are currently being developed.The tumour environment is highly immunosuppressive and locally regulates the anti-tumour response of T lymphocytes infiltrating the tumour. Generally, tumour-infiltrating T lymphocytes express PD-1, and tumour cells express PD-1 ligands (PD-L1 and/or PD-L2)6. A low level of PD-1 is sufficient to ensure the inhibitory role of T-cell activation. In the case of PD-1 deficiency, the administration of PD-L1 does not inhibit the activation of T cells. This lack of inhibition confirms that the inhibitory function of PD-L1 is tightly connected to its interaction with PD-17.PD-1 is a type I transmembrane glycoprotein composed of 288 amino acids. It belongs to the immunoglobulin superfamily, which also includes the CD28 and CTLA-4 molecules. PD-1 consists of an extracellular domain, a transmembrane domain and a cytoplasmic domain. The cytoplasmic domain possesses two tyrosines, one in the immunoreceptor tyrosine-based inhibitory motif (ITIM) and the other in the immunoreceptor tyrosine switch motif (ITSM), which are essential for the inhibitory role of the protein. PD-1 is expressed on the surface of CD4+ cells, CD8+ cells, NK cells, B cells, peripheral T cells, dendritic cells and monocytes8. PD-L1 is expressed on B and T lymphocytes, macrophages, mesenchymal cells and dendritic cells9. Unlike other members of this family, PD-L1 is also present on the surface of non-haematopoietic cells such as endothelial, cardiac, pulmonary, pancreatic, muscular and placental cells. The PD-L1 protein was discovered in 1999 as a new member of the B7 molecule family10 and was identified as the first known PD-1 ligand the following year11. PD-L1 and B7–1 both interact via their IgV-like domain11.The PD-1 protein interacts with two known ligands: programmed death ligand 1  and programmed death ligand 2 . The PD-L1 molecule is a type I transmembrane protein with 290 amino acids. It is encoded by the CD274 gene, which is found on chromosome 19 in mice and on chromosome 9 in humans. This protein consists of an extracellular domain, a transmembrane domain and an intracellular domain12. Nivolumab, an antibody targeting the PD-1/PD-L1 pathway, has also recently gained FDA approval based on its significant tumour response in clinical trials for the treatment of melanoma13.Various therapeutic approaches that target the blocking of the PD-1/PD-L1 axis are currently being developed. Blocking receptors on immune effector cells can help eliminate cancer, as described recently with regard to clinical trials evaluating ipilimumab, a blocking antibody of the CTLA-4 receptor, which was accepted as an anti-cancer treatment in 201114. Bristol-Myers Squibb has also recently shown that new PD-L1 inhibitors ((2-methyl-3-biphenylyl) methanol derivatives) under patent can bind to PD-L1 and dissociate the PD-1/PD-L1 complex at stoichiometric concentrations. However, these compounds induce the dimerization of hPD-L1 in solution15.Low-molecular-mass inhibitors have also been studied for their ability to modulate the PD-1/PD-L1 signalling pathway. These inhibitors are based on different types of molecules, such as macrocyclic peptides or oxadiazole derivativesd). Equilibrium binding assays were performed to determine the Kd between murine PD-1 and PD-L1 and yielded a 4 µM dissociation constant16. The cross-species protein interaction of murine PD-L1 and human PD-1 has also been reported in a few studies17. In 2007, the equilibrium binding responses between PD-1 and immobilized PD-L1 or PD-L2 were measured by SPR, and a 0.77 µM dissociation constant was obtained for the binding of PD-1/PD-L118. More recently, PD-1 ligands were once again characterized using SPR-based assays, and the results gave a Kd of 8 µM for the binding of hPD-1 to hPD-L1 and a Kd of 29 µM for the binding of mPD-1 to mPD-L119.The binding interactions of PD-1 with PD-L1 have been studied by surface plasmon resonance (SPR) and isothermal titration calorimetry (ITC) over the years, but these investigations led to controversy regarding the values of the dissociation constant  with low sample consumptionTo determine the best formulation for analysis of the interaction between a protein and its ligand, several lysis buffers and several buffers for the analysis of thermographs during thermophoresis were studied. The lysis buffer modulates the fluorescence of the labelled protein. As shown for the PD-1-eGFP protein lysis, the use of a buffer without detergents .CHO-K1 cells (ATCC® CCL-61) were cultured in Ham’s F-12 Nutrient Mixture  with 1% PS  and 10% FBS . Cell lines were cultured at 37 °C in a 5% COSeveral lysis buffers, including some containing detergents, were tested for their extraction efficiency , HEPES buffer , SSB buffer , and PBS-T buffer .Various buffer solutions were used to determine which ones led to the best stability and homogeneity within capillaries when processing microscale thermophoresis experiments: MST buffer  or a calibration curve . Different types of additives such as Tween 20, various MgCld constants between a protein and its ligand can be calculated using the saturation binding curve at equilibrium27. The fitting function is derived from the law of mass action:MST experiments were performed on a NanoTemper ® Monolith NT.115 with blue/red filters . Samples were prepared in the different buffers listed in the MST buffer section and loaded into standard/premium treated capillaries. Measurements were performed at 22 °C using 20% MST power with laser off/on times of 5 s and 30 s, respectively, and 60% MST power with laser off/on times of 5 s and 20 s. All experiments were repeated three times for each measurement. Data analyses were performed using the NanoTemper® analysis software. The K[LP]: Bound complex concentration[Ptot]: Total protein concentration[Ltot]: Total ligand concentrationKd: Dissociation constantA pcDNA3.1 plasmid containing an mPD-1-YFP fused protein was purchased from Life Technologies . The pcDNA3.1 Hygro plasmid was also purchased from Life Technologies. The plasmid was digested by two restriction enzymes, HindIII and EcoRI (New-England-Biolabs 2000), to allow the insertion of our mPD-1-YFP construct. The pVITRO eGFP plasmid was purchased from InvivoGen and was used for PCR amplification to obtain the eGFP amplicon. The plasmid containing hPD-L1-eGFP was purchased from GeneCopoeia (CS-GS402L-M10/pReceiver-M10). The plasmid containing the mutant variation of hPD-L1-eGFP was also purchased from GeneCopoeia (CS-GS406L-M10/pReceiver-M10). Both sequences are based on the crystal structure of the PD-1/PD-L1 complex (PDB code: 3BIK) and are described in Supplementary Information Thermo Scientific webtools were used to design two set of primers, which were purchased from Eurogentec for use in pcDNA 3.1 Hygro constructs. The first set of primers, which flanked the PD-1-linker-YFP gene sequence for insertion into the pcDNA 3.1 Hygro plasmid, was as follows: F: 5′-ATGTGGGTCCGGCAGGTA-3′ and R: 5′-TTATCTGAGTCCGGAGCGGTAC-3′. The second set of primers, which was used to switch the YFP with eGFP, was as follows: F: 5′-GTGAGCAAGGGCGAGGAG-3′ and R: TTACTTGTACAGCTCGTCCATGC  were used for the cloning of DNA fragments and the preparation of plasmids because they possess recA1 and endA1 gene mutations that increase the insert stability and the extracted DNA quality. The strains were stored at −80 °C. The pcDNA3.1 Hygro/PD-1-eGFP plasmid was transformed into the E. coli cells and then purified using the Mini Plasmid Prep Kit . The plasmid concentration was then quantified using a NanoDrop (ThermoFisher Scientific), and the concentration was adjusted to 2 µg/µL to simplify further cell transfection.Mix & Go competent CHO-K1 cells were transfected with the Cell Line Nucleofector® Kit T, Program U-023 and the pcDNA 3.1 Hygro plasmid expressing PD-1-eGFP. Two micrograms of plasmid was transfected into one million CHO-K1 cells suspended in 100 µL of Nucleofector solution. Cells were analysed by flow cytometry 48 h after Nucleofection®. Cells were then subjected to an appropriate selective pressure that allowed the growth only of cells containing the DNA insert. After three weeks of selective pressure, the multiparametric analysis of transfected CHO-K1 cells overexpressing mPD-1-eGFP allowed the definition of sub-populations that could be separated from the global population. The population of cells strongly expressing eGFP was analysed by flow cytometry and retained for microscale thermophoresis analysis  were treated when they reached 80% confluency in T75 flasks. The cells were washed with 5 mL of PBS and then trypsinized with 1.5 mL of trypsin to avoid using a cell scraper. After the cells were incubated for 5 min, 3.5 mL of complete culture medium as described in the cell culture section was added to the trypsinized cells. Cells were then centrifuged at 1200 rpm at 4 °C for 5 min. The supernatant was removed, and the cells were washed again with 5 mL of PBS and then centrifuged again at 4 °C for 5 min. Once the PBS supernatant was removed, cells overexpressing mPD-1-eGFP were suspended in 300 µL RIPA buffer. The cells were kept on ice to minimize local overheating. Protease inhibitor cocktail (1%) was also added to the mixture . The lysate was collected by centrifugation at 15,000 rpm at 4 °C for 45 min to remove large aggregates and cell debris. Strong centrifugation is recommended to reduce the background that can occur in an MST experiment. The lysate was divided into aliquots, which were stored at appropriate temperatures for further investigation. The overall schematic process of this protocol from cell culture to MST measurements is described in Supplementary Fig. MST was used to establish the binding affinity between PD-1-eGFP and PD-L1 . Cell lysate was diluted in PBS-T buffer (0.05% Tween 20) to a final concentration where the fluorescent signals of the GFP proteins were similar and above the typical detection limit of the Monolith NT.115 instrument (NanoTemper Technologies). The final concentration of cell lysate was kept constant at 35 nM. For the binding between mPD-1-eGFP and h/mPD-L1, 10 µL of the 54 µM PD-L1 solution was diluted 2:1 in 10 µL buffer to make a 16-sample dilution series extending to 61.7 nM. Another concentration range was prepared using a 1:1 dilution from 24 µM to 0.7 nM with the other parameters remaining the same. Ten microliters of cell lysate was added to 10 µL of each ligand solution.MST was used to establish the binding affinity between PD-L1-eGFP and PD-1 . Cell lysate was diluted in PBS-T buffer (0.05% Tween 20) to a final concentration where the fluorescent signals of the GFP proteins were similar and above the typical detection limit of the Monolith NT.115 instrument (NanoTemper Technologies). The final concentration of cell lysate was kept constant at 35 nM. For the binding between hPD-L1-eGFP with h/mPD-1, 10 µL of the 48 µM h/mPD-1 solution was diluted 1:1 in 10 µL buffer to make a 16-sample dilution series extending to 0.7 nM. Ten microliters of cell lysate was added to 10 µL of each ligand solution.Supplementary Information


