While social distancing was crucial to slow the COVID-19 virus, it also contributed to social isolation and emotional strain. This pilot study evaluated the impact of stand-alone psychoeducational group sessions designed to build social connectedness and space for people to learn about mental health during the pandemic. The study examined if offering the stand-alone group sessions increased uptake of and receptivity to additional mental health services. People had access to free, online group psychoeducational sessions offered by a digital mental health platform company. Sessions were offered to (1) employees who had mental health benefits offered through their employer, and to (2) members of the general public. Session formats included discussions, didactic lectures, and workshops, were facilitated by a mental health provider, and used live video conference technology. Topics included race and identity, stress management, coping with political events, relationship issues, and self-compassion. First-time session registrations were tracked from June 2020 to July 2021 on 6723 participants . Among the employee subsample, 49.5% attended a group session as their first use of any available service on the platform; 52.5% of these employees sought additional services after their first session. In anonymous post-session surveys of employees and members of the general public, 86% of respondents endorsed knowledge increases, 79.5% reported improved understanding of their mental health, 80.3% endorsed gaining actionable steps to improve mental health, 76.5% said that they would consider group sessions in addition to therapy, and 43.5% said that they would consider group sessions instead of therapy. These results suggest that scalable, brief group psychoeducational sessions are a useful conduit to mental health care and have potential to reach people who may not otherwise access available mental health services. When the COVID-19 pandemic began, loneliness and social isolation drastically increased as a result of the physical distancing methods introduced to slow the spread of the virus . We tracked available information from all people who registered for sessions from June 2020 to July of 2021 when data were extracted for analysis. The data used in analyses were originally designed for programmatic operations and not originally intended for research purposes. Available data included email addresses from registrations, platform utilization, and post-session survey ratings  registration for online, group psychoeducational sessions within the study time frame; (b) aged 18 years or older at the time of registration; (c) access to a smartphone or computer with Wi-Fi or cellular service in order to connect to the online sessions.These study participants could participate in the online group sessions because they received mental health care benefits from their employer. Employees had access to the digital mental health platform offered by the company, and that access included the online group sessions. Employees could register for the online group sessions either through a public webpage on the website of the mental health platform company, or they could establish a personal account on the platform and register through the platform portal. Unique email addresses were used to track employee registrations through either route.In addition to sessions provided to the benefits-eligible employees, the mental health company offered online group sessions free-to-the-public as a corporate social responsibility action during the COVID-19 pandemic. A public-facing web page described the sessions and had a registration link. The only information collected for the free-to-the-public sessions was the email address used for registration. Given the constraints on the data, these session registrants were included in limited analyses described in the “Benefits-eligible employees learned about the sessions through direct communications sent from their employer and/or the platform company, primarily through direct email marketing and social media posts. Public registrants learned about the existence of the free sessions through mass media communications sent from the mental health platform .The online, group psychoeducational and support sessions (named “Circles”) are live community sessions delivered online. The sessions were initiated in response to the impact of social distancing restrictions imposed to slow the spread of the COVID-19 virus. The intent of the sessions was to create a forum for people to virtually connect with others and learn about and discuss their mental health during the COVID-19 pandemic. Sessions addressed a variety of topics such as follows: coping with uncertainty, race and identity, coping with racism, caregiving, parenting, improving sleep, improving health habits, stress management, coping with political events, relationship issues, self-compassion, building resilience, and combating negative thoughts. Session formats included live discussions, didactic lectures, and practical workshops. All sessions were facilitated by a mental health provider who was either a licensed clinician or certified professional coach in the network of providers managed by the mental health platform company. Individuals could register for an unlimited number of sessions, and all were offered at no charge to the attendee.Sessions were designed to be stand-alone, meaning that they were designed to be self-contained, and not expected to be taken in a specific sequence. People could attend as many sessions as they wanted, and could repeat sessions that were offered more than once. Topics were repeated throughout the study time frame, and the dates/times and facilitators varied throughout the year. The variety of session topics, formats, dates, and facilitators was intentional in order to provide people options that were appealing and accessible to them. Session durations ranged from 60 to 90 min. As the sessions were launched during the height of COVID-19 pandemic social restrictions , all sessions were conducted online using videoconferencing technology . The large didactic sessions could accommodate hundreds of participants and encouraged participants to ask questions through the chat feature. Workshops and discussions were intentionally smaller and could accommodate up to 50 participants; participants were encouraged to use their video cameras and audio connections to interact with the facilitator and other attendees during these sessions.The online group sessions are a component of a comprehensive digital mental health platform. The full platform of services was only available to benefits-eligible employees and not to the general public attending the free-to-the-public sessions. The platform was available to employees through an app. As described in more detail in the “Employees created an account on the platform with their email address and password of choice. The app surfaces questions that assess each individual’s clinical needs and care modality preferences to tailor care recommendations. Based on an individual’s baseline clinical severity and preference for care, recommendations are made to tailor services to meet their needs. Employees can follow the recommendations to connect to care, or can choose their own services if desired. In addition to the group sessions, options for care include the following: self-guided digital content ; one-to-one telehealth sessions  and in-app messaging with a licensed mental health specialist or certified professional coach; and the online, group psychoeducational sessions. Employees with full access to the platform could use any modalities of care and combine multiple modalities. We specifically focused on employees who utilized the online, group psychoeducational sessions as their first use of the platform.An email address was the only element of data required to register for a group session. These addresses were the primary data source for all session registrations for both the benefits-eligible employees and for the general public accessing the free-to-the-public sessions. The first time a unique email address was used to register for a group session, an initial time stamp was created for that unique user. We then tracked the total number of subsequent session registrations with the same email address during the study period, along with the topics for each session.Additional data from the mental health benefits platform were available only for the benefits-eligible employees. These participants were identified when the unique email address that was used for a group session registration was also associated with a platform account. Platform service utilization and demographic data were extracted from these accounts. To examine engagement in other services on the platform, we tracked use of all available services on the platform relative to the date of the individual’s registration for their first group session, including (1) use of trackable, self-guided digital content ; (2) engagement in one-on-one sessions with either an in-network coach; or (3) therapist; and/or (4) registration for additional group sessions. Some elements of the digital content usage were not trackable with timestamps and thus were not accessible for analyses. Demographic data extracted from employee platform accounts included gender  and age in years. No platform utilization data or demographic data were available for public registrants for the free-to-the-public sessions.After each online group session, all attendees were asked to complete a survey of their impressions of the session. The surveys were requested from both benefits-eligible employees and from the general public that attended the free-to-the-public sessions. The surveys were anonymous using a single online survey link, and data could not be linked back to the mental health platform or registration records; therefore, we were unable to sort or separate the data based on whether the respondent was a benefits-eligible employee or a member of the general public. All session attendees were asked to rate the group session using the questions outlined in Table We calculated the total count of session registrations received during the study time frame, the total number of session registrations per unique email address, and separated these counts by registrations from benefits-eligible employees or from the community at large.To examine utilization on the mental health platform for the benefits-eligible employee participants, we calculated the proportion of members for whom the group session was their first activity of any kind on the platform. Among these participants, we calculated the percent that accessed additional mental health services or resources from the platform after their first group session, and the percent that completed coaching sessions, therapy sessions, or accessed additional digital content after their first group session. As we only had demographic data on the benefits-eligible employees, we calculated the percentages of participants identifying as female or male and calculated the average age of these participants.From the post-session survey data, we calculated the total number of surveys returned, a breakdown of the most frequent methods through which people learned about the sessions, and the percentage who endorsed the range of responses to the survey questions. As the surveys were collected anonymously, responses could not be linked to the mental health platform or registration records; therefore, all responses were combined for analyses and not separated based on whether the respondent was a benefits-eligible employee, or a member of the general public.n = 3006) of these registrations came from the general public that had no access to the mental health services offered by the care platform. The other 55% of registrations (n = 3717) came from benefits-eligible employees who also had access to the full digital mental health platform and had a platform account with the identical email address that was used for group session registration. A total of 75 unique session topics were attended during the study time frame. Topics related to personal identity