Several detection techniques, including fluorescent, electrochemical, and electrical methods, have been extensively investigated to selectively recognize K+ ions. In this work, a highly sensitive and selective biosensor based on single-layer graphene has been developed for K+ ion detection under Van der Pauw measurement configuration. With pre-immobilization of guanine-rich DNA on the graphene surface, the graphene devices exhibit a very low limit of detection (≈1 nM) with a dynamic range of 1 nM–10 μM and excellent K+ ion specificity against other alkali cations, such as Na+ ions. The origin of K+ ion selectivity can be attributed to the fact that the formation of guanine-quadruplexes from guanine-rich DNA has a strong affinity for capturing K+ ions. The graphene-based biosensors with improved sensing performance for K+ ion recognition can be applied to health monitoring and early disease diagnosis.Potassium (K Graphene-based biosensors have attracted much research interest recently.Potassium  of a thin semiconductor, by placing it in a magnetic field with a four-point electrode configuration [+ ion biosensors exhibit a high sensitivity as low as 1 nM (10−9 M) and an excellent selectivity (≈4 times) for effectively distinguishing between potassium and sodium ions. The results presented here provide helpful guidance for the design of high-performance ion-selective biosensors for use in healthcare and medical monitoring applications.In this contribution, we fabricated the Hall effect biosensors made of CVD-grown single-layer graphene for detecting Kguration . The car4 and H2 (15:15 sccm) was then flowed into the system to form graphene layers on the copper surface at 1050 °C for reaction of 20 min, followed by cooling the furnace down naturally to room temperature.The graphene films were grown using a thermal CVD with the employment of a 25 µm-thick copper foil as the catalyst  with 25 µm in thickness. The pristine copper foil was cleaned in acetone by ultrasonication for 10 min to remove surface-adsorbed organic impurities. In order to grow graphene, copper foil was set in a tube furnace system, which was heated from room temperature to 1050 °C at a heating rate of 17.5 °C/min with 40 sccm hydrogen flow. When the furnace temperature reached 1050 °C, the copper foil was annealed for an additional 40 min for full reduction of native surface oxide layer. A gas mixture of CH2 layer. The copper foil with graphene layers on the surface was first cut into a sheet with a size of 8 mm × 8 mm, and then a ≈200 nm-thick PMMA layer was deposited on the graphene surface by spin-coating at a spin speed of 500 rpm (10 s) and 4000 rpm (1 min), respectively. The copper foil was then etched away by immersing the sample in 0.1 M ammonium persulfate ((NH4)2S2O8) aqueous solution at 60 °C for 5 h. After complete removal of copper, the PMMA/graphene layer was cleaned with deionized water 3 times and fished onto the SiO2/Si substrate. The sample was dried at 60 °C for 30 min on the hot plate, followed by immersing in acetone at 60 °C for 6 min to dissolve the PMMA. Finally, a post-annealing treatment was performed at 450 °C to improve the interface between graphene and the substrate, as well as guarantee the surface cleanness by decomposition of PMMA micro-residues.In order to fabricate the biosensor, the as-prepared graphene films need to be detached from copper foil and then placed on the silicon substrate coated with a 300 nm insulating SiOThe morphology, quality, and surface chemical compositions of graphene films were identified using optical microscope , atomic force microscopy , Raman spectrometer with 532 nm excitation wavelength of He–Ne laser , and X-ray photoelectron spectroscopy , respectively. The transmittance of the sample in the visible light region was determined by UV-Vis spectroscopy . The electrical signals of graphene biosensors for the detection of alkali ions were recorded by Hall effect measurement system .2/Si substrate is very weak. The characteristic peaks of graphene can be found in its Raman spectrum (−1) and a strong 2D-band (≈2700 cm−1) [−1), the high I2D/IG ratio (1.98), and the narrow full-width at half-maximum of 2D-band (≈38 cm−1) demonstrate the nature of high-quality single-layer graphene prepared by the catalytic CVD method. The organic contaminants would be introduced to the graphene surface during the transfer process and also degrade sensor performance [The layer number and quality of graphene films were identified as presented in spectrum b with a 00 cm−1) ,32. The formance . As the formance ,34. The formance ,36. Figu+ ions, a flexible single-stranded DNA with guanine-rich sequences (5′-GGTTGGTGTGGTTGG-3′) was immobilized on the graphene surface as a probe, which could fold into a tetraplex structure (guanine-quadruplexes) with K+ ions due to the formation of intramolecular hydrogen bonding [n-doping and charged impurity scattering from the immobilized DNA strands, respectively [R) is determined by the product of carrier concentration (n) and mobility (μ) based on the Van der Pauw principle: R + ion detection without the interference from the background buffer ions and DNA probes.It is well known that the basal plane of graphene exhibits a strong interaction with foreign molecules, such as antigens, DNAs, proteins, etc., leading to the achievement of a very low detection limit of the biosensors based on graphene . However bonding . Before ectively ,40,41. I∝ 1/(μn) . We foun+ ion specificity of probe DNA-immobilized graphene device, a control experiment using Na+ ions was implemented and the sensor measurements using the graphene without functionalization were also performed for the comparison. The solutions containing K+ and Na+ ions with the desired concentrations were prepared by dissolving KCl and NaCl in 1× TE buffer, respectively. The device after incubation with DNA probes was rinsed with 1 mL 1× TE buffer for 3 times to remove weakly bound DNAs, and the electrical properties of graphene were recorded. The unfunctionalized graphene was also immersed in 1× TE buffer for 15 h, followed by the same rinsing process. A 100 μL drop with 1 nM K+ ions was individually placed on the surface of graphene with and without DNA immobilization for 6 h, and the electrical properties were recorded again after washing with 1× TE buffer. The standard deviation of each data point in + ions to demonstrate the selective detection of our sensors. As shown in + ion recognition, even the graphene surface has been modified with guanine-rich DNA strand. In + and Na+ ions in the case of probe DNA-immobilized graphene, suggesting that the monitoring of carrier concentration of the Hall effect device can effectively distinguish K+ ions from other alkali ions. In order to examine the K+ ion recognition was investigated, as presented in 13 to 1.30 × 1013/cm2) when the K+ ion is the target. In contrast, it decreases only 4.7% (from 1.90 × 1013 to 1.81 × 1013/cm2) for sensing Na+ ions, demonstrating that our graphene sensing platform based on the Van der Pauw measurements provides a high sensitivity and distinct selectivity for the detection of K+ ions. Compared to other graphene-based devices [+ ions was reported using mechanically exfoliated graphene FETs [+ ions (diameter: ≈2.7 Å), a bipyramidal antiprismatic arrangement can be implemented accordingly [+ ions was much larger than other interference ions, even the added concentration of interference ions (10 nM) is 10 times higher than that of K+ ions (1 nM). The signal deviation for K+ ions is 3.2 and 16.3 times higher than that of Na+ and other cations , respectively. The results confirm that the proposed graphene biosensor not only shows a high sensitivity, but also has a pronounced selectivity towards K+ ions.The performance of graphene biosensors functionalized with DNA probes for selective K devices ,44,45, aene FETs . The higene FETs ,47,48,49+ ions. We demonstrated that among the electrical properties determined from Van der Pauw measurements, the change of carrier concentration of the device is extraordinarily sensitive to the added K+ ion concentration, and less dependent on that of Na+ ions. The K+ ion specificity is attributed to the spatial matching between K+ ions and guanine-quadruplexes, which is a tetraplex structure folded from guanine-rich DNA strands immobilized on the graphene surface. As a result, our devices exhibit a low detection limit (≈1 nM), wide dynamic range (1 nM–10 μM), and remarkable K+ ion selectivity against Na+ and other cations. The proposed sensing platform is feasible and effective in monitoring potassium ions in chemical and biological environments.In summary, the Hall effect biosensor fabricated with single-layer CVD graphene shows great sensitivity for highly selective detection of K


Background. The natural history of idiopathic pulmonary fibrosis (IPF) is very complex and unpredictable. Some patients will experience acute exacerbation (AE) and fatal outcomes. Methods. The study included 30 AE-IPF patients, 32 stable IPF (S-IPF) patients, and 12 healthy controls. We measured the plasma concentrations of leptin and KL-6. Simple correlation was used to assess associations between leptin and other variables. Plasma leptin levels were compared between AE-IPF and S-IPF subjects, decedents, and survivors. Kaplan-Meier curves were used to display survival and Cox proportional hazards regression was used to examine risk factors for survival. Results. In subjects with AE-IPF, plasma leptin was significantly greater than in subjects with S-IPF (p = 0.0003) or healthy controls (p < 0.0001). Plasma leptin was correlated with BMI, KL-6, LDH, CRP, and PaO2/FiO2 . Plasma leptin was significantly greater in 33 decedents than in the 23 survivors (p = 0.007). Multivariate Cox regression analysis showed leptin (>13.79 ng/mL) was an independent predictor of survival (p = 0.004). Conclusions. Leptin could be a promising plasma biomarker of AE-IPF occurrence and predictor of survival in IPF patients. The natural history of idiopathic pulmonary fibrosis (IPF) is characterized by decreasing pulmonary function over time. Some patients may experience acute exacerbations (AE)—sudden worsening of pulmonary function, increased oxygen requirements, new opacities on chest imaging, and a diffuse alveolar damage (DAD) pattern of lung injury without an identifiable etiology . EstimatLeptin was first discovered and cloned by Zhang et al. in 1994 . Leptin β1) ..p < 0.00 Cox model that included leptin and controlled for two other clinically important predictors, leptin was the independent predictor of time-to-death (In a multivariableto-death .p < 0.001) (p = 0.004)  and 13.79 ng/mL , respectively. The area under the ROC curve for leptin in distinguishing AE-IPF from S-IPF was 0.761   and for = 0.004) .p = 0.000; 0.729, p = 0.003) was a better biomarker of IPF acute exacerbation and survival than CRP   and 1(B) in Supplementary Material available online at http://dx.doi.org/10.1155/2016/6940480).CRP is also significantly elevated in patients with AE-IPF than S-IPF shown in . By compIn this study, we assessed plasma leptin concentrations in patients with IPF and in healthy controls and found the following: leptin concentration was higher in subjects with AE-IPF than those with S-IPF and higher in subjects who died than in those who survived to vital status ascertainment. Survival was significantly shorter for patients with leptin levels above, compared with those below, 13.79 ng/mL, and leptin was an independent predictor of survival when controlling for age and oxygenation.The causes and mechanism of acute exacerbation in patients with IPF remain unclear, although it is well known that patients with AE-IPF have significant morbidity and high mortality , 4. Idenβ1 signaling in lung fibroblasts; it does so by inhibiting PPARγ. In addition, leptin signaling is required for bleomycin-induced lung fibrosis [Leptin is a proinflammatory cytokine and plays an important role in the pathogenesis of ARDS, liver, and lung fibrosis , 18, 23.fibrosis . Additiofibrosis , 27. We The mortality of AE-IPF subjects was significantly higher than S-IPF subjects, consistent with the published reports –4. In adThis study has limitations. First, the number of patients and normal controls enrolled was small, and the sample was entirely Asian (Chinese). These may substantially limit the ability to generalize results to the IPF universe, including the 13.79 ng/mL cut-off value. We have no data on the within-subject variability of leptin; levels from the same patient in different clinical circumstances  would be informative and provide data to further support the utility of leptin as a biomarker of disease. A prospective, multicenter, and multinational study of a larger patient cohort would be useful to help provide additional data on leptin.In summary, we found that leptin was elevated in AE-IPF and that high plasma leptin concentrations are associated with poor survival. Additional research is needed to confirm and extend these results, to determine whether and how leptin plays a role in the pathogenesis of AE, and to delineate the utility of plasma leptin as a biomarker of AE-IPF occurrence and predictor of survival in IPF patients.Plasma leptin level  was a better marker of IPF exacerbation and survival than CRP .


This value is in excellent agreement with reported macroscopic values and our atomistic simulations. This implies mechanical properties of graphene scale down to a few-nanometre length. The simplicity of our method provides a unique opportunity to investigate the local variability of nanomechanical properties in layered materials.The interest in mechanical properties of two-dimensional materials has emerged in light of new device concepts taking advantage of flexing, adhesion and friction. Here we demonstrate an effective method to measure adhesion of graphene atop highly ordered pyrolytic graphite, utilizing atomic-scale ‘blisters' created in the top layer by neon atom intercalates. Detailed analysis of scanning tunnelling microscopy images is used to reconstruct atomic positions and the strain map within the deformed graphene layer, and demonstrate the tip-induced subsurface translation of neon atoms. We invoke an analytical model, originally devised for graphene macroscopic deformations, to determine the graphite adhesion energy of 0.221±0.011 J m Analysis of the mechanical properties of two-dimensional materials is important for device development. Here, the authors report a microscopic method for measuring the adhesion of graphene on top of highly ordered pyrolytic graphite, which exploits atomic-scale blisters formed upon neon atom intercalation. We intercalate neon atoms into graphite, which in turn deform enclosing graphene sheets to create atomic-scale blisters on the surface. Detailed experimental analysis of these atomic blisters leads to a direct estimate of adhesion energy of ∼0.221 J mh of ∼0.14 nm and full-width at half-maximum of ∼0.93 nm, respectively  charge transfer between the intercalated Ne atoms and surrounding carbon atoms of the graphite, further asserting that we can treat Ne intercalates as essentially neutral atoms.Representative scanning tunnelling microscopy (STM) images of graphene blisters on highly ordered pyrolytic graphite (HOPG) are shown in ectively . For refectively . The vanectively , we esti eV refs , 22. Ourx–y–z coordinate map of atom centres extracted from et al.et al.To map out atomic positions and their local neighbourhoods, we employed image processing as illustrated in et al.h>10 nm). The nonlinear plate model is generally more accurate and suitable for all sized bubbles. Within this model, the adhesion energy (Γ) of the graphene blister having a characteristic radius a and a height h, 10μ represents a function of the Poisson ratio ν:Here h<0.3 nm and h<<a. In such cases the first term in The linear plate model is an approximation of the nonlinear plate model for small sized bubbles generally having h and radius a. Although this linear plate model was derived for a small blister, it's validity for atomic scale is not clear a priori. In this study, we test this model extension by using the simplified version of the linear plate model given in h and the radius a of the atomic blister, we fit the STM line-profile with a Gaussian function:which is simply a function of the blister's height as indicated by the red curve in a and the height h, and obtained the adhesion energy via −2  unit, E2D is the 2D Young's modulus of graphene, D is the bending stiffness, a and h are radius and height of the blister; while μ represents the function of the Poisson ratio ν given in E2D=0.323 TPa nm and ν=0.179, we estimate a pressure of 5.4 GPa within the nonlinear plate model (an estimate for the membrane model is 6.3 GPa). For reference, the pressure of the macroscopic blisters determined in the work of Yue et al.where −2. Notably the adhesion energy does decrease with the increase in the number of intercalated Ne atoms. These results suggest that the local adhesion of graphene layers can be substantially influenced by an increase in the number of intercalated neon atoms, particularly if they are localized in the same region. It is also expected that further increase in concentration of intercalated neon atoms can induce local exfoliation of the top graphene layer.Our approach is further validated by atomistic modelling using DFT calculations. Our experiments further indicate the feasibility of tip-induced manipulation of subsurface Ne atoms. et al.One may question the applicability of STM to measure topographic height. In fact, it is well-known that the atomic corrugation of graphite in STM images depends on the tip conditions3031323334353632333233z-height in this case to make the atomic corrugation in −2 was obtained out of 32 total measurements of the rescaled blister . Nc-AFM detects short-range forces, and the nc-AFM image provides direction information about the corresponding tip–surface interactionIn conclusion, we demonstrate a direct method to measure the adhesion energy of graphene on graphite, by intercalating inert gas atoms between graphene sheets. Measurements are based on the shape and heights of the graphene blisters at the atomic scale and analysed using analytical methods (linear plate models) and DFT calculations. Our results are in good agreement with recently reported direct measurements of adhesion energy for graphite. Local topographic analysis also provides detailed atomic information related to the graphene blisters, such as local strain and the mobility of subsurface noble gas atoms. We envision that this methodology can be applied to other layered materials to estimate the adhesion energy and the related elastic mechanical properties at atomic level. Moreover, intercalation of noble gas atoms may provide a feasible pathway to create electronically interesting ‘Gaussian' impurities39−10 mbar. The nc-AFM measurements were carried out in the same system with a SPECS Kolibri sensor. HOPG was freshly cleaved by the scotch tape method and quickly transferred into ultrahigh vacuum. The HOPG was subsequently annealed up to 500 °C for ∼20 min. The blisters and associated defects on HOPG were created by briefly sputtering the sample with Ne+ ions . These sputtering conditions are necessary for the reproducibility of atomic sized blisters. Lighter neon was chosen over argon to minimize creation of point defects by sputtering. STM images were taken after cooling the sample to both liquid nitrogen (77 K) and liquid helium (4.3 K) temperatures. The STM profile measurements over different blisters taken at 77 and 4.3 K yield consistent results, suggesting in this temperature range adhesion energy shows little change, as may be expected  positions were determined with subpixel precision using a combination of image processing and fitting routines. After the atomic positions were established, a survey of the six nearest neighbours was conducted to obtain the data in An HOPG sample (Grade SPI-1) was purchased from SPI Supplies. The experiments were conducted by using the SPECS Joule-Thomson (JT) cryogenic STM/AFM in an ultrahigh vacuum chamber with a base pressure ≤1 × 10cted see . Atomic-ab initio simulation package (VASP)434649−1 k-point separation was used for STM image calculations.The adsorption properties of Ne atoms in the gap between two parallel graphene layers were investigated based on DFT calculations using Vienna The data that support the findings of this study are available from the corresponding author upon request.How to cite this article: Wang, J. et al. Atomic intercalation to measure adhesion of graphene on graphite. Nat. Commun.7, 13263 doi: 10.1038/ncomms13263 (2016).Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.Supplementary Figures 1-6, Supplementary Notes 1-3 and Supplementary References.


