LITERATURE REVIEW
Graphene material
Graphene, silicene, germanene, phosphorene, hexagonal boron nitride (h-BN), molybdenum disulphide (MoS2), graphitic structures of carbon nitride (g-C3N4), and zinc oxide (g-ZnO) [12] which are typical representatives of two-dimensional (2D) ultrathin materials have recently exploited on a wide range of applications such as electrical appliances As far as graphene was concerned, a 2D sp 2 -bonded carbon monolayer, has drawn tremendous attention owing to its notable electronic and mechanical properties [14] It is known to have remarkable electronic properties, such as a high carrier mobility [8][19], but the absence of a band gap restricts its applications of large-off current and high on-off ratio for graphene-based electronic devices [14] Fig 1.1 illustrates the structure of monolayer of graphene and its applications [23]
Figure 1.1 Structure of monolayer of graphene and its applications
Initially, it was believed before the accomplishment of experimental fabrication of graphene that strict 2D crystals could be difficult to stabilize from theoretical and experimental perspectives due to the effects of thermal expansion
Nevertheless, in 2004, a single layer of carbon in atoms-level thickness was fabricated by Geim and Novoselov using micromechanical exfoliation and studied the electronic field effect and carried out a series of studies [8]
On the other hand, graphene oxide and its reduced form are graphene’s derivatives and are all semiconductors but with lower carrier mobility (Fig 1.2) [24]
Figure 1.2 Structure and properties of other graphene’s derivatives
In comparison with other 2D materials (Fig 1.3) [12], graphene is considered to be an excellent sensor material with high conductivity, electron mobility and the gapless and approximately linear electron dispersion around the Fermi level
Although graphene exhibits a very promising material with excellent electronic properties, there will be quite questionable to adopt graphene into sensors using nano- electric devices [19] Therefore, the introduction of the substrates such as h-BN and SiO2 can be an innovative way to help open up the band gap of graphene, thereby enhancing the sensor properties of graphene
Figure 1.3 Structure and physical properties of other 2D materials
Figure 1.4 Topology and charge density map of G/h-BN and G/SiO2
A comparison of topology of G/h-BN and G/SiO2 is depicted in Fig 1.4 [17][29] It is clear that while a similar lattice structure of graphene with both h-BN and SiO2 is seen, h-BN seems to have a smooth surface without any charge traps and
SiO2 surface is usually impure and uneven The surface optical phonon energy of h-
BN is two-fold magnitude greater than that of SiO2 [4] It indicates that G/h-BN will have a better performance compared with G/SiO2.
Heterostructure of Graphene/Hexagonal boron nitride (G/h-BN)
Hexagonal boron nitride (h-BN) is a representative of 2D material with a wide band gap Hexagonal boron nitride (h-BN) is called “white graphene”, consists of alternative boron and nitrogen atoms in a sp 2 -hybridized 2D honeycomb arrangement and 2D h-BN monolayer is isolated from bulk BN (Fig 1.5) [6] The bond length of B-N is around 1.45Å The interaction between boron and nitrogen is basically a covalent bond
Due to the fact that hexagonal boron nitride (h-BN) has a wide band gap, it could lead to its excellent properties of electrical insulations, high thermal conductivity and superior lubricant properties [28] Additionally, it can be useful as an important complementary 2D dielectric substrate for graphene electronics A direct band gap of h-BN which is the gap between HOMO and LUMO levels is attained by π and π ∗ located on the N atom and B nucleus, respectively [9]
Dean et al studied the quantum Hall effect of graphene with h-BN substrate for the first time in 2011 [7] Wang et al conducted the combination of graphene and h-BN crystals by physical force [26] Later on, other researchers have investigated and proposed G/h-BN heterostructure functional devices G/h-BN heterostructure can act as a high-capacity cathodes with high voltage for Aluminum batteries in the study of Pretti Bhauriyal et al [3] Furthermore, gas sensing properties has been studied for 2D G/h-BN lateral interface, specifically for NOx gas in Paquin et al studies [21].
Heterostructure of Graphene/Silicon dioxide (G/SiO 2 )
Table 1.1 Physical properties among graphite, SiO2, and h-BN
SiO2 Graphite Graphite diamond h-BN
Lattice constant Orthogonal a =1.383 Å, b = 1.741 Å, c = 0.504 Å Face-centered 1.936 a = b 2.46Å c = 6.67Å
First of all, SiO2 is known as nano-silica and has been used for a great deal of biomedical research owing to its functionalized ability and stability Furthermore, SiO2 substrate was widely applied on integrated circuits working as a dielectric medium It is explained by the good physical properties of SiO2 (Table 1.1) [10] For graphene supported by SiO2, Ishigami et al [13] indicated that single layer graphene mainly follows the underlying morphology of SiO2 and estimated the adhesion energy between graphene and SiO2 Otherwise, DFT calculations of graphene on SiO2 surface have been published Whilst SiO2 is generally experimentally found in amorphous, DFT calculation typically limited to crystalline SiO2 structures There are two kinds of SiO2 represented in Fig 1.6 [8]
They are α-quartz and cristobalite with multiple layers of SiO2 In reality, α- quartz is the most stable configuration under ambient conditions X F Fan et al [8] has studied the interaction between graphene and the surface of SiO2 in both α-quartz and cristobalite using first principles DFT It is found that by applying oxygen defect, the SiO2 surface could shift the Fermi level of graphene Nguyen et al [20] has also studied oxygen-terminated SiO2 (0001) surface interacted with graphene and concluded that G/SiO2 is a semiconductor Furthermore, Zhimin Ao et al [2] has also worked with G/α-SiO2 (0001) for interaction study and concluded that the vdW forces mainly serves as the interacting force in this system and is stronger than interaction of graphene layers in graphite
Figure 1.6 Configurations of (a) α-quartz and (b) cristobalite of SiO2
On the other hand, the studies of gas adsorption on G/h-BN and G/α-SiO2 are still limited and the gas adsorption mechanism is still a questionable problem for these systems even there have been a lot of studied investigating the gas adsorption on pristine graphene Hence, the significance of depicting the gas adsorption has motivated us to study more deeply in these heterostructures.
