Graphene-based nanohybrids are good candidates for various applications. However, graphene exhibits some unwanted features such as low solubility in an aqueous solution or tendency to aggregate, limiting its potential applications. On the contrary, its derivatives, such as graphene oxide (GO) and reduced graphene oxide (RGO), have excellent properties and can be easily produced in large quantities. GO/RGO nanohybrids with porphyrins were shown to possess great potential in the field of photocatalytic hydrogen production, pollutant photodegradation, optical sensing, or drug delivery. Despite the rapid progress in experimental research on the porphyrin-graphene hybrids some fundamental questions about the structures and the interaction between components in these systems still remain open. In this work, we combine detailed experimental and theoretical studies to investigate the nature of the interaction between the GO/RGO and two metal-free porphyrins 5,10,15,20-tetrakis(4-aminophenyl) porphyrin (TAPP) and 5,10,15,20-tetrakis(4-hydroxyphenyl) porphyrin (TPPH)]. The two porphyrins form stable nanohybrids with GO/RGO support, although both porphyrins exhibited a slightly higher affinity to RGO. We validated finite, Lerf–Klinowski-type  structural models of GO ( Graphene is a two dimensional (2D) single layer of graphite, that possesses unique mechanical, optical and electrical properties such as superconductivity and high Young’s modulus1. Functionalization of this novel material broadened the physicochemical properties ranges and the field of possible applications6. However, pure graphene exhibits very low solubility in water and tend to aggregate due to 8. Both species have tunable properties and can form stable aqueous suspensions. GO is typically produced by chemical exfoliation of graphite through strong oxidization and is widely considered as an individual sheet of graphene decorated with various oxygen-containing functional groups 10. The chemical reduction of GO leads to RGO with partly restored structure and properties of pure graphene, depending on the reduction process applied12. Among various graphene-based materials, the dye-functionalized graphenes are attractive candidates for nanohybrid platforms with peculiar photoactive properties.Ever since the explosion of interest to graphene following its successful fabrication in 200416. Non-covalent chemical modification of GO or RGO with dyes is based on fundamental concept of molecular interactions, such as electrostatic attraction, 17.The synthesis of nanohybrids involving non-covalent interactions between GO or RGO and dyes have important advantages, such as high yields, facile synthetic routes and maintenance of the main properties of each component25. Up to now, several groups have reported on improved photocatalytic activity of porphyrin/graphene nanohybrids toward pollutant photodegradation25. Yuan et al.20 presented enhanced photocatalytic activity toward hydrogen generation in a non-noble metal system for photocatalytic N-methylpyridyl) porphyrin and RGO decorated with 21 and biological28 sensing, drug delivery29 or cancer therapy16.Scientific community’s deep interest in porphyrin- and graphene-based hybrid materials is reflected in a number of reports6. Surprisingly, in spite of all these recent advances in the field of porphyrin/graphene nanoassemblies there are just few reports that combine experimental and theoretical investigations of such materials35.In spite of the rapid progress in experimental research on the porphyrin-graphene hybrids some fundamental questions about the structures and the interaction between components in these systems still remain open. Elucidation of the mechanism of the interaction between the graphene materials and porphyrins including electronic properties of these materials is crucial for knowledge-driven design of nanomaterials and devices with desired properties39. Other approach focus on local interactions of the adsorbate with graphene-derivative surface that is modeled as a graphene sheet decorated with very few oxygen-containing groups40. Out of various finite structural models proposed over the years43, the model of Lerf et al.44  was explicitly or implicitly assumed in many successful functionalization studies43. It contains 46. We have recently demonstrated the use of a finite, LK-based 31. On one hand side, the model allows for detailed analysis of frontier molecular orbitals thus provides basis for spectra interpretation30. On the other hand, we noted that it may be used for efficient absorption spectra simulation of zinc-substituted porphyrins31.GO and RGO are amorphous systems and as such constitute challenge to any computational protocol. Periodic density functional theory (DFT) calculations most often assume some degree of repeating order in oxygen atoms distribution on graphene sheets31 while appropriate RGO model The main aim of this study is to explore the robustness of the proposed LK-based models to describe nanohybrids’ formation processes. We focus on the nanoassemblies of two porphyrins, 5,10,15,20-tetrakis(4-aminophenyl) porphyrin (TAPP) and 5,10,15,20-tetrakis(4-hydroxyphenyl) porphyrin (TPPH) with GO and RGO  and TAPP-RGO (27 nm). Moreover, the Soret bands of the nanohybrids exhibit approximately two times lower extinction coefficients compared to free TPPH/TAPP molecules with a slight broadening of the bandvide infra) that predict the dihedral angle between the phenyl and porphyrin plane decreases upon complexation with GO/RGO. We also note that absorption spectra of nanohybrids with RGO feature significant alternation in high-energy region (> 350 nm) as compared to the free RGO. This indicates strong electronic interaction and orbital mixing upon nanohybrid formation.The bathochromic shifts of the Soret band observed upon nanohybrid formation could be explained by a flattening of the porphyrin molecules. Our hypothesis about porphyrin flattening when adsorbed on the GO/RGO sheet is supported by the theoretical calculations  we investigated the increase of the absorbance of the Soret band (after subtracting the GO/RGO absorbance) of the porphyrins adsorbed on GO or RGO as a function of their concentration SI Fig. c and S5c48. Interestingly, the spectral changes occurring upon addition of GO to the aqueous solutions of cationic porphyrins were more pronounced than for TAPP and TPPH since approximately ten times lower concentration of GO was required to achieve detectable spectral changes. Therefore, it is reasonable to conclude that the interaction of GO with neutral porphyrins TAPP and TPPH is weaker in comparison to positively charged porphyrins. It can be explained by the electrostatic attraction between cationic porphyrin and negatively charged GO that facilitate assembly of the naonhybrid material.Batochromic shift of the Soret bands together with the decrease of the molar absorption coefficients upon addition of GO was previously reported by us for cationic porphyrinsThe interaction of the excited states of the porphyrins with the GO and RGO sheets was investigated by the emission spectroscopy. It is worth mentioning that comparisons of the emission data require a matching of the absorbances at the excitation wavelength. In the current work, emission experiments were performed with the excitation at the isosbestic points which ensured constant absorbance Table . In addiely Fig. a. The emely Fig. a.Figure 48. More efficient emission quenching for cationic porphyrins was evidenced by ca. ten times higher slope of A decrease in the fluorescence intensities of both porphyrins is observed with increasing GO and RGO concentrations see Figs b, 4b. In48.By applying the time-correlated single photon counting technique it was found that the emission decay profiles of TAPP and TPPH did not change upon addition of either GO or RGO .Figure For each computed spectrum we identified five key transitions (representatives of the most prominent bands) and traced their presence in experimental spectral curves. The computed transition densities for these transitions (1)–(5) are shown in the bottom of Fig. 57. However, most of the reported reactions of the epoxy ring-opening require prolonged stirring or sonication, usually at elevated temperatures. In our case, the suspensions were mixed, followed by immediate spectroscopic measurement. However, if the covalent functionalization would take place in our set-up, it would lead to the porphyrin system being located perpendicularly to the GO plane. In this way, The comparison of experimental and computed UV–Vis spectra can also be used to distinguish the non-covalent and covalent functionalization of the graphene oxide. Many reports show that GO epoxy groups can, under certain circumstances, undergo nucleophilic attack that causes ring-opening and covalent linkage of the porphyrin to the GO supportFurther insights into the nature of low-energy excited states can be obtained with multireference ab initio calculations. Our state-averaged approach provides access to singlet and triplet states simultaneously. Moreover, the underlying CASSCF wave-function covers static (strong) correlation issues while DLNO-NEVPT2 corrects excitation energies for the missing dynamic correlation. Thus, the method can efficiently handle near-degeneracies within the active space.31). The first singlet excited state of TAPP (1.70 eV) is found 0.03 eV lower in energy than in the case of TPPH, while the first triplet state is found in both cases around 1.6 eV.The outcomes of CASSCF/DLPNO-NEVPT2 calculations are summarized in a form of state-energy diagrams shown in Fig. Once the nanohybrids with GO are formed, the nature of the first excited singlet and triplet states changes from porphyrin-centered to charge transfer (CT). The low-lying The nanohybrids that involve RGO model are more complex to analyze. We found high density of states close to the ground state. In fact 5 electronic states were found to be no more than 0.7 eV apart from each other. These are only RGO-centered excitations but this underlines the complex behavior of the RGO material. For both porphyrins, their complexes with RGO feature CT-capble excited states around 1.5 eV. However, in contrast to GO these states have strong multireference character, i.e. CT configuration state functions (CSFs) are accompanied with CSFs that involve only RGO-centered orbitals. This once again points to strong orbital interaction between porphyrins and RGO species.Presented study has two major outcomes. On one hand side, by carrying out careful spectroscopic analysis, we found the two examined porphyrins form stable nanohybrids with GO/RGO support. Here, for the first time we showed that both porphyrins exhibit higher affinity to RGO. On the other hand, we demonstrated that LK-type models allow for robust representation of the GO/RGO surfaces in quantum chemical calculations. The models pave the way for applications of high-level ab initio methods to solid-state problems owing the local nature of adsorbate-GO/RGO interaction.The spectra simulated with efficient The origin of strong porphyrin-RGO interactions was traced back to the small deformation energy of the RGO upon nanohybrid formation as well as to more extended availability for Taking into account the variety of the possible porphyrin/graphene materials the development of theoretical methods that could properly predict spectroscopic properties of those materials can serve as a guidance for fabrication of such materials with desired properties.5,10,15,20-tetrakis(4-aminophenyl) porphyrin (TAPP) and 5,10,15,20-tetrakis(4-hydroxyphenyl) porphyrin (TPPH) were purchased from Porphyrin Systems, graphite powder was purchased from Acros Organics and ascorbic acid was purchased from Sigma Aldrich. Ethanol (HPLC grade) was bought from J.T. Baker. Solutions were prepared with millipore distilled water  and FTIR as described previously60. All spectroscopic measurements were performed in EtOH-UV–Vis absorption spectra were recorded using a dual-beam spectrometer Cary 100 (Agilent) UV–Vis scanning from 200 to 800 nm with 1 nm increments. Quartz cuvettes with 10 mm optical path lengths were used.The fluorescence spectra for solutions with 0.1 and lower absorbance at the excitation wavelength were collected on LS 50B spectrofluorometer (Perkin Elmer). The samples were excited at the isosbestic point obtained during UV–Vis titration experiments with GO and RGO. Emission lifetimes were measured using a FluoTime300 fluorescence spectrometer (PicoQuant) operating in the time-correlated single photon counting mode (TCSPC). A light-scattering Ludox solution  was used to obtain the instrumental response function (prompt). The emission decay lifetimes were measured following excitation with 440 nm or 405 nm photodiodes. Emission data was corrected for inner filter effect I and II44 We consider a model system with a C/O atomic ratio of 2.3, that is close to the one reported for GO used in the experimental part of work59.The chosen molecular structure of the graphene oxide (GO) model 61, this is in good agreement with XPS data that shows decreased content of 62. The RGO’s C/O ratio is ca. 4 which indicates that large amount of the oxygen-containing groups are successfully removed from GO upon reduction59. Therefore, in our calculations, we have initially considered three RGO models derived from our GO structure: Similarly to GO, RGO is a finite system. The available structural information does not provide a clear understanding of the local microscopic structure. TEM data indicate the presence of quasi-amorphous SI Fig. The GO and RGO models that have been used throughout the work are shown in Fig. 63 supplemented with D3BJ dispersion correction65 was chosen as an optimal compromise between cost and accuracy. Geometrical counterpoise correction (gCP)66 was applied to minimize intra- and intermolecular basis set superposition error. Obtained structures were subject to numerical second derivative calculations and were confirmed to possess only positive normal modes.BP86 functionalBinding energies 69. All states up to 10 eV were considered, resulting in more than 3000 states accounted for in each calculation. Hybrid B3LYP70 and range-separated Spectra calculations were performed with two approximate time-dependent DFT methods: simplified time-dependent DFT (sTD-DFT)69 the author shows that by requiring Coulomb (ii|aa) terms in sTDA to approach Interestingly, the sTDA was found to reproduce the best experimental curve shapes in our study. In the original sTDA work71 calculations were obtained from MP2 natural orbitals. Strongly occupied orbitals with occupation numbers smaller than 1.90 and weakly occupied orbitals with occupation numbers of more than 0.10 were selected to enter the active space in subsequent CASSCF iterations. In the case of free porphyrins, the procedure provided active space consisting of four essential Gouterman’s orbitals73 along with four electrons. This space is abbreviated as CAS. The complexes with GO and RGO were treated with spaces CAS and CAS that contain in addition to porphyrin-centered Gouterman’s orbitals also contain the orbitals of the graphene species (strongly and weakly occupied). Isosurface plots of all active space orbitals are provided in the SI.Starting vectors for complete active space self-consistent field (CASSCF)The CASSCF wave-function was optimized in a state-averaged way. For TAPP/TPPH and their nanohybrids with GO the averaging was over 5 singlet and 4 triplet states. In the case of RGO the number of states was increased to 10 singlets and 10 triplets due to high density of states in the relevant energy window.74. Due to the size of the systems under study, we employed the domain based local pair natural orbital approximation with the default settings (DLPNO-NEVPT2)75. The calculations were performed using compact def2-SVP basis set76. Test calculations for TPPH shown that an adapted set-up provides excitation energies within 0.02 eV error with respect to much more demanding canonical NEVPT2 computations that use def2-TZVP basis77.To account for dynamic correlation outside the active space, excitation energies were calculated with the n-electron valence state perturbation theory at the second order (NEVPT2)77 was used throughout the study. Resolution-of-the-identity78 along with corresponding auxiliary basis set79 was employed in Coulomb integrals evaluation. Exchange integrals were evaluated seminumerically80. Geometry optimizations, interaction energies and multireference calculations were performed with ORCA 4.2.0 package81. sTDA and sTD-DFT computations were carried out with standalone stda 1.6.1.1 code obtained from author’s github repository82 and interfaced with ORCA and Turbomole 7.4 software83. The former was used for spectra generation while the latter allowed us to compute transition densities using escf module84 provided with sTDA-generated ciss_a file that contains excited state vectors in Turbomole’s format. Isosurfaces of transition densities (85.If not stated otherwise, def2-TZVP orbital basis setSupplementary Informations.


Biopolymers are a solution to solve the increasing problems caused by the advances and revolution in the electronic industry owing to the use of hazardous chemicals. In this work, we have used egg white (EW) as the low-cost functional layer of a biocompatible humidity sensor and deposited it on gold (Au) interdigitated electrodes (IDEs) patterned through the state-of-the-art fabrication technology of thermal vacuum evaporation. The presence of hydrophilic proteins inside the thin film of EW makes it an attractive candidate for sensing humidity. Usually, the dependence of the percentage of relative humidity (%RH) on the reliability of measurement setup is overlooked for impedimetric humidity sensors but we have used a modified experimental setup to enhance the uniformity of the obtained results. The characteristics of our device include almost linear response with a quick response time (1.2 s) and fast recovery time (1.7 s). High sensitivity of 50 kΩ/%RH was achieved in the desirable detection range of 10–85%RH. The device size was intentionally kept small for its potential integration in a marketable chip. Results for the response of our fabricated sensor for dry and wet fingertips, along with determining the rate of breathing through the mouth, are part of this study, making it a potential device for health monitoring. Environmental sensors are becoming significantly important in applications related to our daily life for controlling and monitoring various ecological parameters, such as temperature, pressure, light intensity, humidity, and various gases ,2,3,4. A3. The above reports clearly show the importance of using biopolymers as the functional layer of various electronic devices due to their immense potential of providing a green solution to the increasing toxic effects caused by the electronic industry, but not many researchers have used these natural materials for the application of sensing humidity.Biomaterials have already been successfully tested as the functional layer for different types of electronic devices, including resistive random-access memory (RRAMs) ,17, fiel2 NWs) as the active layer, however, this functional layer was not completely biocompatible due to the addition of SnO2 NWs as the biopolymer of chitosan alone was not able to efficiently sense humidity. Natali et al. [Sisman et al.  fabricati et al.  studied i et al.  also meai et al.  reportedAmong four different classes of biomaterials, including carbohydrates, nucleic acids, green plants, and proteins, egg white (EW) has shown interesting characteristics in different electronic devices, such as solar cells , super cIn this work, we have explored the humidity response of EW as the functional layer of a humidity sensor by spin coating a thin film on a transparent glass substrate on the surface of gold (Au) interdigital electrodes (IDEs) patterned through the state-of-the-art fabrication technology of thermal vacuum evaporation. The fabricated humidity sensor was used successfully for monitoring human health with promising characteristics, including high sensitivity in a wide humidity range with high repeatability. This efficient performance could be attributed to the presence of crosslinked amino acids connected with each other through peptide bonds inside the EW thin film, forming long chains. These amino acids are bonded to each other by various types of chemical bonds, including hydrogen bonds, ionic bonds, hydrophobic bonds, etc. These intra/inter-molecular chemical bonds present in the crosslinked amino acids are hydrophilic in nature and, therefore, play a vital role in sensing humidity changes in the environment.+, K+ and Na+), and nearly forty proteins . The schematic diagram of a chicken egg with an image of a chicken egg is shown in First, 99.9% pure gold was used for patterning Au IDEs. EW was extracted from a fresh chicken egg that was randomly picked from the market and was used as the functional layer of the humidity sensor. EW was carefully separated from the egg yolk in a clean laboratory with the help of a stainless-steel spoon. The separated EW was collected in a test bottle and mixed with highly purified deionized water with the help of a pipette. Pure EW was not preferred because it could not form a uniform thin film owing to its high viscosity. The dilute solution of EW was bath sonicated for 10 min and dispersed thoroughly, followed by filtration to remove any solid particles. It was found that the raw EW was highly soluble in deionized water owing to the presence of vitamins, fats, salts . IDEs can be considered as two chemristors connected in a parallel combination. The state-of-the-art fabrication technology of thermal vacuum evaporation was used for patterning Au IDEs owing to its high controllability and extremely efficient results, and a schematic diagram is shown in The biomaterial-based sensor and its thin film were characterized to find their structural, morphological, and electrical characteristics. These characterizations were helpful in determining the conduction mechanism effectively. The surface roughness of the functional layer was measured through a 3D nanoprofiler  in phase shifting interferometry (PSI) phase. Dimensions of patterned Au IDEs were determined by using an optical microscope . The contact angle of the spin coated thin films was measured using a contact angle tester . The chemical composition and structure of the EW biopolymer were determined by using Fourier transform infrared (FTIR) spectroscopy (ALPHA II FTIR spectrometer).2 gas to dehumidify the sealed chamber was located on the perpendicular wall of the chamber at a 15 cm distance from both the sensors, while the inlet for the humidifier was located at the bottom of the chamber at 17.5 cm from both sensors. The reason for maintaining this distance between the inlets and sensors for humidification and dehumidification was to avoid sudden changes in the level of humidity inside the sealed chamber. Real values of