There are many reasons why microbial community composition is difficult to model. For example, the high diversity and high rate of change of these communities make it challenging to identify causes of community turnover. Furthermore, the processes that shape community composition can be either deterministic, which cause communities to converge upon similar compositions, or stochastic, which increase variability in community composition. However, modeling microbial community composition is possible only if microbes show repeatable responses to extrinsic forcing. In this study, we hypothesized that environmental stress acts as a deterministic force that shapes microbial community composition. Other studies have investigated if disturbances can alter microbial community composition, but relatively few studies ask about the repeatability of the effects of disturbances. Mechanistic models implicitly assume that communities show consistent responses to stressors; here, we define and quantify microbial variability to test this assumption. A central pursuit of microbial ecology is to accurately model changes in microbial community composition in response to environmental factors. This goal requires a thorough understanding of the drivers of variability in microbial populations. However, most microbial ecology studies focus on the effects of environmental factors on mean population abundances, rather than on population variability. Here, we imposed several experimental disturbances upon periphyton communities and analyzed the variability of populations within disturbed communities compared with those in undisturbed communities. We analyzed both the bacterial and the diatom communities in the periphyton under nine different disturbance regimes, including regimes that contained multiple disturbances. We found several similarities in the responses of the two communities to disturbance; all significant treatment effects showed that populations became less variable as the result of environmental disturbances. Furthermore, multiple disturbances to these communities were often interactive, meaning that the effects of two disturbances could not have been predicted from studying single disturbances in isolation. These results suggest that environmental factors had repeatable effects on populations within microbial communities, thereby creating communities that were more similar as a result of disturbances. These experiments add to the predictive framework of microbial ecology by quantifying variability in microbial populations and by demonstrating that disturbances can place consistent constraints on the abundance of microbial populations. Although models will never be fully predictive due to stochastic forces, these results indicate that environmental stressors may increase the ability of models to capture microbial community dynamics because of their consistent effects on microbial populations.IMPORTANCE There are many reasons why microbial community composition is difficult to model. For example, the high diversity and high rate of change of these communities make it challenging to identify causes of community turnover. Furthermore, the processes that shape community composition can be either deterministic, which cause communities to converge upon similar compositions, or stochastic, which increase variability in community composition. However, modeling microbial community composition is possible only if microbes show repeatable responses to extrinsic forcing. In this study, we hypothesized that environmental stress acts as a deterministic force that shapes microbial community composition. Other studies have investigated if disturbances can alter microbial community composition, but relatively few studies ask about the repeatability of the effects of disturbances. Mechanistic models implicitly assume that communities show consistent responses to stressors; here, we define and quantify microbial variability to test this assumption.Author Video: An author video summary of this article is available. Many central questions in ecology focus on the sources of variability in populations. Accuracy of predictions is highly valued in ecological studies, and population size is necessarily more predictable when populations are less variable , 2. StilSome variability naturally exists in all populations. Disturbances could act either to increase or to decrease this level of variability , 7. The Predicting the composition of microbial communities using environmental disturbances is a major objective of microbial ecology . Here, w16–To address the strong interest in understanding drivers of variability in microbial community composition, some studies have analyzed the range of compositions observed in bacterial communities following novel disturbances. These experiments have found consistent changes in community composition due to the disturbance , 21. ThuIn this study, we imposed several disturbance regimes upon periphyton communities in order to examine the effects of disturbances on the variability of populations within the periphyton. Our goal was to determine whether disturbances have repeatable effects on periphyton communities. After initially growing 108 periphyton communities on Plexiglas slides in a common environment, we then randomized each of these replicate communities into one of nine treatments, each corresponding to a different disturbance regime. To generate these nine treatments, we subjected periphyton communities to one of three possible conditions  at two time points. These two disturbances were selected because they are both potential consequences of the high-wind events that occur in our study system . This 3 We quantified the variability of populations between communities within each treatment using the coefficient of variation (CV) of each taxon. The coefficient of variation is calculated as the standard deviation of the populations divided by the mean abundance of the populations and therefore has the advantage of accounting for variance-mean scaling . We tranPeriphyton colonized Plexiglas slides suspended in a shallow  eutrophDiatom taxa on slides were enumerated by light microscopy to measure the abundance of each taxon within the periphyton biofilm. We used linear mixed models to analyze how the variability of taxa in the disturbed treatments compared to the variability of taxa in the undisturbed treatment, AA. The fixed effects in the model were 4 binary variables corresponding to whether the community received the depth disturbance at T1, the scouring disturbance at T1, the depth disturbance at T2, or the scouring disturbance at T2. A random effect for taxon was included, under the assumption that taxa have differing amounts of inherent population variability. The response variable in the linear mixed models was the square root CV of the taxon populations, measured in density per square centimeter. A lower CV corresponded to lower variability of a taxon between communities in the same treatment. The estimated treatment effects from the mixed model represent the mean differences in square root CVs between a given treatment and the undisturbed treatment, AA.P values were obtained from the linear mixed model for the diatom taxa. The scouring disturbance reduced the square root CV of the diatom communities by a mean of 0.155 at T1 (P = 0.0343) and by 0.158 at T2 (P = 0.0307). The altered-depth disturbance reduced the square root CV by 0.156 at T1 (P = 0.0330) and by 0.230 at T2 (P = 0.0016). Thus, densities of diatom taxa became more consistent as a result of experiencing one disturbance, regardless of whether the disturbance was applied at T1 or T2.The treatment that had the highest mean taxon square root CV was the undisturbed treatment, AA. Thus, taxon populations in the AA treatment were the most variable of any treatment. The four treatments that received one disturbance, SA, AS, DA, and AD, all had significantly lower square root CVs than the AA treatment . These tP = 0.0458 and P = 0.0363, respectively). In these treatments, which received the same type of disturbance at T1 and T2, the taxa were more variable than would be expected from the independent effects of the disturbances at T1 and T2. However, there was no significant interaction between disturbances in communities that experienced different types of disturbances at T1 and T2 (corresponding to treatments DS and SD). Therefore, communities that received different disturbances at the two time points continued to become less variable as a result of experiencing another disturbance, whereas communities that experienced the same disturbance twice did not become as consistent.In both the DD and SS treatments, there were significant positive interactions between the disturbances at T1 and T2  to determine if the community composition shifted as a result of the disturbances. We compared the undisturbed treatment, AA, to the disturbed treatments to identify whether the disturbed communities separated from the AA treatment in community composition. Strong separation of disturbed and undisturbed communities would indicate novel community development in the disturbed treatments. The PCA for the diatom communities captured 97.2% of community variability in the first two axes. The first axis, responsible for 92.8% of variability, represented the tradeoff between communities dominated by The communities in the undisturbed treatment, AA, occupied a