The atomic-thick anticorrosion coating for copper (Cu) electrodes is essential for the miniaturisation in the semiconductor industry. Graphene has long been expected to be the ultimate anticorrosion material, however, its real anticorrosion performance is still under great controversy. Specifically, strong electronic couplings can limit the interfacial diffusion of corrosive molecules, whereas they can also promote the surficial galvanic corrosion. Here, we report the enhanced anticorrosion for Cu simply via a bilayer graphene coating, which provides protection for more than 5 years at room temperature and 1000 h at 200 °C. Such excellent anticorrosion is attributed to a nontrivial Janus-doping effect in bilayer graphene, where the heavily doped bottom layer forms a strong interaction with Cu to limit the interfacial diffusion, while the nearly charge neutral top layer behaves inertly to alleviate the galvanic corrosion. Our study will likely expand the application scenarios of Cu under various extreme operating conditions. Atomically thick anticorrosion coatings on Cu are desired for future applications, but still at its infancy. Here, the authors report a Janus-doping mechanism in bilayer graphene on Cu substrate that results in an enhanced anticorrosion performance. However, the susceptibility of Cu to oxidation greatly limits its advanced applications6. For example, Cu will lose more than 99.99999% of its electrical conductivity at 200 °C in air for only 30 min7. Conventional organic coating8 and sacrificial anode9 anticorrosion techniques have made significant success in traditional industries, unfortunately, these methods typically rely on a thick coating and fail to comply with the miniaturisation requirements of the integrated circuits industry2. Currently, the rise of two-dimensional (2D) materials has provided new opportunities for the development of anticorrosion technology12. Graphene, in particular, has emerged as a promising candidate for an ultimate anticorrosion coating due to its excellent characteristics at the atomic thickness, including absolute impermeability, high electrical and thermal conductivity, excellent chemical stability, and great optical transparency15. However, previous studies have shown that the anticorrosion performance of graphene is far from satisfactory under real working conditions, especially in complex and diverse environments29, which limits its application to an early stage.Cu is widely used in the modern semiconductor industry as electrical connectors due to its high conductivity23. Second, graphene is cathodic to most metals and will lead to local galvanic reaction24. As a result, corrosive molecules will interact with the free electrons on graphene surface and thus accelerate the electrochemical corrosion process28. Recently, efforts have been made to enhance the graphene-Cu couplings to prevent interfacial molecular diffusion, for example, by forming a commensurate graphene/Cu(111) system30 or producing an ultra-flat Cu surface13. However, these methods impose overly restrictive limitations on Cu or graphene and still cannot address the electrochemical corrosion issue. Therefore, there is an urgent need to develop a robust and effective anticorrosion strategy for graphene coating that can address all those three requirements.In principle, an ideal anticorrosion coating material should comply with three requirements: (i) intrinsically, being impermeable to corrosive agents and having low penetrating defect density; (ii) interfacially, being tightly coupled with metal to prevent further horizontal diffusion once corrosive agents reach the interface, and (iii) surficially, being electrically inert to prevent electrochemically facilitated corrosion reactions. A defect-free graphene film naturally fulfils the first requirement, but it generally fails to meet the interfacial and surficial ones. First, the easily formed wrinkles on graphene and intrinsic step bunches on Cu allow for the diffusion of corrosive molecules at the interface31. It is found that the bilayer coating strategy not only integrates the advantages of the monolayer , but also demonstrates excellent prospects far beyond expectation (with a Janus-doping effect for improved anticorrosion). Specifically, it can simultaneously satisfy the demands of both reinforcing the graphene-Cu interactions to limit interfacial molecular diffusion and maintaining the intrinsic charge neutrality of the top layer graphene to suppress surficial electrochemical reactions  arbitrary-twisted bilayer graphene coating on Cu by wet transfer method (see Methods for more details). After being oxidized at 250 °C for 6 hours, the monolayer graphene coated Cu quickly deteriorated and turned black , whereas the bilayer coated area maintained the initial Cu state with shining metallic lustre  images further confirmed that the Cueps Fig. . Previou34 (see Methods for more details), and deduced from the model that bilayer graphene could effectively protect Cu for more than 1000 h at 200 °C, while monolayer graphene only works for ~36 h  of bilayer graphene is confirmed to be orders of magnitude lower than that of monolayer graphene  were readily estimated from the Arrhenius equation36  to track the evolution of the penetrating defects on graphene film Fig. . After bFurthermore, the oxidation process under extreme working conditions was investigated by in situ environmental scanning electron microscopy (ESEM), which allowed for real-time observations with an oxygen pressure of 150 Pa, a hydrogen pressure of 80 Pa, and a temperature of 600 °C. Under such oxygen-rich and high-temperature conditions, monolayer graphene could not withstand even one second of exposure Fig. . In cont2O became increasingly prominent, proving the chemical state of Cu has risen from 0 to +1  was carried out to gain insight into the chemical state of Cu during oxidation. As the oxidation progressed at 150 °C, the satellite peak and Auger peak of Cu +1 Fig. . Notablyess Fig. , demonstene Fig. . These fene Fig. . By comb38. Based on these findings, we propose that the bilayer graphene/Cu system demonstrates a Janus-doped characteristic, where the bottom layer is heavily doped and forms an enhanced interaction with Cu which limits the interfacial diffusion and migration of corrosive molecules, while the top layer is nearly charge neutral, thus can cut off the electron pathway and block the catastrophic electrochemical reactions. By successfully manipulating the electronic structures of the two layers, both the interfacial diffusion and surficial electrochemical reaction pathways are suppressed, finally resulting in the ultraslow corrosion of Cu.We further utilized first-principles calculations to understand the ultrahigh anticorrosion performance in the bilayer graphene/Cu system  experiments were performed to investigate the detailed electronic structures. The calculation results demonstrate an energy shift between the Dirac point and the Fermi surface in the graphene/Cu system, and the shift of the bottom layer graphene is significantly larger than that of the monolayer , such an upshift of 12 cm-2 versus ~1.4 × 1012 cm-2). This evident doping effect leads to a strengthened interaction between bottom graphene and Cu, thus effectively blocking the interfacial diffusion pathway for corrosive agents at the graphene-Cu interface  measurements revealed that the surface potential of bilayer graphene on Cu was ~135 mV higher than that of monolayer graphene Fig. , indicatyer Fig. . Accordiace Fig. .In the case of substantial electron transfer for monolayer coating, graphene is more likely to provide electrons to corrosive agents, and its high electrical conductivity will provide a channel for electrons to migrate on the surface and participate in the cathodic reactions. Regarding the top layer of bilayer graphene, both our calculations and nano-ARPES results confirm that there are negligible electrons transferring onto the top layer Fig. . Such an5. As a further demonstration, we transferred bilayer graphene coatings onto Cu conductors on a printed circuit board (PCB). After annealing at 120 °C for 20 h, the bilayer graphene successfully protected the Cu conductors with no visible signs of oxidation -1 (NH4)2S2O8 solution in a water tank. After that the obtained free-standing PMMA/graphene film was smoothly placed onto another as-grown monolayer graphene/Cu without deliberately controlling the twisted angle. Finally, the obtained PMMA/bilayer graphene/Cu sample was baked at 80 °C for 10 min and then annealed in Ar and H2 atmosphere at 400 °C for 10 h. The second way is using the typical chemical vapour deposition (CVD) growth method, and these bilayer domains are of several tens of micrometres. In detail, a Cu foil was first placed on a quartz substrate and loaded into the CVD furnace. Then the system was heated to 1040 °C under a reducing atmosphere of 500 standard cubic centimetres per minute (sccm) Ar and 30 sccm H2. After holding at 1040 °C for 1 hour, 0.05 sccm/50 sccm of CH4/H2 was introduced into the system for 10–30 min to obtain bilayer graphene on Cu.Bilayer graphene coated Cu samples are prepared in two ways. The first one is using the typical wet transfer method, and the bilayer coating area can be on the decimetre scale. Specifically, 8% polymethyl methacrylate (PMMA) in anisole solution was spin-coated onto the surface of the as-grown monolayer graphene/Cu sample and then the sample was baked at 120 °C for 2 min. Then the Cu was etched by 0.2 mol LThe oxidation experiments were carried out by baking the samples in a CVD chamber in air at 120–275 °C for up to 15 days. The room temperature oxidation experiments were carried out in Beijing with the temperature controlled within 20–30 °C and the relative humidity controlled between 30 and 50%.