relative humidity (RH%) were recorded with the help of a reference sensor (HTU-21D) that was placed near the EW-based humidity sensor to maintain the desired level of humidity inside the measurement chamber through a feedback signal. An LCR meter (Applent AT-825) was used at a 1 kHz frequency with an AC output of 0.6 Vrms to measure the impedance values. The measurement chamber was completely sealed, and its humidity level was decreased to 0 RH% from ambient conditions with the help of a controlled inflow of N2 purging gas through the nozzle. Atomized water vapor was used to gradually increase the humidity level inside the sealed chamber with the help of a humidifier, while its temperature was maintained at 25 °C to avoid the effect of temperature on humidity measurements.The change in values of the impedance response relative to the change in humidity were recorded with the help of a custom designed and highly controllable sealed environmental chamber, whose schematic diagram is shown in −1 corresponds to O–H stretching vibrations. The absorption peak at 1635 cm−1 corresponds to the amide-I (N–H) region of egg albumin due to C=O stretching vibrations; there is another peak at 1547 cm−1 in the FTIR spectra which corresponds to the amide-II region due to N-H bending in plane and C–N stretching. These characteristic peaks are in good agreement with already reported IR spectra of egg albumin [2 gas and increased gradually from 0–100% RH with the help of a humidifier and the resulting values of impedance were recorded. The thin film of EW-based humidity sensor exhibited an inversely proportional relation between its impedance and RH, as shown in the electrical characteristic graph, which is consistent for each set of recorded data.The electrical response of the EW thin film-based humidity sensor was recorded by keeping it close to the reference sensor inside the sealed measurement chamber. Electrical contacts were made by using silver (Ag) epoxy to make firm contact with the Au IDEs. The RH% was decreased to 0% with the help of NThe results show that the sensor does not respond to changes in RH% from 0–10% RH and its impedance begins to decrease gradually after 10% RH. The sensor showed an almost linear decrease in the impedance values, which is highly desirable for humidity sensors. The sensor did not respond to changes in the water content of its environment at RH > 85%, which signifies that the EW sensor has a wide sensing range of 10–85% RH. The drop in impedance values was mainly due to a decrease in the resistance of the EW thin film which may have been due to the rapid adsorption of water molecules in the porous surface of the biopolymer.2 > 0.99) that allows easy conversion of the sensor’s response to relative humidity by solving the equation with high accuracy. The stability of the biopolymer-based humidity sensor was also recorded at four different RH% levels  and the obtained results exhibited highly stable output for more than 36 h, as shown in EW is considered a good insulator and, therefore, it has high impedance values in dry conditions. Experiments have shown that the impedance value is highly dependent on the water content absorbed by this material, which makes it a useful functional material for sensing humidity. Adsorption of water molecules in the thin film of EW may dissolve organic material in the cells, resulting in the easy flow of the current and reduction in the impedance value. Water itself is a good conductor of electric currents, therefore, its successful penetration into a thin film of an insulating biopolymer will have a definite effect on its impedance values. A thin film of EW tries to attain equilibrium when there is a difference in the content of water vapor in its surrounding environment by allowing the water molecules to diffuse through it. The obtained results show that the impedance value decreases almost linearly with increasing RH%, as shown in 2 forms a peptide bond among multiple amino acids, resulting in water release, and for this reason it is known as a dehydration reaction. Amino acids exist in four different forms depending on the formation and bonds between their long chains. Peptide and disulfide bonds are the strong bonds which protect EW from the process of denaturation, thus providing high thermodynamic stability. The denaturation of proteins modifies the paths for oxygen to diffuse, hence resulting in a reduction in oxygen scattering and an increase in the probability of forming conductive channels throughout the EW thin film. The porous structure of EW provides a large surface area for the dispersion and transmission of water molecules to become adsorbed. To understand the conduction mechanism of charge carriers taking place inside the functional layer of the proposed humidity sensor, it is important to understand the chemical structure of EW. It is composed of proteins that contain long chains of amino acids. These proteins are recognized based on these amino acid chains, consisting of a carboxylic acid group and central alpha (α) carbon part that is connected to one of the side chains and hydrogen (H).Chemical characteristics of amino acids, such as hydrophobic, hydrophilic, basic, and acidic, are determined based on the side chains. Linkage between COOH and NH3O+) in large quantities. Proton hopping takes place between two adjacent molecules of water, as depicted by the equation of the Grotthuss reaction. Thus, the hydrophilic nature of the EW thin film and its humidity-sensing behavior can be linked to the side chains attached to these disulfide and peptide bonds. As a result of these chemical reactions, thio and amino acids lose H atoms, resulting in covalent bonding between two S atoms of distinct amino acids. Loss of a couple of H atoms results in a decrease in the concentration of charge carriers because each H atom consists of one electron and hole pair. There are various amino acids present in EW but only six of them are the cause of its hydrophilic nature, owing to their polar side chains. The reaction of humidity with these polar chains causes a change in the capacitance and impedance values of EW that can be used for sensing humidity changes. Threonine and serine are two of the polar amino acids whose hydrophilic property is due to the alcohol functional group as these groups can form hydrogen bonds with the water molecules present in the environment of the sensor. Cysteine plays a critical role to form quaternary and tertiary protein structures and it exhibits a hydrophilic nature due to its parallel chemical bonds between a hydroxyl group and sulfhydryl group. Side chain reactions of cysteine enable it to form a bond between two S atoms through oxidation. Furthermore, due to the neutral nature of NH2 bonded with a carbonyl group in standard conditions, the formation of an amide takes place, causing its hydrophilic behavior. Among the amino acids, proline has a somewhat different nature as it is a part of polypeptide chain and has no H atom attached to its N atoms, thus it does not have any polarity.Physical adsorption of water vapor in the thin film of EW results in decreasing its impedance because the oxygenated hydrophilic groups are ionized due to the presence of a highly electrostatic field. This ionization process results in the formation of hydronium ions  groups present in EW, and due to this, no protons can take part in the conduction process, owing to the restriction caused by hydrogen bonds. Water molecules continue to be adsorbed on the surface of the EW thin film to form a less ordered second layer of water molecules on its surface due to the presence of local hydrogen bonds. The porous structure of an EW thin film biopolymer might cause a large contact area between moisture and hygroscopic groups present on the surface of the EW, resulting in faster transmission and diffusion of water molecules in the functional layer of the humidity sensor. With the passage of time, more layers of water molecules keep forming without any order, known as the physisorption process, thus making room for the protons to take part in the conduction process, as explained by the Grotthuss mechanism . Apart f+ jumping owing to the low absorption rate of water molecules. Increasing the RH% level in the surroundings of the humidity sensor results in the creation of more H+ ions and the formation of hydrogen bonds between the biopolymer and water molecules, which accelerate their flow in the functional layer.Conduction at a relatively low level of RH% is primarily based on HThe response time is 10% to 90% of the total change in impedance value, while recovery time can be defined as the time required to drop from 90% of the maximum impedance value to 10% of the maximum impedance value. The transient response of our sensor was recorded to evaluate its performance for different applications, as shown in The fast response and recovery time of our sensor enables it to detect the rate of breathing and categorize it as normal (average person), fast (athlete), and slow (patient), so that one can check the status of respiration. The performance of our fabricated sensor was also determined for the application of monitoring human health. Real-time monitoring of the human respiratory system can play a vital role in providing intensive health care to patients. The surface of the developed sensor was exposed to human breathing to check its sensitivity. The obtained results were encouraging, with a quick response and recovery time and the ability to sense even small changes in RH%. Conductivity of the functional layer was increased with exhaled human breath due to the presence of water content. Resistance of the functional layer increased while inhaling due to a decrease in water content, hence proving the application of the EW thin film for monitoring human health. The literature suggests that exhaling air at a slow speed has a larger amount of moisture content as compared to breathing at a rapid speed. This difference in the level of humidity can be sensed by our sensitive humidity sensor by monitoring the variance in the value of its impedance, as shown in We tested our device for the application of distinguishing between a moist and dry finger by applying hand cream on a fingertip and moving it close to our sensor. The change in the impedance value for the wet and dry finger was due to the absorption of water molecules by the EW thin film generated from the surface of fingertip and these water molecules were desorbed upon lifting the fingertip, as shown in In summary, a biocompatible thin film of egg white (EW) biopolymer was prepared by diluting EW with deionized water and depositing it on Au IDTs to fabricate a humidity sensor. Various characterizations of EW, including surface roughness (3D nanoprofiler), FTIR, contact angle, and electrical response, were investigated in detail to understand its humidity-sensing behavior. The sensor showed an almost linear response, short response/recovery time , high average sensitivity (50 KΩ/%RH), and a wide range relative humidity response (10–85%RH) by 10 orders of magnitude (3–0.3 MΩ). Due to the wide range of our humidity sensor, it can indicate uncomfortable humidity levels of <30%RH and >75%RH after attaching an additional circuit to it. We tested our fabricated EW-based humidity sensor for different applications, including environmental monitoring, breath monitoring, and skin care. The obtained results were highly encouraging for various aspects of health monitoring with fast response time and high sensitivity.