Gas molecules
These days, the process of industrialization and urbanization are booming sharply, one of the most pressing problem worldwide is air pollution As a result, the detrimental effect of this serious phenomenon is that it can be linked to the damage of human health in a direct or indirect way As WHO data reported, air pollution could cause 1 in 9 deaths worldwide while ambient air pollution caused 7.6% deaths over the world in 2016 [27] It is estimated that 4.2 million premature deaths universally are associated to the pollution of atmosphere [1] It mainly causes some serious health problem related to breathing such as lung cancer, and acute respiratory infections in children as well as heart disease, stroke, chronic obstructive pulmonary disease, etc For the purpose of mitigating the impacts of air pollution, the detection of toxic gases on air with a good sensitivity and favorable selectivity plays an essential role in research and manufacturing process Thus, this study aims to discover and propose promising materials that can not only be economical but also produce a better sensitivity and selectivity with toxic gases in the air The mechanism of gas adsorption is also one of the aspects drawing a lot of interest for understanding the interaction of material and gas adsorbate
In reality, outdoor air pollution can root from natural and anthropogenic sources Regarding natural sources, the contribution of local air pollution is more prone to forest fires and dust storms [1] On the other hand, human activities are the key factor leading to polluted air problems and far exceeds natural sources Adverse health consequences of air pollution can occur as a result of short- or long-term exposure [27] Herein, we investigate the adsorbability of 5 pollutants (CO2, CO, NO,
NO2, NH3) which have strong impacts on human health as well as the earth climate i.e global warming and water vapor H2O acting as an essential element in air There are some physical properties and toxicity of 5 toxic gases and water vapor below: a) Carbon dioxide (CO 2 ): CO2gas is colorless gas and is called “greenhouse gas” due to its main contribution into greenhouse effect CO2 is naturally traced in the Earth’s atmosphere and could be released from the dissolution of carbonate rocks in water and acids It is a by-product of burning fossil fuels and land-use changes and other industrial processes In geometric aspect, CO2 is a linear molecule with sp hybridization, with the bond length of C=O is 1.163 Å b) Carbon monoxide (CO): CO is a colorless and odorless gas, which at high levels can be harmful to humans by binding with hemoglobin, so it will be easily absorbed through the lungs That leads to hypoxic injury, nervous system damage, and even death The dizziness and nausea phenomenon are recognized in 45-min exposure of
CO The origin of CO in the atmosphere is believed coming from the exhaust of transport activities and machinery that burn fossil fuels According to VSEPR, CO has a linear molecular shape and the bond length of CO is originally 1.128 Å The hybridization of CO is sp with the bond order of 3 CO is a diamagnetic molecule with fully paired electrons c) Nitrogen monoxide (NO): There is a natural spontaneous reaction transforming NO in the atmosphere environment into NO2 during oxidation process Generally, nitrogen oxides are mainly produced from natural phenomenon such as lightning in thunderstorms NO gas is a colorless gas and is a main factor in acid rain deposition
Some common symptoms with breathing of low levels of NO are cough, tiredness, and nausea Nonetheless, NO can damage seriously our lung over the next one to two days after breathing Basically, NO has 1.15 Å of bond length and bond order is 5 2
NO is a paramagnetic molecule with one unpaired electron d) Nitrogen dioxide (NO 2 ): NO2 is a reddish-brown gas with origin from motor- vehicle emissions The shape of NO2 molecule is bent Due to acute toxicity of NO2,
NO2 has a serious harm to health like chlorine and CO gases in equal measure It can be directly adsorbed through human lungs and its inhalation, then cause heart failure and even to death NO2 is also a paramagnetic molecule with single unpaired electron
The bonding angle of NO2 is 134.3 o with 1.197 Å of bond length e) Ammonia (NH 3 ): Ammonia is a colorless alkaline gas with a characteristic of pungent smell Ammonia is considered as one of the abundant nitrogen-based substances in the air Breathing over the threshold of concentration of NH3 can expose to sinusitis, upper airway irritation, and eye irritation Some diseases of the lower airways and interstitial lung are found as acute exposures occur to concentrated ammonia [27] The bond length of N-H is 1.017 Å Geometrically, NH3 has one lone pair of electrons and has a tetrahedral structure in sp 3 hybridization f) Water vapor (H 2 O): The bond length of O-H in water vapor is 0.9584 Å According to VSEPR, H2O is in a bent shape with sp 3 hybridization Geometrically, H2O has two lone pairs of electrons In this study, H2O is in gas phase and is not classified as a toxic gas Nonetheless, H2O serves as an indispensable factor in air, so it can be as a reference for other toxic gases studies Apart from investigating the toxic gas adsorption on constructed heterostructures, the study on adsorption of water vapor could be adopted for hygrometer.
Physisorption mechanism of gas sensor
Figure 1.7 Schematic mechanism of gas sensor and its signal measurement
Toward developing gas sensor materials, the mechanism for physisorption is taken into account Therefore, the rationale of signal measurement plays an essential role in understanding it (Fig 1.7) Basically, there are three phases that physisorption has occurred during detection (Fig 1.7a) The first stage is the stage before gas adsorption (1) The gas molecule is in the proximity of the surface of sensor and there has not been any interaction yet Then, the second stage is the stage being completely adsorbed on surface of sensor material (2) This is the time that the gas molecule is close enough to interact with surface of material and the interaction of gas and sensor fully achieved the most preferable positions for adsorption After being completely adsorbed on sensor, the gas turns to desorption stage (3) The adsorption process will last for several seconds
From practical aspect, the signal measurement of gas sensor can be estimated by impedance measurement It is based on the change of resistance (R) Due to n- type nature of graphene, if the gas molecule serves as an acceptor which gains electron from sensor material, the signal of resistance will immediately increase and reach a peak during being completely adsorbed and vice versa (Fig 1.7b) In desorption phase, the value of resistance will suddenly come back the initial value due to the fact that there is not any interaction between gas molecule and surface For each adsorption, the response of sensor will get a peak of resistance during a contact time If the sensor is well qualified, the response should get the same height and wide of the peak at each different adsorption.