were most popular , with 58% of all registrants (n = 3899) signing up for those group sessions.A total of 6723 unique emails were used to register for an online group session for the first time during the study time frame. Forty-five percent  registered for only one session; 17% (n = 1143) went on to register for a second session; 16% (n = 1076) went on to register for 3 or more additional sessions. The employees who had employer-sponsored access to the mental health platform were more likely to sign up for more than one group session compared to members of the general public, X2  = 166.4, p < 0.001.Among all first-time group session participants , 67%  identified as female, 14% (n = 520) identified as male, and the remaining 41%  did not disclose gender identity. The average age of these participants was 36.9 years (range = 20 to 80 years).Among the benefits-eligible employees, 45% (n = 3717), the group session was the first activity of any kind on the platform for 49.5% (n = 1841). These individuals did not create an account or engage in any other platform care activity until they signed up for their first online, group session. The other 50.5% (n = 1876) of the benefits-eligible employees who signed up for their first group session during the study period had previously set up an account and used at least one other care option before they attended their first online, group session.Among the benefits-eligible employees who registered for their first group session during the study time frame (n = 967) went on to use at least one additional care component of the mental health platform after their first group session. Specifically, 21.9% (n = 213) went on to utilize at least one telecoaching session, 9.3% (n = 90) utilized at least one tele-session with a licensed therapist, and 90% (n = 870) used some combination of digital content  after their first group session.Among the 1841 employees who had not previously used any platform services, 52.5% .When asked how they learned about the group sessions, 31% of survey respondents said that they learned about the sessions from an email sent from their employer, 18% learned from an email sent from the mental health platform company, 17% learned from a public website of the company, 13% learned from the mental health platform mobile app, and 10% learned from a friend or co-worker.When asked about the impact of the group session, 79.5% of respondents agreed or strongly agreed that attending the session increased their understanding of mental health, 80.5% agreed or strongly agreed that the session gave them useful skills, and 80.3% agreed or strongly agreed that the session gave them actionable steps to improve their mental health. When asked about their receptivity towards using group sessions in addition to or instead of therapy, 76.5% said they were somewhat likely or very likely to use the group sessions in addition to therapy, and 43.6% were somewhat or very likely to use group sessions instead of therapy.The results of this pilot study evaluation suggest that online, group psychoeducational sessions were attractive and acceptable to many people during the height of the COVID-19 pandemic, and reached a segment of the population that had not previously accessed mental health care through other modalities . Among the benefits-eligible employees who had full access to the platform mental health resources, over 1800 had not previously utilized their available services before their first group session; the online group session was their first point of entry. The finding that 52.5% of these benefits-eligible employees went on to use other elements of care after their first group session suggests that the sessions may have helped to increase interest in or receptivity to additional care among employees who had full access to mental health services but had not previously used them. Our results are consistent with the extant literature that single online group sessions can serve as an important starting point or conduit to additional care Brown, .instead of therapy, and the majority being open to using groups in addition to therapy. Individual visits with a mental health provider are not necessarily the right solution initially or exclusively for many people’s mental health needs.Less than one-third of the benefits-eligible employees who had not previously used their available services went on to use either therapy or coaching; the majority (90%) used digital resources and/or additional group sessions. This finding suggests that for many individuals, receiving care in a one-on-one setting from a coach or therapist is not necessarily the first step in attending to one’s mental health. The post-session survey responses about attitudes and intentions for additional mental health care add further support to this argument, with almost half (43.6%) of the respondents with survey responses  stating that they would be open to using group sessions Thousands of people from the general public also sought participation in these group psychoeducational sessions. Almost half of the registrations for the online group sessions were from people in the public who did not have access to the mental health platform through their employer. These people would not have received personal email invitations to participate, which implies that they found the group sessions through website searches, word of mouth, or from seeing content on the mental health company website or through company posts on social media. We found that benefits-eligible employees were more inclined to register for additional group sessions than the registrants from the general public; this may be because employees may have been made more aware of their employer-sponsored benefits as a result of the session, and took advantage of the available services afterwards. Given the limited data collected on the public session participants, we do not know if the registrants from the general public had access to mental health services elsewhere. While it is possible, it is also highly likely that access was quite challenging, both due to resource constraints imposed by the pandemic  evidence that online, single sessions of group psychoeducation can be helpful for improving help-seeking attitudes and intentions , but we are not able to differentiate the results to examine this. The registration system for public users did not ask for any personal data beyond an email address, and limits our ability to understand more about the public participants . Ideally, we would want comparable demographic information to examine differences/similarities in who sought out the group sessions, and confirmation of whether or not public participants had access to mental health services elsewhere. There is also a chance that people who had employer-sponsored access to the platform chose to register through the public registrations with different email addresses, and thus, we may have some false-negative cases of public registrations. However, this would result in an under-reporting of cases of people accessing services through the platform; we may be undercounting the people who utilize group sessions and no other modalities, despite having coverage for additional care.These group sessions by design were quite diverse in terms of content topics, dates and times they were offered, formats, and facilitators that supported them. While this breadth of variety has its advantages, it also limits our ability to determine if there are any central, active ingredient(s) of these sessions that produce the desired effects. Additionally, while we were able to track registrations, we did not collect identifiers of session attendees; there is the likelihood that some individuals registered but did not attend. The observational nature of the real-world data also limits any implications about causality. Further studies will need more rigorous designs, control conditions, and intentional isolation of the hypothesized active ingredients to more precisely determine the cause(s) and their magnitude of effect.The post-session surveys were optional, and there is the likelihood of a positive response bias in that those who benefitted the most from the sessions were more likely to complete the optional feedback survey. Additionally, while social connectedness, stigma reduction, and reduced loneliness/isolation are viable outcomes for group psychoeducational sessions, we did not have measurements of these constructs incorporated into the sessions. We have since added a post-session survey question inquiring if the session helped build a sense of community and are working on other ways to collect outcomes of interest on participants without adding burden to their experience. While the data had their limits and challenges, the group sessions have been highly popular and continue to endure. This provides us with future opportunities to improve upon data collection and tracking of individuals to more closely understand how the group sessions have helped guide people towards other elements of mental health care.The results of this evaluation suggest that scalable, brief, online group educational sessions can be a useful conduit to draw people to mental health care and can be an important element in expanding the reach of mental health services to people who may underutilize their available mental health resources. During the height of the COVID-19 pandemic when social distancing measures were widespread, the introduction of these online, group psychoeducational sessions were met with a large volume of interest, and attendees who shared their experiences revealed encouraging signs of their impact . Online group sessions that are primarily psychoeducational and supportive in nature have exciting potential to be a point-of-entry; they can engage people who might not make full use of the mental health services available to them. Furthermore, some may choose to use them as a stand-alone or preferred option if given the choice. They can have a positive impact in improving people’s understanding about their mental health and giving them a sense of direction. They can also empower and encourage people to take further steps to access care for their mental health.


Tremendous research efforts have recently focused on the synthesis of graphene from graphitic materials, while environmental issues, scalability, and cost are some of the major challenges to be surmounted. Liquid phase exfoliation (LPE) of graphene is one of the principal methods for this synthesis. Nevertheless, sufficient information about the mechanisms of exfoliation has yet to emerge. Here, a microreactor based on the hydrodynamic cavitation (HC) on a chip concept is introduced to exfoliate graphite in a totally green process which involves only natural graphite flakes and water. HC-treated graphitic materials were characterized by UV-Vis and Raman spectroscopy, DLS (Dynamic Light Scattering), AFM (Atomic Force Microscopy), and SEM (Scanning Electron Microscopy) analyses. The present sustainable reactor system was found to exfoliate thick and large graphite particles to nano-sized sheets (∼1.2 nm) with a lateral size of ∼500 nm to 5 μm. LPE of graphene with a hydrodynamic cavitation microreactor is a totally green process which involves only natural graphite flakes and water. During the past decade, many research efforts have been focused on graphene due to its outstanding electrical, optical, chemical, and mechanical properties, as well as its unique 2D honeycomb lattice.13 Over the years, various methods have been proposed to produce graphene, which can be categorized into two major approaches: top-down and bottom-up.14 Top-down approaches involve the separation of the stacked layers of graphite into graphene sheets. Mechanical exfoliation,15,16 liquid-phase exfoliation (LPE),17,18 unzipping of multi-wall carbon nanotubes (MWCNTs),19,20 and arc discharge21,22 are some examples of this approach. In contrast to top-down methods, bottom-up methods involve synthesizing graphene from carbon-containing sources such as chemical vapor deposition,23,24 epitaxial growth,25 and pyrolysis.26Production of graphene and related materials at