The transmission and transport properties of biperiodic graphene superlattices are studied theoretically. Special attention is paid to the so-called transparent states of biperiodic superlattices. A Dirac-like Hamiltonian is used to describe the charge carriers in graphene. The transfer matrix method and the Landauer–Büttiker formalism are implemented to obtain the transmittance and conductance, respectively. Similar results to those reported for Schrödinger electrons are obtained. However, in the case of Dirac electrons the splitted bands and the transparent states associated to the biperiodicity depend strongly on the angle of incidence as well as the character of the charge carriers. In fact, the dynamic of the splitted bands and transparent states is inverted for holes. The origin of transparent states is unveiled by obtaining an analytic expression for the transmittance. It is found that resonant transmission through single and double barriers gives rise to transparent states. Regarding the transport properties, it is possible to identify the fundamental changes caused by the biperiodicity. In particular, it is found a splitting, shifting, and diminishment of the conductance peaks with respect to the case of regular periodicity. This opens the door to corroborate experimentally the fundamental characteristics of biperiodic gated graphene superlattices through transport measurements. Moreover, the plethora of phenomena intrinsic to these structures are the basis of multiple device applications, with quantum cascade lasers being a well-known example3. The vast majority of works are devoted to single-period semiconductor superlattices. However, biperiodic or double period semiconductor superlattices have some characteristics that are interesting from both the fundamental and technological standpoint. In particular, the minibands are splitted into two subminibands, one of the subminibands presents narrow energy resonances and the other broad energy ones. In addition, a special energy resonance named transparent state arises at the edge of one of the subminibands. These characteristics were experimentally verified by Coquelin et al.5 in finite biperiodic GaAs/AlGaAs superlattices using hot electron spectroscopy. Later, Sprung et al.6 studied theoretically the origin of transparent states in biperiodic superlattices. They found that the Bragg resonance turns into a transparent state located close to the band edge of the low (high) energy subminiband when the first (second) well is wider. Furthermore, the transparent state occurs at a fixed energy, regardless of the number of unit-cells in the superlattice.Semiconductor superlattices have been fundamental to demonstrate quantum size effects in artificial structures8. Extra Dirac points arise once the periodic electrostatic potential surpasses a critical value. The extra Dirac points are located at the Fermi energy for the case of equal barrier-well widths, and present an energy shift for unequal barrier-well widths. Furthermore, the group velocity of the charge carriers in the extra Dirac points and even the original one is renormalized, becoming in extreme cases zero in one direction and unchanged in another. The extra Dirac points have been experimentally confirmed in lateral and moiré graphene superlattices10. This transition from isotropic to anisotropic properties is not exclusive of the periodic modulation. For instance, graphene nanoribbons with different edge orientations exhibit edge-dependent electronic and optical properties14. Here, it is also important to mention that there are recent breakthroughs in the fabrication of the so-called gated (electrostatic) graphene superlattices (GGSLs)16. One of the most attractive aspects of this type of superlattice is the tunability that can be achieved through electrostatic gating in contrast to moiré graphene superlattices. As in the case of semiconductor superlattices, most of the works in graphene superlattices are devoted to the study of single-period structures. In fact, there are extensive studies in electrostatic23, magnetic29, and strain34 graphene superlattices. Regarding biperiodic superlattices in graphene the few works found in the literature address aspects related to the electron transport, band structure, and resonant peak splitting38. For instance, Huo et al.35 investigated the transmission properties of biperiodic magnetic superlattices with asymmetric barriers, finding superior wave vector filtering characteristics of biperiodic magnetic superlattices over single periodic ones. The same authors36 studied the transport properties of asymmetric biperiodic magnetic graphene superlattices for parallel and antiparallel magnetic configurations. They found a giant magnetoresistance effect with a strong dependence on the asymmetry and interval of the magnetic barriers. The superior wave filtering characteristics and the giant magnetoresistance effect of biperiodic magnetic graphene superlattices are attractive for electron wave filters and magnetic reading devices, respectively. Tashima et al.37 studied the generation of new Dirac cones in graphene under double-periodic potentials. They found that the Dirac cones are generated sporadically following the Diophantine equation, in contrast to the consecutive appearance of the Dirac cones in single-periodic potentials. They also found that the energy cutoff of the linear dispersion relation in graphene is directly implicated in the generation of the sporadic Dirac cones. Xu et al.38 investigate the resonant peak splitting in finite biperiodic magnetic graphene superlattices. General expressions for the transmission probability and the resonant peaks were derived. They also found resonant peaks splitting induced by the periodicity and a resonant peak related to the unit-cell of two barriers and two wells. The unit-cell related peak unchanged as the period varies and drops quickly as the unit-cell asymmetry increases. The splitting characteristics are also confirmed in the conductance and shot-noise. As it is documented there is some progress in the understanding of the resonant peaks splitting in biperiodic magnetic graphene superlattices. However, we consider that transparent states have not been studied in detail in biperiodic GGSLs (BPGGSLs). Specifically, the role played by the angle of incidence, the character of the charge carriers (electrons–holes), and the resonant characteristics within the unit-cell. Taking into account the relevance of BPGGSLs from both the fundamental and technological standpoint, we consider that a thorough assessment of its characteristics, including the transparent states, is necessary.In the case of graphene, a periodic potential gives rise to extra Dirac points in the band structure and a highly anisotropic propagation of the charge carriersIn this paper, we address biperiodic superlattices and transparent states in graphene. We first show the general characteristics of biperiodic superlattices and transparent states for Dirac electrons, highlighting the fundamental differences with respect to Schrödinger electrons. We then proceed to analyze the origin of the transparent states. Our analysis is based on an analytic expression for the transmission coefficient. Finally, we assess the impact of the biperiodic modulation on the transport properties. In particular, we analyze the linear-regime conductance at zero temperature varying the degree of biperiodicity as well as correlating it with the contour maps of the transmission.n and p type regions in the superlattice structure are also highlighted. Depending on the energy of the incident charge carriers In Fig. mentclass2pt{minimThe charge carriers in BPGGSLs can be described by the low-energy effective HamiltonianThe wave function and wave vector in the barriers are given asW as superscript, In the case of the wells and the left and right semi-infinite regions the wave function and wave vector are given in similar fashion. Actually, we can obtain them by simply setting 41 we can write the transmittance as40The transmission properties can be obtained with the help of the transfer matrix method. In fact, by requiring the continuity of the wave function along the superlattice structure as well as the conservation of the transverse wave vector Likewise, the trace of n as Eq. , but whaThis set of expressions allows us to compute the transmittance of BPGGSLs. More importantly, they give us the possibility to know the origin of the different resonances in the transmittance.The transport calculations are based on the Landauer–Büttiker formalism. In particular, the linear-regime conductance at zero temperature is computed with the formula37. So, the formation of extra Dirac points is not relevant for our analysis.Here, we will show firstly the general characteristics of the transmission properties of BPGGSLs, paying special attention to the dependence of transparent states on the angle of incidence, the width of the quantum wells, and the character of the charge carriers. Then, we will proceed to analyze the origin of transparent states based on an analytic expression for the transmission coefficient. In addition, we will analyze the band structure and group velocity characteristics of transparent states in single and double periodic GGSLs. Finally, we will address the transport properties of BPGGSLs. Specifically, we will analyze the impact of the biperiodicity on the linear-regime conductance at zero temperature. It is also important to mention that throughout the study the height of the barriers will be 42. As we can notice the minibands and minigaps are better defined as the angle of incidence increases. Moreover, the minigaps get larger and the minibands tend to degenerate as the angle increases. We can also see the splitting of the minibands as a consequence of the biperiodicity, however, the splitting is not the same for all minibands as in the case of Schrödinger electrons6. Similar transmittance characteristics are obtained when In Fig. a and the angle of incidence considered is a to 75a. The subminibands also shift to lower energies, about 12 meV for the same variation of In Fig. Now, it is turn to unravel the origin of transparent states. In order to do so, we will analyze all ingredients involved in the determination of the transmittance, see Eqs.  and 20)20). Specmentclasspt{minimamentclasspt{minimamentclasspt{minima38. For instance, the role played by the charge carriers, the relevance of the angle of incidence, and the impact of the details of the biperiodic unit-cell. Regarding the latter, Xu et al.38 talk about unit-cell related peaks in generic terms, however, the resonant peaks associated to the unit-cell can be caused either by 6. So, we proceed to analyze this condition in more detail. Actually, As we can realize there are several characteristics of biperiodic graphene superlattices that were not properly addressed by Xu et al.However, when these states are in the biperiodic environment they are not necessarily states with high group velocity within electron energy minibands as shown in Fig. a for either 38.Finally, we will analyze the impact of biperiodicity on the transport properties. Specifically, we want to see if an identifiable hallmark associated to the biperiodic potential is manifested in the zero temperature linear-regime conductance. In Fig. In summary, we have studied the transmission and transport properties of BPGGSLs. We paid special attention to the characteristics and origin of the transparent states. The transfer matrix method and the Landauer–Büttiker formalism were used to obtain the transmittance and the zero temperature linear-regime conductance, respectively. We found that once the biperiodicity is incorporated the superlattice transmission bands are splitted and transparent states arise in the edges of the splitted bands as in the case of Schrödinger electrons. However, the splitted bands and the transparent states of BPGGSLs depend strongly on the angle of incidence and the character of the charge carriers. More importantly, we obtained an analytic expression for the transmission coefficient that allows us to unravel the origin of transparent states. In fact, transparent states owe their origin to the resonant tunneling through single and double barriers. We also identify the fundamental changes caused by the biperiodicity and particularly by the transparent states on the band structure. In the case of the transport properties, we found that the splitting of the transmission bands results in additional peaks in the conductance and a diminution of it as the contrast between the width of the quantum wells increases, opening the door to corroborate experimentally the fundamental effects of BPGGSLs. Finally, we would like to remark that further studies with other external effects such as strain, interacting substrates, magnetic proximity effects, electromagnetic radiation, etc. and other 2D materials such as silicene, transition metal dichalcogenides, and phosphorene are needed in order to have a better understanding of biperiodic superlattices and transparent states for Dirac electrons.Supplementary Information.