+ cluster at 30 keV with an incidence angle of 45°. The dual sputtering beam uses Cs+ cluster at 500 V and 27 nA with an incidence angle of 45°. The ARPES measurements were performed at the nano ARPES beamline BL07U of the Shanghai Synchrotron Radiation Facility, with a beam spot size of ~500 nm and energy/momentum resolution of 50 meV per 0.2°. Graphene sample was measured in an ultrahigh vacuum with a base pressure of more than 5 × 10-11 mbar and photon energy of 91 eV, and the data were collected by DA30L analysers. NAP-XPS was performed on a system which is manufactured by SPECS Surface Nano Analysis GmbH. The facility is composed of three chambers, an analysis chamber, a preparation chamber, and a load-lock chamber. The X-ray source in the vacuum environment is separated from the high-pressure analysis chamber using a Si3N4 window. The analysis chamber is equipped with a PHOIBOS NAP hemispherical electron energy analyser, a microfocus monochromatized Al Kα X-ray source with beam size of 300 μm, a SPECS IQE-11A ion gun, and an infrared laser heater. The base pressure of the main chamber is kept below 1 × 10-9 mbar.Optical images were obtained using an Olympus BX51 microscope. Raman spectra were obtained with a Witec alpha 300 R system with a laser excitation wavelength of 514 nm. EBSD characterizations were carried out using PHI 710 Scanning Auger Nanoprobe. AFM images were acquired using a Bruker Dimensional ICON system under ambient conditions. KPFM measurements were performed using Asylum Research Cypher under ambient conditions. Depth resolution mass spectra were conducted on a ToF-SIMS 5–100 instrument (ION-ToF GmbH), which relates to a UHV preparation chamber. The primary ion source uses BiThe in situ experiments were conducted in a specially modified commercial ESEM (Thermo Fisher Quattro-s), using oil-free pre-vacuum pumps for the vacuum system, a homemade laser heating stage for temperature control, and a K-type thermocouple for temperature monitoring. A gas supply module facilitated by mass flow controllers (Bronkhorst) was employed, together with a mass spectrometer (Pfeiffer OmniStar) to analyse the atmosphere in the chamber. Prior to the experiments, the ESEM chamber was cleaned using plasma. The acceleration voltage was set between 3.0 and 7.5 kV, and images were captured using a large field detector. Throughout the experiments, no influence of the electron beam on the oxidation process was detected.We divide the oxidation of Cu into two processes, the first is the formation of graphene point defects, at a rate 40. The interaction between the valance electrons and ion core were described by the projector augmented wave (PAW) method42. The exchange-correlation potential was formulated by the generalised gradient approximation (GGA) with the Perdew-Burke-Ernzerhof (PBE) scheme43. The kinetic energy cut-off of plane wave basis is set to 417 eV. First, the bulk Cu was relaxed until the force is less than 0.02 eV/Å, and the obtained primitive lattice constant is 2.5412 Å, which is about 3% mismatch of the graphene lattice constant (2.46 Å). This relaxed Cu lattice constant was employed in the following calculations. The Cu substrate was cleaved from the bulk phase with three Cu atom layers. The bottom two layers are fixed to simulate bulk Cu, while the topmost Cu layer and bilayer graphene are relaxed until the force less than 0.02 eV/Å. As determined from the ARPES results, the bilayer graphene has ~27.5° rotation, therefore, a superlattice matrix 45. The adsorption energy was calculated by The calculations were carried out using Vienna ab initio simulation package (VASP)Supplementary InformationPeer Review FileDescription of Additional Supplementary FilesSupplementary Movie 1


The fatigue crack growth rate (FCGR) of aluminium alloys under the combined influence of temperature and humidity remains a relatively unexplored area, receiving limited attention due to its intricate nature and challenges in predicting the combined impact of these factors. The challenge was to investigate and address the specific mechanisms and interactions between temperature and humidity, as in coastal environment conditions, on the FCGR of aluminium alloy. The present study conducts a comprehensive investigation into the combined influence of temperature and humidity on the FCGR of the Al6082 alloy. The fatigue pre-cracked compact tension specimens were corroded for 7 days and then subjected to various temperature and humidity conditions in a thermal chamber for 3 days to simulate coastal environments. The obtained data were analysed to determine the influence of temperature and humidity on the FCGR of the Al6082 alloy. An empirical model was also established to precisely predict fatigue life cycle values under these environmental conditions. The correlation between FCGR and fracture toughness models was also examined. The Al6082 alloy exhibits a 34% increase in the Paris constant C, indicating reduced FCGR resistance due to elevated temperature and humidity levels. At the same time, fatigue, corrosion, moisture-assisted crack propagation, and hydrogen embrittlement lead to a 27% decrease in threshold fracture toughness. The developed model exhibited accurate predictions for fatigue life cycles, and the correlation between fracture toughness and FCGR showed an error of less than 10%, indicating a strong relationship between these parameters. Aluminium alloys in the 6xxx series have gained significant popularity and are widely utilised in diverse structural applications such as marine applications , rotor bThe connection between FCGR and fracture toughness is essential in understanding the fatigue behaviour of aluminium alloys . VariousThe coastal environment, characterised by high humidity levels and fluctuating temperatures, poses unique challenges to materials due to the corrosive nature of the atmosphere . Middle Several factors, including corrosion, temperature, and humidity, influence the aluminium’s FCGR. Corrosion can lead to localized weakening of the material, accelerating crack growth. Temperature variations can affect the diffusion of atoms along the crack front, influencing crack growth rates. Additionally, higher humidity levels can promote crack propagation due to moisture and environmental factors.The correlation between FCGR and fracture toughness is critical in understanding the fatigue behaviour of the Al6082 alloy. Fracture toughness represents the material’s capability to resist crack propagation and absorb energy before failure. Higher fracture toughness values indicate better crack resistance. Meanwhile, FCGR measures the rate at which cracks extend under cyclic loading. The FCGR is influenced by factors such as stress levels and crack size.The Paris model, also known as the Paris Law or Paris–Erdogan Law, is a mathematical relationship used to predict the growth of fatigue cracks in materials over time. Three distinct regions are observed in a da/dN vs. ΔK plot. The threshold region, characterized by low ΔK values, shows minimal crack growth due to closure effects. The Paris region, with intermediate ΔK values, displays a linear connection between da/dN and ΔK, representing stable crack growth. At high ΔK values beyond the Paris region, the accelerated growth region significantly increases da/dN, leading to failure .In coastal conditions, environmental factors such as temperature and humidity impact the corrosion FCGR of aluminium alloys. Hassaan Bin Younis et al.  utilizedHowever, despite utilising various models ,22,23 toThis research aims to address this knowledge gap by studying the Al6082 alloy’s FCGR under controlled temperature and humidity conditions that simulate a coastal environment. This study focuses solely on investigating the stable crack growth regime in the da/dN vs. ΔK plot. The research is limited to examining crack growth behaviour within this region, where crack growth is predictable and stable. The influence of temperature and humidity variations on the crack propagation characteristics will be evaluated by subjecting the alloy to cyclic loading and monitoring crack growth. The novelty of this work lies in the thorough investigation of FCGR under combined temperature and humidity conditions in a coastal environment, the development of an empirical model for accurate fatigue life prediction, and the correlation between FCGR and fracture toughness models. These contributions significantly advance the understanding of the fatigue behaviour of the Al6082 alloy in coastal environments, leading to a comprehensive understanding of aluminium alloy for potential applications in coastal environments.3, elastic modulus of 70 GPa, yield strength of 320 MPa, tensile strength of 348 MPa, and elongation of 17.5%. Its fracture toughness is 28.63 MPa√m in non-corroded conditions and 23 MPa√m in high humidity conditions at room temperature [The Al6082 alloy is well-known for being strong and lightweight, making it popular in the aerospace, automotive, and marine industries . Table 1The preparation of the compact tension (CT) specimen from a 7 mm thick sheet of Al6082 alloy was undertaken following the specified geometry, as depicted in The fatigue pre-cracked CT specimens were placed in a 3.5% NaCl solution for 3 days at room temperature in order to conduct localised corrosion testing. Subsequently, the specimens were removed, air-dried, and subjected to harsh coastal environmental conditions using a thermal chamber. This chamber simulated temperatures of 20, 40, 60, and 80 °C along with humidity ranging from 40% to 90%, as shown in FCGR investigation on the Al6082 alloy is performed using a servo-hydraulic testing apparatus on a 7 mm thick specimen with a 3 mm initial fatigue pre-crack size. The servo-hydraulic testing machine can apply controlled cyclic loads to the specimen shown in In this experiment, the fatigue life cycles and related crack lengths of the Al6082 alloy were recorded under cyclic loading conditions. The change in crack size over the number of fatigue cycles provided valuable data by which to analyse the FCG behaviour. The FCGR values were also determined under different temperature and humidity conditions.I Alqathani et al.  has estaOne of the crack growth functions, the Paris–Erdogan model, is given in Equation (2) . The ParFurther understanding of the connection between FCGR (da/dN) and SIF range (ΔK) involved using the obtained data to plot da/dN against ΔK. The plot, often presented on a log–log scale, allows for a linear representation of the FCGR within a specific SIF range. By fitting the experimental data on the da/dN vs. ΔK plot, the FCG coefficients (C and m) can be determined. The da/dN vs. ΔK plot for the power law regime  was drawIt is evident from From The constant m values as humidity increases indicate that the material’s crack growth behaviour remains consistent, and that the da/dN vs. ΔK curves a–d remaiThe information presented in th), were calculated from the Paris constants C and m, as per the equation mentioned by Robertson and Ritchie [FCG was investigated by subjecting fatigue pre-cracked Al6082 alloy samples to a 3.5% NaCl solution for 168 h, followed by 72 h of temperature and humidity exposure. The presence of moisture can accelerate corrosion processes, further contributing to crack growth. Thus, the pre-crack fatigue becomes smaller as it gets deeper into the material. Small-crack fatigue thresholds, represented by the threshold SIF range (ΔK Ritchie  and Nest Ritchie .