COMPUTATIONAL METHODS AND MODELS
Density Functional Theory (DFT)
Density Functional Theory (DFT) is a computational quantum mechanical modelling method applied for natural and materials sciences in order to study the electronic structure of many-body systems In 1964, Pierre Hohenberg and Walter Kohn proved that for molecules with a nondegenerate ground state, the ground-state molecular energy, wave function, and all other molecular electronic properties are uniquely determined by the ground-state electron probability density ρ0(x, y, z), a function of only three variables [16]
Hohenberg and Kohn proved their theorems only for nondegenerate ground states Subsequently, Levy proved the theorems for degenerate ground states [16]
The procedure of DFT can be summarized as in the below diagram [30]
Figure 2.1 Flow chart of the solution procedure of DFT
The Kohn-Sham (KS) Method
If we know the ground-state electron density ρ 0 (𝐫), the Hohenberg-Kohn theorem tells us that it is possibe in principle to calculate all the ground-state molecular properties from ρ0 without having to find the molecular wave function
The Hohenberg-Kohn theorem does not tell us how to calculate E 0 from ρ 0 , nor does it tell us how to find ρ 0 without first finding the wave function A key step toward these goals was taken in 1965 when Kohn and Sham devised a practical method for finding ρ0 and for finding E0 from ρ0 Their method is capable, in principle, of yielding exact results, but because the equations of KS method contain an unknown functional that must be approximated, the KS formulation of DFT yields approximate results [16]
Kohn and Sham considered a fictitious reference system (denoted by the subscript s and often called the noninteracting system) of n noninteracting electrons that each experience the same external potential-energy function νs(𝐫 i ), where νs(𝐫 i ) is such as to make the ground-state electron probability density ρs(𝐫) of the reference system equal to the extact ground-state electron density ρ 0 (𝐫) of the molecule we are interested in; ρ s (𝐫) = ρ 0 (𝐫) Since Hohenberg and Kohn proved that the ground- state probability-density function determines the external potential, once ρs(𝐫) is defined for the reference system, the external potential ν s (𝐫 i ) in the reference system is uniquely determined, although we might not know how to actually find it The electrons do not interact with one another in the reference system, so the Hamiltonian of the reference system is
2∇ i 2 + νs(𝐫i)] = ∑ ĥ i KS n i=1 n i=1 ĥ i KS is the one-electron Kohn-Sham Hamiltonian
Since the reference system s consists of noninteracting particles, the ground- state wave function ψs,0 of the reference system is the Slater determinant of the lowest-energy Kohn-Sham spin-orbitals u i KS of the reference system ψs,0 = |u 1 KS u 2 KS … un KS|, u i KS = θ i KS (𝐫i)σi
Kohn and Sham rewrote the Hohenberg-Kohn equation as follows Let ΔT̅ be defined by ΔT̅[ρ] ≔ T̅[ρ] − T̅s[ρ] ΔT̅ is the difference in the average ground-state electronic kinetic energy between the molecule and the refence system of noninteracting electrons with electron density equal to that in the molecule Let ΔV̅ ee [ρ] ≔ V̅ ee [ρ] −1
2∬ρ(𝐫 1 )ρ(𝐫 2 ) r 12 d𝐫 1 d𝐫 2 The Hohenberg-Kohn equation now becomes
The functionals ΔT̅ and ΔV̅ee are unknown Defining the exchange-correlation energy functional E xc [ρ] ≔ ΔT̅[ρ] + ΔV̅ ee [ρ], we have
This formula expresses E ν [ρ] in terms of three quantities, the first three terms on the right side, that are easy to evaluate from ρ and that include the main contributions to the ground-state energy, plus a fourth quantity E xc , which, though not easy to evaluate accurately, will be a relatively small term They key to accurate
KS DFT calculation of molecular properties is to get a good approximation to Exc The electronic energy including nuclear repulsion is found by addition of the internuclear repulsion [16]
The Kohn-Sham orbitals are found as follows The Hohenberg-Kohn variational theorem tells us that we can find the ground-state energy by varying ρ (subject to the constraint ∫ ρ d𝐫 = n) so as to minimize the functional E ν [ρ] Equivalently, instead of varying ρ, we can vary the KS orbitals θ i KS , which determine ρ In doing so, we must constrain the θ i KS ’s to be orthonormal, since orthonormality was assumed when we evaluated T̅ s
One can show that the Kohn-Sham orbitals that minimize the energy for the molecular ground-state energy satisfy
+ ∫ρ(𝐫2) r12 d𝐫 2 + ν xc (1)] θ i KS (1) = ε i KS θ i KS (1) where the exchange-correlation potential ν xc is found as the functional derivative δE/δρ of the exchange-correlation energy E xc : ν xc (𝐫) ≔δExc[ρ(𝐫)] δρ(𝐫)
If Exc[ρ] is known, its functional derivative is readily found from the above formula, and so νxc is known
There is only one problem in using the Kohn-Sham method to find ρ and E 0
No one knows what the correct functional E xc [ρ] is Therefore, both E xc in the energy expression and νxc are unonwn Various approximations to Exc will be discussed shortly [16]
The Kohn-Sham orbitals θ i KS are orbitals for the fictitious reference system of noninteracting electrons, so, strictly speaking, these orbitals have no physical significance other than in allowing the exact molecular ground-state ρ to be calculated The density-fucntional molecular wave function is not a Slater determinant of spin-orbitals In fact, there is no density-functional molecular wave function However, in practice, one finds that the occupied Kohn-Sham orbitals resemble molecular orbitals calculated by the Hartree-Fock method, and the Kohn- Sham orbitals can be used (just as Hartree-Fock MOs are used) in qualitative MO discussions of molecular properties and reactivities Note that, strictly speaking, Hartree-Fock orbitals also have no physical reality, since they refer to a fictitious model system in which each electron experiences some sort of average field of the other electrons [16]
For a closed-shell molecule, each Hartree-Fock occupied-orbital energy is a good approximation to the negative of the energy needed to remove and electron from that orbital (Koopmans’ theorem) However, this is not true for Kohn-Sham orbitals energies The one exception is ε i KS for the highest-occupied KS orbital, which can be proved to be equal to minus the molecular ionization energy With the currently used approximations to Exc, ionization energies calculated from KS highest-occupied- orbital energies agree poorly with experiment [16]
Various approximate functionals E xc [ρ] are used in molecular DFT calculations To study the accuracy of an approximate Exc[ρ], one uses it in DFT calculations and compares calculated molecular properties with experimental ones
The lack of a systematic procedure for improving E xc [ρ] and hence improving calculated molecular properties is the main drawback of the DFT method [16]
In a “true” density-functional theory, one would deal with only the electron density (a function of three variables) and not with orbitals and would search directly for the density that minimizes E ν [ρ] Because the functional E ν is unknown, one instead uses the Kohn-Sham method, which calculated an orbital for each electron
Thus, the KS method represents something of a compromise with the original goals of DFT [16].