Atomic resolution imaging through STM shows that the Cp*Ru+ fragments are localized above the hollow position of the hexagonal structure, and that the first graphene layer adsorbed with the fragments on the graphite redeveloped morphologically to minimize its geometric energy. For a better understanding of the adsorption site and molecular geometry, experimental results are compared with computed calculations for the graphene surface with Cp*Ru+ fragments. These calculations show the adsorption geometries of the fragment on the graphene surface and the relationship between the geometric energy and molecular configuration. Our results provide the chemical anchoring geometry of molecules on the graphene surface, thereby imparting the theoretical background necessary for controlling the various properties of graphene in the future.To comprehensively investigate the adsorption geometries of organometallic molecules on graphene, Cp Bandgap control in graphene is one of the most important and tantalizing research topics in the graphene community because it may ultimately enable new applications in digital electronics7, pseudospintronics8, terahertz technology10, and infrared nanophotonics12. A number of approaches have been proposed or implemented to control the bandgap in graphene, such as using uniaxial strain14, graphene–substrate interactions16, lateral confinement17, and breaking the inversion symmetry in bilayer graphene18. Among them, adhering or bonding the atoms/molecules on the graphene surface can effectively control the bandgap because of the large surface-to-volume ratio of atoms/molecules that can be easily adsorbed on its surface20. However, comprehensive investigations into the adsorption behavior of molecules on graphene surfaces are insufficient, although the understanding and interpretation of the molecule–graphene interaction is a fundamental research field.Recently, graphene with highly ordered carbon nanostructures has garnered significant interest as a smart material with high electrical and thermal conductivities and excellent mechanical properties21, tribology22, molecular electronics23, and molecular magnetism25. In particular, an organometallic molecule containing the Cp*Ru+ fragment (Cp* = pentamethylcyclopentadienyl) is ubiquitous in complex chemistry and their thermal and photochemical behaviors as well as reactive intermediates for selective reactions have garnered significant attention28. The Cp*Ru+-graphene complex can be obtained via the reaction between Cp*Ru(CH3CN)3PF6 and arenes, in which the relatively labile acetonitrile ligands are readily substituted by a 6π-electron donor29. To analyze individual Cp*Ru+ fragments adsorbed on arene structures, it is important to select graphene substrates that are highly uniform over a wide area. Hence, highly oriented pyrolytic graphite (HOPG) was selected in this study to model an atomically perfect graphene surface using the mechanical exfoliation method.As a model to investigate the adsorption behavior of molecules on graphene, organometallic compounds were considered in this study because of their diverse applications in surface science and nanotechnology, such as catalysis*Ru+ fragments on a graphene surface exfoliated from high-quality HOPG surfaces. The purpose of this study was to comprehensively investigate the identification of individual organometallic adsorbates via specialized local measurements and then to test the design criteria for adsorbing an organometallic compound on graphene. The advent of surface probing techniques such as atomic force microscopy (AFM) and scanning tunneling microscopy (STM) has resulted in increasing interest in the study of the adsorption behavior and geometric configuration of individual molecules on substrate surfaces. Furthermore, a comprehensive theoretical geometry of the Cp*Ru+ fragment on the graphene surface was developed by performing computational functions of molecular mechanics calculations.We investigated the adsorption behavior of Cp*Ru(CH3CN)3PF6] and HOPG with ZYH grade were purchased from Aldrich Chem. and Advanced Ceramics Corp., respectively. To prepare Cp*Ru+-graphite, the HOPG was mechanically cleaved using 3M scotch tape in air and immediately dipped into a Cp*Ru(CH3CN)3PF6 solution based on ethanol at room temperature. After the reaction or prior to the characterization, the HOPG surface was sufficiently washed with copious amounts of ethanol and distilled water and then dried by blowing N2 gas.Pentamethylcyclopentadienyltris(acetonitrile)ruthenium(II) hexafluorophosphate + residue on the substrate, the substrate was washed with copious amounts of ethanol prior to the measurements. To visualize the Cp*Ru+ fragments on the HOPG surface, we used an atomic force microscope  and a scanning tunneling microscope . PtIr tips were used in the STM measurements. During the STM measurement, an insulating liquid, 1-phenyloctane (Aldrich Chem.) was used between the tip and the surface to allow high-quality atomic-scale imaging. During operation, the bias voltages and tunneling currents were varied from -10 to -500 mV and from 50 pA to 1 nA, respectively, to obtain high-quality images. A confocal backscattering Raman spectrum with a spot size of approximately 4 μm2 was measured using a 40X objective focused through the cell window. Furthermore, 3.2 mW of 633 nm He–Ne laser was used as the excitation source.The presence of the Cp*Ru+-graphite were calculated from the molecular mechanics force field using the Polak–Ribiere algorithm in HyperChem Professional 8.0. To realize the graphite structure in the program, we used a five-layer graphene structure with 18 × 16 unit cells for each graphene .The geometric configurations of Cp*Ru(CH3CN)3]+ reacts readily with a various types of arenes to form η6-bound metal-arene complexes by coordination covalent bond, as shown in Fig. *Ru+ fragments on the graphene surface, we used the dipping method. The presence of Cp*Ru+ fragments on the graphene substrate was verified via FT-IR and XPS. Figure 3-related peaks. As the reaction time progressed, the bands at 2922 and 2870 cm−1, assigned to the asymmetric and symmetric methyl (CH3) stretching modes of the methyl groups in Cp*, respectively31, increased sequentially. These results show that the Cp* fragments originating from Cp*Ru+ reacted to the graphene surface as the reaction time progressed. Other verifications of the Cp*Ru+ fragments bound on the graphene surface can be confirmed through changes in Ru conditions, derived from XPS analysis. As shown by the XPS results in Fig. 3/2 was observed in the case of dried Cp*Ru(CH3CN)3PF6 solution on the glass substrate (blue). Meanwhile, the presence of Ru 3p3/2in the dropped Cp*RuL3PF6 solution on the graphene (or HOPG substrate), was confirmed by the peaks at 462.3 eV, which induced a coordinative reaction between the Cp*Ru+ fragments and the graphene surface (green and red)34. This peak shift is important for explaining the reaction between Cp*Ru+ and the HOPG surface. The Ru+ atoms in [Cp*Ru(CH3CN)3]+ and Cp*Ru+-graphene have different atomic environments. In particular, the Ru+ in [Cp*Ru(CH3CN)3]+ is bound to acetonitrile ligands with relatively stronger electronegativity compared with the case involving reaction with the arene structure, where electrons (or the electron density) were attracted toward itself in a bond. Before discussing our results, it is noteworthy that the chemical shifts in the core-level binding energy of XPS are often used to investigate the electronic redistribution or charge transfer upon elements37. The general rule in the interpretation is that the binding energy of the atom increases with the electronegativity of the attached atoms or groups37. In other words, the Ru 3p3/2 peak in [Cp*Ru(CH3CN)3]+ shifts toward a higher binding energy compared with that in Cp*Ru+-graphite, as indicated by the XPS results shown in Fig. *Ru+ fragments were successfully bound on the graphene surface to form η6-bound metal-arene complexes by a coordination covalent bond during dipping the HOPG substrate in the [Cp*Ru(CH3CN)3]+ solution.To obtain an atomically flat graphene surface that exhibits a perfect lattice of thousands of angstroms, HOPG was used by applying the mechanical exfoliation method. +, inducing sp3 carbon structures in the honeycomb structure on graphite. Hence, the D peak evolved at the step edge by binding to the fragments, as shown in Fig. To consider the possibility of defect formation on the graphene (or HOPG) surface during the adsorption of Cpband ~ 130 cm−1 anband ~ 130 cm−1 anband ~ 130 cm−1 anband ~ 130 cm−1 an*Ru+ fragments on a HOPG surface with a highly ordered arene nanostructure using STM measurements and calculations. Our results showed that a Cp*Ru+ fragment was localized above the hollow position of the hexagonal carbon structure in the STM images, and that the HOPG surface adsorbed with the fragments was morphologically redeveloped by minimizing the geometric energy. In particular, by calculating the geometric energy variation, we discovered that the system geometric energy of Cp*Ru+-graphite increased significantly at distances less than 7.65 Å between the Cp*Ru+ fragments, as a result of the steric effect of Cp*. These findings indicated that a combination of geometric configuration calculations and experimental studies can provide valuable insight into the behavior of adsorbed molecules for the identification of geometric characteristics and eventual design of more effective organometallic complexes.In summary, we demonstrated the adsorption behavior and geometric configuration of CpSupplementary Information.