A dynamic Ni2C reordering process, accompanied by slow carbon loss to subsurface regions, is proposed to increase the Ni2C 2D carbide long-range order via ripening toward coherent domains, and to increase the local supersaturation of near-surface dissolved carbon required for spontaneous graphene nucleation and growth. Upon transformation, the intensities of the surface carbide reflections and of specific powder-like diffraction rings vanish. The associated change of the specular X-ray reflectivity allows to quantify a single, fully surface-covering layer of graphene (2 ML C) without diffraction contributions of rotated domains. The simultaneous presence of top-fcc and bridge-top configurations of graphene explains the crystal truncation rod data of the graphene-covered surface. Structure determination of the |4772| precursor surface-carbide using density functional theory is in perfect agreement with the experimentally derived X-ray structure factors.Surface X-ray Diffraction was used to study the transformation of a carbon-supersaturated carbidic precursor toward a complete single layer of graphene in the temperature region below 703 K without carbon supply from the gas phase. The excess carbon beyond the 0.45  monolayers of C atoms within a single Ni CVD of graphene has, thus, been studied extensively on a variety of metal substrates4. Some of these metals exhibit a rather poor solubility of carbon in the bulk, whereas others – such as the Ni(111) substrate used in this work – dissolve carbon quite well in the surface near bulk regions already at temperatures above 673 K. Poor solubility favours a surface-limited growth mechanism, proceeding via continuous decomposition of different gaseous carbon feedstocks. In contrast, substantial antisegregation of carbon into the metal near-surface and bulk regions at elevated temperatures allows for subsequent (sub)monolayer re-segregation of graphene5 or even multilayer re-precipitation of graphitic carbon6 upon cooling, depending on the experimentally provided degree of carbon supersaturation of the Ni bulk.Controlled chemical vapour deposition (CVD) of well-defined, highly ordered large-area graphene layers is mandatory for a variety of potential technological applications, et al. in a comprehensive review on graphene-nickel interfaces7. The temperature-dependent growth mechanisms of graphene by chemical vapor deposition under UHV conditions by exposure to ethylene (10−8 to 10−6 mbar) are reviewed and the thermal stability of graphene and the surface-confined Ni2C nickel carbide are compared. At least three different growth regimes are distinguished:On Ni(111), both cases have been verified, as discussed by Dahal 2C surface carbide phase forms rapidly at the surface. The ambiguous role of Ni2C, serving on the one hand as a carbon reservoir for subsequent graphene growth and, on the other hand, as a kinetic obstacle suppressing the nucleation of the more carbon dense graphene8 is pointed out. The role of intermediate Ni2C on the way to graphene as a potential kinetic barrier is assigned to its reduced ability to dehydrogenate ethylene and because surface-confined Ni2C is a carbon-dilute (0.45 ML C) low energy line phase in the Ni–C surface-phase diagram. Therefore, it is believed to exhibit a considerable kinetic barrier of rearrangement toward graphene, since large carbon and Ni density fluctuations are required to achieve the local C-coverage of 2 ML required for graphene nucleation. As a consequence put forward in our present study, nucleation of graphene is likely to become easier once additional carbon supersaturation of the surface-near regions below the 2D Ni2C layer is provided.(1) Below 770 K, the Ni9, a carbon-denuded transition zone between the initially formed metastable Ni2C domains and the advancing graphene front was observed, highlighting the complex function of subsurface carbon during the transition from Ni2C toward the final product monolayer graphene.(2) Between 770 and 920 K no stable surface carbide is formed and graphene grows on the apparently pure Ni(111) surface. In LEEM studies of the same group7.(3) Between 920 and 1070 K the high mobility of C atoms in the Ni bulk renders it hard to establish a sufficient C-supersaturation of the near-surface regions, which is both mandatory for graphene nucleation and growth and for thermodynamic stabilization of already formed graphene domains. In UHV this was so far only achieved on up to 300 nm thick Ni-films, which can be more easily presaturated with carbon as compared to a bulk single crystal, at temperatures up to 1070 Ket al.10 suggest that, according to the Brønsted–Evans–Polanyi (BEP) relation, the activation energy for non-epitaxial graphene nucleation should be larger than for the much more stabilized epitaxial graphene, in order to explain the increasing contribution of rotated domains at higher temperatures at and above 813 K. Using LEEM, they show that perfectly epitaxial and unrotated graphene islands nucleate and grow via decomposition of the Ni2C surface carbide at about 673 K, which is fully in line with the results of our present study (see results and discussion section 3.). This is in contrast to a mixture of epitaxial and non-epitaxial graphene domains growing on Ni(111) with an initially partial Ni2C coverage, which becomes continuously replaced by graphene at 810 K. With respect to the role of near-surface dissolved carbon, they show that switching off the carbon gas phase supply does not immediately halt the ongoing graphene growth. As shown in11, the presence of a highly localized carbon-rich near-surface reservoir is suggested to explain the ongoing graphene formation, which proceeds in absence of the immediately decaying Ni2C surface carbide layer at ~810 K.As a general trend, an increasing fraction of rotated graphene domains was observed with increasing growth temperature. Yang et al. for the temperature region below ~770 K, based on complementary in-situ XPS and STM measurements12. These authors discuss a temperature-dependent graphene growth mechanism in ethylene, switching from an in-plane single layer conversion  or two layer carbide conversion below ~773 K to a direct Ni(111)-mediated conversion mechanism without intermediate carbide above 773 K. Again, at T < 773 K only epitaxial unrotated graphene directly attached to bulk Ni(111) was observed after conversion, whereas both rotated and unrotated graphene domains were observed above 773 K.To account for the complex situation of a growth mechanism with simultaneous carbon gas phase deposition and resegregation of carbon from the bulk, a “combined” mechanism was proposed by Patera 7 suggest that at least two of the possible high-symmetry graphene binding states on Ni(111), namely the top-fcc and top-hcp Ni binding configurations, are energetically almost degenerate, so that both configurations are likely to occur and to give rise to a large contribution of domain boundaries upon completion of the full graphene layer . In order to reduce the nucleation density, to modulate the kinetic barrier between Ni2C and graphene, and to modulate the solubility/supersaturation of carbon in the near-surface regions, Weatherup et al. successfully introduced Au doping of Ni surfaces to achieve deliberate kinetic control of graphene growth with respect to thickness, attainable coverage, optimized epitaxy, domain size, domain orientation etc.14.As a practical consequence of the above-mentioned salient features of temperature-dependent graphene growth on pure Ni surfaces, low growth temperatures (<773 K) are in principle desirable, mainly to avoid rotated graphene domains and to trigger optimized epitaxy. On the other hand, a lowering of the temperature will enhance the nucleation density and thus reduce the average domain size, so that a large amount of small domains with a large contributions of domain boundaries must result. DFT results reviewed in ref.et al.15, which was achieved by C-supersaturation with the highly carburizing CVD agent toluene at ~923 K. Upon cooling of this highly carbon-enriched state of the near-surface regions, a large contribution of metastable structures, the most prominent being a layered Ni(111)-Ni2C-rotated graphene structure, was observed, likely because of fast and rich carbon segregation. The given interpretation of the role of the Ni2C surface carbide as a source of graphene grain rotation was later questioned, and for the cooling process a post-segregation of “interlayer” Ni2C domains beneath already rotated grown graphene domains on Ni(111) - which exhibit intrinsically weaker net binding to the substrate as compared to the epitaxial domains - was proposed as an alternative explanation12.The other extreme of the “carbon supersaturation scale” of Ni(111) is represented by a study of Jacobson 3C or other carbidic Ni-C phases has been deduced so far - e.g. from diffraction experiments, which also holds for our present study - the above-reviewed Ni(111) surface science studies and also our present work suggest the formation of a more or less carbon-rich “quasi-3D” Ni-C subsurface reservoir as a necessary precondition for graphene growth. In this context, an amorphous carbidic NixCy precursor in between the energetically most stable hexagonal Ni3C bulk carbide polymorph and graphene has been postulated recently on the basis of quantum chemical molecular dynamics (QM/MD) simulations of graphene formation16, which would be necessarily invisible in diffraction measurements. Nevertheless, the critical role of local carbon supersaturation within this amorphous precursor for the ongoing graphene nucleation and growth was highlighted.Despite the fact that on Ni(111) no direct evidence for 3D-crystalline carbidic graphene precursors such as Niin situ surface X-ray diffraction provides a look at both the supersaturated carbidic precursor and the resulting graphene-covered Ni(111) surfaces at long-range ordering, thus complementing the local microscopic measurements of the Ni2C carbide and graphene structures presented in previous STM works. Moreover, we aimed at an unambiguous experimental clarification of the suspected Ni(111)-Ni2C coincidence cells denoted either as |2772| or |4772|, which is still lacking from the so far known details of LEED and STM-FFT data (see ref.17 and literature therein). Also, subtle, but potentially graphene-growth-relevant, changes of the Ni2C carbide superstructure with increasing ethylene exposure at T~673 K, being necessarily accompanied by increasing supersaturation of the Ni(111) near-surface regions with dissolved C, were anticipated. Moreover, the SXRD data of intermediate stages between the supersaturated carbidic precursor and the final graphene-covered Ni(111) surface were expected to reveal if rotated graphene domains and/or layered Ni2C-(un)rotated graphene regions are measurably abundant below 773 K. Regarding the choice of the ethylene CVD temperature, we aimed to revisit the complex structural scenario just “at the edge of graphene growth” at and above 673 K in the 10−6 mbar pressure range, as chosen previously by Patera et al.12. Under these conditions, a complete Ni2C layer is still stabilized in presence of the ethylene gas phase, but it can already convert quasi “by chance” (i.e. via stochastic graphene nucleation) to a full monolayer of epitaxial graphene, as postulated in ref.7.The central aim of this study is, thus, to revisit and clarify the issue of a coexistence of near-surface dissolved and carbidic Ni-C species in a sufficiently C-supersaturated scenario to induce graphene growth. Our approach using 18 using an X-ray energy of 18.0 keV. A polished single Ni(111) crystal was mounted in a dedicated UHV setup, which is connected to a 6-circle diffractometer. This sample chamber enables cleaning of the surface by sputter-anneal cycles, involving heating in 5 × 10−7 mbar O2 and final desorption of oxygen, exposure to ethylene and analysis of the surface composition by Auger Electron Spectroscopy (AES). The temperature was measured with a thermocouple directly spot-welded to the side wall of the disk-shaped sample, which leads to an estimated off-set of at maximum 10 K. The gas pressure was measured with a state-of-the art calibrated ionization gauge using the gas-specific sensitivity factors provided by the manufacturer. According to the specifications, the error at a pressure of 1*10−6 mbar is around 5%.The surface X-ray diffraction experiments were performed at beamline ID03 of the European Synchrotron Radiation Facility (ESRF), France19. Structural models were refined against the experimental structure factors using the program ROD20.X-ray scattering from surfaces gives rise to crystal truncation rods (CTRs) and surface rods (SRs), where the former include a contribution from the bulk and the latter arise solely from the topmost atomic layer, which can have different periodicity and symmetry than the bulk underneath. Integrated diffraction intensities were obtained in