The Local-Density Approximation (LDA)
Hohenberg and Kohn showed that if ρ varies extremely slowly with position, then Exc[ρ] is accurately given by
Exc LDA[ρ] = ∫ ρ(𝐫)εxc(ρ) d𝐫 where ε xc (ρ) is the exchange plus correlation energy per electron in a homogeneous electron gas with electron density ρ
Jellium is a hypothetical electrically neutral, infinite-volume system consisting of an infinite number of interacting electrons moving in space throughout which positive charge is continuously and uniformly distributed The number of electrons per unit volume in the jellium has a nonzero constant value ρ The electrons in the jellium constitute a homogeneous electron gas Taking the functional derivative of E xc LDA , we find νxc LDA =δE xc LDA δρ = εxc(ρ(𝐫)) + ρ(𝐫)∂ε xc (ρ)
∂ρ Kohn and Sham suggested the use of Exc LDA and νxc LDA as approximation to Exc and ν xc , a procedure that is called the local density approximation (LDA) One can show that ε xc can be written as the sum of exchange and correlation parts: εxc(ρ) = ε x (ρ) + ε c (ρ) where εx(ρ) = −3
The correlation part ε c (ρ) has been calculated, and the results have been expressed as a very complicated function ε c VWN of ρ by Vosko, Wilk, and Nusair (VWN) Thus, εc(ρ) = εc VWN(ρ), where εc VWN is a known function [16] We get νxc LDA = νx LDA+ νc LDA, νx LDA = −[(3/π)ρ(𝐫)] 1/3 , νc LDA = νc VWN
VASP – Vienna Ab initio Simulation Package
The Vienna Ab initio Simulation Package (VASP) is a computer program for atomic scale materials modelling, e.g electronic structure calculations and quantum- mechanical molecular dynamics, from first principles VASP computes an approximate solution to the many-body Schrửdinger equation, either within density functional theory (DFT), solving the Kohn-Sham equations, or within the Hartree- Fock (HF) approximation, solving the Roothaan equations [30] Hybrid functionals that mix the Hartree-Fock approach with density functional theory are implemented as well Furthermore, Green’s functions methods (GW quasiparticles, and ACFDT- RPA) and many-body perturbation theory (2 nd -order Mứller-Plesset) are available in VASP [30]
In VASP, central quantities, like the one-electron orbitals, the electronic charge density, and the local potential are expressed in plane wave basis sets The interactions between the electrons and ions are described using norm-conserving or ultra-soft pseudopotentials, or the projector-augmented-wave method [30].
Implemented computational scheme
In this work, all the first-principles calculations were based on the density functional theory (DFT) implemented in the Vienna Ab intio Simulation Package
(VASP) [16] The calculations employed periodic boundary conditions and plane- wave expansion of the wave function The generalized gradient approximation (GGA) in the scheme of the Perdew – Burke – Ernzerhof (PBE) function was used for the exchange-correlation potential of interacting electrons and the projector- augmented wave (PAW) pseudopotential was used to describe electron–ion interactions The visualization for structural figures and charge density drawings using in this work was produced by VESTA package developed by K Momma and
Electronic structure methods, such as DFT, can be used to study the interaction of materials with adsorbed molecules from first principles An essential detail is the inclusion of dispersion interactions and van der Waals (vdW) interaction, which are omnipresent in adsorption phenomena As these interactions are not adequately indicated in standard DFT, various methods have been proposed to incorporate them
In this work, revPBE-vdW method was employed for the correction of van der Waals interactions for the potential energies and interatomic forces of small molecules adsorbed on the graphene/hexagonal boron nitride (G/h-BN) and graphene/silicon dioxide (G/α-SiO2) The optimized structures were fully relaxed until the Hellman–Feynman forces acting on each atom were less than 0.01 eV/Å
The total energy convergence was chosen as 10 -5 eV between two steps, and a vacuum layer of over 15 Å was employed along the z direction to eliminate the interaction with spurious replica images
All calculations for G/h-BN heterostructure were done with a plane-wave cut- off energy of 520 eV and a 8×8×1 k-point mesh in the Brillouin zone of 33 supercell
In terms of G/ α -SiO2 system, cut-off energy of 600 eV was applied for all calculations and 6×6×1 k-point mesh in the Brillouin zone of 22 supercell was utilized for gas adsorption
In order to calculate adsorption energy, the system was fully relaxed, except for the bottom layer of h-BN in the single slab For non-gas adsorption, the stacking stability E stack of the G/h-BN heterostructure was calculated using the equation:
E stack =EG/h−BN− EG− Eh−BN n where E G ,E h−BN , and E G/h−BN are total energies of isolated graphene, isolated h-BN substrate, and G/h-BN system, respectively, and n is the total number of atoms in the heterostructure
Adsorption energy is the quality for estimating the adsorptive ability of toxic gases on the constructed heterostructure material It presents the correlation between total energies of system before and after adding gas molecule The less the adsorption energy reaches, the more the adsorptive ability of gas molecule of heterostructure will achieve The adsorption energy E ads will act as a quantitative measurement for gas adsorption study And for gas adsorption, the adsorption energy Eads was conventionally computed by this formula:
𝐸 𝑎𝑑𝑠 = 𝐸 𝑔𝑎𝑠/𝐺/𝑆𝑖𝑂 2 − 𝐸 𝐺/𝑆𝑖𝑂 2 − 𝐸 𝑔𝑎𝑠 for G/SiO2 where E G/h−BN , E G/SiO 2 , and E gas are energies of the G/h-BN, G/SiO2 systems and isolated gas molecule, respectively, E gas/G/h−BN and E gas/G/SiO 2 are total energies of G/h-BN and G/SiO2 with gas adsorption, in turns [3][20]
For the purpose of confirming and checking the result from site optimization, the scanning method was investigated by applying Computational DFT-based Nanoscope tool developed by V A Dinh (2017) The principle of this scanning method is that the minimum energy configurations and optimized distance from gas molecule to the surface will be determined Utilizing this tool, it avoids the error from conventional formula for adsorption energy The orientation of gas molecules on the surface can be optimized at each configuration The procedure of calculation can be summarized into two steps: (1) horizontal scanning in order to determine the stable position of the adsorbate, and (2) vertical scanning in order to calculate the adsorption energy profile [25]
The result from adsorption energy profile is elucidated by a formulation
Adsorption energy and response distance will be shown as a graph The x-axis illustrates the distance (Å) from the center of mass (COM) of the gas molecule to the graphene surface The y-axis represents to the adsorption energy, which is defined as:
𝐸𝑎𝑑𝑠 = 𝐸𝑔𝑎𝑠/𝐺/𝑠𝑢𝑏𝑠𝑡𝑟𝑎𝑡𝑒− 𝐸𝑠𝑎𝑡𝑢𝑟𝑎𝑡𝑖𝑜𝑛 where Egas/G/substrate is the total energy of the system G/substrate and gas molecule, E saturation is the total energy of the configuration of the complex system when graphene and h-BN substrate are isolated from each other This formula is equivalent to conventional calculation.