a reasonable cost from graphite is a long-lasting scientific challenge and puts an obstacle against graphene-based emerging applications. The properties of graphene and related materials are closely related to their synthesis method, which could enable the precise control of their shape, size, and surface properties, thereby leading to versatile physical, chemical, and biomedical characteristics.27,28 Typically, the mechanical routes for exfoliation of flakes apply in the form of two forces. The vertical impacts act on the flakes, which causes to overcome energy between layers to peel them apart , and the sliding relative movements between layers occur due to the exerted lateral force (shear force).In general, in top-down methods, the process involves mechanical and chemical energies to break down weak van der Waal forces in high-purity graphite sheets.29,30 Generally, there are three main steps in LPE synthesis: (i) dispersion of graphite in a suitable solvent, (ii) exfoliation, and (iii) purification of the final products.31 In the second step, the formation and collapse of bubbles on the flake surfaces instantly result in a compressive stress wave propagation throughout the particle. Based on the theory of stress waves, the particle is also exposed to a reflected tensile stress wave. The cycle of creation and collisions of bubbles leads to intensive tensile stress in the flakes. Additionally, the other potential scenario is the exertion of unbalanced lateral compressive stress. This kind of stress can also break down adjacent layers by the shear effect.32 As a result, it is an efficient and fast approach to develop nano-sized particles, where the prominent role belongs to cavitation bubbles.33LPE, one of the most widely used top-down methods for graphene production, was first introduced in 2008. In this method high energy sonication or mixing are conducted to exfoliate graphite to graphene sheets in a solvent with addition of surfactants to avoid oxidation or reduction. On the other hand, spontaneously exfoliation of graphene sheets under the effect of high energy liquid–liquid interface is another approach, where graphite particles act as a surfactant in aqueous based medium.34,35 The collapsing bubbles (cavities) in the liquid provide the energy source to initiate and enhance a wide range of chemical processes and introduce physical effects to break down graphite layers into graphene.36 The resulting bubble collapse could generate very high energy densities (energy per unit volume), which causes a rise in the local temperature and pressure as large as 5000 K and 500 atm, respectively, over an extremely short period of time.37 In general, acoustic-based exfoliation is carried out with an ultrasonic water bath or probe-tip sonicator, which can be scaled up to no more than a few hundred milliliters.38 Indeed, because of the inefficient energy transfer from the source to the liquid medium, the increase in the volume will exacerbate the production rate. Thus, exfoliation of graphite to graphene by ultrasonication is not a suitable way for large scale graphene production.39Cavitation is a phase change phenomenon involving the nucleation, growth, and collapse of gas or vapor-filled bubbles in liquids.40,41 Recently, the generation of hydrodynamic cavitating flows in microfluidic devices has gained much attention because of the scalability, cost-effectiveness, and energy-efficiency. Furthermore, facile flow generation processes besides the stationary section of hydrodynamic reactors make them even more popular and effective.42,43Due to the significance of hydrodynamic cavitation in fluidic systems, many studies have been dedicated to provide an understanding about the effects of major parameters such as thermophysical properties of the working fluid, geometry of the reactor, and surface roughness elements.et al.44 attempted to prepare single and few-layered graphene flakes in a cavitation reactor by employing a water–acetone mixture. Their process yield was 4%, and they introduced this method as a promising mass production tool with advantages of low cost and green process. In one of the recent studies conducted by Qiu et al.,45 a 50 g L−1 graphite suspension with a sufficient amount of surfactant (sodium cholate) was processed by passing around 2000 times through a microreactor (∼3 hours). The hydraulic power and relative energy consumption of their system were about 5 W and 2 MJ L−1, respectively. They reported that the surfactant might undergo destruction under intense cavitation, which can prevent the increase in the yield of process. In another study, graphene and its analogues materials were produced by the use of liquid phase exfoliation and microreactor, where Yi et al.46 introduced the fluid dynamics method for scalable and efficient production. They performed the experiments with the help of a high-pressure plunger pump, and the suspensions were under the effect of N,N-dimethylformamide (DMF) as a dispersion medium. They treated the working fluid in 5-cycles.Some studies on liquid exfoliation inside a microreactor are capable of generating hydrodynamic cavitation. For example, Liu Motivated by the emerging studies on LPE in microfluidic devices, herein, a sustainable hydrodynamic cavitation reactor system with a nozzle, which lead to a sudden decrease in the cross-sectional area of the fluid path and an increase in the velocity of the working fluid, was designed. This system was shown to be highly efficient in the large-scale preparation of stable graphene solutions from natural graphite powder in water. Accordingly, we developed an eco-friendly hydrodynamic cavitation induced microreactor, which could exfoliate graphene with the use of just pure water instead of harmful and expensive solvents and chemicals.2.2.1.−1 solid concentration was prepared using de-ionized water without the use of any surfactant or dispersant agent. In a typical experiment, graphite flakes in water were sonicated using an ultrasonic bath sonicator  for 30 min. The resulting graphite solution was kept on a side for 15 min to precipitate out the unstable large graphite flakes, and the supernatant  was separated to be used in the hydrodynamic cavitation reactor, where it was passed through the reactor.Natural graphite powder was purchased from Alfa Aesar . The graphite solution with 25 mg L2.2.The microfluidic device (hydrodynamic cavitation reactor) used in this study was fabricated using the semiconductor microfabrication techniques on silicon and was bonded to a glass cover to make sure that the reactors are leakproof. Thus, a fixed upstream pressure can lead to a stable flowrate in the reactors. The fabricated reactor consists of three main regions, namely inlet, nozzle, and extension zone. The widths of the inlet and extension are identical, while the width of the nozzle is smaller so that a sudden decrease in the flow cross-sectional area can be achieved.According to the Bernoulli's principle, velocity and static pressure are inversely related. Hence, the increase in the fluid velocity as a result of the change in geometry of the flow restrictive element in the reactor leads to a decrease in the static pressure, which triggers the formation of cavitating flows.47 The microfluidic device in this study is also equipped with wall roughness elements so that hydrodynamic cavitation can incept at lower upstream pressures. The reactor is resistant to high pressures and can withstand very high upstream pressures up to 1200 psi.Since the energy released from the collapsing bubbles provides the input of our system, it is vital to make sure that the majority of the bubble collapse occurs inside our reactor. For this purpose, the nozzle length in our reactor is significantly longer than the available studies in the literature, which facilitates the pressure recovery within the system. Hence, the bubbles face a relatively high-pressure region in the extension area of the reactor, which results in the collapse within the reactor. The second feature of the fabricated reactor lies on the engineered wall of the nozzle area, where roughness elements were formed. Our previous studies reported that the presence of roughness elements on the walls facilitated the formation of cavitating flows.Ln of the nozzle length is equipped with triangular roughness elements with a height of 4 μm. One inlet and two outlets are formed on the reactor to realize the flow path. The detailed geometrical parameters of the microfluidic device are listed in As mentioned before, the microfluidic device in this study consists of three regions with the same length of 2000 μm. The widths of inlet and extension zones are 900 μm, while this value for the nozzle is 400 μm. 2/348The process flow of the fabrication of the reactor in this study is the repetition of material deposition, patterning, and material removal using the standard microfabrication techniques. Accordingly, a layer of silicon dioxide was deposited on a double-side-polished silicon wafer. The inlet and outlet ports were patterned on the surface by the photolithography and dry etching processes. Then, second photolithography and deep reactive ion etching (DRIE) were performed on the wafer to obtain the final design. The silicon wafer was then bonded anodically to a glass cap to finalize the nozzle configurations. Three pressure ports were patterned on the surface along with the inlet and outlet ports to assist in the measurements of the static pressure at the inlet, nozzles, and extension zones. More detailed information about the fabrication process flow can be found in our previous studies.2.3.47 The working fluid (the starting graphite dispersion) was kept in a stainless-steel container , which was connected to a high-pressure pure nitrogen tank, was introduced to the system via proper fittings and stainless-steel tubing. The microfluidic device was installed and sandwiched into a homemade aluminum package, which facilitated flow visualization and prevented any leakage. The sandwich holder consists of one inlet connected to the fluid container and one outlet, where the fluid leaves the reactor. The pressure sensors  were also installed on the package to measure the static pressures at three different locations of the reactor. A double-shutter CMOS high-speed camera (Phantom v310) along with a macro camera lens with a focal length of 50 mm was used to record the flow patterns during the experiments, while the volumetric flowrate of the system was measured at different upstream pressures.Graphene nanosheets were prepared using a hydrodynamic cavitation reactor system shown in , which wρ and μ are the fluid density and dynamic viscosity, respectively. The density of water at 20 °C is 998.2 kg m−3, and the dynamic viscosity is 1 cP in this study. Since the concentration of the graphite suspension is low, its effect on the density and viscosity of this working fluid is neglected. The velocity of the system, on the other hand, is calculated from the measured volumetric flow rate and cross-sectional area. Dh is the hydraulic diameter of the nozzle. Cavitating flow characterization is of great importance to assess the intensity and flow pattern formation. For this purpose, the cavitation number is used and defined as:Pi is the upstream pressure, Pvap is the saturation vapor pressure of the working fluid, V is the characteristic velocity of the fluid in the reactor, which is calculated at the beginning of the nozzle based on the volumetric flow rate of the system .The prepared solution was introduced to the tubing system by applying the upstream pressure supplied by the nitrogen tank. The solution was propelled to the hydrodynamic cavitation reactor, where the exfoliation process happened in the nozzle and extension regions. The increase in the upstream pressure leads to a faster fluid flow in the system. One of the major parameters, Reynolds number, is expressed as:2.4.