The results provided a fundamental understanding of the interfacial properties of graphene papers, which will be useful for developing paper-based devices with mechanical integrity.The emergence of graphene paper comprising well-stacked graphene flakes has promoted the application of graphene-based materials in diverse fields such as energy storage devices, membrane desalination, and actuators. The fundamental properties of graphene paper such as mechanical, electrical, and thermal properties are critical to the design and fabrication of paper-based devices. In this study, the interlayer interactions in graphene paper were investigated by double cantilever beam (DCB) fracture tests. Graphene papers fabricated by flow-directed stacking of electrochemically exfoliated few-layer graphene flakes were mechanically separated into two parts, which generated force-displacement responses of the DCB sample. The analysis based on fracture mechanics revealed that the interlayer separation energy of the graphene paper was 9.83 ± 0.06 J/m Howevertch tape , chemicatch tape , and oxitch tape . The oxitch tape . GO and tch tape ,18, nanotch tape ,19, electch tape ,21, trantch tape , and higtch tape . Howevertch tape . The dirtch tape ,26. Electch tape ,31,32,33Macroscopic paper-like materials, among the multiple applications of graphene-based materials, exhibit high potential for utilization in free-standing, lightweight, and flexible devices, such as energy storage devices, membranes, sensors, and actuators ,35. MechIn this work, the interlayer separation in graphene paper was investigated using mode I fracture tests. Graphene flakes were obtained using electrochemical exfoliation of graphite; subsequently, graphene papers were fabricated by flow-directed assembly of the obtained graphene flakes. The double cantilever beam (DCB) specimens for the mode I fracture tests were prepared by gluing both sides of the graphene paper to two Si substrates. The interlayer separation energy was estimated using the force–displacement responses obtained from the mechanical separation of the graphene paper. 4)2SO4; Sigma-Aldrich, St. Louis, MO, USA) in water and subsequent stirring at 100 rpm for 10 min. Electrochemical exfoliation was initiated by applying a DC voltage (2 V) to the graphite for 3 min. This facilitated wetting of the graphite electrode and intercalation of the electrolyte anions that induced lattice expansion in graphite. Exfoliation was completed under an applied voltage of 10 V. Thereafter, the suspended graphene sheets were collected using vacuum filtration through a polytetrafluoroethylene (PTFE) membrane filter (pore size = 0.2 µm) and washed several times with ethanol and deionized water , respectively. The EEG papers and their fracture surfaces were characterized by Raman spectroscopy  with a laser wavelength of 532 nm. The chemical structures of the EEG papers were characterized using Fourier-transform infrared (FTIR) spectroscopy  and X-ray photoelectron spectroscopy , Thermo Fisher Scientific, Waltham, MA, USA). The C 1s peak of the XPS spectra was deconvoluted using Gaussian–Lorentzian peak shapes after Shirley background correction [The EEG papers were subjected to morphological analysis using scanning electron microscopy . The EEG flakes were placed on a SiOrrection . The cryThe DCB specimens (5 × 30 mm) were prepared by sandwiching the EEG paper between two Si substrates using a high-viscosity adhesive . The prepared DCB specimens exhibited a configuration of Si/adhesive/graphene paper/adhesive/Si . The lamoa) was determined from the distance between the center point of the loading tab and the crack front. The DCB specimens were mechanically separated by mode I fracture tests at a constant displacement rate of 0.5 mm/min using a universal testing machine  (a) at any point during the DCB fracture test was estimated from the force–displacement responses using simple beam theory, according to the following equation [P and E, b, and h denote the in-plane Young’s modulus, width, and thickness of the substrate, respectively. The interlayer separation energy of the graphene paper was determined from the energy release rate (G) obtained using the following equation [Glue was not applied at one end of the substrate, where the loading tabs were attached, to allow the formation of an initial crack. The initial crack length ( Taiwan) . The craequation ,42:(1)a3equation ,42:(2)G=2/Si substrate, and their lateral sizes were estimated from the SEM images  was similar to that for chemically or thermally reduced GO flakes (~1.2–1.5) [The interlayer structure of the EEG paper was characterized by thin-film XRD analysis. The XRD pattern of the EEG paper exhibited a prominent peak at 26.46° corresponding to a d-spacing of 0.3364 nm a. The XR1.2–1.5) ,44.−1 corresponded to the hydroxyl, carboxyl, and alkoxy groups, respectively [The results of FTIR spectroscopy indicated the presence of oxygen functional groups in the EEG flakes c. The chectively ,46,47. Tectively ,49,50,51ectively ,53,54. Hectively . Moreoveectively . In addiectively .−1) revealed the presence of EEG flakes near the epoxy terminus (The EEG paper was subjected to mode I fracture to elucidate the interlayer interactions between the graphene flakes. The photographs of the upper and lower Si substrates (USi and LSi) after the fracture showed the uniform dark color of the entire substrate a. This iterminus c,e. The terminus .J), determined from the energy release rate (G), represented the interlayer bonding energy of the EEG paper (2 (2 substrate was reported to be 0.45 J/m2 [2 [2 [2 [EG paper b. The inpaper (2 d, as dep.45 J/m2 . The adh J/m2 [2 , while tm2 [2 [2 . The adh[2 [2 [2 . The hig[2 [2 [2 . The lay[2 [2 [2 . Therefo[2 [2 [2 ,62.2. Since the EEG flakes were oxidized during the exfoliation process, the high separation energy was attributed to the strong interactions induced by the oxygen functional groups in the flakes. Furthermore, the interlocking of the individual EEG flakes in the paper might be another reason for the high separation energy. A better understanding of the interlayer interactions in graphene paper will facilitate the development of paper-based devices. Mechanical integrity of graphene papers is important for developing reliable paper-based devices. In this study, a classical fracture test was performed to induce interlayer separation in graphene paper, and the interlayer interactions between the graphene flakes were elucidated. Graphene flakes were obtained by electrochemical exfoliation of graphite; thereafter, graphene papers were fabricated via vacuum filtration of the obtained graphene flakes. The mode I fracture tests successfully separated the EEG paper into two parts; SEM and Raman spectroscopy observation on the fracture surfaces confirmed a complete separation of the paper. Therefore, the force–displacement responses obtained from the fracture tests revealed the interlayer separation energy in the EEG paper of 9.83 ± 0.06 J/m


A theoretical formulation of the electromagnetic response in graphene ribbons on dielectric substrate is derived in the framework of the ab initio method. The formulation is applied to calculate the electromagnetic energy absorption in an array of potassium-doped graphene nanoribbons (KC Recently, graphene-based plasmonics and photonics are being used in various applications, such as bio-chemical sensing enhancement ,2, photoOne of the biggest challenges in applied plasmonics or photonics is finding a way to excite and manipulate the 2D plasmons directly by the incident electromagnetic field. Even though 2D plasmons modes produce a strong localized electric field, that field is evanescent and therefore cannot be excited directly by light. In single-layer graphene, the Dirac plasmon can be excited only indirectly, e.g., by exciting the localized plasmons on the AFM tip, which then excites the Dirac plasmon in the graphene . HoweverThe measurements of the electromagnetic field transmission through the GNR arrays on SiOickness) ,16. Morene edges ). The plectivity . In the ectivity  in polarThus far, the theoretical description of the optically active plasmon resonances in submicrometer graphene ribbons, despite providing useful information, such as plasmon wave functions or analytical dispersion relations, is limited to semi-analytical modeling, mostly based on the simple Drude model conductivity, which does not take into account the substrate polarization ,21. The A way of approaching the creation of a Dirac plasmon (DP) in GNRs has been explored via the synthesis of alkali-metal-doped graphene on metallic substrates, being extensively studied experimentally and theoretically ,27,28,29In this paper, we explore the electromagnetic response in an array of potassium-doped graphene nanoribbons . The dik, with incidence perpendicular to the surface,c is the speed of light. The electromagnetic energy absorption in the array of KCIf we assume that the sample is driven by an external electromagnetic field of unit amplitude, frequency pression :(2)A(ω)=y), Equation σμν  9) and aEquation ), the DyEquation  transforAfter inserting the Fourier expansion of the screened conductivity  is ,32(14)ΓThe propagator of the scattered electric field in the region z>0 is (15)Γ^scz directions, respectively. More specifically, z) direction are Here, the unit vectors of the z direction. For this reason, we define the spatially dependent conductivitySince we study a 2D crystal which consists of just two atomic layers, its electromagnetic response is strongly dispersive in the perpendicular fined as (16)σμν,z direction, s’ is merged with the band quantum number, i.e., S is the normalization surface, L is the superlattice unit cell in the z direction and T. Here, the current vertices areL. The KCIt should be noted that this defined conductivity do not depend on lattice parameter rding to , the nonivity is (19)σμνiHere, ivity is (21)σμνiAn alternative modeling of the KCximation , but takWe assume that the dielectric media is vacuum  in  in 21) ifunction  of the A100 meV)  are stilFinally, in d influences the absorption spectra In this section, we first demonstrate how replacing the KCd. As expected, as d increases, the energy of the DPR decreases and the energy difference between them becomes smaller. Considering that the sample is driven by the electromagnetic field, homogeneous in the y direction, the peaks appearing in the absorption spectra obviously represent optically active dipolar modes. According to the continuity equation The blue lines in d is quite large, and the interaction between the dipolar modes in the different nanoribbons is negligible; thus, they can be considered as almost decoupled resonances of the individual nanoribbons. However, we show below that these modes are still weakly dispersive as we increase the wave vector On the other hand, the induced densities of the other non-dipolar modes d, as can be seen by comparing l. All these manipulations are experimentally feasible, which could have a significant impact on the applied plasmonics.These results show us that we can fold the fragments of the Dirac plasmon  is likely to play a significant role in profiling the higher-order plasmon resonances g phonon , which iOur scanning electron microscopy (SEM) analysis of GNRs placed on a carbon tape and analyzed with 5 kV Helios NanoLab DualBeam scanning electron microscope showed multilayer GNR structures with lengths of several microns and widths ranging around 100 nm. the GNRs b–i reveaoribbons . At ∼267tic GNRs ,46. An iompounds . It is pompounds . Thus, h34 cm−1) . From thFinally, our theoretical results are in excellent agreement with the experimental results, confirming the credibility of the presented method and the above-stated conclusions.l causes the ‘projection’ of the Dirac plasmon into the radiative region, turning it into a series of IR-active Dirac plasmon resonances. This encourages the fabrication of graphene nanoribbons with the desired electromagnetic response in the IR or THz frequency range, which could be used in plasmonic, photonic or optoelectronic applications. We showed that the DPR band structure (band gap W) can be tuned by changing the period l. By creating a large band gap We developed the ab initio theoretical formulation of the electromagnetic response in doped graphene nanoribbons and used it to calculate the optical absorption in an array of potassium-doped graphene nanoribbons deposited on a dielectric Al