Heterostructure configurations
2.6.1 Unit cell of the graphene/substrate heterostructure
In general, the interaction between graphene and substrate is simulated using the repeated-slab model
Blue: Nitrogen Green: Boron Brown: Carbon
Figure 2.2 Two different AB-stacking patterns of G/h-BN
For G/h-BN monolayer, 1×1 graphene unit cell was designed above 1×1 h-
BN unit cell with initial interlayer distance 3.43 Å of the G/h-BN heterostructure layer which is also quite similar to other papers [3] The total z-axis in the slab model was 25 Å In the purpose of avoiding the spurious vertical periodic coupling effect,
(1) C on top N (2) C on top B the vacuum separation was set to be more than 20 Å For the 1×1 surface of h-BN, the 1×1 cell of graphene can be matched properly with a small difference of lattice constants The surface of h-BN at the bottom of heterostructure was fixed in z coordinate
Theoretically, there are several stacking positions for matching between graphene and h-BN The major three stacking patterns in most studies are: (1) AA stacking, with C atoms are positioned directly above both B and N atoms; (2) AB stacking, with several C atoms are positioned above N atoms (C on top N), while the other B atoms are placed below the center of C ring; (3) AB stacking, with several C atoms are located above B atoms (C on top B), while the other N atoms are placed above the center of C ring Nonetheless, in this study, two AB stacking patterns were investigated in order to opt the most stable configuration for further gas adsorption study There are two different AB stacking patterns of G/h-BN heterostructure above (Fig 2.2)
In G/α-SiO2 system, graphene was placed above 5 layers of SiO2 (α-quartz) with initial interlayer distance 3 Å and z-length is 30 Å Five layers of SiO2 is around
10 Å, which is good enough in thickness value for study the interaction with graphene
Therefore, the vacuum separation is around 18 Å helping eliminate the interaction with spurious replica images In addition, Si atom at bottom will be saturated by attaching a H-passivated in order to reduce the surface’s interaction (Fig 2.3) In Fig
2.3b, several carbon atoms of graphene are on top of all silicon atoms of α-SiO2 As far as oxygen atoms of SiO2 were concerned, some oxygen atoms are relatively on hollow of hexagonal center of graphene and some relatively coincide with positions of carbons above
Figure 2.3 G/α-SiO2 heterostructure with (a) side view and (b) top view of G/SiO2
2.6.2 Supercell of the graphene/substrate heterostructure 2.6.2.1 G/h-BN heterostructure
For G/h-BN heterostructure, after optimization of unit cell of G/h-BN heterostructure, the lattice constants for the G/h-BN system are a = b = 2.51 Å Due to the fact that the lattice constants of both graphene and h-BN are around 2.5 Å, the
3×3 supercell of G/h-BN heterostructure was simulated for further study with gas adsorption In order to avoid the interaction between the gas with the adjacent gas molecule in the repeated model, the lattice constants a = b = 7.5 Å of the 3×3 supercell of G/h-BN system seem to be suitable for further studies
Based on two different AB stacking configurations constructed for stability analysis, Table 2.1 and Table 2.2 are the summaries for optimization structure results of both heterostructures
It can be seen that the total energy of AB stacking pattern with C on top B (Etotal≈ -266.66 eV) is smaller than the total energy of AB stacking pattern with C on top N (Etotal≈ -266.59 eV) in two times of optimization process To confirm the result in quantitative calculation, the stacking stability 𝐸 𝑠𝑡𝑎𝑐𝑘 of the G/h-BN heterostructure is calculated
For AB stacking pattern with C on top B, 𝐸 𝑠𝑡𝑎𝑐𝑘 = −0.025eV For AB stacking pattern with C on top N, 𝐸𝑠𝑡𝑎𝑐𝑘 = −0.023eV
Table 2.1 The optimization results of AB stacking pattern with C on top B
Table 2.2 The optimization results of AB stacking pattern with C on top N
Hence, the heterostructure of AB-stacked bilayer with B facing C, and N in the hollow site of the graphene hexagon (C on top B) seems to be more stable than the other one This result is coincident with the conclusion of the other previous papers [26] The reason for this phenomenon stems from the nature of interaction of electrons between graphene and h-BN In graphene structure, the electron cloud is much more concentrated around C-C bonds in hexagonal honeycomb Otherwise, N has a larger electron affinity than B in nature (ꭓ N = 3.04> ꭓ B = 2.04), so N can act as anion and B would be cation attracting electron cloud of graphene Hence, N anions positioned in the center of graphene’s hexagon satisfy the electron repulsion with electron cloud of graphene in AB stacking pattern with C on top B This elucidation can be clearly exemplified by Fig 2.4 below
Figure 2.4 Electron distribution of G/h-BN heterostructure with C on top B
All in all, the final heterostructure for gas adsorption study is the 3×3 supercell of AB stacking configuration with C on top B with lattice constants a = b = 7.4991 Å, c = 25 Å The vacuum separation is 21.47Å and the interlayer between graphene and h-BN after optimization is 3.53Å
The band structure and DOS analysis of G/h-BN is showed below (Fig 2.5)
After calculation, the Fermi energy level of G/h-BN is -1.692 eV and the band gap is equal to 0.050 It elucidates the fact that h-BN already helps open the band gap of pristine graphene