−1, resonance frequency of 50–200 kHz, and tip radius of 10–20 nm. UV-visible measurements were conducted on the samples in disposable cuvettes using a double-beam device (Varian Cary 5000 UV/Vis-NIR spectrometer) in the range of 200–800 nm. Raman spectroscopy was performed on a Renishaw inVia Reflex with the laser frequency of 532 nm as an excitation source. Raman spectra were obtained and normalized from at least 15 different spots on each sample. The size distribution of flakes after the specific cycles was determined using the dynamic light scattering (DLS) method. In this method, 1 mL of each sample was characterized in disposal cuvettes. The experiment was carried out with a Zetasizer Nano ZS  device equipped with a He/Ne laser operating at 633 nm as a light source.After different cycles of hydrodynamic cavitation, the collected samples were subjected to sequential centrifugations  to remove any unexfoliated material. The procedure for the sequential centrifugations is given in the Discussion section. The optical microscopy, Raman spectroscopy, scanning electron microscopy (SEM), and atomic force microscopy (AFM) for the samples were performed by transferring several drops of the supernatant (the top two-thirds of the dispersion from S3U samples) of second centrifuged suspension on silicon wafer substrates. The microscopic size and morphology of graphite/graphene were characterized by optical microscopy  and SEM . SEM images were taken after coating a very thin layer of gold–palladium alloy to observe the physical morphology and thickness of existing layers of the graphene. AFM measurements of graphene were made under ambient conditions at 60% relative humidity and 22 °C with a Digital Instruments Bruker Multimode 8 in tapping mode. The characterization was obtained using a NanoAndMore tip with a bending spring constant of 40 N m3.Graphene nanosheets were produced in the hydrodynamic cavitation reactor system , where a3.1.Pi) corresponding to cavitation inception is 350 psi. The corresponding flow velocity is 68.2 m s−1, while the corresponding Reynolds number can be found as 15 861. Thus, it is evident that the flow is turbulent even at cavitation inception.Under cavitating flow conditions, the static pressure at the nozzle area drops to a critical value due to a sudden change in the flow geometry. The high-speed camera system captures cavitating flows at the beginning of the nozzle area. The upstream pressure , where the gas phase is elongated along the nozzle are, leads to the developed flow regime .As can be seen in th cycle are shown in th cycle, while fully developed cavitating flow is seen at the upstream pressure of 300 psi. This indicates that more heterogeneous sites as a result of the fine exfoliation are formed inside the introduced suspension, and the nucleation is triggered more vigorously after the 80th cycle.Regarding the application of the fabricated microfluidic device in this study, developed flow regime corresponding to the upstream pressure of 650 psi is suitable for cyclic treatment of the graphite suspension and subsequent exfoliation due to the optimum conditions regarding the input power and output of the process. The experiments include 0–80 cycles so that the graphite suspension is thus treated with cavitating flows. Cavitating flows corresponding to inception and developed flow after the 803.2.via 20-cycles, the starting graphite dispersion was circulated 20 times through the hydrodynamic cavitation system, and the obtained solution of the graphene nanosheets was analyzed using spectroscopic and microscopic techniques. To maintain the homogeneity in the produced graphene nanosheets, a sequential centrifugation method was developed and applied for all samples. In this method, the graphene dispersions after the hydrodynamic cavitation treatment were first centrifuged at 2000 rpm for 1 hour; thus, the exfoliated graphene nanosheets and small fragments of graphite were obtained in the supernatant solution (S2U). This supernatant was subjected to a second centrifugation process at 3000 rpm for 1 hour to remove large particles and to isolate the highly exfoliated stable graphene nanosheets (S3U). In the hydrodynamic cavitation-assisted graphene production process, the starting graphite dispersion was circulated through the system to evaluate the effect of the number of cycles on graphene production. The pre-defined cycles of 20, 40, 60, and 80 were used to study this effect. For example, to prepare a graphene-containing solution 49,50 and graphene.51,52 In a typical Raman spectrum of graphene, there are three commonly reported peaks as D, G, and 2D bands at around 1350, 1580, and 2700 cm−1, respectively.53 The D band in the spectrum is related to the structural disorders, edges, and topological defects in the flakes. The area ratio of D-band to G-band (AD/AG) is often used to define the relative amount of surface defects on the graphene.54,55 Besides, the 2D-band for graphene is attributed to two-phonon double resonance and can be used as a measure to evaluate the number of layers in the graphene nanosheets. More specifically, the intensity ratio of 2D-band to G-band band (I2D/IG) is an indication for the number of layers of graphene.The isolated graphitic materials and the starting graphite dispersion were first characterized by Raman spectroscopy to evaluate the effect of the hydrodynamic cavitation on the exfoliation of graphite flakes. Raman spectroscopy is a versatile tool to analyze the structure of carbon nanomaterials, including carbon nanotubes56 No significant change is observed in the maxima of the 2D-band of the S3U-20, S3U-40, and S3U-60 compared to the starting graphite dispersion (2D-band ∼2716 cm−1). However, there is a significant downshift (∼25 cm−1) in the maximum of the 2D-band for the S3U-80 and, the band appeared at 2692 cm−1. In agreement with the literature,52 the observed shift can be attributed to the formation of bilayer graphene nanosheets after 80-cycles of hydrodynamic cavitation. Furthermore, the enhanced I2D/IG ratio after 80-cycles further supports the formation of a few layer graphene nanosheets.57ID/IG ratios of 0.10, 0.48, 0.32, and 0.87 for the S3U-20, S3U-40, S3U-60, and S3U-80, respectively, suggesting a gradual defect formation.58When the defect density was analyzed, almost no defect was observed for the starting graphite dispersion. In contrast, the isolated graphene nanosheets have 59 and it was shown that the intensity ratio between the D-band and D′-peak (at ca. 1620 cm−1) could be used as a measure to probe the nature of the defects. In general, this ratio (ID/ID′) was found to be ∼13 for sp3-defects, while it was ∼7 and ∼3.5 for vacancy-like defects and boundaries in graphite, respectively. After the application of hydrodynamic cavitation, the intensity of D′-peak gradually increases with an increase in the number of cycles. In parallel, as above-mentioned, the intensity of D-band ∼1620 cm−1 also gradually increases. The isolated graphene nanosheets have ID/ID′ of 1.93, 2.31, 1.91, and 3.63 for the S3U-20, S3U-40, S3U-60, and S3U-80, respectively. From the observed ratios, it can be concluded that the hydrodynamic cavitation creates surface defects on the exfoliated graphene nanosheets, and the defect density becomes more pronounced after 80-cycles of cavitation. However, it is worth pointing out that the calculated ID/ID′ ratios are lower than the ratios reported for the graphene nanosheets with sp3 and vacancy-like defects.The nature of defects in graphene was previously studied,60 The lateral size of the analyzed nanosheets is in the range of 1–5 μm. Furthermore, close inspections on the AFM image of the few-layer graphene nanosheets produced after 60-cycles display large holes, which vary in sizes between 100 to 600 nm  characterization was used to determine the size and thickness of produced graphene nanosheets. The results complement the Raman spectroscopy data. AFM image and height profile of the produced graphene nanosheets after 80-cycles of hydrodynamic cavitation further confirm the exfoliation of graphite flakes into bi-layer graphene nanosheets having a thickness value of ∼1 nm . The thio 600 nm . The pre−1), the concentrations of the obtained graphene nanosheets are calculated as ∼2.1 (S3U-20), 1.1 (S3U-40), 1.0 (S3U-60), and 1.1 (S3U-80) μg mL−1 using the molar absorption coefficient of 3620 mL mg−1 m−1 at the wavelength of 660 nm for the graphene in water.61 Using the concentrations of the isolated graphene nanosheets, the process efficiencies after 20-, 40-, 60-, and 80-cycles are calculated as 8.4%, 4.8%, 4%, and 4.4%, respectively. It is worth noting that the efficiency of the hydrodynamic cavitation-assisted graphene production process after 40-cycles is higher than the previously reported study.58 However, the yield of exfoliated graphene showed a fast decrease after 20-cycles. The observed concentration loss may be related to the trapping of exfoliated graphene in the cavities and the porosities of the system. The efficiency of the system can be improved by reducing the length of the pipes, porosities of the exposed surfaces, and using a closed-loop system. Moreover, the UV-Vis analysis of a control sample prepared by centrifuging the starting graphite dispersion exhibits almost no absorbance at 660 nm (1.4 μg mL−1). This result indicates that the stability of the isolated graphene nanosheets is higher than that of the starting graphite dispersion, probably due to the size shortening of graphite flakes.UV-Vis spectroscopy was performed to assess the concentration of the isolated graphene nanosheets and the starting graphite dispersion  technique. The DLS results of the centrifuged samples of carbon-based (graphite/graphene) colloids at the end of different hydrodynamic cavitation cycles are demonstrated in The scanning electron microscopy (SEM) image of the starting graphite dispersion displays large flakes having a lateral dimension of over ∼5 μm . The lat−6 s). Therefore, the energy density (E = J m−3) can be calculated using the pressure differential along the channel.62 All of the cycles were performed at 650 psi (4.48 × 106 J m−3) for having consistent results. However, the pressure sufficient to have graphene exfoliation decreases to 300 psi (2.06 × 106 J m−3) with the number of cycles due to exfoliation and fragmentation of graphite powder in lower cycles, which provides active sites for nucleation of the cavitating bubbles. 63,64 The results on hydrodynamic cavitation show a higher yield by consuming a lower energy density for graphene exfoliation. As a well-known technique for graphene exfoliation, sonication consumes 25–540 watts of power (5 times more than hydrodynamic cavitation) for an extensive amount of time (3000 times more than hydrodynamic cavitation) to exfoliate a fraction of 1 liter of graphite solution.61,65–68 Although the size of used graphite powders limits the hydrodynamic cavitation method, 300 times more energy is required to achieve the same yield for the sonication method.The residence time of the fluid in the hydrodynamic cavitation device is rather short  on cavitating flows were visualized and studied. Then, the impact of cavitating flows on graphite exfoliation was investigated. This method does not involve any surfactants or dispersion agents. According to the results, the suspensions with graphite flakes led to an increase in the number of the sites of heterogeneous bubble nucleation and to a decrease in the upstream pressure needed for cavitation inception and a developed cavitating flow pattern. Fragmentation of flakes and then exfoliation of layers was observed after exposures of 60–80 hydrodynamic cavitation cycles inside a microfluidic device and were rigorously characterized with different methods. With the implementation inside the reactor, it is possible to have a green, scalable, cost-effective, and energy-efficient process. The produced graphene nanosheets  meet the requirements well in many applications such as bioengineering, composites, and electronic devices. The results on hydrodynamic cavitation show a higher yield compared to the sonication and shear methods for graphene exfoliation.The data that support the findings of this study are available from the corresponding author upon reasonable request.The authors declare that they have no conflict of interest.RA-011-D1RA03352B-s001RA-011-D1RA03352B-s002