large area of the PCA space see . CommuniP values reported for the bacterial communities were obtained from this analysis.Bacterial community composition in the periphyton was determined using a PCR-based DNA fingerprinting method called automated ribosomal intergenic spacer analysis (ARISA) . This meThe analyses for the bacterial communities used the residuals from detrended taxon CVs as the response variable. Detrending was performed because the CVs of the OTUs showed a strong relationship with mean OTU abundances, whereby OTUs with higher mean abundances had lower CVs. To remove the effect of mean abundance, we fitted an exponential model of the OTU CVs as a function of log(OTU mean abundances) . We thenFor the bacterial communities, AA had the median level of variability out of the nine treatments. However, no treatment was significantly more variable than the AA treatment. No single disturbance at either T1 or T2 had significant effects on the variability of OTUs . Thus, tAs with the diatom communities, we compared the bacterial community composition of the AA treatment to those of the disturbed treatments using a PCA. We evaluated whether the communities in the AA treatment separated from the communities in disturbed treatments to determine if there were consistent compositional differences between the undisturbed and disturbed communities. The PCA for the bacterial communities captured 51.2% of community variability in the first two axes. The first axis accounted for 27.6% of community variability, and the second axis accounted for 23.6% of the variability. The loadings on these two axes were primarily from the most abundant OTUs across all treatments.The communities in the undisturbed treatment, AA, occurred in close proximity to disturbed communities in PCA space . FurtherP = 0.540, P = 0.554, and P = 0.754 for Sorensen, Euclidean, and Bray-Curtis metrics, respectively).We used three different dissimilarity metrics  in Mantel tests to evaluate whether differences in the diatom communities were related to differences in the bacterial communities. There was no significant relationship between the bacterial and diatom communities for any of the three metrics used  disturbances decrease the variability of populations within diatom and bacterial communities and that (ii) multiple disturbances have interactive effects. For the diatom communities, every treatment that experienced a single disturbance had a significantly lower square root CV than did the AA treatment. This consistent result shows that communities that were disturbed once became less variable than communities that were undisturbed. However, double disturbances did not necessarily cause the communities to become increasingly more consistent. Both the SS and the DD treatments had significant positive interactions, showing that these communities were more variable than would be expected based on the independent effects of the single disturbances. However, the treatments that experienced different disturbances at the two time points (SD and DS) continued to become less variable as a result of the second disturbance. Thus, for the diatom communities, different disturbances continued to increase the consistency of the diatom communities, although the same recurring disturbance appeared to be saturating in effect. Therefore, the interactions between sequential disturbances were important to understanding community dynamics in treatments that were disturbed twice.For the bacterial communities, no single disturbance had a significant effect on the variability of OTUs within the communities. However, three of the four treatments that experienced two disturbances had interactive effects, all of which led to lower population CVs. Thus, multiple disturbances to the bacterial communities generally created communities that were less variable than communities that were disturbed once. The strong interactions indicate that multiple disturbances had novel effects on the communities, such that the communities that experienced two disturbances demonstrated much-different responses than the communities that experienced only one disturbance. Additionally, it appears that high levels of disturbance were necessary to generate changes in the bacterial communities, because the only treatments to show significant effects were disturbed twice. This was not surprising, as pelagic lake bacterial communities were previously found to be highly resilient to disturbances  and therDespite differences in how the diatoms and the bacteria responded to individual treatments, there were several broad similarities between the diatom and bacterial responses to disturbances. For instance, none of the disturbed treatments in either the diatom or bacterial communities showed significantly greater variability than the undisturbed treatment, AA. Additionally, in both the diatom and the bacterial communities, at least two of the three least variable treatments were highly disturbed, having experienced two disturbances . These rThe differences in the diatom and bacterial responses to individual disturbance treatments may be due to additional drivers of population variability within these two communities. For example, the strength and number of species interactions in a community can also be an important determinant of population variability . AlthougGomphonema species have been found to be tolerant of turbulent conditions, showing high abundances in water currents , whereas the altered-depth disturbance was a sustained perturbation (press disturbance). The similar responses of the communities to these two disturbances are in line with a recent review showing that a high proportion of microbial communities are sensitive to both press and pulse disturbances; of the experiments reviewed, 92 of 112 microbial communities showed a change in composition or function in response to a pulse disturbance, and 141 of 178 communities changed in response to a press disturbance . Thus, tIn addition to the experimental disturbances, there are many other possible factors that could have influenced the variability of populations within the periphyton. For instance, the periphyton communities experienced environmental variability throughout the duration of the experiment due to natural weather conditions and small-scale variability in environmental forces. Acknowledging this environmental stochasticity, we intentionally implemented experimental disturbances that were more extreme than the natural variability that we observed during this time period. Additionally, we did not account for colonization of diatoms or bacteria after disturbances were implemented, which may have generated additional variability in these communities. However, because the Plexiglas slides were rerandomized between disturbances, we expect systematic bias from immigration to be minimal between treatments. Furthermore, the diatom and bacterial data sets are complementary in their strengths; the diatom data were obtained through direct counts, meaning that there is high accuracy in identification, although only a subsample of the community was measured. Conversely, nearly the entire bacterial community was sampled but with some degree of bias from using ARISA . Thus, bPrediction of microbial communities is an oft-cited goal of microbial ecology. However, predictive models can be accurate only if the process that they are describing is inherently repeatable. For instance, statistical models will produce a good fit to microbial community composition data only if these microbial communities show consistent responses to environmental drivers. The results of these experiments indicate that microbial communities do show repeatability in their response to environmental stress, because communities became more similar to one another after experiencing the same disturbance. This finding could be tested in other systems by examining whether predictive models of bacterial community composition  lake inDisturbances were implemented at two time points. At the first time point, day 20, we randomly assigned 36 of the 108 slides to each of the following conditions: ambient (no disturbance), altered-depth disturbance (relocation to an 0.5-m depth), or water-scouring disturbance. Weekly water column profiles showed that Secchi depth during the summer of 2013 varied between 1.5 m and 3.3 m, with 11 to 33% of surface photosynthetically active radiation (PAR) reaching 3-m depth. We chose these two disturbances  because they mimic natural disturbances to periphyton communities in the lake due to the high-wind events that are common at our study site , 47. DurSimilarly, on day 25, we again randomized the slides into three groups and manipulated the slides with the disturbances described above, incubating the slides for another 5 days. On day 30 of the experiment, we retrieved the Plexiglas slides from the lake and froze the slides at −20°C until further processing. Additional details about the experimental manipulations are provided in 10.1128/mSystems.00013-16.3Figure S1 Figure S1, PDF file, 0.1 MB.At the start of the experiment, the 108 Plexiglas slides were distributed across 6 identical metal racks. All 6 racks were deployed side by side on buoy lines in Lake Myvatn and were suspended 0.3 m from the sediment surface. After 20 days of periphyton colonization (T1), slides were again randomized before experiencing the first disturbance. Again, on day 