(3)∆Kth−6 mm/cycle. The threshold SIF values have been calculated and are listed in Using Equation (3), it is possible to predict the threshold SIF range for small cracks by extending the linear stable growth-rate curve downward to a level as low as 10From the data, it can be observed that an increment in the temperature leads to an increment in the threshold SIF. This means the material exhibits greater resistance to crack initiation and propagation at higher temperatures. The higher threshold SIF values indicate that the material can withstand higher SIF ranges before cracks propagate. On the other hand, as humidity increases, the threshold SIF decreases. Higher humidity levels make the material more susceptible to crack initiation and growth at lower SIF ranges. This suggests that moisture and increased corrosion potential under humid conditions can reduce the Al6082 alloy’s resistance to crack growth.th value of 0.61 MPa√m, indicates that the Al6082 alloy is susceptible to crack initiation under varying temperature and humidity conditions. The combination of fatigue, corrosion, moisture-assisted crack propagation, and hydrogen embrittlement due to high humidity contributes to the reduced threshold SIF. These factors act together, promoting crack initiation and propagation at relatively low stress levels.The observed range of threshold SIF values, with a low ΔKThe effect of temperature and humidity is discussed in two sections, focusing on the effects of temperature and humidity. This is considered an effective approach to present the findings clearly and in an organised fashion.In (a) Reduced Corrosion:As temperatures increase, the Al6082 alloy experiences a reduction in the corrosion rate, which can impact crack initiation and growth behaviour. As the temperature increases, the rate of oxide formation accelerates, resulting in a thicker and more protective oxide layer on the surface of the Al6082 alloy, as shown in 2O3) on the surface [This enhanced oxide layer acts as a barrier , effecti surface . This oxMoreover, the more stable oxide layer formed at higher temperatures adheres more firmly to the metal surface, enhancing its resistance to degradation. This increased stability and adhesion make it more difficult for aggressive agents to dislodge or degrade the oxide layer, further reducing the overall corrosion rate.The data also reveal that the activity of aggressive agents, represented by their respective values (0.46 to 0.26), decreases at higher temperatures, as shown in (b) Crack Closure:As temperatures increase, the Al6082 alloy undergoes the formation of an oxide layer, develops the presence of phase particles in dimples, and plastic deformation ahead of the crack tip, among other mechanisms . These fThe roughness around the crack tip leads to interlocking and meshing of the crack surfaces, causing crack closure and slowing down FCGR . Additio(c) Presence of Phase Particles:As the temperature rises from 20 °C to 80 °C, the Al6082 alloy’s percentage elongation also increases, resulting in improved ductility and enhanced resistance to FCGR. The samples subjected to testing at 60 °C and 80 °C exhibited noticeable phase particles, whereas their presence was considerably diminished at 20 °C and 40 °C a,b. This2Si intermetallic compound [Upon reaching a temperature of 70 °C and above and then cooling, elements such as Mg within the Al6082 alloy tend to aggregate, creating stable particles referred to as precipitates, specifically the Mgcompound . These fAt room temperature, dislocation motion is low. It increases rapidly from 30 °C to 60 °C but slows down after 60 °C. An increment in temperature from 60 °C to 80 °C minimally impacts resistance to FCG in the Al6082 alloy due to reduced dislocation motion. This reduction allows phase particles to act as effective barriers, regulating void formation, reducing crack nucleation at the crack tip, and slowing down the crack propagation, increasing resistance to fatigue crack growth.In (a) Corrosion/Corrosion Fatigue:Varying humidity levels can significantly influence the corrosion process in the Al6082 alloy and subsequently impact crack initiation and growth. The presence of chloride ions, which increase with higher humidity levels, is critical in initiating aggressive localized corrosion on the metal surface, such as pitting corrosion.At 60 °C and 40% humidity, the chloride content is relatively low (0.11%), which may result in minimal localized corrosion. As humidity increases to 60%, 70%, and 90%, the chloride content rises to 0.27%, 0.35%, and 0.53%, respectively, as shown in This increase in chloride content significantly enhances the potential for localized corrosion, particularly in pitting . The syn(b) Moisture-Assisted Crack Propagation:When a material is exposed to higher humidity levels, the absorption and diffusion of moisture into it promote the formation of a thin electrolyte layer (TEL) , this caAt low humidity conditions (40%), the reduced moisture on the material’s surface slows down the corrosion process, resulting in a less aggressive corrosion rate than in higher humidity conditions. Typical corrosion products that can form under such conditions include oxides and hydroxides . At high(c) Hydrogen Embrittlement:As humidity increases, aluminium becomes more susceptible to hydrogen embrittlement, reducing its ductility and toughness and promoting a transition from ductile to brittle fracture behaviour . The obsThese hydrogen embrittlement effects extend beyond the crack tip region, influencing the material’s mechanical behaviour. As humidity increases, the material’s crack growth behaviour becomes more influenced by hydrogen-induced embrittlement, leading to an accelerated crack growth rate. The presence of hydrogen in the material can lower the threshold for crack initiation and promote faster crack propagation, reducing the material’s fatigue life and overall resistance to crack growth. The combined impact of hydrogen embrittlement (HE) contributes to the observed reduction in aluminium’s resistance to fatigue crack growth at higher humidity levels.Hydrogen embrittlement (HE) is common in various aluminium alloy series when exposed to humid environments . HoweverDuring stage II of FCG, the distance separating fatigue striations is equal to the rate at which the fatigue crack expands within a single cycle ,58,59. AAs humidity increases from 40% to 90%, the environmental conditions become more conducive to corrosion and crack propagation. This can lead to an acceleration in the FCGR of the material. The faster crack growth rate means that the crack propagates over a larger distance during each fatigue cycle, resulting in wider spacing between individual striations on the fractured surface, as shown in Therefore, the experimental observation of increased striation spacing with increasing humidity is consistent with the higher FCGR and larger C values. The combination of these factors indicates that, as humidity increases, the material’s FCGR becomes more rapid, leading to wider spacing between the striations on the fractured surface.The study of crack propagation paths at different temperatures (ranging from 20 to 80 °C) under 80% humidity has revealed a consistent trend, i.e., that the fatigue cracks propagate along relatively straight paths , as showThis observation indicates that the fatigue cracks growth behaviour in the Al6082 alloy remains relatively stable across the tested temperature range and under specific humidity conditions. The material exhibits a consistent crack propagation pattern, indicating that the environmental conditions, including humidity and temperature, have a relatively uniform influence on the crack propagation mechanism. The consistent and relatively straight crack propagation paths imply that the material’s fatigue behaviour remains predictable and reliable under temperature and humidity conditions.The significance of this study lies in its comprehensive examination of FCGR in an Al6082 alloy under combined temperature and humidity conditions within a coastal environment. By subjecting the material to varying temperature and humidity levels, we have gained valuable insights into the material’s fatigue crack growth behaviour, crack initiation, and propagation mechanisms. This work aims to develop an empirical model to predict fatigue life cycles and the Paris constant C . BecauseThis study employs a novel curve fitting technique to develop an empirical model that predicts fatigue life cycles and the Paris constant C for the Al6082 alloy under various temperature and humidity variations within a coastal environment. The curve fitting process is applied to the experimental data points to identify the mathematical relationship that best represents the correlation between fatigue life cycles and crack growth rates with temperature and humidity.A 3D scatter plot, as shown in The equation indicates that the fatigue life cycles of the material are influenced by both temperature and humidity. A positive coefficient for T suggests that an increase in temperature is associated with an increase in the predicted fatigue life cycles. On the other hand, a negative coefficient for H implies that an increase in humidity leads to a decrease in the predicted fatigue life cycles.Similarly, a 3D scatter plot, as shown in The equation represents how temperature and humidity levels influence the Paris constant C. A negative coefficient for T suggests that an increment in temperature reduces the predicted Paris constant C. In contrast, a positive coefficient for H signifies that an increase in humidity is associated with an increase in the predicted Paris constant C. Therefore, as humidity increases, the C value increases, and the material’s resistance to FCGR decreases, and as temperature increases, the C value decreases and the resistance to FCGR increases.The novelty of this work lies in conducting a comprehensive investigation of the FCGR under combined temperature and humidity conditions in a coastal environment, developing an empirical model for accurate fatigue life prediction, and establishing a correlation between FCGR and fracture toughness models.The established empirical model of fracture toughness  is repreIn Ic) has been developed as Equation (6):The empirical model for fracture toughness ) was derived through fracture toughness testing . EmpiricLikewise, the comparison between experimental and empirical model results of fatigue life cycle values is documented in Similarly, the comparison between experimental and empirical model results of fracture toughness values is presented in The strong correlation observed between the experimental and developed models, with a maximum error of 10%, can be attributed to the alignment of the validation conditions  within the broader investigated range of temperature (20–80 °C) and humidity (40–90%). This strategic selection facilitated the verification of the consistency of the equations across diverse environmental scenarios.The combined influence of an increase in temperature and humidity levels, in line with coastal environmental conditions, decreases the FCGR resistance of the Al6082 alloy. The corrosion under higher humidity levels reduces the threshold fracture toughness, facilitating crack initiation and propagation at relatively low stress levels. This is evident from the notable decrease in threshold fracture toughness by 27% and the increase in the fatigue crack growth constant C by 34% as temperature and humidity increase.Higher temperature conditions enhance the alloy’s resistance to FCGR by introducing precipitated phase particles, facilitating the formation of an oxide layer, and inducing crack closure. In contrast, heightened humidity conditions diminish the resistance of the Al6082 alloy to FCGR due to escalated corrosion, moisture-assisted crack propagation, and hydrogen embrittlement.The precision of the developed empirical models is remarkable, showcasing an error of less than 10% in predicting Paris constant C, fatigue life cycles, and the relationship between fracture toughness and FCGR. This robust correspondence underscores the models’ reliability for both researchers and engineers. The alignment between experimental and developed models, confirmed through validation experiments, establishes a solid foundation for predicting FCGR in diverse environmental conditions.This research investigated the combined influence of temperature and humidity on fatigue crack growth rate in the Al6082 alloy within a coastal environment. The outcomes of this study hold considerable significance for the scientific community, shedding light on the complex relationship between temperature, humidity, and fatigue crack growth rate in the Al6082 alloy within coastal conditions. Through the comprehensive experimental study, the following significant conclusions were drawn:


L1 and L2, containing a fluorescent pyrene unit, and their Zn(II) complexes are proposed as fluorescent probes for the detection of PFOA in aqueous media. Binding studies carried out by means of fluorescence and NMR titrations highlight that protonated forms of the receptors can interact with the carboxylate group of PFOA, thanks to salt bridge formation with the ammonium groups of the aliphatic chain. This interaction induces a decrease in the fluorescence emission of pyrene at neutral and slightly acidic pH values. Similarly, emission quenching has also been observed upon coordination of PFOA by the Zn(II) complexes of the receptors. These results evidence that simple polyamine-based molecular receptors can be employed for the optical recognition of harmful pollutant molecules, such as PFOA, in aqueous media.The globally widespread perfluorooctanoic acid (PFOA) is a concerning environmental contaminant, with a possible toxic long-term effects on the environment and human health The development of sensible, rapid, and low-cost detection systems is a current change in modern environmental chemistry. In this context, two triamine-based chemosensors,  Perfluorooctanoic acid (PFOA) and perfluorooctane sulfonic acid (PFOS) are two chemicals composed of a fully fluorinated carbon chain and a hydrophilic polar end group . They arThe strongest evidence of PFOA and PFOS toxicity is related to endocrine disorders, in particular dyslipidaemia. However, animal and epidemiological studies regarding communities exposed to contaminated drinking water and the general population established a positive association between PFOA levels and kidney and testicular cancer along with a statistically significant association between PFAS exposure and suppressed immune response ,16.−1) 3+ and [H2L1]2+ in the case of L1 and [H3L2]3+ in the case of L2 . The latter displays a higher sensing ability for PFOA with respect to L1 and L2 (LOD 26.4 nM), but does not discriminate between PFOA and PFOS. From this point of view, the ability of L1 and L2 to selectively bind PFOA over PFOS is a peculiar characteristic of these receptors in the panorama of molecular hosts for these pollutants. As a preliminary investigation of the effects of interfering agents on the emission of the PFOA complexes with L1 and L2, we analyzed the fluorescence response of L1 and L2 in the presence of PFOA (100 equivs.) and an excess (200 equivs.) of a few model compounds, which, for their anionic nature, can be considered suitable candidates as interfering agents. We choose 1,3,5-nitrophenol, benzenesulphonic acid, 4-nitro-benzoic acid, and simple metansulphonic acid, which are in anionic form at neutral pH value, and may represent good candidates as organic interfering pollutants. Fluorescence measurements reported in L1 and L2 adducts with PFOA. No changes in the emission properties and sensing abilities of L1 and L2 for PFOA are also found when environmentally relevant cations  or anions  are present in solution in excess with respect to PFOA  processes from the ammonium groups of L1 or L2 to the pyrene unit, inducing fluorescence emission quenching. To evaluate the influence of temperature in PFOA binding to the two chemosensors, the fluorescence titrations of L1 and L2 in the presence of increasing amounts of PFOA at pH 4 were also repeated at 288 K and 308 K , likely due to the formation of an insoluble adduct between this analyte and the two receptors, preventing the determination of the stability constants of the adducts formed.Potentiometric measurements confirmed that no interaction occur between the two receptors with PFOS. In the case of PFOA, precipitation is observed at an acidic pH value (below pH 7) in the condition of the potentiometric titrations . We partially solved this drawback by performing 1H NMR titrations at pH 7 and 4 in D2O/CD3OD 40:60 (v/v) mixture. However, L2 suffers low solubility even in this medium at pH 4, and therefore, the system L2-PFOA was analyzed only at pH 7. In the case of L1, the addition of increasing amounts of PFOA, up to 20 equivs., to a solution of the receptor induces a progressive upfield shift both at pH 7 and 4 . The addition of more than 20 equivs. of PFOA does not significantly affect the spectra. The signals of the 1AL and 2AL methylene groups , in keeping with a stronger host-guest interaction at this pH. In an attempt to clarify the role of the pyrene unit in PFOA binding, we also performed 19F titrations by adding increasing amounts of L1 or L2 to 10−2 solutions of PFOA. Unfortunately, in these conditions, precipitation at pH 4 prevents spectral analysis, while the spectra recorded at pH 7  mixture, shows negligible shift for both the aliphatic methylene groups and the pyrene protons, confirming the suggestion derived for fluorescence emission analysis. Similarly, the addition of PFOS to a solution of L1 at pH 7 and to the solution of L2 at pH 4 and 7 did not induce any relevant shifting of the signals of the receptors.Interestingly, L1 and L2 form stable 1:1 complexes with Zn(II) that can be isolated as solids from H2O/EtOH 1:1 solutions. Potentiometric titrations have been also used to determine the binding constant of the receptors toward the Zn(II) cation. The measurements have been carried out in an H2O/EtOH 50:50 (v/v) mixture in the presence of 0.8 equivs. of metal ions, and the explored pH range was 2.5–9 for L2 and 2.5–8.5 for L1 . The binding constants of both receptors are reported in As expected, both L1 and L2 are able to form Zn(II) complexes in neutral or slightly alkaline pH conditions. The higher formation constant of L1 (log K = 8.69) with respect to that of L2 (log K = 7.88) is in agreement with the lower ability of the dipropylentriamine chain in first-row transition metal coordination than diethylentriamine + is also found in solution, as often observed for Zn(II) complexes in which the coordination sphere of the metal is not saturated by ligand donor atoms. Similar species most likely exists also for L1, yet complex precipitation prevents a confident determination of such species. We decided to compare the emission of the Zn(II) with L1 and L2 at pH 8. At higher pH values, in fact, precipitation could prevent a correct analysis of the emission phenomena. At pH 8, the Zn(II) complexes of L1 and L2 are the most abundant species present in solution, although in the case of L2 a not trascurable amount of the receptors is also present in solution in its metal-free form. As discussed above, both receptors are poorly emissive at pH 8 (TRIS buffer) in water/ethanol solution (50:50 v/v). As often observed for Zn(II) complexes with fluorescent polyamine ligands, Zn(II) binding to both L1 and L2 results in the formation of emissive 1:1 complexes. When increasing amounts of Zn(II) is added to a solution of L1 at pH 8, the fluorescence emission linearly increases up to a 1 metal-to-ligand molar ratio (R), achieving a constant value for R > 2  up to an R value of ca 1, suggests the formation of complexes with 1:1 stoichiometry.A similar behavior is also observed in the case of L2 , althoug2O/EtOH (v/v) solution containing L2 and ZnCl2.6H2O in 1:1 molar ratio in the presence of an excess of NaClO4 (10 equivs.). In the asymmetric unit of [ZnL2Cl](ClO4) (compound 6) one [ZnL2(Cl)]+ cation and one ClO4− anion are present. The Zn(II) metal ion is bound by the three nitrogen atoms of the polyamine, while a chloride ligand completes the tetracoordinated environment (see 3) or larger macrocyclic derivatives unable to provide further donor atoms. In the present case, steric hindrance from the large pyrene pendant is likely to subtend to the adopted coordination geometry.Slow evaporation of an Hment see . The cooment see , are com…O24 3.199(1) Å), yet collinear to the Cl-Zn bond (Cl1-Zn1-O24 177.43(3)°): this long electrostatic interaction virtually completes a trigonal bipyramidal environment. The presence of outer sphere donor-acceptor interactions has been observed in Zn(II) polyamine complexes and generally happens along the expected direction for the addition of a further inner sphere ligand. For instance, prototypical square planar Zn(II) porphyrin complexes, when they interact with a fifth out-of-sphere oxygen donor, do so axially . Mononuclear examples of tetracoordinated Zn(II) centres bound to three nitrogen donors further showing out of sphere Zn…O contacts, as in our case, are rare, yet the FOJTAZ 2+ fluorescence emission decreases up to a [PFOA]/[ZnL1]2+ molar ratio of 1, to achieve an almost constant value for a [PFOA]/[ZnL1]2+ molar ratio greater than 1,4 suggesting the formation of 1:1 stoichiometry complexes. The quenching effect is only partial and can be ascribed to the weakening of the Zn-N bond upon PFOA binding, which can partially restore the PET effect from the amine groups to the fluorescent unit.The presence of a coordinated Zn(II) cation, which features an unsaturated coordination sphere can be exploited in the coordination of PFOA, through the interaction of the anionic substrate  with the metal center. The binding features of the Zn(II) complexes of L2, although, in this case, the minimum of the fluorescence intensity is reached with a higher amount of PFOA (15 equivs.). Apparent constants of 3.2 and 3.4 log units for the addition of PFOA to the Zn(II) complexes with L1 and L2, respectively, were calculated by data treatment with the Hypspec program, with detection limits (LODs) values 6.2 (L1)and 11.2 µM (L2). Both complexes show a binding ability lower than that found for the metal-free receptors at pH 4 and 7. However, as already observed for the polyammonium receptors, addition of PFOS to solutions of L1 or L2 at these pH values does not change the pyrene emission, indicating that, differently from PFOA, PFOS is not bound by the Zn(II) complexes. This result is in agreement with the known lower affinity for transition metal cations of the sulphonate group with respect to the carboxylate one.A similar result was also obtained for the Zn(II) complex of 1H NMR spectra of the Zn(II) complexes with L1 or L2 show a remarkable line broadening in D2O/CD3OD (40:60 v/v) preventing their interpretation. The addition of PFOA or PFOS does not affect the fluxional character of the spectra. Therefore, 1H NMR experiments cannot be used to infer a hypothesis on the observed lower binding ability of the Zn(II) complexes with respect to the metal-free triamine at neutral or slightly acidic pH values. We also performed FT-IR spectra on the solid-state ternary complexes ZnL1(PFOA)Cl and ZnL2(PFOA)Cl obtained by slow evaporation of H2O/EtOH 50:50 (v/v) solutions containing L1 or L2, ZnCl2.6H2O (1 equiv.) and PFOA (1 equiv.). The spectra show a slight, but not negligible (15 and 20 cm−1 for ZnL1(PFOA)Cl and ZnL2(PFOA)Cl, respectively) shift toward lower energy for the C=O stretching band, suggesting an interaction of the carboxylate group to the metal. Interestingly enough, the C-F stretching bands do not show significant shifts in the complex with respect to ‘free’ PFOA, suggesting that the perfluoroalkyl chain is not involved in complex stabilization. On the other hand, the crystal structure of the [ZnL2Cl]+ shows that Zn(II) complexation induces receptor stiffening which can prevent the interaction between pyrene and the perfluoroalkylchain of PFOA. Although the conclusion on structure in solution derived from X-ray structure can be misleading, we can tentatively suppose the