A reconfigurable Substrate-Integrated Waveguide (SIW) filter operating in the THz region was designed in this work. Two SIW resonators were coupled through a magnetic iris to form a second-order filter with a double-layer substrate. The first substrate was silicon of permittivity 11.9; on top of it, silicon dioxide of permittivity 3.9 was placed. The ground and upper plane were composed of gold plates. Graphene material was then used for the tunability of the filter. A thin graphene sheet was sandwiched between the silicon dioxide substrate and the upper gold plate. An external DC bias voltage was then applied to change the chemical potential of graphene, which, in turn, managed to change the operational center frequency of the filter within the range of 1.289 THz to 1.297 THz, which translated to a bandwidth range of 8 GHz. The second part of this work centered on changing the aspect ratio of the graphene patch to change the center frequency. It was observed that the frequency changed within the range of 1.2908 THz to 1.2929 THz, which gave a bandwidth of 2.1 GHz change. Microwave filters are a fundamental component of communication systems. With recent technological advances, tunable/reconfigurable filters are becoming useful to achieve the requirements of modern filters. Beyond 5G, communication systems are required to operate at high frequencies in the region of THz. Various filters use planar technologies, which suffer considerable losses in the THz region, including various materials ,7,8,9,10In terms of tuning the filters, different methods have been explored in the literature ,10,11,12Qian  used a lLi and Yang  placed vFor high-frequency structures in the THz region, graphene has been used for frequency and bandwidth tuning ,16,17,18mn modes to be excited from the structure, which helped the filter to be configured as a single- or dual-band notch filter. The variation in the chemical potential of graphene also changed the center frequency. Moazami et al.  presenteGraphene has the property of negative permittivity, and such materials are vital for the propagation of waves in the terahertz region. Negative permittivity is important in confining the propagation of surface plasmonic waves, which are waves that are transmitted on the surface of a metal and dielectric interface. Graphene is a two-dimensional (2D) material with semi-metallic properties. It is a single layer of graphite crystals with a single atomic layer of covalently bonded hexagonal carbon atoms. Graphene is composed of carbon atoms arranged hexagonally .Graphene can support Surface Plasmon Polariton (SPP), which makes it a good candidate for electrical tunability. SPP is an electromagnetic excitation that occurs on the interface between a dielectric material and a metal surface . Surface2). This filter can be used in bio-medical devices, such as sensors operating in the terahertz region. It can be used to let the required signals pass and forbid all other signals outside of the target frequency. This paper is organized as follows. In this research work, a second-order filter was built, which operates in the THz region. SIW technology was used. Two substrates were employed; the first was attached to the ground plate of silicon (SI) and the second was attached to the upper plate of silicon dioxide σg1=−bV is the bias voltage and t is the substrate thickness. The relationship in Equation (5) shows that, as the external bias voltage changes, the chemical potential also changes; hence, we can control the chemical potential of graphene using an external bias voltage, which, in turn, can be used to vary the center frequency.The tuning of the filter can be achieved by changing the voltage across the graphene sheet. This provides an easier alternative method for changing the central frequency of the filter than changing the entire geometry of the filter. The geometry of the filter can be changed in case there is a need to operate in a dual-band mode. The relationship between the surface conductivity and chemical potential is given as :(5)μc=ћv2), with permittivity of 11.9 and 3.9, respectively, was also included. Graphene of thickness 0.0034 µm was placed between the Si02 substrate and the top gold plate. The applied external DC bias voltage is indicated as Vb.A band-pass filter was designed for operation at a resonant frequency of 1.2 THz. The structure was simulated at first with no graphene, as shown in b was used to change the chemical potential of graphene. The values of chemical potential started from 0.04 eV to 0.40 eV. The other parameters of graphene are shown in In this work, the external voltage bias VWhen the chemical potential was 0.1 eV, the SIW filter resonated at first and second frequencies of 1.2894 THz and 1.2398 THz, respectively, with return losses of −36.441 dB and −28.502 dB, respectively, as shown in b; hence the external voltage was varied to obtain different chemical potential values, and in turn, the center frequency changed.As shown in Equation (5), the chemical potential of graphene is directly proportional to the applied bias V1 and z1. Here, yellow circles represent the via holes.The length and width of graphene, as shown in 1, representing the width, and z1, representing the length of the graphene patch, were changed, and the results are shown in 1 = 50 µm and z1 = 100 µm, as shown in 1 and z1 were changed to 100 µm and 300 µm, respectively (The chemical potential was kept constant at 0.1 eV. The parameters wectively , the firFrom In this research work, a second-order SIW filter was designed to operate at 1.2 THz. The magnetic iris of length d1, as shown in The aspect ratio of the graphene sheet was also changed to change the frequency of the filter. As the width and the length of the graphene patch changed, the center frequency also changed; however, this method requires modifying the physical filter structure for a change in frequency, which may be undesirable, as compared with a change in frequency by simply changing an external voltage without changing the geometrics of the physical filter structure. More work in this research will be conducted on adding more layers of graphene sheets instead of one to improve the range in which the frequency can be tuned. Furthermore, the orientation of the graphene sheets will be interchanged between the horizontal and vertical positions.


In this work, we benchmark non-idealities and variations in the two-dimensional graphene sheet. We have simulated more than two hundred graphene-based devices structure. We have simulated distorted graphene sheets and have included random, inhomogeneous, asymmetric out-of-plane surface corrugation and in-plane deformation corrugation in the sheet through autocorrelation function in the non-equilibrium Green’s function (NEGF) framework to introduce random distortion in flat graphene. These corrugation effects inevitably appear in the graphene sheet due to background substrate roughness or the passivation encapsulation material morphology in the transfer step. We have examined the variation in density of state, propagating density of transmission modes, electronic band structure, electronic density, and hole density in those device structures. We have observed that the surface corrugation increases the electronic and hole density distribution variation across the device and creates electron-hole charge puddles in the sheet. This redistribution of microscopic charge in the sheet is due to the lattice fields’ quantum fluctuation and symmetry breaking. Furthermore, to understand the impact of scattered charge distribution on the sheet, we simulated various impurity effects within the NEGF framework. The study’s objective is to numerically simulate and benchmark numerous device design morphology with different background materials compositions to elucidate the electrical property of the sheet device. However, large-scale commercial production and market adoption are still very far from the horizon. The possible utilization of graphene sheets is in various applications from the transparent electrode, electronics, telecommunication equipment, and internet of thing (IoT) sensors. To realize this commercial adoption in the electronics and optoelectronics industry, the main challenge for graphene is in the controllability, homogeneity, and uniformity in the electronic property in the mass roll-to-roll production process. The growth and transfer process, such as temperature variation and gas flow fluctuations in the chemical vapor deposition reactor, give rise to long-range spatial variation in the electronics performance parameter of the large-area graphene sheet. It prevents the seamless stitching of graphene single grain, which gives rise to imperfect lattices and grain boundary interfaces, causing a decrease in conductance8. Moreover, the geometrical circumstance of the graphene sheet transfer scheme gives rise to spatial variation in the doping density. Therefore, for homogeneous and uniform graphene sheets, defect density is an important measure. However, we must consider the graphene sheet’s average defect density and spatial defect distribution profile to quantify the effect9. Moreover, all those issues, as mentioned above, are a challenge to scale up the production. There are various methods proposed to fabricate the graphene sheet on an industrial scale, such as exfoliation, the epitaxial method10, chemical vapor deposition (CVD)11, Roll-to-Roll plasma-enhanced chemical vapor deposition (PECVD) method15. However, the synthesis of graphene on metal catalysts by CVD has been the most scalable process until now. Besides, all these process steps have their underline chemistry and influence on the quality of the graphene sheet16. Therefore, the electrical quality of CVD/PECVD grown graphene sheets varied broadly from process to process and batch to batch. Besides, the transfer and isolation process are bottlenecks in the production scale and incorporate defects in the sheet and degrade the sheet’s electrical quality20. These nanoscale atomistic effects during the growth and transfer steps influence the vital electrical properties of the sheet through variation in background carrier density, carrier mobility, and sheet resistivity. Electrical property mapping is critical for the process optimization and quality control of large-area graphene sheets in Roll-to-Roll production. In terms of throughput and quality, all the electrical characterization method available is far behind the Roll-to-Roll production process. In recent times to numerically probe the above-mentioned microscopic variations and non-idealities in the macroscopic device, some notable theoretical and numerical efforts have been made in the community, e.g., Stegmann et al. investigate the current flow paths in the deformed graphene by using modified hopping parameters in a tight-binding approach and connecting it with the current classical trajectories in curved space21. Also, the influence of a Gaussian strain on sublattice selectivity of impurities in graphene is investigated by modified tight-binding parameters and investigated the local density of states variation25. However, unlike our multi-scale study, they investigate a single strain defect of Gaussian curvature in the flat graphene sheet or nanoribbon. In a realistic device scenario, however, many fluctuations exist and are random in nature. Also, local sublattice symmetry breaking and electron-hole puddles formation in graphene is theoretically discussed in some detail26, and our numerical results match their prediction. Other than the above work, multi-scale quantum ballistic transport calculations have been performed in the recent past on flat graphene28. Furthermore, our flat graphene sample calculation matches with them. To the best of the author’s knowledge, very few multi-scale incoherent and phase-coherent quantum transport calculations are performed in the graphene and two-dimensional system. All the scattering mechanisms are left as the residual calculation for future work. In this study, first, we will discuss and summarize the various numerical simulation results for the graphene device’s various aspects, variabilities, and