25, slides were randomized onto new racks corresponding to the disturbance experienced at T2. Download Copyright © 2016 Herren et al.2016Herren et al.Creative Commons Attribution 4.0 International license.This content is distributed under the terms of the Slides were removed briefly from the freezer to obtain diatom counts on a microscope before being frozen again. Diatoms were identified to the lowest taxonomic resolution possible, which was genus or species. A minimum of 500 individuals per slide were identified by counting half-transects across slides. The mean number of individuals identified per sample was 1,063, for a total of 114,843 individuals across the 108 Plexiglas slides. We then transported the slides to Madison, WI, USA, for analysis of the bacterial communities in the periphyton using automated ribosomal intergenic spacer analysis (ARISA) , 49. BriNitzschia holsatica, Cymbella spp., Synedra spp., Gomphonema spp., Rhoicosphenia spp., Cocconeis spp., colonial Fragilaria spp., and singular Fragilaria spp.). Together, these 8 taxa accounted for 99.4% of all individuals counted. We standardized all data to densities of each taxon per square centimeter. For each of the nine treatments, we calculated the coefficient of variation (CV) for each of the 8 taxa across the 12 slides in that treatment. We chose the CV as the indicator of population variability because it did not change in response to the mean abundance of the taxa and because it showed homogeneity of variance between treatments. Additionally, the CV integrates across all 12 slides within a treatment and mitigates the effects of any single anomalous communities. We transformed the CVs by taking their square root because the distribution of CVs was slightly skewed toward larger values.Because some taxa were rare and therefore were inconsistently present in samples, we analyzed only the 8 most common diatom taxa  were binary vectors corresponding to whether or not the taxon was in a treatment that received the depth disturbance at T1, the scouring disturbance at T1, the depth disturbance at T2, or the scouring disturbance at T2 (equation 1). We also included all interactions between these four predictor variables to assess the interactive effects of multiple disturbances. We recognized that the taxa may have different inherent levels of population variability, and so we included a random intercept by taxon, denoted by αtaxon. This term assumes that the square root CVs of taxa are normally distributed but estimates only the distribution from which the square root CVs are drawn, rather than an effect for each taxon.We analyzed square root CVs using a linear mixed effects model. The four predictor variables  against the mean abundance of that population. We found that the population CV was not biased by the mean population abundance. Download Copyright © 2016 Herren et al.2016Herren et al.Creative Commons Attribution 4.0 International license.This content is distributed under the terms of the 10.1128/mSystems.00013-16.5Figure S3 Cocconeis spp., Rhoicosphenia spp., Cymbella spp., Synedra spp., Gomphonema spp., Nitzschia holsatica, single Fragilaria spp., and colonial Fragilaria spp. Download Figure S3, PDF file, 0.3 MB.We plotted the estimated random effect from the mixed model against the log of the mean abundance of each diatom taxon. We found no relationship between the fitted random effects and the mean abundances of the diatom taxa. Abbreviations refer to Copyright © 2016 Herren et al.2016Herren et al.Creative Commons Attribution 4.0 International license.This content is distributed under the terms of the 10.1128/mSystems.00013-16.6Figure S4 Figure S4, PDF file, 0.3 MB.Mixed model residuals were not biased by treatment and were approximately normally distributed. Download Copyright © 2016 Herren et al.2016Herren et al.Creative Commons Attribution 4.0 International license.This content is distributed under the terms of the 10.1128/mSystems.00013-16.7Figure S5 Figure S5, PDF file, 0.4 MB.A principal component analysis for the diatom communities shows that the AA treatment polygon overlaps strongly with every other treatment polygon. The AA treatment polygon (red) spans a large portion of the first axis (PC 1), as well as the entire length of the second axis (PC 2). Download Copyright © 2016 Herren et al.2016Herren et al.Creative Commons Attribution 4.0 International license.This content is distributed under the terms of the 10.1128/mSystems.00013-16.8Figure S6 Figure S6, PDF file, 0.5 MB.A principal component analysis for the bacterial communities shows that the AA treatment polygon (red) overlaps strongly with every other treatment polygon. Download Copyright © 2016 Herren et al.2016Herren et al.Creative Commons Attribution 4.0 International license.This content is distributed under the terms of the We performed principal component analyses (PCAs) on the diatom and the bacterial communities. Our main goal for these analyses was to evaluate whether the composition of the disturbed communities consistently differed from the composition of undisturbed communities. Because there was a wide range in the mean densities of diatoms on the slides, we transformed the diatom counts into relative abundances before running this analysis. Again, we used only the 8 most common taxa in the diatom PCA. Similarly, in the PCA of the bacterial communities, we removed all OTUs present in fewer than 30 samples.To assess whether there were correlations between the diatom communities and the bacterial communities, we performed Mantel tests on the 106 slides for which we had data on both the diatom and bacterial communities. We used these tests to determine if changes to either the diatom or the bacterial community on a slide could predict changes in the other community.10.1128/mSystems.00013-16.1Text S1 Text S1, DOCX file, 0.1 MB.We provide additional details about the design and data collection of our experiment. We performed diagnostics on the mixed models used to statistically analyze our results so as to verify the appropriateness of these models. Download Copyright © 2016 Herren et al.2016Herren et al.Creative Commons Attribution 4.0 International license.This content is distributed under the terms of the 10.1128/mSystems.00013-16.2Text S2 Text S2, PDF file, 0.1 MB.Approximations for community proportion CVs. We performed simulations to demonstrate that the pattern seen in the CVs of the bacterial data set is an expected result of relativizing the data. Download Copyright © 2016 Herren et al.2016Herren et al.Creative Commons Attribution 4.0 International license.This content is distributed under the terms of the 10.1128/mSystems.00013-16.9Table S1 Table S1, DOCX file, 0.1 MB.Definitions of community properties and their relationships to population variability. Download Copyright © 2016 Herren et al.2016Herren et al.Creative Commons Attribution 4.0 International license.This content is distributed under the terms of the 10.1128/mSystems.00013-16.10Table S2 P value, which was the fraction of the null distribution of mixed model coefficients that was lower than the observed mixed model coefficient. *, P < 0.05; **, P < 0.01. Download Table S2, DOCX file, 0.1 MB.For each treatment, we calculated a pseudo-Copyright © 2016 Herren et al.2016Herren et al.Creative Commons Attribution 4.0 International license.This content is distributed under the terms of the


On the other hand, misorientation angles have weak influence on the resistance across MoS2 GBs, ranging from about 130 Ω μm for low mismatch angles to about 6000 Ω μm for 21°. The interface resistance across graphene-MoS2 heterojunctions also exhibits a strong dependence on misorientation angles with resistance values ranging from about 100 Ω μm for low-mismatch angles in Class-I (symmetric) interfaces to 1015 Ω μm for 14° mismatch in Class-II (asymmetric) interfaces. Overall, symmetric homo/heterojunctions exhibit a weak dependence on misorientation angles, while in MoS2 both symmetric and asymmetric GBs show a gradual dependence on mismatch angles.We study the impact of grain boundaries (GB) and misorientation angles between grains on electronic transport in 2-dimensional materials. Here we have developed a numerical model based on the first-principles electronic bandstructure calculations in conjunction with a method which computes electron transmission coefficients from simultaneous conservation of energy and momentum at the interface to essentially evaluate GB/interface resistance in a Landauer formalism. We find that the resistance across graphene GBs vary over a wide range depending on misorientation angles and type of GBs, starting from 53 Ω  Besides graphene, transition metal dichalcogenides (TMDs) are another class of two-dimensional (2D) materials which have attracted intense research interests in recent years. The potential applications of graphene and TMDs have motivated mass scale production of large-area films. Among the most popular methods, chemical-vapor deposition (CVD) on transition metal substrates is relatively cheap and extensively used to grow high quality large two-dimensional sheets1. However, CVD-grown films are typically found to be polycrystalline in nature, consisting of many single crystalline grains each with random crystal orientation and separated by grain boundaries (GBs)2. Several studies have reported that grain boundaries in 2D materials impact both their electronic7 