The adsorption of graphene is thermodynamicallyfavorable with interfacial adsorption energies of −0.08 and−0.32 J/m2 to pristine SrTiO3 and La-dopedSrTiO3 surfaces, respectively. We find that graphene introducesC 2p states at the Fermi level, rendering the composite semimetallic,and thus the electrical properties are predicted to be highly sensitiveto the amount and quality of the graphene. An investigation of thelattice dynamics predicts that graphene adsorption may lead to a 60–90%reduction in the thermal conductivity due to a reduction in the phonongroup velocities, accounting for the reduced thermal conductivityof the composite materials observed experimentally. This effect isenhanced by La doping. We also find evidence that both La dopant ionsand adsorbed graphene introduce low-frequency modes that may scatterheat-carrying acoustic phonons, and that, if present, these effectslikely arise from stronger phonon–phonon interactions.We present a detailed theoretical investigation of the interactionof graphene with the SrO-terminated (001) surface of pristine andLa-doped SrTiO The thermalconductivity has contributions from the electrical thermal conductivityκel and the lattice (phonon) thermal conductivityκlatt. Methods for optimizing ZT include doping and dimensionality reduction9 through nanostructuring12 and nanocompositing.14 However, improving TE performance is a complex process due to theinterdependence of the electrical properties—increasing σby increasing the carrier concentration n improvesthe power factor S2σ but also increasesκel and tends to decrease S.The performance of a TE material is determined by the dimensionlessfigure of merit 18 which are rare, toxic, and/orexpensive. While the highest ZT are currently obtainedwith chalcogenide TEs,20 recent work has shown that metaloxides22 such as CaMnO3,23 SrTiO3,27 M2CoO3,28 BaTiO3,29 tungsten bronze,31 Bi2Sr2Co1.8Oy,32 In2O3,33 and La1/3NbO334 may be promising alternatives to conventionalTE materials while being made from cheaper, more earth-abundant, andless toxic materials.36 Among the potential oxide TEs,strontium titanate  shows promise due to itsthermal stability at high temperature and tolerance to doping.37 Bulk SrTiO3 has arelatively poor ZT, and thus doping has been extensivelyexplored as a possible route to improving its performance with examplesincluding substituting Sr sites with rare-earth elements such as La39 and Ti sites with other transition metals such s Nb.42 La doping has been shown to promote the formation of A-site vacancies,which both increases the electrical conductivity and decreases thethermal conductivity through enhanced phonon scattering.43 Doping with La under reducing conditions furtherleads to the formation of oxygen vacancies, which decreases the thermalconductivity while having minimal impact on the electrical conductivity.Wang et al.38 showed thatdoping SrTiO3 with 12% Dy and 8% La increased the ZT from 0.05 to 0.36 at ∼800 °C.Most TE materials currently on the market are alloys containingbismuth, antimony, and tellurium,45 grain boundary engineering,47 and nanocompositing SrTiO3 with materials such as graphene also have the potential toimprove the TE performance. In the latter case, whereas a graphene-basedTE would perform poorly due to its large thermal conductivity, theaddition of graphene to conventional-49 and oxide-based51 TEs has been shown to produce synergisticimprovements in the ZT. Lin et al.13 investigated the addition of grapheneto lanthanum-doped (LSTO) and noted a widening of the operating windowto room temperature, a decrease in the thermal conductivity, and asignificant increase in the electrical conductivity. The best resultswere obtained when 0.6 wt % of graphene was added, achieving a ZT of 0.42 at room temperature and 0.36 at 750 °C,amounting to a 280% improvement over pure LSTO. Bantawal etal.50 and Baran et al.52 investigated the electronic structureof graphene–SrTiO3 composites and found that carbonstates were present at the Fermi level within the SrTiO3 band gap. The latter study52 also showedthat by altering the SrTiO3 surface termination the electricalproperties of the material could be tuned to optimize the electricalconductivity and to obtain both p and n-type transport.As an alternative to doping, strain engineering,In this work, we extend these previous studies by performing furtherdetailed characterization of STO/LSTO–graphene composites,including modeling the structural dynamics and elucidating the impactof graphene adsorption on the thermal transport. We find that thenanocompositing produces surface interactions that impact both theelectronic and thermal properties of the composite. Analysis of theelectronic density of states displays characteristic fingerprintsof graphene, which are reflected in the electrical properties of thecomposite, and analysis of the phonon spectra and group velocitiesindicates that the La doping and graphene adsorption are both likelyto suppress the heat transport in the composite materials. These resultsprovide further fundamental insight into how surfaces and interfacescan be exploited through nanocompositing, providing a firm foundationfor the discovery and optimization of future high-performance TEs.Abinitio Simulation Package (VASP) code.56 We employed the Perdew–Burke–Ernzerhof (PBE) generalized-gradientapproximation (GGA) functional58 with the DFT-D3 dispersioncorrection59 to account for van der Waalsinteractions. The projector augmented-wave (PAW) method was used todescribe interactions between the core and valence electrons, withthe following valence configurations: O—2s22p4; C—2s22p2; Sr—4s24p65s2, Ti—3d24s2, and La—5s25p66s25d1.61 A kinetic energy cutoff of 520eV was used to represent the Kohn–Sham orbitals, which wasdetermined from explicit convergence testing. Γ-centered k-point grids with 6 × 6 × 6 and4 × 4 × 1 subdivisions were used to integrate the Brillouinzones of bulk SrTiO3 and surface models, respectively.Surface models were generated with an initial vacuum spacing of 20Å between periodic images, and a dipole correction was appliedin the direction of the surface normal. The electronic energies wereconverged to 10–6 eV, and geometry optimizationswere performed until the magnitude of the forces on the atoms werebelow 10–2 eV/Å. For the surface models, geometryoptimizations were performed with the cell shapes and volumes fixed.Calculations were performed using pseudopotential plane-wave densityfunctional theory (DFT) as implemented in the Vienna 62 The band energies of bulk SrTiO3 and the surface modelswere calculated non-self-consistently on dense 50 × 50 ×50 and 20 × 20 × 1 k-pointmeshes, respectively, and Fourier interpolation was used to increasethese densities by a further 5×. The BoltzTraP results were comparedto calculations using the BoltzWann code,64 details of which are given in the SI.To obtain the charge carrier concentration, we used Boltzmann transportanalysis, where the chemical potential is directly related to thecarrier concentration. As the chemical potential is shifted into thevalence or conduction bands, the number of hole or electron carriersincreases. By interpolating the density of states (DOS), the numberof carriers at any given chemical potential can thus be determined.To validate the BoltzTrap and BoltzWann methods, we calculated theSeebeck coefficient of bulk SrTiO3 as a function of carrierconcentration  and as a functionof temperature at a fixed carrier concentration corresponding to thebottom of the conduction band .65 The calculations with the two methods givesimilar results . Wealso compared the band structures of bulk SrTiO3 and thesurface models obtained from our DFT calculations and by Wannier interpolationusing the Wannier functions employed in our transport calculations.Transport coefficients were evaluated by solving the linearizedBoltzmann transport equations within the constant relaxation-timeapproximation using the BoltzTraP code.66 andPhono3py codes68 to compute for the slabmodels the harmonic force constants, phonon spectra, phonon groupvelocities, and quantities related to the lattice thermal conductivity.In these calculations, VASP was used as the force calculator to obtainthe harmonic force constants using the supercell finite-displacementmethod.67 Atomic displacements were generatedin 2 × 2 × 1 supercells, and accurate single-point forcecalculations were performed with a 500 eV cutoff energy and proportionallyreduced 2 × 2 × 1 k-pointmeshes. For these calculations, the PAW projection was performed inreciprocal space, and an auxiliary charge–density grid with8× the density of points was used when evaluating the forces.Finally, we employed the Phonopy72 based on which we chose the SrO-terminated {001}surface of SrTiO3 as our starting point. An appropriateslab model was constructed from bulk cubic SrTiO3, consistingof 20 SrTiO3 and 5 SrO formula units  surfaces of 0.056 eV per C atom calculated by Zou et al.74 The difference in energymay be due to the lower level of strain in the graphene sheets inthis work  surfaces,indicating that the energetic penalty for La doping is substantiallyreduced in the presence of graphene.Finally, the energies for La doping were calculated as3 . The former may be compared to valuesof 2.74 eV using the LDA75 and 2.34 eVusing the PBE GGA.76 Similarly, our calculatedindirect gap can be compared to values of 2.1477 and 1.85 eV using the LDA78 and 1.99eV using PBE.76 Our calculations deviatefrom the experimental values of 3.75 and 3.25 eV (direct/indirect)due to the well-known band gap underestimation inherent in (semi-)localDFT.79 The underestimation of our calculatedband gaps compared to other computational literature is likely dueto the inclusion of a van der Waals correction (DFT-D3); indeed, Holmström et al.81 calculated a band gap of 1.76–2.00eV with PBE-D3, which is in keeping with our results. Despite theband gap underestimation, our calculations still correctly predictSrTiO3 to be a semiconductor and thus do not affect thequalitative analysis of the electronic structure, and, most importantly,the quantitative comparison between the slab models.We calculate direct and indirectband gaps of 2.0 and 1.65 eV for bulk SrTiO3 and La-doped SrTiO3 surface models indicate them to be semiconductors. As forbulk SrTiO3, the surfaces are predicted to have an indirectband gap . The orbital-projectedpartial density of states  surface, which estimated band gaps of1.72–2.01 eV80 (PBE-D3) and 1.86eV (LDA).78 In agreement with both theoryand experiment, we find that the valence band maximum and conductionband minimum are dominated by O 2p and Ti 3d states, respectively.79 The addition of graphene to the surface introducesC 2p states into the SrTiO3 band gap  PBE functionalpredicted a similar introduction of C 2p states at the Fermi levelwhen SrTiO3 is composited with porous graphene , irrespective of the concentration of pores.50The electronicdensity of states (DOS) of SrTiOf states 2a,c showband gap 2b,d. How3 surfaces intrinsically alters the electronicstructure and as such is expected to impact upon the electronic transportand thermoelectric properties. The three crucial properties controlledby the electronic structure are the Seebeck coefficient S, the electrical conductivity σ, and the electronic part ofthe thermal conductivity κel.It is clear from Figure S10. 