non-idealities in device simulation, to elucidate the nature of variability in the measurand electrical properties for benchmarking purposes. In the subsequent article under preparation, we will also report the effect of each scattering mechanism in multi-scale simulation, their combined effect as self-energy incorporating explicitly in the NEGF loop as self-consistent Dyson equation in graphene sheet devices. Furthermore, The multi-scale non-equilibrium Green’s function formalism framework detail, its incoherent extension, implementation, important assumption, approximation, bottom-up atomistic tight-binding models, and numerical truncation to treat these non-ideal graphene devices are discussed in the method section and great detail at supplementary information section. Next, in the following result and discussion section, we will discuss the multi-scale non-equilibrium Green’s function formalism numerical results and their physical interpretations. Finally, in the last section, we conclude the article by summarizing the results, observations, and future work in the two-dimensional material field.Since the isolation of single-layer graphene in 2004, graphene has shown promising research results in laboratories across the globeNext, in the following methods section, we will discuss the multi-scale non-equilibrium Green’s function formalism used to get these results in the aforementioned section.29. The electronic band structure derives from the tight-binding method. The method is similar to the linear combination of atomic orbitals (LCAO) used to construct molecular orbitals31. However, in the tight-binding approximation, electron-electron interactions of the orbital are neglected, but it gives an excellent approximation to electronic band structure. Furthermore, for more rigorous treatment, the Hubbard model was employed. The graphene is a two-dimensional sheet of carbon atoms arranged in a hexagonal lattice. At the nano-scale atomic composition, crystal symmetry and the spatial disorder affect the material’s bulk properties as quantum mechanics effects come into the picture and modify the electronic-phononic structure. Therefore, atomistic simulations are more appropriate to model the quantum device’s electronic properties in the entire Brillouin zone33,c annihilation operators, and summation runs over entire n lattice point, and l is first and m is third nearest neighbor site of n lattice point. First nearest-neighbor hopping parameter 34. In the tight-binding framework dangling bonds at the surface or edge is passivated by primarily two numerical methods. In the first strategy, passivation atoms are implicitly incorporated without distinguishing passivation atom types and add a passivation potential to the dangling bonds’ orbital energies. This method works well with a relatively large system, arbitrary crystal structures, and hybridization symmetries. Furthermore, with appropriate parameters, it is applied to any passivation scenario35. The second approach is explicit, including the passivation atoms and their coupling to the surface or edge atoms Hamiltonian matrix and limited to small molecules and systems36. In this explicit treatment, ab-initio results for different passivation atoms used to fitting targets. The unsaturated dangling bonds at the edge or surface will result in edge or surface states at the electronic band structure. These unwanted states iron out by coupling the hydrogen passivation atoms to the surface’s or edge’s unsaturated dangling bonds in the device. We have used the 38. The adaption of NEGF formalism to semiconductor devices first demonstrated by Lake and Datta42, in 1992 and later in 2002 by Wacker43. Through NEGF formalism, the time evolution of many-body quantum fields in thermodynamic equilibrium and non-equilibrium state can be investigated49. These quantum fields constitute carriers such as electrons, phonons, spin, and electric-field in semiconductor devices60.The primitive lattice vectors in graphene are,A is spectral function related to the spectral peak of Green’s functions in energy spectrum, E is energy space, n, m, l, v are discrete lattice point of device where Green’s propagator travel in coupled system of Eq.  is,62. Its modular architecture parallelizes in a five-level message passing interface (MPI) in the position, momentum, energy, bias, and random seeding space. Due to the modular architecture of the transport kernel, various physical models add up and extend into it, the detailed discussion provided in the article’s supplementary information.The theoretical framework of Non-equilibrium Green’s function formalism with detailed reference is given in the supplementary information. Here we briefly summarize the NEGF formalism on a discrete device grid as,from Eq. , \documementclasspt{minimaWe have employed multi-scale, multi-physics-based bottom-up, non-equilibrium Green’s function mechanism-based quantum transport simulation techniques to investigate various device aspects and deduce the observable and measurable at the final stage in the computationally simulated devices. Moreover, most reported publications in the graphene and two-dimensional material field calculate electrical parameters of coherent transport limit and leave scattering interaction behind as a residual. The scattering nature and origin depend on graphene’s different fabrication process steps, the device orientation and substrate, and surface encapsulation in the device preparation step. The complete stepwise description of the theoretical framework provides in the article’s method section and supplementary information. This industrial research work was envisioned to show the opportunity of improving the electrical characterization of the roll-to-roll CVD graphene production process. Therefore, our results in this work are directed to corrugations and impurities effect in the reasonably clean state-of-art industrial production and transfer process. Here we will discuss the main results from numerical calculation.64. Due to thermodynamic instability, the corrugation and ripple have been observed in the free-standing and substrate-born graphene sheet devices. There is modest work reported on deformed graphene. Most of the previous work concentrated on a uniform, uniaxial or biaxial strain and centrosymmetric deformations69. Katsnelson et al. derived the mathematical formulation for microscopic defects and generic random potential by ripples for the Dirac fermions from the semi-classical Boltzmann transport view70. The fluctuating interatomic distances and angles between carbon bonds are described by in-plane and out-of-plane atomic displacements deformation tensor in the corrugated graphene. This work tried to elongate their original idea in the non-equilibrium Green’s functions formalism (NEGF) based quantum transport domain. Based on the substrate material type and fabrication process, the corrugation profile has considerable variation from 0.30 71. Due to corrugation, 72. The surface corrugation effect in the graphene sheet modeled through the gaussian auto-correlation function in the transverse x and y-direction as,We have investigated the out-of-plane random, inhomogeneous, asymmetric structural corrugation effect in the electrically open infinite reservoirs contacted geometry of graphene sheet to examine the large variability across the electric properties of CVD graphene sheet. Graphene is a single atom thin sheet of the carbon atom and needs a substrate to work as a device. The substrate’s effect is manifold, such as corrugation in the graphene sheet by the substrate surface profile and scattering through the substrate’s impuritiesfrom Eq. , electrofrom Eq. , the denfrom Eq. , and elementclass2pt{minimmentclass2pt{minimmentclass2pt{minimmentclass2pt{minimmentclass2pt{minimmentclass2pt{minimmentclass2pt{minimmentclass2pt{minimmentclass2pt{minimmentclass2pt{minimmentclass2pt{minim73. Moreover, the sharply peaked Van-Hove singularity point slowly shifts from low energy towards higher energy and slowly smoothing at these higher energies with the increased deformation in the sample. Even a tiny randomized inhomogeneous in-plane or out-of-plane deformation strain will break the local sublattice and inversion symmetry in the one atom thin graphene. It will give rise to an inhomogeneous pseudo magnetic field that produces the additional density of the state’s low-energy peaks and increases the scattering probability with a deteriorating conductance. Moreover, inhomogeneous pseudo field incipient a non-equivalent charge density localization and distribution across the asymmetric sublattices of deformed regions. Furthermore, creating the electron-hole puddles in the graphene sheet can be seen from the numerical calculation from the electronic density Fig. 74. From density of modes M(E) Fig. We have observed from Fig. entclass1pt{minimaentclass1pt{minimaentclass1pt{minimaentclass1pt{minimaentclass1pt{minimaentclass1pt{minima75. However, this shift is minuscule in comparison to a small geometry corrugated structure from Fig. M point in the band structure for these deformation values. From Figs. et al. perform Metropolis algorithm-based Monte-Carlo simulations for intrinsic ripples in graphene with varying samples size of atoms from N = 240 to 1994076. For varying samples size at T = 300K, they found the ripples latent size of 5 to 10 nm long matching with the experiment values77. In our work from NEGF calculation from comparing Figs. The density of state from Figs. entclass1pt{minimaentclass1pt{minima75. The In-plane deformation profile also influences the electronic properties of the narrow-width graphene device and graphene nanoribbon. However, for the wide graphene sheet device on the substrates, the surface corrugation will always impact and fluctuate the device performance characteristics. Furthermore, in the corrugated device structure, the electron density distribution is nonuniform in the sheet implies that scattering rate and carrier conductivity are also spatially varying phenomena in the device. A highly corrugated device will complicate the band diagram with the mixing and split of various branches. In the corrugated device structure, we have observed the density fluctuation with the increase of corrugation compared to the flat configuration. In addition, the local density of state variation suggests that the scattering probability should be in the spatial domain, momentum-dependent, and energy-dependent. Moreover, the current path will be highly disordered and nonlinear in such a device and follow the minimum resistance path. In the corrugated structure, density variations from the average density valuation in the flat configuration arise due to random quantum fluctuation due to variable atomic bond length and bond angle in the microscopic description of the material at the atomistic scale, and inversion symmetry and lattice symmetry breaking. These effects influence the macroscopic electronic and charge transport properties of the sample.We have also simulated a two-dimensional orthorhombic device structure to investigate whether a four atom per unit supercell will influence similarly or have different characteristics. This geometrical structure can be further tailored to make an armchair and zigzag nanoribbon configuration based upon confinement direction, boundary condition, and edge topology. In the article’s supplementary information, simulation results are rendered in the full-text page resolution from Supplementary Figs. 78. Auto-correlation function is used to statistically model the in-plane deformation effects79. In the transport direction of z, the graphene sheet has a uniform ideal width of W. At position 80. By using the exponential nature of the auto-correlation function,81. Using NEGF formalism, we have created various numerical roughness profiles and evaluated the graphene sheet’s electronic transport properties.We have investigated the in-plane deformation effect on the electronics properties of the graphene sheet. In-plane, inhomogeneous deformation acts as a scattering source and affects the graphene sheet’s transport propertyWe will discuss the results of 10x10 graphene supercell Fig. 82. Also, the modest increase in deformation amplitude will introduce these localized states, and transmission current through these new states will progress83. However, a radical increase in the in-plane deformation will effectively decrease the sheet width available for propagating modes, increase the transport bandgap, and decrease the current value. One of the main contributions of roughness scattering through non-equilibrium Green’s functions formalism (NEGF) transport is that we have shown the corrugations scatterers is a long-range scattering potential, as depicted in Figs. From Fig. et al. mathematically formulated the impurity scattering using linear response theory Kubo formalism. Furthermore, gauged robust minimal conductivity independent of disorder of sample in the Boltzmann conductivity limit by applying mean-field approximation to the Kubo conductivity tensor in a weak scattering regime exploiting the liner Dirac electronic bandstructure of graphene84. However, our simulation work is based upon the Landauer formula in the non-equilibrium Green’s functions formalism, which is more generic to handle linear as well as non-equilibrium transport regimes and derived through Keldysh’s generalized perturbation theory for the non-equilibrium system. In the non-equilibrium Green’s functions formalism, the generic interacting current ansatz has been given by Caroli et al.87 from the fluctuating electronic density between the interacting contact, and it corresponds to equation (5) of the Landauer formula for the current through an interacting electron region88. We have numerically incorporated the spatial distribution of impurities atoms in graphene by solving the Poisson equation of spatially fluctuating impurities potential with NEGF formalism. Henceforward, we calculate the spatial charge distribution in terms of density of state, electronic and hole density, and variation in transmitting density of modes. Furthermore, we have investigated the change in electronic properties with the interpretation of impurity density variation. We have varied the number of carbon atoms involving a substitutional impurity atom to consider these effects, effectively changing the device’s doping density. Furthermore, We have changed the impurity atom type, e.g., Nitrogen and Phosphorous atoms, with varying atomic radius. Besides, in the Phosphorous impurity study, we intentionally change the electronic valency of the ion with ten electronic charges. This fictitious super ion configuration is simulated to mimic a larger diameter atomic or molecular defect with the high electronic charge concentrated at a particular lattice site on graphene sheet in the substitutional or adsorbent configuration pattern during the fabrication or transfer step. To circumvent the high computational cost of non-local scattering self-energy term in the NEGF framework. Adsorbed or substrate charged impurities trap are modeled in the graphene sheet as charge impurity center and truncated at the Q is element charge, and T is temperature, k is the Boltzmann constant, and 89. In our impurities, NEGF calculation similarly minimum conductivity value is observed. However, our calculation scenario is more complex. We calculate the transmission at room temperature and mix up all the propagating modes at thermal energy as it happens in the room temperature measurement in the CVD graphene sheet for any practical application. We have calculated the Density of state from Eqs. et al. marom Eqs.  and (19)equation  of the Lequation  of the Lequation  of the Lequation  of the Lequation  of the Lequation  of the Lequation  of the Lequation  of the Lequation  of the Lequation  of the LIn Fig. In Fig. The impurity atoms, inhomogeneous impinging applied electrical field, and various strain fields through ripples, corrugation in the graphene sheet increase the energy mixing of propagating density of modes. Furthermore, the extra state density assists in propagating electrons to scatter more, therefore reducing overall conductance. Nevertheless, at the same time, even the slight variation in band structure dispersion gives rise to variation in the effective mass of Dirac fermion from idealistic values, and overall observed mobility and conductivity deteriorate furthermore from the flat characteristic. We have observed the slight kink in the density of state around zero-energy Dirac point due to substitutional impurity and the start of band branch splitting around the high symmetric points of the Brillouin zone, which broadens the original graphene band at these points. These additional band branches will influence the energy landscape in the next few nearest-neighbor carbon atoms. Hence, more accuracy can be achieved in band structure calculation by adopting a higher-order tight-binding model for an impurity-driven sheet in an open boundary device or using an electrically close boundary sheet in the ab-initio calculation with few ten of thousand atoms device with additional computation overhead. Next, we have a doped graphene sheet with substitutional Phosphorus impurity. Although intentionally replace the electronic valency of the ion with ten electronic charges to create a fictitious super ion to mimic a larger diameter atomic or molecular defect with the high electric charge concentrated at a specific lattice site on the graphene sheet. In the figure Fig. In Fig. 92, Furthermore, the most prominent mechanisms of these various physical effects determine the final device characteristic. In the NEGF loop, these various mechanisms are adopted as Dyson’s self-energy loop to solve self-consistently. The macroscopic sample’s characterization properties are defined by the microscopic averaging out of competing scattering statistics rather than individual scattering events of the order of the femtosecond process. Finally, we conclude the article with a summary of the results and observations.In Fig. We have numerically investigated various random, non-idealities, e.g., inhomogeneous out-of-plane surface corrugation, in-plane deformation, and excess atomistic charge impurities in the 2-dimensional graphene sheet. These non-idealities primarily arise in the Roll-to-Roll chemical vapor deposition (CVD) and plasma-enhanced chemical vapor deposition (PECVD) manufacture process. Mitigating these variances is necessary for the practical application success of the graphene industry, and the high fidelity and uniformity require in the graphene production, transfer, benchmark process is the utmost requirement for developing the graphene-based industry. We have employed a multiscale, multi-physics-based non-equilibrium Green’s function framework in a third nearest-neighbor tight-binding configuration. The Tight-binding model is computationally efficient to incorporate atomistic effects on mesoscopic electrical properties. Our detailed study provides an essential understanding for evaluating and benchmarking the electronic properties of graphene sheets. It also oversees the nanoelectronics device design aspect on graphene and 2-D material for practical application in industry. Our calculation has not explicitly treated surface roughness scattering as a self-energy term in the NEGF framework, which is numerically cumbersome, affecting the device’s performance. In future investigations, we will attempt to incorporate that in an equal mathematical footing in the framework. Also, a more sophisticated local density of state-dependent scattering model should be employed for a more detailed investigation of the highly corrugated device. Also, surface passivation treatment can influence the device’s electrical characteristics. Theoretical modeling of capping material effect, doping efficiency, long-range electrostatic screening, interface effect, interlayer phenomena, contact quality, and heat transfer in the low-dimensional material-based device should be examined further for quantitative evaluation. However, scattering is omitted and treated as residue in the most published articles in the 2-D materials domain and ignored without sufficient justification. In addition, the atomistic resolutions are critical for the charge in the self-consist computations. The theoretical treatment of defect situations is even challenging at the multiscale simulation. However, these are challenging transport situations at the nanoscale’s theoretical modeling in the graphene and 2-D material domain.Supplementary Information.


Rapid detection of heavy metals in solution is necessary to ensure human health and environmental protection. Some heavy-metal compounds are present in solution as compounds instead of as ions owing to their low ionization. Therefore, the development of sensor devices for the detection of heavy-metal compounds is important. In this study, as a proof of concept, we propose a sensor device using graphene and a chelating agent, which were used to develop an identification technique for three types of cadmium compounds. Pristine-graphene and two types of chelator-modified graphene-based sensors were successfully used to detect cadmium compounds at concentrations ranging from 50 to 1000 μM. The detection time was less than 5 min. The three type of graphene-based sensors responded differently to each cadmium compound, which indicates that they detected cadmium as a cadmium compound instead of as cadmium ions. Furthermore, we successfully identified cadmium compounds by operating these three types of sensors as a sensor array on the same substrate. The results indicate that sensors that focus on heavy-metal compounds instead of heavy-metal ions can be used for the detection of heavy metals in solution. Heavy metals are highly biotoxic and extremely dangerous, not only to humans but also to all living organisms; therefore, early detection of heavy metals is important ,2,3. WheN,N,N′,N″,N‴,N‴-hexaacetic acid (TTHA) and terpyridine were used as chelating agents, as these molecules are less water-soluble and can be modified without introducing defects on graphene via CH-π or π-π interaction.Graphene is a two-dimensional material composed of carbon atoms, and it has a high potential for sensor applications owing to its high mobility and surface sensitivity  15,16,1,116,17. In this study, sensor arrays with pristine or chelator-modified graphene-based sensors are fabricated to identify cadmium compounds in solution. We determine three cadmium compounds by evaluating the response of the sensor array to the introduction of cadmium compounds.2 (290 nm) substrate via photolithography and thermal evaporation, as shown in 2/97% Ar to remove oxidized impurities and promote catalysis. Graphene was synthesized by flowing 1500 sccm of 3% H2/97% Ar with 15 sccm of 5% CH4/95% Ar at 1058 °C for 50 min. After the chemical vapor-deposition process, graphene was transferred onto the substrate using a conventional transfer method. Graphene, except for that in the channel area, was removed using an oxygen plasma [2 at 300 °C for 1 h to remove the residues on the graphene surface, such as the resist.Cr/Au electrodes were formed on a Si/SiOn plasma ,35. The 2 at 300 °C for 1 h to remove adsorbates. After H2 annealing of the graphene-based sensor array, the solution in which these molecules were dissolved was placed onto the graphene via drop casting and modified on the graphene for 1 h. After deposition, the graphene-based sensors array was dried using compressed air and placed in a vacuum chamber overnight to remove residual molecules, such as tris-HCl buffer or dimethyl sulfoxide.TTHA, and terpyridine were purchased from Tokyo Chemical Industry Co., Ltd., Tokyo, Japan. TTHA was dissolved in 10-mM tris-HCl buffer solution at a concentration of 50 μM, and terpyridine was dissolved in dimethyl sulfoxide at a concentration of 50 μM. The graphene device was annealed again under Ar/H−3 Pa. The field-effect mobility was calculated using the following equation:gC represents the gate capacitance; W and L represent the width and length of the channel, respectively; and DSI and BGV represent the drain current and back-gate voltage, respectively [A graphene-sensor array was placed in a vacuum probe  for device