and thermal properties10.Graphene, a monolayer of spμm11 to tens of kΩ μm4. Huang et al.12 showed a wide distribution of misorientation angles between adjacent grains in a polycrystalline monolayer graphene sheet with a preferential low angle growth of about 7°. The GB resistance across such GBs was found to be about 240 Ω μm. Contrasting this to the sheet resistance of 700 et al.13 observed a reduction in mobility in CVD-grown graphene and attributed it to the strong carrier scattering at grain boundaries. Clark et al.14 found resistance across graphene GBs to be varying between 40–140 Ω μm for samples with misorientation angles ranging from 9° to 21°. The resistivity of GBs was more than 3 times the bulk resistivity of the grains consistently across all of their samples. There was a positive correlation between misorientation angles and GB resistance, but the width of the transition region surrounding the GB also played a role.The earliest of these studies focused on the electrical resistance across graphene GBs. Experimentally, graphene GB resistance has been found to vary over a broad range from a few Ω 19 which have helped to gain more insight on transport across graphene GBs. Yazyev and Louie15 found that GBs across grains represented by the same translational vectors are highly transparent to charge carriers with a transmission of about 80%, whereas GBs formed by grains with different translational vectors behave as perfect reflectors of carriers. Vancso et al.16 performed wave packet dynamical transport calculations to show that transmission properties across graphene GBs depend on misorientation angles as well as localized structures at the boundaries. Zhang et al.17 showed that intrinsic (defect-free) GBs are almost transparent to carrier transport in highly symmetric GBs. They concluded that the degradation in transmission mainly comes from the extrinsic defects at the boundaries which results in the passivation of the π-orbital. Recently, Sun et al.18 investigated electrical properties along different transport directions with respect to the GB direction using Density Functional Theory (DFT) calculations combined with Green’s function technique. They showed that the zero band gap nature of graphene bandstructure remains intact even in the presence of GBs. They also found that there is an at least 50% current suppression in the transport across GBs as compared to the current in pristine graphene. Despite the numerous studies on various types of graphene GBs, the dependence of GB resistance on misorientation angles is still inconclusive.Besides experimental measurements, there are several theoretical studies225; however, little is known about the impact of misorientation angles on its GB resistance. Najmaei et al.20 studied the individual and collective effect of GBs on electronic transport properties and found that the carrier mobility shows a weak dependence on channel length up to 75 μm. Kang et al.21 also reported a similar dependence of field-effect mobility on channel length, again indicating that GBs don’t significantly degrade the electronic transport properties in CVD-grown MoS2. This observation was further corroborated by Schmidt et al.22, where they demonstrate that the electronic properties of CVD-grown monolayer MoS2 are comparable to those of their exfoliated counterparts. In contrast, Ly et al.25 showed that MoS2 sheets exhibit very poor electrical transport properties (mobilities below 70 cm2 V−1 s−1) for all their devices with different misorientation angles. They observed a positive but non-linear correlation between field-effect mobility and misorientation angles.There has also been a growing interest in electrical transport of CVD-grown MoS29 as well as vertical32 2D heterostructures has recently gained significant research attention with particular focus on graphene-contacted MoS2 lateral (in-plane) heterostructures36. Graphene has been reported to form an ohmic contact with MoS237, resulting in an increase in mobility up to an order of magnitude as compared to that of in metal-MoS2 field-effect transistors (FETs). This calls for investigating the role of misorientation angles in determining the graphene-MoS2 interface resistance in such heterostructures. Throughout the numerous studies of the resistance of GBs and interfaces, a common thread is that the resistance spans a wide range of values depending on mismatch angle. A definitive trend explaining this variation, especially in MoS2 GBs and graphene-MoS2 interfaces, still requires further investigation.Electronic transport in lateral2 grain boundaries, as well as graphene-MoS2 heterojunctions. We use the transmission coefficients to compute the conductance of the boundaries/interfaces as a function of both mismatch angle and carrier concentration. In Sec. 2 we further detail our approach and delineate two different classes of GBs (twin and tilt homojunctions) and interfaces (Class-I and II heterojunctions). In Sec. 3, we discuss our results showing that transport across twin homojunctions and Class-I heterojunctions show a weak dependence on mismatch angles, whereas the resistance across tilt homojunctions and Class-II heterojunctions exhibits a strong dependence on mismatch angles. We conclude in Sec. 4 that GBs play a moderate role in MoS2 due to its parabolic bands, but can be quite significant in graphene and large-mismatch graphene-MoS2 heterostructures owing to graphene’s steep linear Dirac cones.In this paper, we focus on the fundamentals behind the impact of grain misorientation angles in 2D homojunctions and heterojunctions. Starting from electronic structure obtained through first principles Density Functional Theory (DFT), we calculate the transmission coefficients and boundary/interface resistances for graphene and MoS15 to calculate the transmission coefficient of electrons across a graphene grain boundary. The interface resistance is calculated in the following steps: bandstructure calculations for graphene and MoS2 individually from the first principles, rotation of the Brillouin zones (BZ) to account for the misorientation angle between adjacent grains, calculation of electron transmission across the interface from the energy and momentum conservation, and finally computing the interface resistance in the Landauer formalism. For heterojunctions between dissimilar materials, an additional second step involves band alignment at the interface based on the Schottky-Mott rule.To study the impact of misorientation angles on interface resistance, we have developed a numerical model based on first-principles DFT electronic bandstructure calculations and electron transmission coefficients from simultaneous energy and momentum conservation. The latter is an extension of the approach originally proposed by Yazyev and Louie2 individually from first principles using Density Functional Theory (DFT) as implemented within the open-source distribution Quantum Espresso38 . It is followed by the alignment of the bands at the interface. In homojunctions such as graphene-graphene GBs and MoS2-MoS2 GBs, the bands are always well-aligned at the interface, whereas in heterojunctions, such as the graphene-MoS2 GBs, the bands need to be aligned. In contrast to the planar charge in a 3D interface, a 2D heterojunction forms a line dipole at the junction39. It has been shown that in 2D heterojunctions, the effect of this interfacial dipole vanishes when the overall dimensions of the device are much larger than the characteristic junction-width, typically about 10 nm39. As a result, the band alignment in 2D heterojunctions is far less sensitive to the interfacial details and the band alignment closely follows the Schottky-Mott rule39.First, we calculate the electronic bandstructure for single-layer graphene and MoS2 are treated as semi-infinte, so we use the Schottky-Mott rule40 and align the vacuum levels of the two materials at the interface. Next, the work function of graphene (ϕgraphene = 4.55 eV41) and the electron affinity of MoS2 (42) are used to align the respective bands away from the interface relative to the vacuum level. Due to the difference in the work function of graphene and electron affinity of MoS2, an energy barrier 2 side near the interface to account for the energy barrier height in equilibrium. The amount of band-bending on MoS2 side, which is also a function of carrier concentration nC, is given by 26. The carrier concentration typically depends on the level of impurities, doping, or gating45.In our case, the graphene and MoSL and ΘR, each being the angle of rotation between the grain on the left and the right side with respect to the interface, taken here as reference, as shown in Fig. L is taken to be positive for anticlockwise rotation of the left grain, whereas ΘR is positive for clockwise rotation of the right grain. We define misorientation angle as ΘM = ΘL + ΘR. To include the effect of the misorientation angle in our calculation, the wavevectors in the first Brillouin zone are rotated by ΘL for the left grain and ΘR for the grain on the right hand side of the interface. The rotation of the Brillouin zone does not affect the aforementioned band structure alignment at the interface.The orientation of the grains with respect to the GB/interface is defined by two angles ΘL = ΘR = ΘM/2) and the second is when only one of the grains is rotated away from the interface . In literature, the former type of