carboxylate group replaces the chloride anion in the coordination sphere of the metal observed in the solid state structure shown in Unfortunately, the L1) and 1-(1-Methylpyrenyl)-1,5,9-triazanonane (L2) were prepared in accordance with the methods described in the literature 2+, and [ZnL2]2+ fluorescence spectra at pH 4 and 7 in H2O/EtOH 50:50 (v/v) were made, and the standard deviation of the blank measurements was calculated. The fluorescence intensity I0/I at 375 nm  in the presence of increasing amount of PFOA was plotted as a concentration of PFOA and gave a straight line, whose slope (K) was calculated. The detection limit was calculated by using the equation:The detection limit was determined from the fluorescence titrations data based on a reported method . Six mea2.6H2O (1 equiv.) and PFOA (1 equiv.) to a solution of the ligand L1 or L2 in an H2O/EtOH 50:50 (v/v) mixture. The pH of the solution was adjusted at pH 8 by the addition of a small amount of a 0.1M solution of NaOH in an H2O/EtOH 50:50 (v/v) mixture. Solid complexes were isolated by slow evaporation of the resulting solution. The spectra were recorded with an IRAffinity-1S Shimadzu instrument.FT-IR measurements were performed on freshly prepared complexes obtained by adding ZnClL1(PFOA)Cl, C29H20ClF15N3O2Zn: C 42.05, H 2.43, N 5.07. Found: C 41.23, H 3.57, N 6.34. Anal calcd. for ZnL2(PFOA)Cl, C31H24ClF15N3O2Zn: C 43.48, H 2.82, N 4.91. Found: C 44.76, H 3.54, N 4.21.Anal calcd. for Zn2F using all data (SHELXL-2018/3) [23H25N3)Cl]ClO4 (M = 543.73 g/mol): triclinic, space group P-1 (no. 1), a = 8.7070(2) Å, b = 11.4358(2) Å, c = 12.7837(3) Å, α = 77.662(1)°, β = 93.3735(9)°, γ = 68.582(1)°, V = 1157.50(4) Å3, Z = 2, T = 100 K, μ(CuKα) = 3.903 mm−1, Dcalc = 1.560 mg/cm3, 33,464 reflections measured (3.539° ≤ Θ ≤ 72.429°), 4558 unique (Rint = 0.0448) which were used in all calculations. The final R indices [I > 2σ] are 0.0281/0.0803, R indices  are 0.0305/0.0834 and the GoF is 0.884. CCDC 2237493 contains the supplementary crystallographic data for this paper. These data can be obtained free of charge via http://www.ccdc.cam.ac.uk/conts/retrieving.html .Single crystal X-ray diffraction data of 6 were collected on a Bruker Apex-II diffractometer equipped with a CCD detector . Data were collected with the APEX2 software,  The crys-2018/3) . All the-2018/3)  and mole-2018/3) . CrystalL1 and L2, that, at neutral or slightly acidic pH values, form protonated species. Despite their simple structures and their straightforward synthetic accessibility, they can form complexes with PFOA featuring stability higher than those formed by most of the previously reported receptors and, at the same time, selectivity for PFOA over PFOS. The ability of triamine to form complexes with Zn(II), a metal ion known for its ability to change/expand its coordination sphere in order to bind exogenous species represents an ‘added value’ of these molecular receptors. In fact, this metal ion can be exploited as an anchoring point for the carboxylate group of PFOA, a structural characteristic that leads to the formation of stable complexes between the Zn(II) complexes with L1 and L2 and PFOA and selectivity for the latter over PFOS. The Zn(II) complexes with PFOA, however, are less stable than that formed by the protonated species of the receptors, likely due to the rigidity of molecular architecture of the Zn(II) complexes with the present receptors, well outlined by the crystal structure of the [ZnL2Cl]+ cation. As a result, binding of the carboxylate of PFOA to Zn(II) can force the perfluoroalkyl chain to stay far from the pyrene unit, preventing the formation of stabilizing hydrophobic interactions with this aromatic moiety.These results point out that the straightforward coupling of a polar hydrophilic section is able to interact via charge-charge and H-bonding with the negatively charged perfluoroalkyl carboxylate groups, with a large aromatic unit, which can give hydrophobic interactions with the perfluorinated aliphatic chain may result in molecular receptors able to form stable complexes with PFOA, with great selectivity for this analyte over PFOS, whose sulphonate group shows a poor tendency to give H-bonding. This is the case of the triamine receptors L1 and L2 in the polyamine chain and/or in the fluorogenic moiety used, in order to develop a library of fluorescent probes. From this point of view, the assembly of arrays of chemosensors may be exploited to optimize the selectivity of the recognition process.Pyrene can be exploited not only to bind PFOA in cooperation with the polyamine aliphatic chain (when protonated or bound to Zn(II)), but also to signal the binding event through changes in its emission properties. Indeed, the binding of PFOA induces fluorescence quenching, more marked in the case of the metal-free receptors. Although the limit for PFOA detection is not particularly exceptional, PFOA is selectively detected over PFOS by both receptors, a peculiar characteristic in the panorama of molecular optical sensors for these analytes. Furthermore, the performance of the chemosensors in PFOA detection can be, in perspective, enhanced by their incorporation in nanostructured materials, in which energy transfer cooperative effects may occur between closely placed fluorescent probes. At the same time, the simple synthetic procedure used can be exploited to develop different chemosensors, differing from The above considerations outline that coupling a polyamine chain with a nearby fluorescent hydrophobic moiety may represent a novel approach for the development of new optical PFOA chemosensors, simultaneously displaying high stability of the adducts, fluorescence response and particular selectivity properties. Altogether, these characteristics make fluorescent polyamine-based receptors a promising tool for the binding and detection of this environmental contaminant.


Our objective was to assess their Kp clinical isolates were selected. Minimum inhibitory concentrations (MICs) were determined by broth microdilution in triplicate. Time-kill analyses were used to test CZA and MVB alone (1 and 4x MIC) and in combination with colistin , fosfomycin , gentamicin , meropenem , and tigecycline  against 1x108 cFu/mL. 24 hour log-kill was calculated as log cFu/mL decrease from time 0.15 KPC-ompK36 WT, IS5, or GD. 27% and 73% were KPC-3 and KPC-2, respectively. 100% were susceptible to CZA and MVB. None were resistant to COL. 3 were non-susceptible to GEN, which were all IS5 (Table 1).5 isolates each had Figure 1). Mean log-kills did not vary for CZA + COL, GEN, or TGC against ompK36 mutants vs WT; however, log-kills were significantly lower for CZA + FOS  or MEM  against ompK36 mutants compared to WT. Synergy rates were reduced from 100% against WT to 80%, 60%, and 40% against mutant isolates for CZA + COL, MEM, and FOS, respectively .In combination with CZA 1x MIC, each of COL, GEN, and MEM were bactericidal against all isolates; mean ± standard error (SE) log kills were -7.39 ± 0.3, -6.58 ± 0.93, and -5.81 ± 0.21, respectively . Mean ± SE log kills were significantly greater against porin mutants compared to WT for MVB + COL , FOS , or TGC . Rates of synergy were also higher against porin mutants vs WT for MVB + FOS or COL .MVB 1x MIC in combination with COL, FOS, GEN, and TGC were bactericidal 67, 27, 80, and 47% of the time, with corresponding log kills of -3.96 ± 1.1, -1.56 ± 0.83, -5.05 ± 0.82, and -2.53 ± 0.28, respectively  and MVB (meropenem-vaborbactam) at 1X MIC, stratified by ompk36 status: wild-type (WT) versus mutant (MUT). Bactericidal is defined as -3 log kill from time 0 at 24 hours and indicated by the dotted horizontal line. COL = colistin; FOS = fosfomycin; GEN = gentamicin; MEM = meropenem; MIC = minimum inhibitory concentration; TGC = tigecycline.Figure 2Proportion of bactericidal, synergistic, and antagonistic outcomes for ompK36 wild-type  versus mutant  KPC-Kp isolates tested against CZA (ceftazidime-avibactam) or MVB (meropenem-vaborbactam) at 1X MIC as single agents and in combination with colistin (COL), gentamicin (GEN), tigecycline (TGC), meropenem (MEM), or fosfomycin (FOS). Bactericidal activity was defined as -3 log kill from time 0 at 24 hours; synergy and antagonism were defined as -2 or +2 log kill at 24 hours compared to most active single agent, respectively.Porin mutations negatively impact CZA synergy with other antibiotics compared to WT, though 24-hour log kills for COL, FOS, GEN, and MEM remained below the bactericidal threshold. Conversely, porin mutations potentiate synergy between MVB and COL, FOS, or TGC.Ryan K. Shields, PharmD, MS, Allergan: Advisor/Consultant|Cidara: Advisor/Consultant|Entasis: Advisor/Consultant|GSK: Advisor/Consultant|Melinta: Advisor/Consultant|Melinta: Grant/Research Support|Menarini: Advisor/Consultant|Merck: Advisor/Consultant|Merck: Grant/Research Support|Pfizer: Advisor/Consultant|Roche: Grant/Research Support|Shionogi: Advisor/Consultant|Shionogi: Grant/Research Support|Utility: Advisor/Consultant|Venatorx: Advisor/Consultant|Venatorx: Grant/Research Support


The efficient conductivity of graphene-polymer systems is expressed supposing graphene, tunneling and interphase components. The volume shares and inherent resistances of the mentioned components are used to define the efficient conductivity. Besides, the percolation start and the share of graphene and interphase pieces in the nets are formulated by simple equations. Also, the resistances of tunneling and interphase parts are correlated to graphene conductivity and their specifications. Suitable arrangements among experimented data and model’s estimates as well as the proper trends between efficient conductivity and model’s parameters validate the correctness of the novel model. The calculations disclose that the efficient conductivity improves by low percolation level, dense interphase, short tunnel, large tunneling pieces and poor polymer tunnel resistivity. Furthermore, only the tunneling resistance can govern the electron transportation between nanosheets and efficient conductivity, while the big amounts of graphene and interphase conductivity cannot play a role in the efficient conductivity. The early studies on polymer graphene nanocomposites have focused on the preparation of products with small percolation start to achieve a big conductivity by a slight filler amount13. Generally, the percolation start is linked to the aspect ratio of graphene as the ratio of diameter to thickness15. So, the dimensions, dispersion quality and aggregation/agglomeration of graphene nanosheets manage the percolation start and thus, the nanocomposite’s conductivity (denoted as conductivity here). In addition, some novel parameters attributed to nanoscale including tunneling effect and interphase area can control the percolation start and conductivity.Graphene has a high stiffness and good electrical conductivity causing the stiff and conductive nanocomposites19. In fact, electrons can be easily transported via tunnels between nanoparticles. Therefore, the conductivity does not require the physical joining of nanoparticles. Figure 25. Figure 29. The interphase pieces can also connect to the nets, since they cover the nanoparticles31. This attractive subject have been studied for rigidity of nanocomposites33. Nevertheless, the impress of interphase on the conductivity was improperly studied.The