characterization. The transfer characteristics of the graphene-based sensors were measured using a source-measurement unit  at 23 °C at 10ectively ,37,38.Atomic force microscopy (AFM) and Raman spectroscopy analyses were performed to confirm the modification of the chelating agents on the graphene surface. For pristine graphene, graphene devices were prepared using the above process without modifying the chelating agents, and the AFM  and Raman spectra were measured . A laser with an excitation wavelength of 523 nm was used for the Raman measurements.A handheld data-acquisition device was fabricated using a commercially available semiconductor chip. The data-acquisition device consisted of a 6-channel analog-to-digital converter with 24-bit resolution and multiplexer switches, and it is capable of multiple measurements via up to 24 channels. A 16-bit digital-to-analog converter was implemented as a voltage application system. The data-acquisition device was controlled by an Arduino and connected to a clip connector for array operation b.A pristine graphene and two chelator-modified graphene-based sensors were prepared. The substrate on which the graphene-based sensor was fabricated was fixed to a clip connector and connected to the above data-acquisition system, as shown in Three types of graphene-based sensors, pristine, TTHA-modified, and terpyridine-modified, were assembled on a chip with three devices per type on a substrate for identification of cadmium compounds. Nine sensors were operated simultaneously to measure cadmium compounds. The drain voltage was fixed at 50 mV and the sampling interval was 1 s. Each cadmium compound was dissolved in 100 mM acetate buffer, and 20 μL of the solution was dropped into the rubber pool to achieve final concentrations of 10, 50, 100, 500, and 1000 μM at 23 °C. Solutions of each concentration were introduced at 5-min intervals as in 2/Vs, respectively. The Raman spectrum of the graphene-based sensor is shown in −1 [−1, respectively. The intensity ratio of the G and G’ peaks and the FWHM results indicate that the graphene is monolayer graphene [First, the transfer characteristics of the fabricated graphene-based sensors were measured in a vacuum chamber before they were modified with the chelating agents. The typical transfer characteristics of the pristine graphene-based sensor are shown in wn in −1 ,40. The graphene . These r2/Vs, respectively. This decrease in mobility was considered to be owing to increased doping and carrier scattering caused by the modification of TTHA. However, the TTHA-modified graphene retains higher mobility than molecular immobilization via direct chemical modification [2/Vs, respectively, as shown in −1  to prevent variations owing to differences in the device characteristics. The results also indicate that the detection limit is between 10–50 μM. Similar to the pristine graphene-based sensor, the drain currents of the TTHA- and terpyridine-modified graphene-based sensors also respond quickly to the introduction of cadmium compounds, as shown in Graphene-based sensors were used to measure three types of inorganic cadmium salts: cadmium chloride, cadmium sulfate, and cadmium nitrate. A silicon rubber pool was attached to the graphene-based sensor, and measurements were made in acetic acid buffer. A drain voltage of 50 mV was applied, and the time response of the drain current was measured with a sampling interval of 1 s. The difference in the response of these sensors is may be owing to a change in the electrostatic potential of the chelating agent when the cadmium compound is coordinated to the chelating agent ,50,51. WBased on the above results, the graphene-sensor array was used as a logic circuit to identify cadmium compounds. Three types of graphene-based sensors, pristine, TTHA-modified, and terpyridine-modified, were assembled on one chip with three devices per type on one substrate. We performed simultaneous measurements using nine sensors. These measurements were performed under the same conditions as those in We fabricated graphene-sensor arrays comprising pristine and chelator-modified graphene for the identification of cadmium compounds in solution, which exhibited different sensor responses to three different cadmium compounds. This indicates that the graphene-based sensors do not detect cadmium as cadmium ions, but as cadmium compounds. This result is consistent with those of previous studies on the state of cadmium compounds in solution. Furthermore, in this study, an array of graphene-based sensors was used to identify cadmium compounds. The sensor arrays exhibited specific responses to each cadmium compound, and we successfully identified the cadmium compounds using the fabricated graphene-sensor arrays. Thus, this study established a detection method for heavy metals that focused on heavy-metal compounds instead of heavy-metal ions. These results represent an important step toward fundamental technologies for the development of sensors for heavy-metal detection. In the future, sensors for other heavy-metal compounds are expected to be realized by optimizing chelating agents.


Although the CVD synthesis of graphene on Cu(111) is an industrial process of outstanding importance, its theoretical description and modeling are hampered by its multiscale nature and the large number of elementary reactions involved. In this work, we propose an analytical model of graphene nucleation and growth on Cu(111) surfaces based on the combination of kinetic nucleation theory and the DFT simulations of elementary steps. In the framework of the proposed model, the mechanism of graphene nucleation is analyzed with particular emphasis on the roles played by the two main feeding species,  Since its discovery in 2004 , graphenAmong the mentioned methods, CVD is most frequently used for the production of high-quality graphene having high homogeneity, imperviousness, high purity, and fine grains. It is used nowadays to produce hundreds of thousands of square meters of graphene annually .This resulted in an intensive study of the CVD graphene growth process, which showed that on different surfaces/substrates and in different conditions qualitatively different graphene samples may be obtained. For instance, while on Ru, Ni, Ir, and Co surfaces, the segregation growth mechanism takes place, typically yielding bi- or multilayer graphene . The groSince single-layer graphene is usually of higher interest, a large amount of experimental and theoretical studies were dedicated to this process with the aim to find optimal conditions. As a result, low-carbon-source conditions have been found to be preferable, and they are typically used in industrial production. Moreover, high temperature, which suppresses the formation of dendritic domains, is usually used. In this work, we concentrate on the CVD growth process on Cu(111) that uses methane as a carbon source and occurs at high temperatures (c.a. 1300 K).The surface-catalyzed pyrolysis of hydrocarbons that lead to numerous carbon species on the surface;The aggregation and nucleation of these species on the metal surface, which produces graphene nuclei;The growth of the nuclei due to the attachment of feeding species;The coalescence of the flakes when high coverage is reached.Theoretical methods are widely used to support experimental findings and reveal important details of the mechanisms underlying the CVD production of graphene. From a theoretical point of view, if side-processes  are ignored, one can distinguish the following essential steps involved in the CVD:Each of these steps involve different elementary reactions, and the majority of steps occur simultaneously, influencing each other. This impacts the overall kinetics of the CVD process and, consequently, the quality of the resulting material. Due to such complexity of the process, its modeling requires multiscale approaches for a proper description.The most popular way to study CVD within multiscale settings is to combine a kinetic Monte Carlo (kMC) approach with DFT calculations ,21,22,23Simulations are performed in the range of up to several hundred nanometers, whereas the typical sizes of the nuclei observed in experiments are in the micrometer scale ;kMC calculations are usually limited to the steady growth of a single graphene nucleus, so there is no information on the nucleation step included. Consequently, no size distribution or nuclei density can be obtained, which are known to be crucial characteristics of CVD graphene;Simulations on the hexagonal kMC lattice are complicated by the formation of the pentagon edge (the pairwise closing of the Klein edge of graphene on the Cu(111) surface) and its opening by the next attaching particle.Although the kMC+DFT methodology allows the simultaneous accounting for many species and reactions which can take part in the process, it is important to point out a few significant limitations of this approach:To our best knowledge, there has only been a very restricted number of attempts ,31 to detheories ,34,35,36Moreover, we re-evaluate the DFT barriers of the most important elementary reactions and find out significant deviations from values used in recent studies. These differences qualitatively influence the results of kinetic modeling.Small Well-defined graphene nuclei which are immobile on the surface and grow due to the attachments of At the first stage of the CVD process, methane adsorbs and decomposes on the Cu(111) surface, producing carbon adatoms, which then agglomerate and eventually form the graphene nuclei. For our further discussion, it is convenient to divide carbon containing surface particles into three classes:n reaches a certain value I depending on the surface concentration of We also assume that when the number of atoms in the cluster lusters"  known inr with the number of atoms n in it:As it may be evidenced from various microscopic images ,40,41,42In addition, we assume that the edges of the growing nuclei have the most stable zigzag form, so the attachment/detachment processes may be characterized by the respective barriers calculated with DFT for the zigzag edge as described below.J as the rate of the dissociative adsorption of Within all introduced approximations, we consider the following kinetic scheme (see c.a. <10%) so that the whole surface area is assumed to be available for the dissociative adsorption of methane.We also note that the model is derived for the case of low surface coverage  tog tog14) t in Ref. . TherefoI as a function of the effective oversaturation To solve the system of kinetic equations described in the previous subsection, one has to define the rate of nuclei formation –Slyozov ,35 or Be–Slyozov  theoriesA and U are extracted from experimental data as discussed in To avoid these obstacles, we introduce a semiempirical nucleation rate, in which functional dependence on the effective oversaturation U defining a barrier to nuclei formation must depend on the relative concentrations of monomers and dimers; however, in the present contribution, we consider it as an effective parameter which remains constant throughout the process.Strictly speaking, the parameter It is important to note that the nucleation mechanism considered here cannot be described in terms characteristic for theories applied to multicomponent nucleation. This is due to the fact that Elementary reactions and reaction rates have been calculated at the DFT level as follows: We employed the BEEF-vdW  and PBE Despite the fact that there are just a few reaction barriers required in our model and that those were previously reported by Li et al. , our re-t widths  using thzag edge , which iIn Overall, our DFT results show that the barriers of the two crucially important concurrent reactions, the attachment of A and U entering Equation , and the main reason for this substantial difference lies in the high values of the attachment rate constants  to experimental data, we were able to construct a consistent description of the process. Among the most important results, the role of We developed an analytical kinetic model of the nucleation and growth of graphene on Cu(111) that simultaneously includes