Figure 2.5 Band structure of G/h-BN and DOS of (a) h-BN, (b) graphene and (c) total system
With regard to the lattice constants of constructed G/ α-SiO2 heterostructure (a = b = 4.91239 Å , c = 30 Å), the 2×2 supercell of this system was taken into consideration in order to suffice space for gas adsorption studies and avoid the gas- gas interaction although z-axis is intact with 30 Å Hence, the new lattice constants for further study is estimated with a = b = 9.82478 Å The supercell of G/α-SiO2 heterostructure for gas adsorption is illustrated in Fig 2.6 with both top and view sides A rationale for it’s stability is based on the interaction between graphene and α-SiO2
Figure 2.6 Optimized configuration and electronic density of G/α-SiO2 using revPBE-vdW (a) top view and (b) side view Yellow in (c) presents the locations of the electron cloud
Fig 2.6c indicates the close look at the electron contribution and the attractive – repulsive interactions of single layer of graphene and 5-layer SiO2 From the electron cloud, it can be seen that electrons of graphene concentrate mainly around C-C bonds and a low electron density is recognized at the centre of C hexagon In α- SiO2 structure, electron of SiO2 tends to be mainly distributed at O atoms rather than at Si atoms due to the fact that the electronegativity of O is theoretically much higher than its Si (ꭓO = 3.44 > ꭓSi = 1.9) It results in the attraction of electron in O, turning
O into more negative atoms (anion) and the losing of electron in Si towards O, turning
Si into more positive atoms (cation)
Furthermore, carbons of graphene were mostly placed on top of silicon atoms of SiO2 substrate and oxygen atoms of SiO2 were close to the center of C hexagon
This configuration helps avoid the repulsive interaction of carbons of graphene and oxygen atoms of SiO2 and reinforce the attractive interaction between carbon and silicon This means that the optimized configuration studied in this thesis tends to be promisingly stable owing to avoidance of strain and stress during matching
2.6.3 Positions for adsorption of toxic gases on G/h-BN and G/α -SiO 2
In general, for each adsorbate, three adsorption sites are considered, namely on top of a carbon atom (T), the center of a carbon hexagon (H), and the center of a carbon-carbon bond (B)
Otherwise, in this study, there are two top positions: T1 with C on top N, and
T2 with C on the center of h-BN hexagon in G/h-BN heterostructure (Fig 2.7) For these positions, two different orientations of the gas molecules were examined: upright orientation (U) and horizontal orientation (H)
Figure 2.7 Three adsorption sites and gas molecule orientations on G/h-BN
In this study with G/α-SiO2 heterostructure, only T and H positions were investigated
Figure 2.8 Different adsorption sites on G/α-SiO2
RESULTS AND DISCUSSION
Study and fabrication the Graphene/substrate heterostructures
3.1.1 The mismatch property between graphene and substrates
In order to decipher the interaction between graphene and substrates (hexagonal boron nitride h-BN and silicon dioxide SiO2) thoroughly, the lattice mismatch (𝜀) should be fully estimated first
For Graphene and h-BN heterostructure, the calculated lattice constants are a
= b = 2.468 Å and a = b = 2.512 Åfor the monolayers of graphene (primitive unit cell) and h-BN, respectively, which are in agreement with the previous studies [5] In the purpose of lessening the mismatch level 𝜀 𝑜 between graphene and h-BN layers, the hexagonal unit cell of the G/h-BN heterostructure was modeled by combining
1×1 unit cell of both graphene and h-BN unit cells Thus, the lattice mismatch 𝜀 𝑜 is defined by formula below where 𝑎 𝐺 = 2.468 Å; 𝑎 ℎ𝐵𝑁 = 2.512 Å
The lattice mismatch between the graphene and h-BN monolayer is quite small in comparison to previously studied heterostructures such as h-BN/phosphorene (5%), silicene/graphene (< 4%), and phosphorene/borophene (< 2%) [12] It can be stated that the strain effect on the electron properties of graphene can be ignored with that insignificant mismatch
In comparison with other previous articles, the difference is summarized in Table 3.1
Table 3.1 Comparison of lattice mismatch with other articles
No Graphene 𝑎 𝐺 (Å) h-BN 𝑎 ℎ𝐵𝑁 (Å) Lattice mismatch 𝜀 𝑜
For graphene and SiO2 heterostructure, the studied lattice constants of SiO2
(α-quartz) whose point group is P3121 (a = b = 4.91239 Å; c = 5.40385 Å) contain a similarity with the values from experimental data (a = b = 4.913 Å; c = 5.405 Å) The mismatch was estimated by constructing the 2 × 2 super cell of graphene (a = b = 2.468 Å) adsorbed on (0001) surfaces of α-quartz The value of mismatch percentage is calculated by
A comparison with different DFT simulation methods and experimental values is summarized in Table 3.2 [10][19]
Table 3.2 Comparison with various DFT simulation methods
DFT-D2 2.4685 4.9259 0.23 vdW-TS 2.4656 4.9764 -0.91 optPBE-vdW 2.4713 4.9891 -0.93 revPBE-vdW (this study) 2.468 4.91239 0.48
From both summaries of G/h-BN (Table 3.1) and G/SiO2 (Table 3.2), the mismatch between graphene and h-BN in G/h-BN heterostructure and graphene and
SiO2 in G/SiO2 system in this study seems to be close to previous reports [13] and insignificant difference in comparison with other methods Therefore, two configurations of two different heterostructures G/h-BN and G/𝛼-SiO2 investigated in this study are qualified for matching from chemical interaction aspect.
Adsorption of different gases on Graphene/h-BN
Overall, the analysis of gas adsorption on G/h-BN was conducted by calculating the adsorption properties (adsorption energy and adsorptive distance from gas to graphene) and DOS analysis of gas molecule before and after adsorption in order to rationalize the adsorption properties of each gas on constructed system As mentioned previously, there are CO2, CO, NO, NO2, NH3 for toxic gas adsorption and water vapor H2O for humidity sensor To be particular, the following studies of these gases will be divided orderly into three groups: (1) carbon-based group: CO2, CO; (2) nitrogen-based group: NO, NO2, NH3, and (3) water vapor H2O
CO2 molecule was adsorbed on G/h-BN heterostructure in all positions (T1, T2, H, and B) with two different orientations (upright U and horizontal H) Fig 3.1 depicts the above-mentioned positions with a specific orientation of CO2 on G/h-BN in top view
Figure 3.1.Atomic structures of all configurations for CO2 molecule adsorbed on G/h-BN (H: horizontal orientation, U: upright orientation; red ball: oxygen, brown ball: carbon, blue ball: nitrogen)
The calculated adsorption energies and adsorptive distances are shown in Table 3.3 in accordance with each optimized structure The adsorption energy of CO2 on G/h-BN is computed by
Then, it leads to final formula:
Table 3.3 Adsorption energy and adsorptive distance for CO2 on G/h-BN
Position Top 1 (T1) Top 2 (T2) Hollow (H) Bridge (B)
As can be seen, the adsorptive distances from CO2 molecule to graphene in all cases are larger than 3Å This suggests the CO2 molecule is physisorbed on G/h-BN
Furthermore, the adsorption energy in horizontal orientation is generally lower than its in upright direction Hence, CO2 tends to be preferably stable in parallel adsorption on G/h-BN All in all, the bridge site in horizontal orientation of CO2 on G/h-BN registers the most stable configuration with Eads = - 0.222 eV
In order to get a deeper understanding of the mechanism of CO2-G/h-BN interaction, molecular orbital (MO) of CO2 [22] and its density of state (DOS) before and after adsorption on G/h-BN are taken into account Fig 3.2 illustrates the similarity of MO diagram of CO2 and DOS of CO2 before adsorption The specific energy levels of CO2 in MO have been labelled in DOS From DOS analysis, the estimated band gap of CO2 is 7.356 eV which is a gap between the highest occupied molecular orbitals (HOMO) and the lowest unoccupied molecular orbitals (LUMO)
The HOMO of CO2 mostly appears from 1𝜋 g orbital of O atoms
Figure 3.2.Molecular orbital (MO) diagram of CO2 (1) and calculated DOS from this study (2)
Figure 3.3.DOS of CO2 before and after adsorption on G/h-BN
A comparison of DOS of CO2 before adsorption and after being completely adsorbed on G/h-BN is analyzed in order to recognize the variation of MO and band gap of CO2 (Fig 3.3) Due to the physisorption of CO2 on G/h-BN, the band gap of
CO2 is unchangeable Nonetheless, HOMO of CO2 is still recognized from 1𝜋 g of oxygen atoms of CO2 and has also shifted backwards Fermi level after adsorption
Otherwise, the Fermi level change from EF = -1.692eV in G/h-BN to – 2.044eV in
CO2/G/h-BN Based on orbital mixing theory and the mechanism of Fermi-level pinning, it can be suggested that a part of electron has been transferred between the
CO2 molecule and graphene, specifically between oxygen atoms of CO2 and G/h-BN
Figure 3.4 Partial DOS of a carbon on graphene mainly interacted with CO2 before and after adsorption
In order to elucidate clearer the electron transfer between CO2 and G/h-BN, a partial DOS of a carbon on graphene is presented in Fig 3.4 This carbon interacting primarily with CO2 molecule during adsorption It is obvious that p z and p x orbitals contribute mainly on DOS of this carbon before and after adsorption A small difference in the change of amplitude of p x orbital in this carbon atom
There are six configurations for CO adsorption on G/h-BN It consists of one Top1 (T1) and one Hollow site in upright (U) orientations, two configurations of Top2 (T2) and two configurations of bridge sites in both orientations (U and H) All configurations are indicated in Fig 3.5
Figure 3.5 Adsorption of CO molecule on G/h-BN in four different sites
After optimization, the calculation of adsorption energy of this system is based on formula below and is summarized in Table 3.4
𝐸 𝑎𝑑𝑠 = 𝐸 𝐶𝑂/𝐺/ℎ−𝐵𝑁 − 𝐸 𝐺/ℎ−𝐵𝑁 − 𝐸 𝐶𝑂 where 𝐸 𝐺/ℎ𝐵𝑁 = −266.662 𝑒𝑉 𝑎𝑛𝑑 𝐸 𝐶𝑂 = −11.352 𝑒𝑉 Hence, the formula for calculation is
Table 3.4 Adsorption properties from optimization of CO/G/h-BN in four sites
From Table 3.4, it is clear that the adsorptive distance is over 3Å which is analogous with CO2 adsorption Therefore, CO is physisorbed on G/h-BN and tends to stabilize in horizontal orientations in comparison with upright orientations From the values of adsorption energy, the most stable configuration is on bridge site in parallel adsorption (Eads = -0.171 eV)
Regarding the molecular orbital of CO [11] presented in Fig 3.6.1, a DOS diagram (Fig 3.6.2) is depicted for the purpose of referring the energy levels in MO
HOMO is on 5𝜎 while LUMO is on 2𝜋 HOMO (5𝜎) of CO is mainly from the contribution of carbon atom The estimated band gap of CO is 6.954 eV
Figure 3.6 Molecular orbital of CO (1) and DOS of CO before adsorption (2)
As far as DOS analysis is concerned, the HOMO (5𝜎) and LUMO (2𝜋) of CO have been altered and shifted back to lower energy levels It indicates that there is a charge transfer between CO and graphene Due to the similar symmetry, the orbital overlap between HOMO (5𝜎) of carbon atom of CO and p orbital of carbon of graphene has been established while LUMO (2𝜋) of CO is closer to the Dirac point than HOMO From the DOS of a carbon atom of graphene interacting mainly with
CO before and after adsorption (Fig 3.8), it can be stated that there is a bonding combinations of the pz atomic orbital of C atom of graphene with HOMO (5𝜎)of CO below 3eV to the Dirac point By contrast, the completely anti-bonding mixing mostly occurs in DOS of C of graphene above the Dirac point and LUMO of CO After adsorption, only py orbital in C of graphene is recognised in DOS even though there is no py orbital before adsorption This can be attributed to the Coulomb interaction of carbons in graphene making p x , p z shift in the space and p y appear on Oxy plane
Figure 3.7.DOS of CO before and after adsorption on G/h-BN
Figure 3.8 Partial DOS of a carbon on graphene mainly interacted with CO before and after adsorption
While four normal positions (T1, T2, H, and B) in upright orientation were investigated in adsorption study, another T2 configuration in horizontal orientation was constructed Fig 3.9 depicts details about all structures for adsorption study