tunneling mechanism mainly governs the conductivity35. They have assumed the roles of many terms for CNT such as amount, conductivity, waviness and aspect ratio in the conductivity. Also, some limited studies have exposed the significances of tunneling effect and interphase on the conductivity of CNT products, but their complex analysis limits their application in practice38. The theoretic works on the conductivity of graphene samples are also imperfect. The former authors commonly correlated the percolation start to aspect ratio and estimated the conductivity by old models such as power-law41. However, the interphase pieces and tunneling largely affect the percolation start and conductivity of polymer graphene nanocomposites. Obviously, disregarding of these main terms in the nanocomposites cannot lead to proper prediction of their behavior. Therefore, development of new models for calculation of conductivity considering these terms are valuable.Some novel models were suggested for conductivity of CNT-based nanocomposites42, a model for conductivity of graphene systems was proposed by interphase depth, filler network, network efficiency and tunneling properties. In the present work, the efficient conductivity of graphene-filled products is expressed assuming the volume shares and resistances of graphene, tunneling and interphase parts. Also, the percolation start and the shares of graphene and interphase pieces in the nets are stated by simple equations. The percolation start and the dimensions of graphene, tunneling and interphase parts express the volume shares of these parts in the nets. Additionally, the resistance of interphase piece is correlated to filler conductivity and interphase deepness. The innovative model is justified by the tried data of some examples. In addition, the impresses of factors on the efficient conductivity are explained and discussed.In our previous work43 as:The actual resistance of polymer graphene nanocomposites was expressedThe polymer nanocomposites include the filler, tunneling and interphase pieces, which affect the efficient conductivity. Figure i” and “λ” are interphase deepness and tunneling length, correspondingly.The latter equation can consider the size, resistance and volume share of each component in nanocomposites as:Since only the shares of filler, tunneling and interphase pieces in the nets can affect the actual resistance, the latter equation is expressed as:The efficient conductivity can be suggested by inverse “All parameters should be determinate to calculate the efficient conductivity.15 by:The percolation start in polymer graphite nanocomposites was statedSince D >  > λ, this equation is simplified to:The latter equation can be developed assuming tunneling and interphase pieces as:So, the percolation start can be estimated by filler size, interphase deepness and tunneling length.44 is given by:The interphase pieces also promote the efficiency of nanofillers in nanocomposites. The total volume portion of interphase in polymer graphene nanocompositesSince the interphase pieces can add to filler nets, the actual volume share of nanofiller consists of both graphene and interphase shares as:45 can be calculated by:Also, the percentages of nanosheets contributing to the conductive netsSupposing the contribution of interphase pieces to the conductive nets by “}φp” Eq. , “f” is So, the volume share of networked graphene is calculated by:form Eq. , which sFurthermore, the volume share of interphase pieces in the nets is given by:When “f” Eq.  and “\do}φi” Eq.  are exchm” is top interphase deepness in graphene nanocomposites. “tm” is 40 nm in the present study. This equation recommends the interphase conductivity by interphase deepness and filler conductivity.Also, it can be suggested that the interfacial attachments manipulate the interphase conductivity in nanocomposites. The interphase deepness commonly represents the extent of interfacial attachments. Consequently, the interphase conductivity is related to interphase deepness as:Moreover, the inherent resistances of graphene and interphase parts can be expressed by:Equations  and 18)18) deterNow, the volume share and inherent resistance of tunneling pieces are defined.43.It was found that the graphene nanosheets are overlapped in nanocomposites and the tunneling conductivity occurs by overlapped nanosheets Fig. 43.The total volume share of tunnels around interphase part in nanocomposites can be given like Eq.  by:19\doBut, only the tunnels in the nets are operative on the efficient conductivity. So, the share of tunnels in the nets is assumed as:g) and the polymer tunnel resistivity (Rp) as:The tunneling pieces in nanocomposites contain polymer layer and graphene nanosheets. As a result, the tunneling resistance considers the inherent resistance of graphene nanosheets in tunneling zones (Rg” and “Rp” can be suggested43 by:2).“RAssuming Eqs. –23, the f”   (PET) (48 and styrene acrylonitrile (SAN)  are calculated as , ,  and  nm for PI, PS, PET and SAN nanocomposites, correspondingly. These levels demonstrate the formation of large interphase and big tunnels in the examples. So, it can be concluded that both interphase deepness and tunneling length control the percolation start and efficient conductivity. These calculations are applied in the novel model to guess the efficient conductivity.The novel model is used to calculate the efficient conductivity in several examples from published articles. Several graphene examples including polyimide (PI)  are obtained as 200, 240), ,  and 300, 1000)  for PI, PS, PET and SAN graphene examples, correspondingly. The highest “d” and the lowest “ρ” are shown in PS/graphene nanocomposite, which cause the minimum level of inherent resistance of tunnels , the estimates of the novel model are acceptable. By these signs, the novel model fittingly displays the variations of efficient conductivity at numerous ranges of “t”. The maximum efficient conductivity of 0.14 S/m is shown at f = 0.6 and Rt = 0.02 Ω, whereas the efficient conductivity decreases to 0 at f < 0.3 and Rt > 0.07 Ω. These outputs designate that the efficient conductivity improves by the high shares of nanosheets and interphase in the nets as well as poor resistance of tunneling pieces. Furthermore, it is understood that the poor share of networked structures and high tunneling resistance meaningfully worsen the efficient conductivity.Figure 58. The large nets provide the efficient transference of electrons, but the small nets weaken the electron moving. Thus, it is rational to get a better efficient conductivity by higher “f”. Moreover, the tunneling resistance oppositely governs the efficient conductivity, because its high level restricts the conductivity of tunneling pieces and the charge transpiration. It is also concluded that only the high resistance of tunneling pieces affects the efficient conductivity, because the negligible levels of graphene and interphase resistances cannot control the electron moving. In fact, great tunneling resistance weakens the charge flow, but graphene and interphase components cannot produce actual resistance in the system. Therefore, the tunneling resistance regulates the efficient conductivity, as proposed by the novel model.The size and compactness of nets expectedly manage the efficient conductivity, for the reason that the conductive nets containing nanosheets and interphase pieces control the extent of electron shifting in nanocompositesThe efficient conductivity was expressed by graphene, tunneling and interphase parts. Also, the volume shares of these components in the nets and their inherent resistances were defined by simple equations. The novel model reveals good predictability compared to tested conductivity of examples. Similarly, the parametric examinations properly justify the stimuli of all factors on the efficient conductivity. These indications approve the correctness of the novel model. The predictions reveal that high filler amount, low percolation level, thin and big nanosheets, dense interphase, short tunnels, wide tunneling area and low tunnel resistivity grow the efficient conductivity. However, graphene and interphase components cannot resist against the electron transportation, while the tunneling resistance governs the electron current. Accordingly, only tunneling resistance affects the efficient conductivity. Among the studied factors, the size of tunnels and tunnel resistivity mainly affect the efficient conductivity. The efficient conductivity can grow to 0.7 S/m at


Furthermore, an equivalent circuit model of the CPW used in the measurements was constructed and simulations were performed, which showed good agreement with the measured results. The results validated the transmission properties of the graphene and the contact impedance at the interface between electrodes and the graphene in CPW circuits, which are necessary parameters for designing antennas using graphene. In addition, by comparing the transmission loss of three types of graphene, the parameters for improving the transmission characteristics were clarified.Graphene has been investigated as a transparent conductive film for use in a variety of devices, and in recent years it has shown promise for use in millimeter-wave devices as 5G technology. In this study, we applied single-layer (SL), triple-layer (3L), and P-type doped 3L graphene to coplanar waveguide (CPW) transmission lines and obtained transmission characteristics (S In particular, transparent conductive materials are attracting attention because they can be installed in a variety of locations without compromising their appearance. For example, indium tin oxide4, indium zinc tin oxide5, and meshed Cu formed on a substrate6 are commonly used, however, these materials have drawbacks such as trade-offs between electrical resistance and optical transparency8. Since our previous report, we have been focusing on chemical vapor deposition (CVD) grown graphene10. In general, graphene has excellent optical transparency and can be transferred onto various shapes and types of substrates due to its robustness and flexibility. If graphene can be implemented as a transparent 5G antenna, it can be embedded in transparent objects that require high optical transparency, such as building windows, car windshields, and mobile phones. However, graphene has higher carrier mobility but lower carrier concentration than metals, resulting in higher electrical resistance. This poses a challenge for its application in millimeter-wave devices. Recently, graphene has been extensively studied as an alternative material to metals, and various studies have been conducted to achieve low resistance while maintaining transparency using methods such as multilayering12 and carrier doping14. There have been reports investigating the electrical properties of graphene itself and its application to millimeter-wave devices. Pan et al. fabricated the slot antennas using ink containing graphene and evaluated their radiation characteristics up to 18 GHz15. Sa'don et al. reported printed array antennas with graphene and their radiation characteristics and beamforming capability at 15 GHz16. Hong et al. compared the electromagnetic interference (EMI) shielding performance of graphene with different qualities by changing the CVD process parameters17. On the other hand, there are limited reports evaluating the characteristics