the so-called stationary mode and converted to structure factors F in a standard way2C surface-carbide covered, strongly C-supersaturated Ni2C covered, and eventually graphene-covered surfaces, namely: 7.5 L ethylene deposited on the quasi-clean Ni(111) crystal at 573 K, resulting in a single layer Ni2C superstructure with ~0.45 ML carbon coverage, 379 L ethylene at 673 K, 1353 L ethylene at 723 K, and eventually 6316 L ethylene, first at 773 K for 1 h (corresponding to 5402 L) and then at 673 K for 10 minutes in 2 × 10−6 mbar ethylene (further 914 L). The latter preparation yielded the metastable “carbon-supersaturated carbidic precursor state” and spontaneously converted to a full (2 ML carbon) graphene coverage by slight thermal annealing to 703 K.Several sample preparation conditions were chosen, resulting in quasi-clean, purely Ni2C.We use the term “quasi-clean” here to emphasize the fact that it is practically impossible to obtain truly clean Ni surfaces, because the bulk of the material contains a virtually infinite amount of carbon which can segregate to the surface. The quasi-clean state reported here refers to a Ni(111) surface prepared in such a way that the carbon content is considerably below the saturation level to start forming graphene or Ni22, using PAW potentials23, the PBE exchange-correlation functional24 and a cutoff energy of 400 eV. The surface carbides were modelled by a single carbide layer supported on three Ni layers. The structures were relaxed until the residual forces were smaller than 0.02 eV/A, with the two lowest Ni layers fixed during the relaxation. A 2 × 2 × 1 k-point mesh was employed for the integration of the Brillouin zone. For the calculation of the surface energies, Ni atoms are referenced to bulk Ni and C to graphite, respectively.The calculations were performed using the VASP code25, which can be modelled by ‘missing’ electron density and the value obtained for the occupancy here would correspond to a root-mean-square (rms) roughness less than 0.5 Å, i.e. to a very smooth surface. If the refined value for the occupancy would be interpreted as resulting from residual carbon, one can calculate the carbon concentration from the difference in atomic scattering factors between Ni (Z = 28) and C (z = 6) to be about 6%. The AES spectrum of the quasi-clean state  data between different preparations, we also include the results concerning the quasi-clean surface. Figure see Fig.  does not2C surface carbide diffraction pattern, which is relatively complex and composed of many spots. In literature, several unit cells and domain structures, based on coincidence lattices with the Ni(111), have been proposed. The dominant structural motif consists of a nearly square ~0.5 nm2 mesh, which is built up from 2 carbon atoms, arranged in a centered way at the corners and the middle of the unit cell, whereby the central carbon atom is surrounded by 4 Ni atoms. The Ni atoms have the freedom to rotate around their central C atom, thereby making up a so-called clock-reconstructed network. In fact, as early as 196926, it was found by LEED that the actual carbide superstructure unit cell is larger than the dominant nearly-square top layer lattice, due to the occurrence of weak spots close to the main reflections and spots at relatively low scattering angles near the direct beam. At that time, a |2772| coincidence cell was proposed and later the larger |4772| superstructure cell was postulated17. Because of the P3m1 symmetry of the underlying Ni(111) surface, such a larger cell of lower symmetry fits in different ways on the substrate. Due to the 6 symmetry operations valid in this planar space group27, 6 co-existing carbide domains appear on the Ni(111) surface. The diffraction pattern shown in Fig. 2C structural motif and the weaker spots  and the 6316 L supersaturation experiment yield a typical NiFigure 2 of the within the carbide layer, the |4772| yields a smaller mismatch to the metallic Ni layer below, thus facilitating the formation of additional bonds. In addition, we find a strong buckling of both the Ni and the C atoms in the carbide layer: In the case of the |4772| surface the Ni atoms in the Ni2C layer are buckled for 0.16 Å, slightly smaller than the value of 0.20 Å for the the |2772| surface. The buckling is more pronounced for the C atoms, with values of 0.65 Å (|4772|) and 0.99 Å (|2772|). The binding of the surface carbide to the metallic Ni layer below also induces a buckling in this layer, with a comparable value of 0.29 and 0.32 Å for the |4772| and |2772|) interface, respectively.This trend is confirmed by the DFT calculations, which also predict a slightly higher stability of about 6 meV/Å2C reflections, data from two preparations of the Ni2C top layer were combined: 7.5 L at 573 K and the supersaturated precursor (6316 L at 773/673 K). This assured a data set large enough to fit all the features of the 2D top layer structure simultaneously and with strongly enhanced accuracy. The diffraction indices  are related to the |4772| unit cell. As a starting point, we have used the results from the DFT calculations and refined this model further. The respective model is shown in Fig. In a next step, the CTRs and surface rods (SRs) are analyzed and compared with the DFT model of the |4772| cell, see Fig. 2C slab to the substrate and the rumpling between the C and Ni layer as well as the rotation angle of the clock-reconstructed motif. The average distance between the carbon and nickel atoms in the Ni2C layer is about the same as obtained from DFT and the average rumpling appears to be 0.1(4) Å smaller. Due to the relatively large error and the enhanced Debye-Waller parameters of around 0.4 Å2, it is concluded that the differences between the DFT and SXRD results are hardly significant and that the proposed structural model has excellent agreement. Table Special care needs to be taken concerning the symmetry of the domain structure when using both the CTR and SR data at once in the refinement. We have measured SRs from one domain only. At the same time, different domains contribute to the CTRs. The refinement was performed by assuming an equal coverage for each of the domains and by transformations based on the symmetry of the Ni(111) surface as described above. A few fit parameters have been further refined, such as the distance of the whole Ni28, the so-called top-fcc and bridge-top configurations, as shown in Fig. 28. The other four stacking possibilities would result in much larger distances, which disagree with the value obtained by SXRD. Due to the perfect epitaxy of the domains with the Ni(111) surface, the graphene scattering contributes exactly to all the CTRs of the substrate; reciprocal space maps did not reveal any signs of abundant randomly rotated graphene domains, which would show up as powderlike diffraction rings, nor of any graphene surface rods. Interestingly, the interference between the scattering contributions of the two co-existing domains leads to almost complete extinction for diffraction with non-zero in-plane momentum transfer, i.e. for all rods except the specular. By calculating the structure factor of the graphene scattering, under the assumptions that the two domains both cover 50% of the surface and that the height above the Ni surface of all the 4 carbon atoms is identical, one obtains: zG the height of the graphene layer above the substrate, fC the atomic scattering factor of carbon. The total structure factor, which is used to fit to the experimental data, is calculated as: Fbulk(hkL) representing the CTR of the Ni(111) surface. The mutual destructive interference of the graphene domains results in a very small contribution to the  rod and even no contribution to the  rod. In contrast, the scattering contribution to the  specular rod can be as high as 2fC, which occurs in the minimum at L = 1.4 along the specular rod, resulting in nearly complete destructive interference. Figure 29 might be a candidate to explain this observation. For the in-plane direction it is probably related to the domain wall density, but because the scattering contribution is already very low, refinement of Here, we describe the structure of the fully surface-covering graphene layer obtained after thermal annealing of the metastable supersaturated precursor state at 703 K. Due to the near-perfect lattice match between graphene a = 0.2456 nm) and the Ni111) surface (a = 0.2489 nm), the former grows in a perfectly epitaxial fashion on the substrate. Because graphene has two atoms in the unit cell and Ni(111) has one atom per surface cell, there exist in principle six different atomic stacking possibilities. Previously, two of these stacking possibilities have been identified to co-exist for energetic stability reasons6 nm and 11 surfac−6 mbar ethylene (5400 L) to obtain “deep” saturation with bulk/ near surface dissolved carbon. After decreasing the temperature to 673 K, additional ~10 minutes of exposure to ethylene followed, resulting in a total exposure of 6316 L and inducing a fully surface-covering Ni2C layer. The Auger spectrum after this preparation and pumping off is shown in Fig. 30. At the same time, the SXRD pattern  surface in its fully carbon-saturated state prior to the nucleation/growth of graphene, and, in due course, to follow the temperature-induced transformation of the deeply “carbidized” surface toward graphene in the absence of external gas phase supply of carbon (i.e. under good UHV conditions). For this purpose, the sample was exposed for 1 h at 773 K to 2 × 102C intensity disappeared completely. The corresponding AES spectrum, shown in Fig. After heating for about 2000 s, the Ni7. By slight heating to 703 K under UHV, this “stochastic” process was deliberately induced, as the gas phase stabilization of the top Ni2C layer is switched off and the supersaturated carbidic precursor is at the same time thermally destabilized. (2) In a LEEM study of the same group9, a carbon-denuded transition zone between the initially formed metastable Ni2C domains and the advancing graphene front was observed at 823 K, but not at 773 K. This leads to a characteristic time-dependence of the Ni2C decay and the subsequent graphene growth process. At around 873 K, immediate decay of the surface carbide is followed by a delayed growth process of the graphene layer (within minutes). In contrast, at 773 K the time-divergence of these processes is much smaller, and an apparently simultaneous carbide-decay/graphene growth process is observed, corresponding rather to the „interfacial“ carbide-graphene conversion/growth picture drawn in the work of Patera et al.12. Our measurement does not allow to resolve the time evolution of the graphene top layer, but the analysis of the specular  rod directly after the 2500 s thermal annealing experiment of Fig. 9. The conclusion is that our 703 K annealing experiment is still dominated by, or at least not far off the „direct conversion mechanism“ put forward in12.This result is interpreted in the context of two previous studies: (1) 673 K ethylene-exposed surfaces can be converted quasi “by chance” (i.e. via stochastic graphene nucleation) to a full monolayer of epitaxial graphene, as discussed in ref.2C |4772| superstructure nor to the integral order spots of the Ni(111) substrate. The corresponding diffraction intensities are highlighted in Fig. 2C |4772| superstructure relative to the ring-like diffraction intensities. We note that their intensity contribution cannot be masked to 100% using this approach. By comparing the d-spacings of the rings to those of the Ni2C spots within the area, especially the intensities below ~2.0 Å are affected by the Ni2C point reflections within the bar. We further note that the optically enhanced b/w contrast in panel (a) provides no direct measure of the real detector intensities plotted in (b).The conversion process from the supersaturated carbidic precursor state toward graphene is accompanied by another interesting effect, namely the decrease in intensity of certain ring-like diffraction features, as will be discussed in more detail in section 5. These features can neither be assigned to the discrete diffraction spots of the Ni2C surface carbide as the initial stage to bulk carbide formation. However, the related intensities appear to be partly developed already after the lowest exposure of 7.5 L, as will be shown in section 5, which might unfavour such a 3D nucleation of bulk carbide phases scenario. In any case, sufficiently flat 3D or 2D surface-covering structures with a certain abundance must be responsible for the ring-like features. The most prominent candidate structure would be Ni3C, because this is the only stable carbide found in the phase diagram. However, the observed d-spacings do not fit to the hexagonal Ni3C phase31. In addition, from the conditions under which we observe the new phase (supersaturated by ethylene exposure) one would expect that the carbon content should be higher than in Ni2C, which would rule out Ni3C from a compositional point of view. A comprehensive theoretical study on metastable nickel-carbides includes a phase stability investigation32, which shows that compounds containing more carbon than Ni2C are drastically less stable. These considerations, together with the experimental fact that the surface carbide’s composition is Ni2C, leads to the assumption that the presently discussed carbide also has a composition close to that. The pronounced structural motif of the surface carbide, the mesh, is assumed to also be present in such a bulk Ni2C phase. Gibson et al.32 have also investigated many different prototype structures for different metastable bulk phases in the Ni-C system by DFT. For Ni2C, the lowest energy structures are found for a rutile  and an orthorhombic (Fe2C-like) type. The projection along the shortest axis of both these structures shows an atomic arrangement which resembles the structural motif of the mesh here, see Fig. hk0, with the coordinate system used by us.Based on these experimental results, we will now postulate a possible crystal structure for this hitherto unobserved and apparently metastable nickel-carbide phase. Since the experimental data are rather limited, we will have to confine our discussion to certain features that should exist in the crystal structure, rather than completely solving it. In analogy to surface oxide formation, i.e. a single 2D oxide monolayer forming during metal oxidation under certain non-ambient conditions, it seems reasonable to view the NiFor the structures discussed here, the strongest reflection hk0 can be used to tentatively index the observed reflections, as shown in Table These reflections can be used to calculate the in-plane lattice parameters of the structure as a = 4.8(1) Å, b = 4.4(1) Å and γ = 92(3)°. Although the angle γ is nearly identical, the side lengths are considerably smaller than the average size of the mesh in the |4772| cell, which are a = 5.08 Å and b = 4.85 Å. This difference in cell parameters can easily be understood by considering that in the proposed bulk structures the Ni and C atoms are not in the same plane; by displacing the C atoms along the c-axis out of the ground plane and keeping the Ni-C bond length constant, the a and b axes will become smaller. Even in the case of a nearly planar 2D structure, such as the surface carbide, the mesh cell parameters can easily be adjusted through rotation of the 4 Ni atoms around the central carbon. This structural geometry feature allows accommodating strain, without changing the Ni-C bond lengths too much, over a relatively large range. The side lengths of an ideal square mesh scale with ~cos(φ) and by changing it from 20 to about 30 degrees, the side lengths change by about 10%. This strain-relieving mechanism plays an important role in the structure formation of the surface carbide and allows to build a nearly strain-free large coincidence cell.As mentioned above, the maps obtained by us only give a 2D, projected view of the crystal structure. Details of the structure along the surface normal are contained in Bragg reflections which have not been observed by us, possibly because of the high scattering angles at which these appear. Most likely the structure is heavily textured having its preferred orientation along the substrate’s surface normal, which complicates the detection of out-of-plane diffraction spots even more.2C surface carbide structure, especially under the highly C-supersaturated conditions used in this work. Possible hints for the coexistence of quasi 3D or bulk-like carbide species and the single-layer Ni2C surface carbide can also be extracted from Ni(111)-based XPS literature data showing an additional C1s component at ≤283.0 eV binding energy, well below the value of 2D Ni2C surface carbide (~283.3 eV)33. The assignment of such low BE components to metastable bulk carbidic phases has been made in Lit.34.As SXRD does not allow for identifying the corresponding real-space structures unambiguously on a tentative model basis, it will be necessary to deliberately look with STM for minority structures within the long-range ordered 2D NiEventually, Figs 2C top layer, which is, around 673 K, just at the edge of decay and thermodynamically only stabilized due to the permanent presence of the 2 × 10−6 mbar ethylene gas phase. In order to explain the increasing long-range ordering, a continuous structural reformation process is suggested, which is necessarily accompanied by ongoing slow carbon loss to subsurface regions, further C supersaturation of near-surface bulk regions and simultaneous structural “ripening” of coherent |4772| domains within the carbide top layer. Also, the nucleation of bulk-like Ni2C domains, giving rise to the diffraction-ring-like features discussed in results and discussion section 4., can be rationalised on this basis. Upon thermal annealing of the supersaturated carbidic precursor in vacuo at 703 K, quantitative loss of all |4772| related point reflections is observed  is observed upon isothermal annealing of the supersaturated carbidic precursor in vacuo at 703 K  precursor state in absence of external carbon supply from the gas phase.A fully surface-covering epitaxial graphene overlayer was formed by thermal decomposition of a carbon-supersaturated/Ni2C surface carbide. DFT calculations of the |4772| structure are in perfect agreement with the SXRD data and show essentially a clock-reconstructed network whereby the carbon atoms are slightly closer to the underlying substrate, of which the last layer of Ni atoms show minor in-plane relaxations.Both the precursor state, the transition process and the resulting fully graphene-covered Ni(111) surface were characterized by surface X-ray diffraction (SXRD). The most prominent, fingerprint-like, signature for the different surface structures is seen in the corresponding specular rod. The X-ray data allow to unambiguously identify the |4772| coincidence cell as the correct one for the Ni2C surface carbide decomposition process without external C supply at 703 K. As described in earlier work7, this low temperature growth mode does not lead to a mixture of epitaxial and rotated  graphene domains. The CTR data indicate the simultaneous presence of 2 high-symmetry configurations of graphene domains, namely top-fcc and bridge-top. The strong modulation of the  specular rod nevertheless allows for a clear assignment of the resulting 2 ML graphene layer.The perfectly epitaxial graphene layer nucleates and grows via a combined C-antisegregation/ NiSupplementary Information


Despite the unique occurrences of structural defects in graphene synthesis, the fracture mechanism of a defective graphene sheet has not been fully understood due to the complexities of the defects. In this study, the fracture mechanism of the monolayer graphene with four common types of defects  were investigated systematically for mechanical loading along armchair and zigzag directions, by using the finite element method. The results demonstrated that all four types of defects could cause significant fracture strength loss in graphene sheet compared with the pristine one. In addition, the results revealed that the stress concentration occurred at the carbon–carbon bonds along the same direction as the displacement loading due to the deficiency or twist of carbon–carbon bonds, resulting in the breaking of the initial crack point in the graphene sheet. The fracture of the graphene sheet was developed following the direction of the breaking of carbon–carbon bonds, which was opposite to that of the displacement loading. Graphene has attracted extensive interests in recent years since its experimental discovery in 2004 . Its twoComputational simulation is a powerful tool and has been widely used in the study of the fracture behaviors of graphene sheets due to the difficulties of precise defect control during the experimental measurements. For example, Zhang et al.  revealedAs mentioned above, many efforts have been made to investigate the fracture of the defective graphene sheets, however, a comprehensive and comparative study of mechanical properties contributed from all the typical defects have not been systematically studied, especially the process of the dynamic fracture of graphene sheet. In this study, the FE model based on molecular structural mechanics was established with the geometric nonlinear effects taken into account, to study the mechanical properties and dynamic fracture of graphene sheet with four different types of defect (single vacancy (SV) defect, divacancy (DV) defect, SW defect and line vacancy (LV) defect). This numerical study revealed the fracture mechanism of these four types of defective graphene sheets, which could serve as a benchmark to search for an effective way for inhibiting the fracture of the graphene sheets.rc, the interatomic force would drop rapidly to zero, and the bond was regarded as broken. The interaction range of carbon atoms was confined within a distance rc = 0.17 nm to avoid unphysical spurious bond forces [c and critical stress σc were 0.197 and 1501 Gpa, respectively. The C–C bond broke when it reached the critical stress σc. The material constitutive relation of beam (Equation (1)) was coded as VUMAT subroutine in ABAQUS/Explicit.In order to simulate the fracture of graphene, an equivalent model of graphene must be established. The large deformation and nonlinear geometric effects shall not be ignored in the fracture analysis process. Considering the realistic distributions of thickness and equilibrium length of the C–C bonds, the covalent bond could be equated to nonlinear Timoshenko beams in this study, as presented by the linear planar beam elements Beam 21) in Abaqus 6.10. The constants of the beam elements were computed and listed in  in Abaqud forces :(1)σ=202D FE models were constructed by Beam21 (shear) and Mass elements in ABAQUS. In the model of graphene, a carbon atom was represented by a node at either end of the beam element, while the beam reflected the reaction between nodes. The dynamic fracture process would be shown by the following breaking of C–C bonds.xl) × 12.6470 nm (yl). It contained 6180 carbon atoms (nodes) and 9159 bonds (elements). To obtain the mechanical properties and dynamic fracture of the graphene model, uniform normal loadings of displacement were applied to nodes on one edge, as shown in Δl/(l·t) = 9.84 × 10–4 fs–1 with a loading time of 18 ps. Along AC direction (l = yl = 12.6470 nm), the displacement loading Δl on the both ends of the model was 1.1200 nm. At the ZZ direction (l = xl = 12.5520 nm), the displacement loading Δl was 1.1116 nm. f) and fracture strain (εf) along the AC and ZZ directions were 104.1 GPa, 122.8 GPa and 0.149, 0.164, respectively. Both of the curves fell within the previous simulation study [f: 90–125 GPa (AC direction), 110–125 GPa (ZZ direction) and εf: 0.14–0.21 GPa (AC direction), 0.14–0.24 GPa (ZZ direction). The Young’s modulus E and Poisson’s ratios μ of the pristine graphene sheet could be calculated as follow:m is number of loading points (120 for AC direction and 103 for ZZ direction), Fp is the force of the single loading point and t is the thickness of the model (0.334 nm). The obtained Young’s modulus and Poisson’s ratios of the pristine graphene sheet also corresponded closely to the experimental values  in the graphene sheet, as shown in c = 1501 GPa, resulting in the crack propagation instantly. As could be seen in these figures, the propagation of the crack presented was radically symmetrical due to the geometric symmetry of the model. The occurrence of the branches was observed during the propagation of crack, which agreed with the previous studies by Omeltchenko [The dynamic fracture and propagation in graphene by FE analysis with the four different types of defects under loading stress along AC and ZZ directions are shown in ltchenko  and Zhanltchenko . From alIt was obvious that the deficiency of the C–C bonds occurred in the SV defect, DV defect and LV defect. When applying loading stress along the AC direction as shown in Under the loading stress along the ZZ direction (as shown in In order to give a comprehensive and comparison studies of mechanical properties of all the typical defects, the fracture strength of graphene with those four defects has been studied. The stress–strain curves of these defective graphene under loading were calculated along both the AC and ZZ directions, as shown in It was found that SW defect had very little impact on the fracture strength of graphene under the loading along AC direction. The fracture stress of graphene sheet with SW defect was 103.7 GPa, which was only 0.3% less than that of the defect-free graphene sheet. Because the Bond A did not miss in this case, no stress concentration occurred on the defective area along the AC loading direction. The initial crack point of the SW defect was not at the defect site but the corners of the graphene sheet. This also could be used to explain that why the fracture stress in SW defect caused by AC loading was similar to that in the pristine graphene.In addition, the fracture stress of graphene with SV defect and DV defect were almost identical, 80.0 GPa and 79.6 GPa, which were decreased by 23.2% and 23.5%, respectively. As shown in However, under the loading along ZZ direction, as shown in In this study, the molecular structural mechanics based finite element models of monolayer graphene with SV defect, DV defect, SW defect and LV defect were developed to study the fracture strength and dynamic fracture, thus revealing the mechanism of fracture failure of the defective graphene. The numerical simulation results demonstrated that the missing and rotation of the C–C bonds may lead to a stress concentration at the defective area along the same direction as the displacement loading, resulting in the breaking of the covalent C–C bonds, and generating the initial crack points. The crack propagated along the crack of the C–C bonds and caused the fracture of the graphene sheet. The breaking of the C–C bonds by the stress concentration significantly reduced the fracture strength of the graphene. The LV defect had the largest effect on the fracture strength of graphene under loading along the AC direction which the DV defect presented the largest effect along the ZZ direction.Overall, the fracture of defective graphene would be attributed to the stress concentration caused by the breaking of C–C bonds and the initial crack point at the defective site along the displacement loading direction. An effective solution to control the fracture is to decrease the stress concentration in the defective area, for example, layer stack to stagger the defective area. Zhi-Min Liao et al.  found th


Some significant advancements have been achieved with the continuous research, such as the corresponding photocatalytic mechanism that has been revealed. Specific influencing factors have been discovered and potential optimizing methods are proposed. The latest developments in graphene assisted TiO2 composite photocatalysts are abstracted and discussed. Based on the primary reasons behind the observed phenomena of these composite photocatalysts, probable development directions and further optimizing strategies are presented. Moreover, several novel detective technologies—beyond the decomposition test—which can be used to judge the photocatalytic performances of the resulting photocatalysts are listed and analyzed. Although some objectives have been achieved, new challenges still exist and hinder the widespread application of graphene-TiO2 composite photocatalysts, which deserves further study.Graphene modified TiO T. T2 unde of TiO2 c. If thelimited) ,120. The, ~2 eV) . Consequan 2 eV) . MoreovemW·cm−2) . Based obe found ,54,122.2, including photoluminescence (PL) spectrum , Electron paramagnetic resonance (EPR) spectroscopy , and Scanning tunneling microscope (STM) .Besides pollutant decomposition experiments, X-ray diffraction (XRD), Scanning electron microscope (SEM), Atomic force microscope (AFM), X-ray photoelectron spectroscopy (XPS), Fourier transform infrared spectroscopy (FTIR) and Raman spectra, some novel characterization technologies can be used to judge the photocatalytic performance of the graphene modified TiO2 . M. M2 , achieving the π-d electron coupling and the following electron transport [Two types of defects can be classified in the RGO, including structure defects and additional functional groups. The former is introduced during the violent redox and exfoliation procedure, such as edge, carbon vacancy and pentagon (heptagon) structure. The latter, including hydroxyl, carboxyl and epoxide groups, is resulted from the strong oxidant to intercalate laminar graphite structure and the total amount is controllable by adjusting the reduction time . Both thradicals ,153. Thelifetime . Similarachieved . With thransport ,54. Therransport . Insuffi2 must be achieved by other ways. Our group found that the surface defects of the 3DGNs play as the bridge and the 3DGNs with moderate defects assisted composite photocatalysts displays the highest performances. On one hand, surface defects of the 3DGNs exert a negative influence to shorten the electron lifetime , simultaneously. Therefore, the 3DGNs with a moderate defect density can realize the balance and endow the best performance for the resulting photocatalysts. Because only the surface defect is useful, the thickness of the 3DGNs becomes another key parameter. Sample with a bi-layer thickness is recommended because all the defects are on the surface .As for the case of the 3DGNs based photocatalysts, in the absence of functional group on its surface (because of the CVD preparation method) means the chemical contact between the graphene basal plane and TiO2 composite photocatalysts include the outputs of the strong oxidizing radicals and the adsorption amount of pollutant molecules. Further, the outputs of the 2. Moreover, the utilization rate of the photo-induced electrons is significantly affected by the electron transport at the interface between these two materials. Therefore, how to give full play to the functions of graphene (an electron tank under UV-light irradiation and a sensitizer under visible light irradiation) is the pivotal issue. As for the adsorption ability, although BET area of a photocatalyst exerts a significant influence, the efficiently adsorbability (chemisorption) is the determinant. In fact, optimizing the surface chemistry of the adopted graphene  is the fundamental approach to enhance the chemisorption ability. The specific relationship between the photocatalytic performance and influence factors (including improvement methods) are shown in Direct determinants of photocatalytic performances of the graphene-TiO2 composite photocatalysts by adopting the 3DGNs (bi-layer thickness) with various defect densities were prepared by our group and all samples possess similar BET area and total adsorption ability at room temperature  and pollutant molecules is weak , additional functional groups (or defects) of graphene enhance the chemisorption. However, the corresponding research on revealing the relationship between the functional group amount (and types) of the RGO and the resulting chemisorption ability of the RGO-TiO2 composite photocatalyst is insufficient.Adsorption experiments manifest that BET area determines the adsorption ability of a photocatalyst ,144,146.2 composites, the bonding capability between the surface functional group  and various pollutants molecules deserves to reveal, which is valuable to design the proper RGO-TiO2 photocatalyst for specific pollutants. As for the 3DGNs-TiO2 composites, the defect density of the 3DGNs deserves further optimizing. Moreover, the theoretical calculation on pollutants adsorption of the graphene-TiO2 is insufficient, lacking enough analog data to support the experimental results. On the other hand, although the major contribution of the adsorption ability results from graphene, corresponding optimizing on depressing the agglomeration of TiO2 also exert a positive effect to adsorb more pollutants. Cai’s group and our group found that TiO2 with a low loading amount is beneficial for depressing the agglomeration behavior [In the future, the major attention should be focused on how to promote the chemical contact between graphene and pollutants. As for the RGO-TiObehavior ,160. Mor2 [As discussed in 2 ,162. The2. Therefore, optimizing the morphology of graphene and TiO2 to increase the contact area between them is one of development directions. The 3D continuous structure of the 3DGNs (and the 3DRGO aerogel) endows an innate advantage for fast electron transport . Moreover, searching proper linkers to achieve a better chemical contact between them is another feasible method.Kongkanand et al. reported that ~32 carbon atoms in the perfect CNTs and graphene can accept one foreign electron . Thereforansport , the fur2, which hinders the electron transport from the Fermi level of graphene to conduction band of TiO2 under visible light illumination. Therefore, how to diminish the impact from this barrier is the crucial factor to achieve the outstanding sensitization of graphene. Besides the similar optimizing parameters discussed in 2 nanocomposite but also dominate their performance in other solar energy conversion devices [Preparing photocatalysts with a visible light activity is the development tendency because of their wide application range. A Schottky barrier is installed because of the electronic structures of graphene and TiO devices .2 and graphene, the Schottky barrier height is mixed. Therefore, decrease its width is a reasonable approach to enhance the electron tunneling at their interface , zero band-gap (acting as a sensitizer), high electron mobility (prolong electron lifetime) and excellent electron storage ability (playing as an electron tank) in theory of graphene endow it a wonderful modifier for traditional photocatalysts. In order to further enhance the resulting photocatalytic performances of the graphene-TiO2 photocatalysts, corresponding optimizations on the mass fraction, morphologies and quality of graphene and TiO2 have been carried out, which are discussed and analyzed in this progress. Moreover, a prospective aiming at three core problems of the graphene-TiO2 composite photocatalysts is provided. Specially, the corresponding discussion of the 3DGNs assisted samples is emphasized. Moreover, some novel technologies on estimating the resulting photocatalytic performances are also discussed here, including the STM, EPR and PL spectra. Although some bottlenecks of the graphene-TiO2 composite photocatalyst still occur, the promising prospects inspire researches continuous modifications and innovations.In this progress, some important evolvements of the graphene modified TiO