symmetric grain boundaries are referred to as twin GBs and the latter as the most asymmetric tilt GBs.In 2D materials, GBs can be of different types depending on both the orientation of each grain with respect to the grain boundary and the orientation of the grains with respect to each other. One extreme is when both the grains are rotated symmetrically by equal angles away from the GB in opposite directions  GBs depending on the position of the boundary itself. For example, given that ΘM is 4° we can have ΘL = ΘR = ΘM/2 (twin GBs), or ΘL = 0° and ΘR = ΘM (the most asymmetric tilt GB), or intermediate cases such as ΘL = 1° and ΘR = 3°, and so on so forth. In order to denote these intermediate tilt cases, we introduce an angle ΘB, which is defined as the angle, in the anticlockwise direction, that the boundary makes with the reference line. So, an intermediate case of ΘL = 1° and ΘR = 3° can be represented as ΘM = 4° and ΘB = 1°.So far, we have discussed the two extreme cases of GBs for a given misorientation angle Θ46. From translational symmetry, transmission requires simultaneous conservation of energy and transverse momentum of the incident electron across the interface. Momentum conservation requires that the parallel component of the incident wave vector b using the perpendicular components of the incident b(E) by averaging the mode-dependent transmission coefficient τb(k) over the constant energy contour, described by δ(E − Eb(k)), using the 2D version of the linear extrapolation approach described by Gilat and Raubenheimer47 asbDb(E), shown in Fig. E) asf/∂E over energyC is the bottom of the conduction band and Emax is the highest electron energy in the first four conduction bands and f(E) is the Fermi-Dirac distribution function f(E) = [1 + exp((E − EF)/kBT)]−1.The effect of GB/interface on transport is incorporated by using boundary conditions based on quantum-mechanical wave continuityentclass1pt{minimaRGB respectively for various misorientation angles in twin GBs. We see in Fig. E) equals 1, is obtained for 0° mismatch angle at any given energy level. However, as the misorientation angle increases, the modes that do not conserve energy and transverse momentum are reflected at the interface, resulting in a reduction of the transmission coefficient, which varies between 0.8 and 0.5 for various mismatch angles. Besides band gap, the energy range for which there is no transmission (Γ(E) = 0) is referred here as transmission/transport gap. In twin GBs, we note that even for large mismatch angles there is no transmission gap in the energy spectrum.We calculate the transmission and resistance of graphene GBs in order to explore the impact of the misorientation angle. The angle dependence of GB resistance largely depends on the type (tilt or twin) of the GB. Figure E) = 1; in contrast, Yazyev and Louie15 reported a linear transmission probability T(E) with energy. They used a non-equilibrium Green’s function (NEGF) formalism to calculate conductance across graphene grain boundaries. In the coherent transport regime, the conductance from NEGF formalism reduces to the conductance in Landauer formalism48, given by49T(E) in the NEGF formailsm is analogous to our transport distribution function Ξ(E). For the graphene GBs with 0° mismatch, Ξ(E) in Eq. Db(E), which is linear with energy [as shown in Fig. T(E) vs. energy plot from NEGF15.For GBs with 0° mismatch angle, we obtain a coefficient Γ which is centered at EF also shifts towards higher energy levels. As the DOS in graphene is proportional to energy near the Dirac point (from Eq. E) also increases with energy away from the Dirac point. Thus the value of the integral in Eq. In Fig. from Eq. , the TDFFigure μm to several kΩ μm3. The wide variation in GB resistance can be fully explained with the trends observed in Fig. μm at 4° mismatch to several thousands of GΩ μm at 14° mismatch, even at high carrier concentration of about 1013 cm−2. The transmission coefficient eventually becomes zero for misorientation angles beyond 14° mismatch due to the large transmission gap in tilt GBs and we observe extremely high values of resistances. In contrast, the resistance of twin GBs in near-intrinsic graphene varies from 400 Ω μm at low to about 1 kΩ μm at high mismatch angles, while at high carrier concentration it varies over a very narrow range of about 90 Ω μm at 4° mismatch to 110 Ω μm at 14° mismatch. Our calculated graphene GB resistances include a ballistic resistance of 53 Ω μm at high carrier concentration of 1013 cm−2 and 424 Ω μm at intrinsic carrier concentration. After removing the ballistic resistance, the calculated GB resistance for a low-mismatch twin GBs of about 1° at high carrier concentration is 8 Ω μm. This is in good agreement with Grosse et al.11.Previously, it was found that the GB resistance across graphene GBs varies within a wide range from a few Ω 2 GBs, we use the same procedure as used for graphene GBs in the previous section. The transmission coefficient as a function of energy is plotted in Fig. 2. We also observe a gradual reduction in transmission coefficient with increasing misorientation angles as compared to that of graphene GBs. However, there is no transmission gap found for MoS2 twin GBs, similar to what we observed in graphene twin GBs. Corresponding to the transmission coefficient for various misorientation angles, the boundary resistance across MoS2 twin grain boundaries vs. carrier concentration is shown in Fig. RGB in MoS2 twin GBs are almost double than the values of GB resistance in graphene twin boundaries for a carrier concentration of 1 × 1012 cm−2, whereas for large carrier concentrations between 6 × 1012 and 9 × 1012 cm−2, MoS2 twin GBs have GB resistance similar to that of graphene twin GBs.To study electronic resistance across MoS2 tilt GBs. It can be seen in Fig. 2 twin GBs. Like in tilt graphene GBs, a transmission gap is also observed in tilt MoS2 GBs for large misorientation angles, however the transmission gap in MoS2 is much smaller than that of graphene. We attribute this trend to the flatter parabolic conduction band bottom of MoS2 as compared to the steep conical bandstructure of graphene around the Dirac point. The variation of GB resistance with misorientation angle is quite distinct in this case as compared to the variation of RGB in graphene tilt GBs. It is important to note that the resistance across MoS2 GBs is much smaller than what we found in graphene tilt GBs. Thus, misorientation of adjacent grains across grain boundaries can cause a significant reduction in electronic conductance in polycrystalline graphene, while GBs in polycrystalline MoS2 might not play such a strong role in electron conduction, which is in good agreement with few recent reports on electronic transport in CVD-grown MoS222.Figure M and ΘB for graphene and MoS2 GBs respectively. The calculated value of resistances across graphene GBs range from few tens of Ω μm to about 1013 Ω μm depending on the ΘM (the angle between the two grains) and ΘB (the position of the boundary with respect to the left grain). However, the GB resistance across MoS2 GBs vary over a relatively narrow range of about 130 Ω μm to 5700 Ω μm for various combinations of ΘM and ΘB. Thus, we can see that for a given misorientation angle, one can have different GB resistance depending on the position of the GB with respect to the grains, and any resistance value falling in this range can be explained by a combination ΘM and ΘB.Figure 2 to differentiate with those of homojunctions. When graphene (taken here to be on left side of the boundary) and MoS2 (right side of the boundary) grains are rotated by equal angles with respect to the interface i.e. ΘL = ΘR, we use the term Class-I interface, whereas when The interfaces formed between two dissimilar materials (heterojunctions) are different from those of homojunctions because of the difference in the properties of the grains on either side of the interface—including electron affinity, work function, and bandstructure. So, before discussing about electron transport across such heterojunctions, we redefine the nomenclature of the interfaces formed between graphene and MoS2 Class-I interface for various misorientation angles at a carrier concentration of 1 × 1012 cm−2. Due to the difference in the work function and electron affinity in graphene and MoS2, the bands bend and an energy barrier  is formed at the interface. Like in homojunctions, the band alignment at the interface is independent of the misorientation angle, and thus, the barrier height is also independent of ΘM. In Fig. 12 cm−2, the interface resistance is in the order of 108 Ω μm because of the large energy barrier. However, at high carrier concentrations between 6 × 1012 cm−2 and 9 × 1012 cm−2, the interface resistance reduces significantly because the energy barrier between graphene and MoS2 almost disappears at such concentrations and they behave like Ohmic contacts.Figure 2 interfaces at a carrier concentration of 1 × 1012 cm−2. The transmission coefficient decreases with increasing mismatch angle similar to the tilt GBs in graphene GBs. A transmission gap is formed in addition to the existing potential barrier, marked in the figure, and this transmission gap widens with increasing misorientation angles. Transmission becomes zero for large mismatch angles beyond 14°. This strong dependence of mismatch angle on transmission coefficient leads to a strong dependence of the interface resistance on misorientation angles in Class-II graphene-MoS2 heterojunctions, which can be seen in Fig. 12 cm−2, the interface resistance varies from about 108 for low mismatch angles to 1014 Ω μm for a mismatch of 14°, whereas at high concentrations the interface resistance ranges from about 102 for low mismatch angles to 108 Ω μm for a mismatch of 14°.Figure 2-MoS2 GBs, the band alignment is independent of the position of the Fermi level so the transmission coefficient is also independent of carrier concentration. In contrast, the barrier height in heterojunctions is a function of carrier concentration via the position of the Fermi level, owing to the difference in DOS between graphene and MoS2. The transmission coefficient in Class-I graphene-MoS2 interface is plotted with carrier concentration in Fig. 2 interface, that is 0° mismatch. The shape of the Γ(E) vs. energy does not change with carrier concentration rather the curves get shifted towards the left in energy due to the decrease in energy barrier height with carrier concentration. In Fig. In homojunctions like graphene-graphene and MoS2-MoS2, and Gr-MoS2 interfaces. It can be seen that, in general, symmetric twin GBs in homojunctions and Class-I interfaces in heterojunctions show a very weak dependence on the degree of mismatch between adjacent grains, whereas tilt GBs in homojunctions and Class-II interfaces in heterojunctions exhibit strong dependence on misorientation angles except in MoS2, where both tilt and twin GBs are found to show a weak dependence on mismatch angles. The weak angle dependence in MoS2-MoS2 GBs can be attributed to the flat parabolic conduction band because of which the underlap in the bandstructures on the either side of the GB is quite small even at large mismatch angles. In order to explain the wide range of the graphene GB resistances in the literature via misorientation angle and type of GBs, the data from the literature has also been included in the figure. The yellow markers in the figure denote the combinations of ΘM and ΘB obtained by fitting the experimental measurements by Kochat et al.50 (ΘB = 2.83° and 3° for ΘM = 12° and 22° respectively), Clark et al.14 , and Yu et al.3 (ΘB = 3.1° for ΘM = 28°).Figure 9 and the presence of localized electronic states, which have been observed at 3D interfaces51 and 2D grain boundaries53. The localized states are not included in our model, but could be treated by modifying Db(E) in Eq. 2 interfaces. Then localized states might introduce additional channels for transmission and lead to slightly higher GB conductance than what we report here without these localized states. In that sense, our conductance values could be thought of as a lower bound.The aim of our study is to understand the effect of misorientation angle on GB conductance. There could be additional effects due to grain boundary roughness2 interfaces varies over a very wide range depending on the degree of mismatch between adjacent grains and type of GBs. The transmission coefficient across symmetric interfaces (twin GBs in homojunctions and Class-I interfaces in heterojunctions) is found to be less sensitive to misorientation angles between adjacent grains because they deflect electrons rather coherently. In these symmetric interfaces, there is no transmission gap. On the other hand, the transmission across asymmetric interfaces (tilt GBs in homojunctions and Class-II interfaces in heterojunctions) is largely diminished by mismatch angles and a transmission gap opens up in the energy spectrum. In contrast to graphene-graphene tilt GBs, the resistance across MoS2-MoS2 tilt GBs show relatively much weaker dependence on mismatch angles. This is attributed to the flat parabolic conduction band bottom in MoS2 as compared to the steep conical conduction band bottom in graphene. As a result, the rotation of the BZ in MoS2 by large angles causes a small transmission gap, whereas even a small misorientation angle across graphene GBs gives rise to a large transmission gap. In homojunctions, the bands are identical on either side of the interface and the response to the carrier concentration, and hence the back-gated voltage, is also uniform on both sides. Thus, for a given misorientation angle, the variation of transmission coefficient vs. energy is independent of carrier concentration in homojunctions. In heterojunctions, the bands are aligned at the interface using the macroscopic variables, including work function and electron affinity, based on Schottky-Mott rule, forming an energy barrier at the interface. The band alignment, and with it the energy barrier between graphene and MoS2, reduces with the carrier concentration because of the differences in their densities-of-states. Consequently, the interface resistance strongly decreases with carrier concentration in heterojunctions in both classes of interfaces. In summary, electrical transport across twin homojunctions and Class-I heterojunctions shows a weak dependence on mismatch angles, whereas the resistance across tilt homojunctions and Class-II heterojunctions exhibits a strong dependence on mismatch angles.In conclusion, we find that misorientation angle between two adjacent grains plays a very significant role in both homojunctions and heterojunctions. We show that the resistance across graphene GBs and graphene-MoS54. For MoS2, we used a nonrelativistic NCPP for Mo and a scalar relativistic NCPP for S. Both potentials employed a Martins-Troullier method with a Perdew-Wang LDA exchange correlation55. The lattice constants are a = 2.459 Å for graphene and a = 3.125 Å, z = 3.11 Å for MoS2, where z is the distance between chalcogen atoms. To ensure that interplanar interactions are neglected, the repeating images of the monolayers are seperated by a 20 Å vacuum. The cutoff energy for plane waves was 120 Ry for graphene and 140 Ry for MoS2. We used a convergence threshold of 10−15 on a Monkhorst-Pack grid sizes of 8 × 8 × 1 for graphene and 6 × 6 × 4 for MoS2 for the initial total energy calculation and then performed a bandstructure calculation on a dense grid of 25,208 k-points (wavevectors) with a convergence threshold of 10−12. We used the central difference method to obtain the electron velocities per band which, in turn, are subsequently used in calculating the electronic density of states (DOS) and other transport properties including interfacial transmission and resistance of the interface.For graphene, we used a scalar relativistic, norm-conserving pseudopotential (NCPP) which implements a direct-fit Von Barth-Car method with a Perdew-Zunger local density approximation (LDA) exchange-correlation functionalM) is 0°. In the diffusive limit (Ohmic regime) when the dimension of the conductor is large compared to the carrier mean free path, the conductance varies inversely with length. One would expect the conductance to become infinite when the conductor length tends to zero. However, it has been experimentally found in both metals56 and semiconductors58 that the measured conductance converge to a finite value called ballistic conductance. The regime where we see this limiting behavior is called ballistic regime. In this regime, characterized by an absence of scattering, the conductor has no resistance–the ballistic resistance is not the resistance of the conductor but the contact resistance48.We derive an analytical expression for the ballistic resistance across graphene GBs and compare it with the numerically computed values of ballistic resistance at different carrier concentrations. We define ballistic resistance as the resistance between two perfectly-matched grains, that is when misorientation angle 〉 is calculated by 2D averaging of velocity of all the modes, vF is the Fermi velocity (≈106 ms−1), which is computed from the slope of the bandstructure (E-k relationship) around Dirac point. DD2(E) is the 2D density of states.The channel number at any energy (E) for a given width of the ribbon is calculated asgs and gv are constants related to the spin of electron and valley degeneracy respectively. For graphene gv = 2 and gs = 2 for electrons. f0(E) is the equilibrium Fermi-Dirac distribution function, Rball in graphene, which is the reciprocal of Gball,2D, is inversely proportional to the square root of carrier concentration. On using the values of the constants in Eq. 10 cm−2, the analytical value of Rball in graphene is about 405 Ω μm.The dispersion of graphene around the Dirac point is approximated by the relation mentclasspt{miniman0 = 8 × 1010 cm−2), the numerically calculated ballistic resistance is 424 Ω μm, which compares quite well with the analytical value of 405 Ω μm. In Fig. E) is 1 for the entire energy range, showing perfect transmission for 0° mismatch (perfectly-matched grains). The curve encompassing the blue area in the figure is the Fermi window function, which is defined as the derivative of Fermi-Dirac distribution function with respect to energy, for intrinsic carrier concentration that is when the Fermi level EF is around the Dirac point and the electron concentration is equal to the hole concentration. Eq. RGB when plotted against carrier concentration as shown in Fig. We compare these analytically calculated values of ballistic resistance for different carrier concentrations with our numerically calculated values as shown in Fig.  The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.