Figure 3.9 Adsorption of NO molecule on G/h-BN in four different sites
To be more specific, a formula for adsorption calculation was derived and stated below Then, a summary for adsorption properties including adsorption energy
Eads and adsorptive distance d was shown in Table 3.5
𝐸 𝑎𝑑𝑠 = 𝐸 𝑁𝑂/𝐺/ℎ−𝐵𝑁 − 𝐸 𝐺/ℎ−𝐵𝑁 − 𝐸 𝑁𝑂 where EG/h−BN= −266.662 eV and ENO = −8.416 eV
Therefore, it is calculated as
Table 3.5 Adsorption properties from optimization of NO/G/h-BN in four sites
Position Top 1 (T1) Top 2 (T2) Hollow (H) Bridge (B)
It can be seen from the table that horizontal orientation is still more predominant than upright orientation in NO adsorption Nonetheless, the position for optimal adsorption of NO adsorption on G/h-BN is on top position, especially T2 in horizontal direction The optimal adsorption energy is Eads = -0.242 eV Additionally, the adsorptive distance d (over 3Å in general) also indicates that NO also physically adsorbed on G/h-BN
Figure 3.10 MO of NO molecule (1) and DOS of NO before adsorption (2)
From calculated DOS diagram of NO, each particular energy level in MO of
NO [22] was matched with each peak in DOS Due to the instinct nature of paramagnetic molecule, NO was calculated with spin polarization HOMO of NO is in 5σ or 3a1 orbital while LUMO is in 2𝜋 ∗ or 2b1 orbital with single unpaired electron
The model of 5σ donation and 2𝜋 ∗ back-donation was seen in NO mechanism [6]
Figure 3.11 DOS of NO before and after adsorption on G/h-BN
Due to spin-polarized calculation, HOMO is degenerate and LUMO is half filled Therefore, there is a mixing orbital between HOMO/LUMO of NO with orbital of carbons of graphene below Dirac point because of analogous symmetry even though there is possibility of orbital overlap above Dirac point
In NO2 adsorption, four basic positions (Top1, Top2, Hollow, and Bridge) are still constructed and optimized for adsorption study (Fig 3.12)
Figure 3.12 Adsorption of NO2 molecule on G/h-BN in four different sites The formula for adsorption energy calculation is also deduced as
𝐸 𝑎𝑑𝑠 = 𝐸 𝑁𝑂 2 /𝐺/ℎ−𝐵𝑁 − 𝐸 𝐺/ℎ−𝐵𝑁 − 𝐸 𝑁𝑂 2 where EG/h−BN= −266.662 eV and ENO 2 = −11.894 eV Replacing these values, we have got: Eads = ENO 2 /G/h−BN+ 278.556 (eV)
Table 3.6 Adsorption properties from optimization of NO2/G/h-BN in four sites Position Top 1 (T1) Top 2 (T2) Hollow (H) Bridge (B)
Likewise, the adsorption of NO2 on G/h-BN gets the optimal position on top sites, especially T1 In comparison with other gases, NO2 has a closer adsorptive distance (around 3Å) although it is still a physisorption mechanism The adsorption energy for T1 is -0.403 eV
Simultaneously, the MO of NO2 [22] and the DOS analysis will ameliorate the understanding of adsorption mechanism NO2 molecule is a paramagnetic molecule, so it is required to consider the spin polarized calculation like NO analysis That is why DOS of NO2 has a spin up and a spin down The band gap of NO2 is estimated and equal to 2.902 eV The 3π * orbital is mainly located on oxygen atoms
Figure 3.13 MO of NO2 molecule (1) and DOS of NO2 before adsorption (2)
Adsorption of CO and NO gases on Graphene/α -SiO 2
In this study, there are two configurations for CO and NO adsorption study on G/α-SiO2 There are one top and one hollow site for each gas which is represented below in Fig 3.22
Figure 3.22 Adsorption of CO and NO on G/α-SiO2 in top and hollow sites
The adsorption energy is estimated by separating system in isolated gas system, G/α-SiO2 heterostructure and gas/G/α-SiO2 system For the isolated gas system, ECO and ENO are – 11.356 eV and – 8.146 eV, respectively Additionally, E G/5SiO 2 = - 567.051 eV Thus, the results of adsorption energy calculation for each gas is given specifically below
Table 3.10 A comparison of adsorption energies of gases on G/α-SiO2
Eads (eV) (gas-pristine graphene)
From the table summarizing the results of adsorption properties, it is obvious that the adsorptive distance d between CO or NO toward G/α-SiO2 is always over 3Å
It shows that CO and NO gases are also physisorbed on G/α-SiO2 In addition, both
CO and NO gases tend to stay more stability on top site compared with hollow site
With regard to the selectivity, the NO molecule gives a better adsorption on G/α-SiO2 than CO molecule It can be rationalized by the single unpaired electron of
NO increase the overlap interaction with orbital of carbons on graphene while CO is classified as a diamagnetic molecule Although the sensitivity of graphene has improved by using α-SiO2 as a substrate, the selectivity was highly recognized The signal of NO will be superior to its of CO which suggested that G/ α-SiO2 can be a promising material sensing for NO in the air
In this work, we have already proposed two different heterostructures G/h-BN and G/α-SiO2 and investigated the gas adsorption of different gases in the air at some typical sites with particular orientations Whilst only CO and NO gas were constructed to adsorb on G/α-SiO2 system in top and hollow sites, all 5 toxic gases in the atmosphere CO2, CO, NH3, NO, NO2 and water vapor were studied the adsorption properties in T1,T2, H, and B sites on G/h-BN system There are some essential conclusions derived from this study
1 The optimal positions and orientation for gas adsorption
It is evident that all gases which are horizontally parallel with graphene gave the better adsorption compared with upright orientation in both G/h-BN and G/α-SiO2 heterostructures With regard to G/h-BN system, the adsorption of CO2, CO, and NH3 on bridge site was more favorable while H2O, NO, and NO2 gained the optimum on top sites
2 Adsorption nature: In both hybrid structures in this study, all gases are physically adsorbed on graphene-based surface
With respect to sensitivity, the introduction of substrate such as h-BN and α- SiO2 has helped to ameliorate the sensitivity for gas adsorption significantly Notably,
NO and NO2 adsorbed more effectively than other gases on G/h-BN It is ascribed to the fact that NO and NO2 are paramagnetic molecules while CO2, CO, H2O, NH3 are diamagnetic molecules From the obtained results of adsorption of CO, NO on G/α- SiO2, it can be concluded that the adsorption of CO and NO on top site was more significant than hollow sites The NO molecule still adsorbed better than CO due to its paramagnetic nature
4 Enhancement of selectivity: More importantly, it is conspicuous that α-SiO2 can enhance the selectivity for NO detection, so it can be used for NO sensor
5 Future research plan: Regarding the selectivity of G/h-BN, it needs to be improved by other methods such as doping For G/α-SiO2, the further investigations should be taken into consideration for other gases Charge transfer studies need calculating in order to understand deeply about the mechanism of adsorption
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