The laser ablation process was carefully optimized to obtain micro-scale and well-resolved electrodes on PET substrate. A functional paste based on cellulose was prepared in order to allow the precise screen-printing of the TiO2 nanoparticles as sensing material on the top of the electrodes. The current against voltage (I–V) characteristic of the sensor showed good linearity and potential for low-power operation. The results of a humidity-sensing investigation and mechanical testing showed that the fabricated miniaturized sensors have excellent mechanical stability, sensing characteristics, good repeatability, and relatively fast response/recovery times operating at room temperature.This paper describes the fabrication and the characterization of an original example of a miniaturized resistive-type humidity sensor, printed on flexible substrate in a large-scale manner. The fabrication process involves laser ablation for the design of interdigitated electrodes on PET  substrate and a screen-printing process for the deposition of the sensitive material, which is based on TiO Humidity sensors are employed today in a wide range of applications, including environmental monitoring, automotive, industrial process, healthcare, agriculture, and increasing indoor air quality in smart buildings. Several kinds of humidity sensors are available based on different transduction principles, such as resistive, capacitive, optical, and surface acoustic wave ,2,3,4. HTypically, rigid substrates like ceramic, glass, or silicon are used as the fundamental building blocks of humidity sensors; but, recent advancements in the field of printed electronics show increased potential for the substitution of rigid substrates by flexible ones, since the latter potentially reduce the cost of sensors and offer good mechanical flexibility. Examples of flexible sensors integrating additional electronic functions like readout electronics ,6, thermIn addition, due to their very small size, silicon-based devices can be integrated with a flexible substrate. For example, a silicon strain sensor and multiplexed silicon non-volatile memory were transferred onto flexible substrate for wearable electronics ,14. MiniIn the case of resistive-type sensors, the size of a device depends mainly on the surface area covered by the electrodes. Low-cost printing technologies such as ink-jet or screen-printing are forecasted to dominate the printed electronics era, since they allow high-volume production ,16. HoweLaser technology is gaining interest as another alternative micropatterning technique due to its high precision and the possibility to use it in open air without clean room facilities. This process was used for the fabrication of ozone sensors, and was compared with photolithography in . It was 2 has received wide attention and has found applications in many promising areas, such as photovoltaics, photocatalysis, and sensors [2 can be found in the literature [2 are the spin-coating, dip coating, or microdroper processes [2 nanomaterials was used for dye-sensitized solar cells and electrodes.Furthermore, to take advantage of miniaturization, it is important to select an adequate sensing material. Among the various sensing materials, metal oxide nanomaterials possess good properties such as chemical and physical stability and high mechanical strength, and they have a high surface-to-volume ratio that makes them a perfect candidate for sensor applications. In recent years, TiO sensors ,24,25,26terature ,28,29,30rocesses , which arocesses ,33, wherIn this context, the aim of this work was to introduce a cost-efficient and low-temperature procedure that allows the large scale fabrication of humidity sensors on flexible PET substrate. The undertaken multidisciplinary approach combines expertise in materials science and chemistry, and fabrication processes and sensor characterization, aiming to present comprehensive bottom-up research in the field of flexible electronics and sensors. One of the main goals of the conducted research is not only to introduce an innovative technology process for the fabrication of sensor devices, but also to provide a proof-of-concept through extensive mechanical testing and a humidity response characterization of the fabricated miniaturized sensors.2-based sensitive layer on interdigitated electrodes (IDE) previously patterned on a flexible substrate  for the design of micro-scale interdigitated electrodes. This powerful technique used for the micromachining of microdevices consists of the creation of an effective heat zone by a focused laser beam, which induces a localized physical state transition allowing the ablation materials . In ordeA screen printing process, which is a cost-effective, time-saving, and mass-production fabrication process, was used for the deposition and patterning of the sensing material. This technique consists in using a squeegee for depositing a paste through a screen stencil, which allows for the direct patterning of functional pastes on a large variety of substrates ,38.2 nanoparticles-based paste was used for the fabrication of the sensitive layer, and was developed specially for the screen-printing process. Water was chosen as the main solvent of the paste because it is readily available and environmentally friendly. First, a 2.5 wt % hydroxypropylmethyl cellulose  was dissolved in water. Next, a 6.1/1 wt % propylene glycol/n-propanol mixture was prepared, where both the propylene glycol and n-propanol were of p.a. quality obtained from Kemika Zagreb, Croatia. Then, a 2.7 wt % solution of a dispersant  in the propylene glycol/n-propanol mixture was prepared. The HPMC solution and the solspers solution were mixed at 1:1 wt ratio by means of an IKA RW20 overhead stirrer for 10 min at 1500 rpm. TiO2 powder  was dispersed  in the mixture to obtain a 7.5 wt % dispersion of TiO2. The screen-printing of the TiO2 paste was performed using a semi-automatized screen-printer , which is a widespread industrially-applied piece of equipment. A screen was fabricated using a 30 μm thick photopolymer film . The mesh used for the screen-printing of the TiO2 paste onto the surface of the electrodes was characterized by a wire diameter of 30 μm. Finally, the samples were kept at room temperature for 2 days to attain complete dryness.In this work, a TiO2 film were examined by scanning electron microscope (HITACHI TM3030) and atomic force microscopy (AFM), whose images were taken with an NTEGRA prima microscope in semi-contact mode. The composition of the TiO2 was investigated by Energy Dispersive X-Ray Analysis (Bruker XFlash), and the electrical characterization was performed using a Yokogawa–Hewlett-Packard semiconductor probe analyzer.The precision patterning of the devices and the morphology of the screen-printed TiO2 and O2) inside a sealed bubbler containing water, and the resulting vapors were then carried to the experimental chamber where the sensors were tested. The humidity level inside the chamber was controlled by adjusting the concentration of the driving gases with mass-flow controllers and flow meters (Brooks Instruments). The humidity sensing response was recorded through the change in resistance caused by varying the RH. A Keithley multimeter, driven by a custom-designed Labview-based interface, was used for monitoring in real time the resistance across the IDEs.The humidity sensing properties of the fabricated sensors were investigated at room temperature (25 °C) by using an indigenously custom-designed humidity setup as described in . The senUsing the process described above, the large-scale fabrication of humidity sensors has been successfully achieved. 2 film. The resulting TiO2 film is well aligned with the film, covering perfectly the surface of the electrodes. This perfect alignment of the screen-printed film is also confirmed at larger scale, as shown in 2 nanoparticle-based film, defining the active area of the humidity sensor, forms a rectangle of 1 mm width and 1.5 mm length  was employed to study the structural composition of the printed titanium dioxide film. 2. The presence of carbon can be clearly observed, and it has been attributed to organic components of the functional paste. Note that, among them, an important component is the binder (hydroxypropylmethyl cellulose), since it assures a strong binding between TiO2 nanoparticles and a good adhesion of the TiO2 film with the substrate, improving the stability of the TiO2 film.The sensing properties are based on the change in the electrical conductance of the sensitive layer with the adsorbed water, which depends on the surface characteristics of the film. The surface morphology of the TiOace area . Figure 2 film should possess good electrical performances to allow for precise and stable resistance measurements. Then, the electrical characteristics of the printed structures should be investigated as well. Current against voltage (I–V) measurements were obtained on sensors printed with one, two, four, and six layers by sweeping the applied voltage from −5 to 5 V. A typical current reading, as shown in 2 film provides a connecting Ohmic electrical contact between pairs of Au electrodes with constant resistance over the supply voltages. That means that a low voltage operation does not hinder the sensitivity, which is essential for low power operation. On the other hand, the conductance of the printed layer should be high enough to be measurable without a high-precision instrument. 2 film. Generally, post-processing steps such as annealing are required to improve the conductivity of the material, leading to an increase in energy consumption and producing additional cost. In this work, in order to develop a low cost and low-temperature process adapted to flexible substrates, we have formulated a recipe for a functional paste that can be used for the printing of several TiO2 layers, and that can preserve the original material physical and transport properties. Indeed, in 2 nanopartices (NPs). This leads to a drop of resistance from about 1 GΩ to 266 MΩ , which was used to ensure that the device response reached its saturated limit without any noticeable drift.2 surface. In that case, the dominant charge transport mechanism is electronic transport, which is much faster than proton conduction. On the other hand, the subsequent layer of the water molecule is generally physisorbed by double hydrogen bonding with the hydroxyl groups formed on the previous water layer [2 film as the humidity level increases. In that case, the proton conduction mechanism becomes dominant, which could explain the slower response times for high humidity levels.er layer ,39. AfteMechanical stability is essential to flexible electronic devices, especially for applications where high stability over the mechanical deformation is required, such as wearable electronic and smart food packaging. Therefore, the influence of the mechanical strain on the electrical behavior of the devices has to be explored. To do so, bending experiments were performed by attaching the flexible sensors to a cylinder a and theTo validate the stable sensing operation under mechanical deformation, humidity measurements were performed when the sensor was in a flat position and bended at 100°.At each indicated position, the sensor was exposed to RH varying from 0 to 35% RH in periods of 10 min. Note that the measurements in a bended position were performed 2 min after bending the sensor in order to leave it enough time to recover its initial resistance value. 2 paste formulation offers high mechanical stability for a TiO2-sensitive layer when it is printed on a plastic substrate, which consequently allows the devices to be used for flexible sensor applications.The obtained results indicate that the TiO2 nanoparticles as sensing material was proposed. This method results from the association of two different approaches: laser ablation and screen-printing. The first approach is coherent for the patterning of micro-scale interdigitated electrodes. The second one is particularly adapted for the industrial integration of metal-oxide-based sensitive film on flexible substrate. Both approaches are fast, cost-effective, and do not require annealing and chemical treatment, which makes them compatible with any kind of flexible substrates. The electrical measurements of the investigated sensors revealed Ohmic behavior, and the electrical properties of the devices were improved by printing successive layers. Mechanical testing showed very good stability of the electrical properties and humidity response of the investigated sensors. The humidity sensing properties were evaluated by the measurement of resistance change with variation in the humidity. The linear response of the fabricated sensitive layer, in range from 5 to 70% relative humidity, reveals great potential for environmental monitoring and humidity sensing applications. In addition, the sensors showed good repeatability and a relatively fast response time. Therefore, the possibility to fabricate miniaturized sensors in a large-scale manner, with preserved good sensing properties, paves the way to low-cost solutions for sensor technologies printed on flexible substrates.An original and innovative process for the large-scale production of flexible and miniaturized humidity sensors with TiO


In addition, PD-L1 levels correlated positively with VEGF  and KI-67  levels when the data were treated as continuous variables. This is the first report suggesting that PD-L1 is important for glioma angiogenesis and proliferation. Thus, further research should be conducted to assess the combination of targeted VEGF therapy and anti-PD-L1 immunotherapy for the treatment of glioma.Programmed death ligand 1 (PD-L1) is highly expressed in many cancers. We investigated the expression of PD-L1 and its relationship with vascular endothelial growth factor (VEGF), matrix metalloproteinase-9 and KI-67 expression in 64 patients with primary glioma. The expression rate of PD-L1 in glioma patients was 78.12%. PD-L1 levels correlated with the tumor grade ( Glioma is the most common type of primary brain tumor of the central nervous system, accounting for 40–50% of all primary brain tumors. Despite advances in therapeutic approaches such as surgery, radiotherapy and chemotherapy over the past decade, the overall survival of glioma patients remains dismal , 2. In pProgrammed death ligand 1 (PD-L1), which binds to programmed death 1 (PD-1) on T cells, B cells, dendritic cells and natural killer T cells, provides tumor cells an important escape mechanism from immune attack, thus leading to immune suppression , 8. In tAberrant PD-L1 expression has been reported to occur in glioma and to contribute to immunoresistance . In precet al. reported a significant inverse correlation between the expression of PD-L1 protein and VEGF-related genes [PD-L1 expression tightly correlates with the pathological grade of glioma , 15; thued genes . The expMatrix metallopeptidase 9 (MMP-9), belonging to the zinc-metalloproteinase family involved in the degradation of the extracellular matrix, appears to facilitate the initiation and progression of multiple biological events required for glioma progression, such as invasion and migration of glioma cells. MMP-9 was also shown to proteolytically cleave PD-L1 in fibroblasts, thus suppressing T cell apoptosis .KI-67 is the most widely used marker for proliferation in clinical practice. PD-L1 expression was found to correlate strongly with KI-67 expression  in breast cancer patients . HoweverWe hypothesized that angiogenesis, invasion and proliferation might be important regulators of the PD-L1/PD-1 axis in glioma, given the association of these processes with the malignant progression of glioma. Thus, we investigated the protein profiles of PD-L1, VEGF, MMP-9 and KI-67 in glioma patients according to the patients' clinical characteristics, and explored the correlations in the expression of these proteins.p = 0.0044)  classification of tumors of the central nervous system, we recruited a total of 23 low-grade glioma (LGG) (WHO I–II) and 41 high-grade glioma (HGG) (WHO III - IV) patients for this study. tumor  than in LGG  (p = 0.013), VEGF status (p = 0.002) and KI-67 index (p = 0.002). Positive VEGF and KI-67 expression were more significant frequently observed in the PD-L1 positive group (85.19% and 86.27%) than in the PD-L1 negative group (14.81% and 13.73%), respectively. In addition, MMP-9 expression was more frequently detected in the PD-L1 positive group (82.69%) than in the PD-L1 negative group (14.81%), although the difference was not statistically significant (p = 0.068). PD-L1 expression was not significantly associated with clinicopathological features such as gender, age, and Karnofsky Performance Status . The correlations between PD-L1 expression and clinicopathological features are shown in Table Overall, PD-L1 protein expression was observed in 78.12% (50/64) of patients with glioma. PD-L1 was expressed in 60.87% (14/23) of LGG cases and 87.80% (36/41) of HGG cases. The correlation of PD-L1 expression with clinicopathological features was assessed with a Mann–Whitney U test. PD-L1 immunopositivity was significantly associated with the pathological grade  and KI-67   .In a microarray study of glioma tissues (2007 WHO grade I–IV), Zeng ectively . NeverthThe rate of PD-L1 protein positivity has varied across studies. For example, in a study with a small sample of 10 patients, PD-L1 protein expression was detected in all nine GBM specimens (WHO IV) and one mixed glioma (WHO III) specimen .p = 0.0044). The results of the present study were similar to those of previous studies [Recent studies found that PD-L1 was overexpressed by GBM and the positive rate of PD-L1 protein expression was ranged from 31.5% to 61.0% –35. Howe studies , 15, whiVEGF is a homodimeric protein identified as a mitogen for endothelial cells and a promoter of angiogenesis. Previous research has demonstrated that vascular proliferation correlates positively with the degree of malignancy in glioma patients , 38. In Monoclonal antibodies blocking the binding between PD-1 and PD-L1 have elicited significant and durable responses in several types of tumors . AntibodHowever, it should be noted that biomarkers identifying patients who are likely to respond to PD-L1 inhibition have not yet been defined. Although PD-L1 immunohistochemistry has been approved by the Food and Drug Administration as the only predictive companion diagnostic test to determine whether pembrolizumab should be used for non-small cell lung cancer patients, improved survival outcomes have been seen in many PD-L1-negative patients . In futuet al. demonstrated that MMP-9 can proteolytically cleave PD-L1 and thus suppress T cell apoptosis [p = 0.743). Thus, MMP-9 expression is likely to be one of several complex mechanisms that may impact the glioma immune microenvironment.MMPs are a group of zinc-dependent proteins that can degrade the extracellular matrix upon their activation. One member of this family, MMP-9, is also an important promoter of tumor invasion . In astrpoptosis . In the et al. found that the expression of PD-L1 in breast cancer patients correlated with KI-67 expression. PD-L1 expression was gradually induced in proliferating cells in parallel with KI-67, and was downregulated in quiescent cells in parallel with the absence of KI-67 [− tumor stem-like cells (lacking the KI-67 marker) derived from gliomas and medulloblastomas [−) may indicate that proliferation is not the only factor involved in the induction of PD-L1.In addition, we found a strong correlation between PD-L1 expression and tumor cell proliferation, as estimated by KI-67 staining. Similarly, Ghebeh of KI-67 . Howeverlastomas . The expWe acknowledge several limitations to our current study. First, the population enrolled in this retrospective study was relatively small, which could result in possible sample selection bias. Second, the expression of PD-L1 has been detected not only in tumor cell but also in vascular endothelial cells, which may impact on the correlation analysis of PD-L1 and VEGF. We do acknowledge the image analysis software used in their correlation analysis of PD-L1 and VEGF could not completely eliminate the interference caused by PD-L1 expressed in endothelial cells, although an AOI was drawn to exclude endothelial cells (blood vessels).In summary, our study revealed that PD-L1, VEGF, MMP-9 and KI-67 are all overexpressed in glioma, especially in HGG. PD-L1 expression was significantly associated with the pathological grade, VEGF status and KI-67 index. As continuous variables, PD-L1, VEGF and KI-67 levels correlated positively with each other. These results indicate that PD-L1 and VEGF are involved in the cascade of the malignant progression of glioma. Thus, therapeutic regimens targeting the T-lymphocyte checkpoint and anti-angiogenesis simultaneously may yield durable responses and herald the resurgence of immunotherapy. Further investigation of the relationship between PD-L1 and VEGF will be necessary, and will contribute to the development of such therapies for human brain glioma.This research was approved by the ethics committee of Shan Dong Cancer Hospital. No informed consent  was obtained for the retrospective analysis. Informed consent was not deemed necessary by the ethics committee, as some of the enrolled patients were deceased, and all samples were anonymous.n = 11), WHO grade II diffuse astrocytoma (n = 12), WHO grade III anaplastic astrocytoma (n = 13), and WHO grade IV GBM (n = 28). The inclusion criteria were as follows: a) no signs of distant metastasis; b) primary glioma confirmed through histopathology; c) well-preserved specimens; d) complete clinical records and pathologic data. Patients who had received antitumor treatment before operation, including radiotherapy and chemotherapy at the same institutions, were not included in this study. Clinical information about the patients was obtained from their medical records.We retrospectively analyzed 64 patients with glioma who underwent surgery at the Shandong Cancer Hospital Affiliated with Shandong University between June 2007 and December 2015. The glioma specimens were from 33 men and 31 women ranging from 39 to 78 years in age, with a median age of 61.3 years. All the tumor specimens were re-evaluated according to the 2016 WHO classification system by two experienced pathologists (P.L. and D.M.), with differences being resolved by careful discussion. The tumor types and grades were distributed as follows: WHO grade I pilocytic astrocytoma . After the sections were cooled, endogenous peroxidase quenching was blocked by incubation with 3% hydrogen peroxidase for 5 minutes at room temperature. Then, the slides were blocked with 5% FBS at room temperature for 15 minutes and incubated for 1 hour with primary antibodies against PD-L1 , VEGF , MMP-9  or KI-67 . EnVision TM+ anti-rabbit HRP labeled polymer (Dako) was used as the secondary antibody for 30 minutes of staining. Then, 3, 3′-diaminobenzidine tetrahydrochloride (DAB) was applied for color development at room temperature for 5 minutes, and sections were subsequently counterstained with hematoxylin. Parallel staining without the primary antibody was performed as a negative control.Two independent observers examined the stained slides in a blinded fashion. The tumor cells exhibiting PD-L1, VEGF, MMP-9 and KI-67 staining were counted under a light microscope at 200× magnification. Five random fields were examined for each tumor specimen. Staining of the cytoplasm or membranes in over 5% of tumor cells was deemed to indicate PD-L1 positivity . VEGF, MThe quantification of PD-L1, VEGF, MMP-9 and KI-67 expression levels was determined using a computerized image analysis system (Image-Pro Plus version 6.0 software). Firstly, image acquisition of IHC stained slides. Briefly, a digital image (Tag Image File Format format) with characteristic glioma on each slides was acquired under an Nikon Eclipse 80i microscopy equipped with an Nikon DS-Fi1 camera. All Images were acquired under high magnification (400×) with a constant set of imaging parameters . Secondly, optical density analysis of the images was performed with the Image-Pro Plus software. Images was calibrated and an appropriate threshold value for DAB-positive hues (brown) was set through histogram . Then, an area of interest (AOI) was drawn to include most of tumor components in the image and exclude endothelial cells (blood vessels), necrosis and slice edge. After the AOI was defined, the integrated optical density (IOD) of the AOI was determined by the software. Lastly, the MOD of the selected area were calculated (IOD/area of AOI) and represented as the immunoreactivity of the candidate protein within tumor tissue. Intra-tumor heterogeneity was minimized through the elimination of the two fields with the highest and lowest MODs, and the average MOD of the remaining five fields was used to represent the PD-L1 level for an individual.t-test. The correlations between PD-L1 expression and clinicopathological features were assessed with a Mann–Whitney U test. The correlation coefficients for the immunoreactivities of PD-L1, VEGF and KI-67 were determined with Spearman's rank correlation test. A p value less than 0.05 was considered significant.All data were gathered in Image-Pro Plus software. Statistical analyses were performed with SPSS . The MODs from the PD-L1, VEGF, MMP-9 and KI-67 image analyses are reported as means ± standard deviations (SDs). The difference in MOD count between the two groups was assessed with a


The buckling of graphene sheets on substrates can significantly degrade their performance in materials and devices. Therefore, a systematic investigation on the buckling behavior of monolayer graphene sheet/substrate systems is carried out in this paper by both molecular mechanics simulations and theoretical analysis. From 70 simulation cases of simple-supported graphene sheets with different sizes under uniaxial compression, two different buckling modes are investigated and revealed to be dominated by the graphene size. Especially, for graphene sheets with length larger than 3 nm and width larger than 1.1 nm, the buckling mode depends only on the length/width ratio. Besides, it is revealed that the existence of graphene substrate can increase the critical buckling stress and strain to 4.39 N/m and 1.58%, respectively, which are about 10 times those for free-standing graphene sheets. Moreover, for graphene sheets with common size (longer than 20 nm), both theoretical and simulation results show that the critical buckling stress and strain are dominated only by the adhesive interactions with substrate and independent of the graphene size. Results in this work provide valuable insight and guidelines for the design and application of graphene-derived materials and nano-electromechanical systems. Graphene has drawn widespread attention due to their excellent properties in electricity, thermology, optics and mechanics, and thus plays an important role in nano-materials and nano-devices ,5,6,7,8.et al. [et al. [et al. [in-situ Raman spectroscopy and atomic force microscopy. They reported a critical compressive strain of around 0.7%. By assuming a simple failure mode, Wilber [In recent years, experimental and theoretical studies have been carried out to investigate the buckling behavior of graphene sheets ,20,21,22et al.  and WangHowever, in previous studies, the buckling modes of substrate-supported graphene sheets are rarely reported. The buckling mode determines the assumption of theoretical model, and it thus affects the critical buckling stress and critical buckling strain significantly. In this paper, the all-atom simulations are carried out to investigate the buckling modes as well as the buckling stress and strain of a monolayer graphene sheet subjected to a uniaxial compressive load on a flat rigid substrate. The effects of sheet size are also studied, and the critical condition for different buckling modes is obtained. Furthermore, the theoretical analysis is carried out based on the energy method to investigate the mechanism of buckling behavior and to reveal the substrate effect on the buckling stress and strain.In this section, the graphene substrate is taken as an example to simulate the buckling behaviors of graphene sheets. The simulation method and the qualitative conclusion are also applicable to the graphene systems with other substrate materials.l and the width w on a rigid graphene substrate. The substrate is modeled as a rigid body because it is much thicker than the graphene and thus the deformation is constrained by the lower-layer material. The compressive loads are applied on the zigzag edges of the graphene sheet, as shown in z-direction) of all the atoms on edges L and R are restrained. Besides, along the armchair-edge direction (x-direction), the displacements of atoms on edge L (or R) are uniform, and their displacements along the zigzag-edge direction (y-direction) are unconfined. When loading, edges L and R move inside along the loading direction, and their displacements are the same in magnitude but opposite in direction.The atomistic simulation on the deformation of graphene on rigid substrate under compressive load is carried out by the atomic-scale finite element method (AFEM) ,27,28, wd is the distance between the two atoms, The second-generation Tersoff–Brenner potential  is adoptubstrate . For gra=0.34 nm ,35.F is obtained by summing up the loading-direction force components of all the atoms on either of the loading edges.The initial configuration of graphene is generated as an ideal perfect two-dimensional sheet with hexagonal lattices in the plane. The initial distance between the graphene sheet and the substrate is 0.34 nm. Before compression, the graphene is relaxed to reach its minimum energy state, which is the initial equilibrium state. Then, the compressive loadings are applied to edges L and R by controlling the displacements. The deformation and buckling behavior of the substrate-supported graphene sheets are investigated by recording the atom coordinates at each displacement increment, and the total compressive force l = 5.4 nm and width w = 5.4 nm. In F is divided by the sheet width w, which is essentially equivalent to the compressive stress of the graphene sheet. The normalized displacement is defined as the relative displacement Δxu divided by the total sheet length l, which is essentially the contraction ratio of the graphene sheet and corresponds to the compressive strain of the graphene sheets before buckling. Here, l of the narrow graphene sheet is 5.4 nm, same as the case of w is 0.74 nm, much smaller than that of the sheet in It is interesting to find that not all graphene sheets buckle following above mode. In the first stage, both stress and strain of the graphene sheet increases linearly with the compression, and the slope of the curve in From For the substrate-supported graphene sheet under uniaxial compression, if the sheet length less than 3 nm or the sheet width less than 1.1 nm, the only possible buckling mode is the one-wave mode similar to that presented in l/w larger than 3.7 still follows the one-wave mode. However, for the graphene sheets with the length/width ratio l/w less than 3.7, the buckling presents two-wave mode, similar to that illustrated in Otherwise, if the sheet length is larger than 3 nm and the sheet width is larger than 1.1 nm, the buckling mode depends on the length/width ratio of the graphene sheet. The buckling of graphene sheets with the length/width ratio The size of graphene sheet can also affect the critical buckling stress and strain, which can be obtained from the peak point of the curves demonstrated in i.e., the critical buckling force per unit width, decreases with increasing sheet length and approaches to 4.39 N/m, as shown in From the simulation results, the critical buckling stress, et al. [It is also found from the simulation results that the critical buckling strain is not sensitive to the graphene size, as shown in et al.  because To obtain a better understanding on the buckling mechanism of the supported graphene sheets, the theoretical analysis is carried out by energy method ,37.The deformation and buckling behavior of the graphene sheets results from the competition between two energy terms ,36,37,38m and the out-of-plane displacement by zu. Suppose the out-of-plane displacement depends only on x as zu = A·cos(πx/λ), in which A is the corrugation amplitude and λ is half of the wavelength. The membrane strain of graphene sheet can thus be obtained from von Karman nonlinear plate theory [When the rectangular graphene sheet in e theory :(2)εm= Et = 289 N/m is the surface Young’s modulus, obtained due to the linearity range of compressive force curve Uad=From Equations (3), (4) and (6), the total energy density of graphene is:TU is a function of contraction ratio A and half wavelength λ. For each given contraction ratio Obviously, the total energy density A = 0 is solved from Equation (8). With increasing The equation set in Equation (8) can be solved numerically. When the contraction ratio TU and its partial differential Besides, Equations (7) and (8) show that the total energy density s are different [i.e., φs and s is determined by s. Therefore, the substrate effect can be presented in versus φs, for substrates with various 2 are also presented in For different substrate, the adhesion parameters ifferent ,45,46. HIt can be investigated in The analytical approximate solution is derived to explicitly present the main factors that influence the critical buckling stress and strain as well as their influence tendency.bU in Equation (4) is simplified as:In order to attain the analytical solution, the bending energy density The adhesion energy density can be simplified by Taylor expansion around Substituting Equations (9) and (10) into Equations (7) and (8) yields:If A > 0, the graphene sheet buckles, otherwise it keeps flat. Thus, the critical condition can be obtained as:Therefore, the critical buckling strain is:The critical buckling stress is:s, which agrees with the numerical results shown in For the system with graphene substrate, the critical buckling stress and strain obtained from the analytical approximate solution Equations (13) and (14) are (1)The buckling mode of the simple-supported graphene sheet is dominated by the graphene size. For graphene sheets with length larger than 3 nm and width larger than 1.1 nm, the buckling mode depends on the length/width ratio only.(2)The critical buckling stress and strain of the substrate-supported graphene sheet with two simple-supported edges are about 4.39 N/m and 1.58%, which are dominated only by the substrate adhesion and independent of the graphene size.(3)The substrate effect is revealed by both theoretical analysis and atomistic simulation. The critical buckling stress and strain can be increased by increasing the adhesive interaction of substrate. The existence of commonly-used substrates can make the critical buckling stress and strain increased by more than 10 times relative to the free-standing graphene sheets.In order to study the compressive buckling behavior of the substrate-supported graphene sheets, both molecular mechanics simulations and energy-based theoretical analysis are carried out to investigate the buckling mode and the critical buckling stress and strain of the monolayer graphene sheets. The following conclusions can be drawn.The estimations on the critical buckling stress and strain obtained in this study can provide guidelines for the design of graphene-derived materials and devices. For example, when the graphene sheet is used as conductive coating materials, the allowable stress of the coated devices should be lower than the critical buckling stress so that the graphene sheet has enough contact area with the substrate to display its high conductivity. Studies have shown that the electrical conductivity of Nano-Electromechanical System and the thermal conductivity of heat conduction element both depend on the smoothness of the graphene sheet ,48 becauOn the other hand, the critical buckling behavior can be utilized to design strain/stress sensors and switches  because