of devices using various types of graphene with different electrical properties in the frequency bands used for 5G technology (24.5 to 27.5 GHz and 37.0 to 43.5 GHz). Zhang et al. have evaluated transmission properties up to 40 GHz by applying graphene to a coplanar waveguide (CPW) with different structures with single layer graphene18. Similarly, Moon et al. evaluated the transmission properties of graphene from 0.5–110 GHz with different number of layers19. Grande et al. evaluated microwave ring resonators with multilayering and SOCl2 doping up to 10 GHz20. While device applications of graphene in the terahertz band23 have attracted much attention, there is insufficient research targeting the millimeter-wave region for 5G applications, which we aim to cover in our study.In recent years, various conductive materials have been considered for applications of millimeter-wave device as fifth generation (5G) technology21) from 1 to 50 GHz. Three types of graphene were fabricated: single-layer (SL), three-layer (3L), and P-type carrier doped 3L graphene with TFSA (Bis (trifluoromethanesulfonyl) amide) as the dopant, and their S21 were measured. Furthermore, the electrical properties of graphene in the CPW were clarified by simulating the S21 using the constructed equivalent circuit model of the CPW and comparing it with the measured S21 of the CPW. The results clarified the behavior of three types of graphene in millimeter-wave devices such as its transmission characteristics and contact characteristics at the interfaces between graphene and electrodes, which are necessary parameter for designing antennas using graphene.In this report, we systematically evaluate the effects of graphene multilayering and carrier doping on transmission characteristics  is required to evaluate optical transmittance evaluation, three types of graphene (10 × 10 mm2) were transferred to a quartz substrate and evaluated optical properties before forming the device. Furthermore, carrier doping was performed on 3L graphene before device fabrication, and the optical transmittance of P-type doped 3L graphene was evaluated. Note that the optical transmittance of the quartz substrate was subtracted for reference to discuss the optical properties of graphene only. As shown in Fig. 24. Being able to improve electrical conductivity while maintaining optical transparency is a unique feature of graphene.The optical transmittances in the visible region of the SL, 3L, and P-type doped graphene are shown in Fig. -1 and 2D peaks at 2680–2700 cm-1, which are characteristic of graphene, were observed as shown in Fig. -1, which may be due to the defects induced during the transferring, stacking and fabricating the CPW processes. Significant damage was not observed with the optical microscope observation in Fig. 2D/IG) correlate with the stacking structure of a multilayer graphene. The obtained I2D/IG of the 3L graphene was 1.5, which is as high as that of SL graphene (I2D/IG = 1.5). As shown in Fig. 2D) from fitting the 2D peak with the Lawrence function indicates that 3L graphene (FWHM2D:35.2) is close to SL graphene (FWHM2D:35.1). These suggested 3L graphene had a turbostratic stacking structure, which is characteristic of multilayer graphene obtained from a layer-by-layer process using polycrystalline graphene grown on polycrystalline Cu foils25. In general, the G peak of graphene originates from the in-plane motion of carbon atoms and shifts toward higher energies with higher carrier density27. In Fig. -1, which supported P-type doping with TFSA.The Raman spectra of the three types of graphene are shown in Fig. 21 of graphene  with guaranteed measurement range from DC to 50 GHz, a probe station , and a vector network analyzer  as shown in Fig. 21 measurement, the CPW was connected to two ports of the vector network analyzer and input impedance of 50 Ω was extracted. After calibrating shorts, opens, loads, and throughs, the S21 was measured.CPWs were used to evaluate the Sene Fig. a. A CPW 30. The contact impedance between graphene and Au in the CPW transmission line was treated as a parallel circuit of contact resistance Rcontact and contact capacitance Ccontact. To prevent delamination of the Au electrodes in the probe measurement, the probe was contacted about 200 µm inside from both ends of the transmission line. For the frequency from 1 to 50 GHz, the areas between the probe contact position and the edge of the transmission line could act as an open stub, so the distance between the probe contacted area and the end of the transmission line was incorporated into the equivalent circuit as a transmission line with a characteristic impedance of 50 Ω  depending on the mobility, Fermi level, and Fermi velocity32. The characteristic exponential relaxation time of τ = 2 picoseconds corresponds to ω/2π = 5.0 × 1011 (500 GHz), which means that the resistor–capacitor (RC) network can be considered constant at least up to 500 GHz34. Furthermore, the skin effect of the conductor is also frequency dependent. The thickness of the skin effect from typical CVD graphene conductivity (1.0 × 106 S/m) is 2.3–16 μm35 from 1 to 50 GHz as calculated using the following equation,36. In parallel with Rgraphene, the parasitic capacitance generation between Au electrodes across graphene channel can also be accounted for, but it was not included in the equivalent circuit model because the electrode thickness (500 nm) is thin and the distance between electrodes across graphene channels (30 μm) in Fig. The graphene channel in the transmission line was expressed only in terms of frequency-independent impedance as Rcontact and Rgraphene of the equivalent circuit model  improved compared to that of SL graphene (1200 cm2/Vs). This suggests that graphene is less likely to be affected by carrier scattering effects from the quartz substrate due to multilayering37. The sheet resistance of graphene (Rsheet) was 758 Ω, 405 Ω, and 125 Ω for SL, 3L, and P-type doped 3L graphene, respectively. The carrier mobility (1090 cm2/Vs) of P-type doped 3L graphene decreased with TFSA doping, while the sheet resistance decreased with high carrier density (4.6 × 1013 cm-2). A comparison of the carrier mobility of SL graphene (4.6 × 1012 cm-2) and 3L graphene (6.8 × 1012 cm-2) shows that carrier doping is effective in lowering resistivity. Rgraphene in the transmission line was determined from Rsheet, taking into account the shape of the signal line of the CPW  and L is the width of the graphene channel in the transmission line  versus SL (42 Ω) and 3L graphene (78 Ω).To determine hod Fig. a. Such phod Fig. b are shoRcontact between graphene and Au electrode, the transfer length method (TLM) was utilized as shown in Fig. RTLM between Au and the graphene40. The value of Rcontact was determined from the contact width between graphene and Au electrode  that contributed to the contact between the Au electrode and graphene. St between the graphene and Au electrodes in the CPW circuit can be expressed asTo obtain W is the width of the CPW signal line (400 μm). P-type doped 3L graphene exhibited an increase in St with P-type doping (5.3 × 10–5 cm2) as shown in Table Rcontact value.Where Ccontact can be treated as a series circuit of the quantum capacitance of graphene (Cq) and the geometrical capacitance (Cg) between Au and graphene.Cq and Cg can be obtained as follows43,EF is the Fermi energy, 8 cm/s), ħ is the reduced Planck's constant, and St' is the effective contact area between graphene and Au in the AC circuit. ε is the dielectric constant, and d corresponds to the distance between the electrode and graphene. Here, in the DC circuit, the effective contact area between graphene and Au (St) can be obtained from the TLM measurement. However, St' in the high-frequency band is difficult to determine because the current distributions in the CPW differ from that in DC measurements due to the current crowding and its frequency dependence. Therefore, Ccontact was treated as a fitting parameter in the analysis of S21, in which the measured S21 is compared to the simulations.21. The simulations were performed using a 3D planar high-frequency electromagnetic software (Sonnet Lite 18.53), and after fitting Ccontact  resulting from the increase in carrier density . This is because the contact area between the Au electrode and graphene in our study . Thus, these results indicated that the large contact area between the Au and graphene enabled the Ccontact to be the dominant factor in the contact impedance.The Au and graphene contacts of the CPW used in this study ware represented by a parallel circuit of udy Fig. a is larg21 of the CPW using the graphene at 1 –50 GHz and comparing them with the constructed equivalent circuit model of the CPW. To our knowledge, our study is the first compare the S21 of various graphene materials with different electrical properties while maintaining transparency. From this comparison, we found that the graphene channel in the CPW can be expressed only in terms of resistance. In addition, multilayering and carrier doping are effective in reducing transmission loss of the graphene, and the contact impedance can be reduced by increasing the contact area between Au and graphene. These are important findings for the design of transparent 5G antenna devices using graphene.Our research clarified the transmission characteristics of graphene for the 5G frequency by experimentally measuring the SIt is evident that graphene will continue to be studied to lower resistivity, increase mobility, and enable processes for larger area, toward a variety of device applications. Our study is one step in that direction, and it has provided valuable insights not only for designing transparent 5G antennas with graphene but also for the design of other devices such as microwave ring resonators, absorber, photodetectors, and terahertz devices using the graphene.21 from 1 to 50 GHz. We also measured the optical and electrical characteristics of the three types of graphene, built equivalent circuit models, and calculated. The agreement between the simulated S21 and measured S21 supports the validity of the constructed equivalent circuit model, in addition, the contact impedance value and the transmission loss of graphene channel were clarified. The comparison of the S21 of the three types of graphene shows that carrier doping and multilayering of graphene are effective in reducing transmission loss while maintaining the transparency of graphene in the operated 5G frequency. The results provide design guidelines for the introduction of graphene as a transparent conductive material in 5G antennas to replace existing materials such as meshed Cu, metal nanowires, and ITO films. Increasing the contact area between Au and graphene was also found to be effective in reducing contact impedance. In designing 5G antennas, it is important to connect the device to the power feed with minimal losses, and our experimental results show that a large contact area between the graphene and electrode is an important consideration as it reduces contact losses.We have fabricated CPWs using three types of graphene and measured the SOur findings provide insights into the design of millimeter-wave devices using graphene and, furthermore, provide the basis for the application of graphene as a radiating element of transparent 5G antennas.Figure 2 (20 sccm) atmosphere for