3 and La-doped SrTiO3 surfaces as a function of carrierconcentration. Within the constant relaxation-time approximation (CRTA)used by BoltzTraP, σ and κel are determinedwith respect to an unknown electron relaxation time τ, while S is independent of this parameter. Within this model, weobtain Seebeck coefficients of 1 333 and 1 475 μV/Kat 600 K for the SrTiO3 and La-doped SrTiO3 surfaces,respectively . A general featureof the DOS of both models is an asymmetry arising from sharper featuresat valence band edges than at conduction band edges. For an intrinsic(undoped) semiconductor, where no charge carriers are present (p–n= 0), the Seebeck coefficient is governed solely by the gradient ofthe DOS at the band edges. In undoped SrTiO3, the largergradient of the DOS at the valence band edge compared to the conductionband edge leads to a larger p-type contribution and a positive S . At higher temperatures,the smoothing out of the Fermi–Dirac distribution reduces theasymmetry in the DOS and S becomes negative, indicatingn-type conductivity.82 The larger Seebeckcoefficient of the La-doped SrTiO3 surface compared tothe SrTiO3 surface is consistent with the steeper statesin the DOS of the former  and about 2.6 × 1020 cm–3 for the SrTiO3 surface model,which is in line with the ∼3.5 × 1020 cm–3 reported by Ravichandran et al.for undoped SrTiO3 thin films.84 Based on recent experiments,13 we alsoreport values of S at carrier concentrations of 3× 1019 cm–3. Figures S5–S7. Theabsolute value of the Seebeck coefficient increases with temperature,as is observed in bulk SrTiO3 at a fixed carrier concentration,and has previously been reported for bulk85 and thin-film samples.84These values represent the maximum theoretical value that couldbe obtained for ideal, defect-free compositions. In reality, all materialscontain defects that promote n or p-type conductivity, and the carrierconcentrations are therefore heavily dependent on the material preparation.Both bulk and thin-film SrTiOk SrTiO3 S6 and ab3 band gap, resulting in a semimetallicelectronic structure for both graphene-adsorbed surfaces. As shownin Figures S10a, et al.,13 this is most likely due to the effectiveconcentration of graphene in our models—whereas we have aneffectively infinite graphene layer adsorbed onto the surfaces ofthe perovskite material, which would correspond to an ∼8 wt% composite, the highest concentration used in the experimental workis a much smaller 1 wt %. However, we can infer from the discrepancythat the electrical performance of these composite TEs is likely tobe highly sensitive to the amount of graphene present and also itsquality in terms of flake size and defect concentration, as thesewould strongly influence both the electrical properties of the graphenesheets and their interaction with the perovskite surfaces. Introducinghigh concentrations of graphene in graphene-oxide composites wouldlead to the thermoelectric properties being driven mostly by the graphenecomponent, and from this perspective, our results are qualitativelyin line with the Seebeck coefficients predicted for graphene fromtight-binding models.86The electronic structures in S decreaseswith temperature , andtemperature  and third-order (anharmonic)force constants. However, obtaining the latter is computationallyvery expensive and is prohibitive for large systems such as our surfacemodels. For this reason, we chose instead to examine the atom-projectedphonon density of states (PDOS), the weighted two-phonon joint densityof states (wJDOS), and the mode group velocities, all of which canbe computed using the second-order force constants, to assess howchanges in the phonon spectrum due to the doping and graphene adsorptionare likely to impact the heat transport.13The latticecomponent of the thermal conductivity κ3+ cations could in principle couplestrongly to low-frequency acoustic modes to suppress transport throughthe TiO6 octahedral framework. There is also a significantcontribution from C to the low-frequency DOS in the graphene models,which likewise suggests that the graphene and SrTiO3 modesmay also couple to suppress the thermal transport of both components.κlatt(T) canbe written as a sum of contributions κλ(T) from the individual phonon modes λ asCλ are the modal heat capacities, νλ are the group velocities, V0 is thevolume of the unit cell, N is the number of reciprocal-spacewavevectors (q) included in the sum over the Brillouinzone, and τλ are the phonon lifetimes givenbyλ are the phononlinewidths obtained as the self-energy from third-order perturbationtheory. Cλ and νλ are calculated within the harmonic approximationasλ are the phononfrequencies, Wλ are the correspondingmode eigenvectors, and D(q) is the dynamicalmatrix for the wavevector q.Within the single-mode relaxation-time approximation (RTA) to thephonon Boltzmann transport equation, the lattice thermal conductivitytensors λ (T) in 88 and compute the sum overharmonic terms to obtain κlatt withrespect to an unknown relaxation time τCRTA aslatt/τCRTA for in-plane transport1/2 (xx + yy), after rotating thetensors to align with the equivalent directions in bulk STO (see Supporting Information). This analysis showsthat one would expect a reduction in κlatt on the order of 60–90% by adsorbing graphene at the surface,based on the changes in the model heat capacities and group velocities(q-point sampling mesh (see the Supporting Information), although despite this, we still predict a reduction in the κlatt due to the graphene adsorption. Thisreduction is more pronounced in the case of lanthanum doping, witha predicted average reduction of 80% over the temperature range 400–1000K compared to a 60–70% reduction without doping. This suggestsa synergy between La doping and graphene addition in suppressing thethermal transport. A possible mechanism for this is that grapheneincreases the “effective mass” of the bulk STO modesand therefore reduces the frequency dispersion and “depresses”the mode group velocities. This would be consistent with the strongergraphene adsorption energies calculated for the La-doped surface.The predicted reduction in thermal conductivity supports the experimentalwork by Lin et al.,13 whichdemonstrated a widening of the operating temperature window for graphene/La-dopedSrTiO3 samples to well below the standard operating temperatureof the undoped material.Although the calculation of τlocities6. We notκlatt/τCRTA functions suggest that La dopingwould lead to changes in the harmonic terms in κlatt. However, the poor convergence behavior means thisfinding may not be reliable. Moreover, as suggested by the phononDOS, it is possible that “rattling” of the La ions wouldcounteract the increase in the harmonic terms by reducing the phononlifetimes, leading to an overall decrease in the thermal conductivity.We explore this point further in the following.We also note in passing that the average λ in λλ′ λ″, which capture the strength of the physical coupling between themodes, requires the third-order force constants, and obtaining theserepresents a substantial computational workload. If the coupling strengthcan be averaged over interacting modes λ′ and λ″,however, Γλ can be approximated as68The ΓPλ is the averaged phonon–phononinteraction strength defined asna is the number of atoms in the primitive cell, and hence 3na is the number of phonon bands at each wavevector q. N2 is the weighted two-phonon density of states (wJDOS) and is a sumof two functions for collision (Class 1) and decay processes (Class2)N2(1) and N2(2) count the number of energy- and momentum-conservingscattering processes for a reference mode with wavevector q and frequency ω. For making comparisons between systems, itis useful to further average the wJDOS functions over wavevectorsto obtain functions of frequency only, i.e.,89 Unlike Pλ in N̅2(ω) can be computed from the harmonic phonon frequencies. N̅21)( and N̅22). To allow for comparison betweensystems, we have normalized the wJDOS functions by (3na)2, which is usually folded into the Pλ term in the expression for the approximatelinewidth (cf. idth cf. 18.N̅2(ω) at low frequenciesare potentially indicative of enhanced acoustic-mode broadening; sincethese modes typically make the largest contributions to the thermalconductivity, this would suppress the overall heat transport.89 However, N̅2(ω) at low frequencies.Similarly, comparing between the pure SrTiO3 and La-dopedsystems suggests that the doping also has little effect on the wJDOS.This suggests that either the changes to the group velocities notedabove are the dominant mechanism for the reduced thermal conductivityof the composites observed by Lin et al.13 or that changes to the frequency spectrum/wJDOSare secondary to changes in interaction strengths in reducing thephonon lifetimes in the composites and doped samples. In particular,our calculations do not indicate significant changes in the harmonicterms between the pristine and La-doped surface models without graphene,and the wJDOS functionals also seem to be generally smaller, so wemight infer from this that any reduction in the thermal conductivityon doping may be attributed to stronger phonon–phonon interactions.To investigate this further would require explicit computation ofthe third-order force constants, which, as noted above, is presentlynot practical.This method allows us to assess whether changes to the harmonicphonon spectrum are likely to increase/decrease the phonon linewidthsand thereby decrease/increase the lifetimes. Since the thermal conductivityis proportional to the lifetimes, this can be a useful means to qualitativelycompare how different dopants might affect the heat transport withoutthe computational expense of a full third-order calculation. Peaksin 3 and La-doped SrTiO3 affects the electronic structure, transport properties, structuraldynamics, and lattice thermal conductivity. Based on our results,we draw three main conclusions from our study.We have performed a detailed study of how the adsorption of grapheneat the surface of SrTiO3 and La-doped SrTiO3, yielding favorable adsorption energies.First, there is a thermodynamic driving force for graphene to adsorbto the surfaces of SrTiO3 band gap, which would account forthe reduced Seebeck coefficient observed by Lin et al.,13 but which is likely mitigated experimentallyby using smaller amounts of graphene in the composites. This highlightsthe sensitivity of the electrical properties to the amount and qualityof the graphene in the composite and indicates that controlling thismay be a simple route to fine-tuning the thermoelectric properties.Our calculations predict that extended graphene layers will inducea change from semiconducting to semimetallic behavior. However, understandingwhether this behavior is localized at interfaces or extends into thebulk will require input from both experiments and modeling to elucidatethe impact of different graphene concentrations on the propertiesof the composite.Second, we find that the adsorption of graphene introduces C 2pstates into the SrTiOFinally, analysis of the phonon spectra shows a remarkable reductionin the phonon group velocities on graphene adsorption, which we predictto lead to decreases of 60–90% of the bulk lattice thermalconductivity. This effect appears to be enhanced by La doping. Furthermore,analysis of the phonon spectra suggests that both La doping and grapheneadsorption introduce low-frequency modes into the density of states.The former, in particular, hints at low-frequency “rattling”modes in La-doped systems that could couple to acoustic modes andsuppress the phonon lifetimes. While calculations of the two-phonondensity of states do not suggest enhanced acoustic-mode broadeningin La-doped or graphene-adsorbed systems, it is possible that a reductionin the mode lifetimes may instead be facilitated by stronger phonon–phononinteractions. This can potentially be investigated in the future byexplicit calculation of the third-order force constants.