cleaning. Graphene was grown by low-pressure CVD on the Cu foil using H2 and CH4 gas. The CVD growth proceeded for 30 min under H2 (20 sccm) and CH4 (2 sccm) flows at 1000 °C. For transfer processes, PMMA  in an ethyl lactate solution (4 wt%) was spin-coated onto graphene as a supporting layer and cured at 180 °C for 1 min.To grow graphene as a uniform monolayer, Cu foil was selected as a catalyst substrate. Before graphene growth, the Cu foil was annealed at 1000 °C for 30 min in H2:30 sccm, power: 20 W, time: 60 s) was performed on the opposite side of the Cu foil from the side where the PMMA film was formed to remove the unwanted graphene. Then the PMMA coated SL graphene sheet was obtained by etching the Cu foil. To form SL graphene on a substrate, the PMMA-coated SL graphene sheet (size: 10 × 10 mm2) was transferred onto a quartz substrate , and the PMMA was removed by immersing it in an acetone for 12 h. The 3L graphene samples were obtained by a layer-by-layer process in which a PMMA-coated SL graphene sheet was repeatedly transferred to another graphene grown on a Cu foil sample. The rest of the process was the same as that for fabricating SL graphene: etching Cu, transferring to the quartz substrate, and removing PMMA to obtain the 3L graphene on the quartz sample.The PMMA was wiped off with acetone during spin-coating because it also spread around to the back side of Cu foil. In the CVD process, graphene grew on both sides of the Cu foil, causing subsequent Cu etching failure. Therefore, oxygen plasma treatment  to completely remove the resist and unwanted graphene residue . The second process is the formation of the graphene channel. Resist coating, UV exposure using a mask for channel formation, immersion in the developing solution, dipping in the Au etchant, followed by immersion in the developing solution again, and oxygen plasma treatment were performed as in the first process. Through these processes, various devices could be fabricated with graphene.Electrode patterning for each device formation was performed in two steps. The first process is to remove unwanted Au and graphene, and the second step is to remove Au on the graphene channel area. For the first process, a photo resist  was spin-coated onto the Au and cured at 90 °C for 1.5 min. After UV exposure, the samples were immersed in a developing solution ) to remove the resist from areas other than the electrode patterns. The samples were then immersed in Au etchant  for 40 s to form the electrode pattern. Finally, the resist on the electrode pattern was removed using a remover , followed by oxygen plasma treatment  in 1-butanol solution (50 mM) onto 3L graphene, allowing it to soak for 1 min at room temperature in air atmosphere, and then spin coating itSupplementary Figures.


Buckled graphene has potential applications in energy harvest, storage, conversion, and hydrogen storage. The investigation and quantification analysis of the random porosity in buckled graphene not only contributes to the performance reliability evaluation, but it also provides important references for artificial functionalization. This paper proposes a stochastic finite element model to quantify the randomly distributed porosities in pristine graphene. The Monte Carlo stochastic sampling process is combined with finite element computation to simulate the mechanical property of buckled graphene. Different boundary conditions are considered, and the corresponding results are compared. The impacts of random porosities on the buckling patterns are recorded and analyzed. Based on the large sampling space provided by the stochastic finite element model, the discrepancies caused by the number of random porosities are discussed. The possibility of strengthening effects in critical buckling stress is tracked in the large sampling space. The distinguishable interval ranges of probability density distribution for the relative variation of the critical buckling stress prove the promising potential of artificial control by the atomic vacancy amounts. In addition, the approximated Gaussian density distribution of critical buckling stress demonstrates the stochastic sampling efficiency by the Monte Carlo method and the artificial controllability of porous graphene. The results of this work provide new ideas for understanding the random porosities in buckled graphene and provide a basis for artificial functionalization through porosity controlling. Buckling is one of the most common phenomena in low-dimensional nanomaterials. Generally, buckling induces delamination , instabiThe causes of bucking in graphene vary . BendingFor the porosities or the local atomic vacancy defects in graphene, the conventional and analytical deterministic models have a shortcoming in the random distribution quantification and computational cost . As mentCompared with molecular dynamics, the finite element model of graphene has competitive merits in computational costs of buckling analysis, especially for the tremendous stochastic sampling procedures . MoreoveIn this paper, a stochastic finite element model is proposed for the efficient quantification and propagation of the random porosities in buckled graphene. The main contents include the graphene geometrical characterization, method description, and result discussion. The buckling patterns of porous graphene are provided and compared under different boundary conditions. Based on the huge sampling space provided by the stochastic finite element model, the discrepancies caused by the numbers of random porosities are discussed. The work provides an important reference for the exploration of buckled graphene in energy harvest, hydrogen storage, and artificial functionalization.The carbon atoms in graphene are combined with the solid covalent bonds to form the periodic honeycomb lattice, which results in extraordinary material and mechanical properties. In order to describe the special periodic microstructure, the beam element is used to simplify the carbon covalent bonds in the finite element model. The corresponding material and geometrical parameters are settled according to the specific values reported in the literature ,31.P), aN) is a deterministic value. The number of the vacancy defect atoms P and aN.In addition, the percentage of random porosities  is settled as in nditions , the in-In addition, the boundary condition (B3) in the third case is more complicated than that in B1 and B2. As presented in Furthermore, the implementation program and numerical computation are performed by the integration of Matlab (Version 2020a) and ANSYS (Version 14.5) commercial software. The corresponding parameter definition, parameter value assignment, and Monte Carlo stochastic sampling are completed under the Matlab programming environment. ANSYS parameter design language (APDL) is used to create the finite element model for porous graphene and perform mechanical computation for elastic buckling. The flowchart of the stochastic finite element model by the combination of Monte Carlo stochastic sampling with the finite element computation is shown in In The critical buckling stress is the key factor in controlling the elastic recycling process efficiently . The eigIn order to compare the impacts of boundary conditions, the buckling patterns of both the porous graphene and the pristine graphene under different boundary conditions are presented in Under the third and fourth boundary conditions, the effects of random porosities in the buckling patterns are more apparent than those under the above-mentioned two boundary conditions. In The buckling patterns provide the deformation shape of porous graphene under compressive loads. For the hydrogen storage and energy harvest by the porous graphene, besides the buckling patterns, the critical buckling stress is the key factor to operate and control the process. The critical buckling stress is the compressive load at which the structure suddenly buckles or loses stability. Therefore, the critical buckling stress calculation for porous graphene needs further exploration. On the other hand, the randomly distributed porosities inevitably exist in the graphene sheets and nanoribbons with the current research and manufacturing technologies. The discrepancies caused by the numbers of random porosities are also essential to be analyzed and discussed.In order to further analyze the effects of random porosities in buckled graphene, the randomly distributed porosities in graphene are propagated by the repeated Monte Carlo stochastic sampling procedure. Different percentages of random porosities and boundary conditions are performed in the stochastic finite element model. The percentages of random porosities propagated in graphene are 0.2, 0.5, 1, 3 and 5%, respectively, and they are represented by P1, P2, P3, P4, and P5.In general, the atomic vacancies lead to the reduction of critical buckling stress compared with that for the pristine graphene under all four boundary conditions, since the mean of the relative value is less than one as in x and y axes are dimensionless units. The x-axis is relevant to the percent of atomic vacancy defects; the y axis corresponds to the relative value between the results of porous graphene and pristine graphene. In Furthermore, the fluctuation levels of the critical buckling stress caused by the location randomness of atomic vacancy defects are also computed by comparison with the pristine graphene. In According to the computational results of the stochastic finite element model, the specific situations caused by the location distribution of atomic vacancies are also tracked. As presented in In order to more precisely analyze the random porosities in the buckled graphene, the probability density distribution of the bucking critical stress under different boundary conditions is computed and presented in The differences in the probability density distribution of the relative variation for critical buckling stress are also presented in In addition, the shapes of the probability density distribution in The buckling patterns and critical stress of porous graphene are sensitive to boundary conditions.The randomly distributed atomic vacancy defects in porous graphene destroy the regularity and symmetry of buckling patterns.The possibility of strengthening effects in critical buckling stress is tracked under the first, third, and fourth boundary conditions.The distinguishable interval ranges of probability density distribution for the relative variation of the critical buckling stress prove the promising potential of artificial control by the atomic vacancy amounts.It is a potentially feasible method to improve the hydrogen storage and release performance by the adaptation and change in the boundary condition of the porous graphene.The approximated Gaussian density distribution of critical buckling stress demonstrates the stochastic sampling efficiency by the Monte Carlo method and the artificial controllability of porous graphene.The results of this work provide new ideas for understanding the random porosities in buckled graphene and provide a basis for energy harvest, hydrogen storage, and artificial functionalization.This paper proposes an efficient numerical model for the random porosity quantification and propagation in pristine graphene. Based on the huge sampling space of the stochastic finite element model, the following points can be concluded: