Impact of Specific PM2.5 Contaminant on Monolayer/Bilayer ArGNR

Elevated Particular Matter (PM<sub>2.5</sub>) may increase the risk of acquiring hazardous health implications, and hence high-performance monitoring of minuscule contaminants might protect people's health. The adsorption behaviour of specific PM<sub>2.5</sub> contaminants on doped/undoped monolayer/bilayer armchair graphene nanoribbon (ArGNR) is analyzed using a hydrogen-passivated layer. By using the first-principles density functional theory (DFT), the influence of doping on the ArGNR substrate is carefully examined. Due to the fragile surface atoms, monolayer ArGNR exhibits roughly twice the adsorption energy compared to the bilayer configuration. However, the specific PM<sub>2.5</sub> contaminants, the CH<sub>4</sub>, NH<sub>3</sub>, and NO<sub>2</sub> molecules demonstrate chemisorption of −2 eV,−2.95 eV, and −4 eV, with extremely less bandgap variation of −65% to −70% and −100% and a gigantic amount of charge transfer of +0.153 eV, +0.156 eV and +0.010 eV, and the DOS peaks at B site are <inline-formula><tex-math notation="LaTeX">$ \pm 110\,\text{eV}, \pm 65{\rm{ eV}}, \pm 80{\rm{ eV}}$</tex-math></inline-formula>, and at the P site are <inline-formula><tex-math notation="LaTeX">$ \pm 130$</tex-math></inline-formula> eV, <inline-formula><tex-math notation="LaTeX">$ \pm 300$</tex-math></inline-formula> eV and <inline-formula><tex-math notation="LaTeX">$ \pm 80$</tex-math></inline-formula> eV on boron-phosphorus (BP) co-doped monolayer ArGNR, for CH<sub>4</sub>, NH<sub>3,</sub> and NO<sub>2</sub>, respectively.


I. INTRODUCTION
In recent, air pollution has exerted a significant hostile influence on the ecosystem, climate, as well as human health.As a result of repercussions, severe diseases, including lung and pulmonic malfunctions, are widespread through micropollutants like PM 2.5 contaminants [1], [2].To address this pressing issue, researchers [3], [4], [5], [6] focused on intelligent gas sensors and actively explored a diverse array of materials for detecting low concentrations of PM 2.5 contaminant in the ambient air.It encompasses a range of materials, including polymers, metal oxides, nanowires, nanobelts, graphene, and carbon nanotubes (CNTs).As the supreme purpose of any sensor is to obtain a high level of sensitivity for contaminants, graphene is viewed strongly as a zero band gap semiconductor.This feature of graphene confines majority of the electrical applications.Recently, CNTs, have also gained significant attention due to their exceptional properties, including high surface-to-volume ratio, thermal and chemical stability, and high charge carrier mobility.However, despite these inherent advantages, these sensors face limitations, such as low sensitivity, that hinder their widespread adoption for PM 2.5 gas sensing applications.Therefore, the prime importance lies in the transition to the next level of the quantum regime, such as GNR (Graphene nanoribbon), for achieving robust adsorption characteristics that are crucial for gas sensing.Commensurately, it can be created by cleaving a ribbon from a graphene sheet, either in the pattern of an armchair or a zig-zag-shaped edge, as per chirality [7].On the basis of symmetry and electronic structure, armchairs (ArGNR) can be further classified as either metallic or semiconducting; nevertheless, zig-zag (ZGNRs) are considered metallic as per tight-binding approximation.As a consequence, the ArGNR substrate, with its semiconducting behavior, possesses substantial potential for the development of gas sensors that exhibit desired sensitivity, reactivity, selectivity, and high surface-to-volume ratio [12].Initially, Ahmed et al. [8] undertook an adsorption study of methane (NH 3 ) contaminants on monolayer ArGNR but neglected the approach of the selection of dopants for gas adsorption.Likewise, Jyoti et al. [9] investigated the adsorption of manganese-doped GNR for CH 4 molecules yet omitted the influence of bilayer ArGNR.Moreover, Kheirabadi et al. [10] neglected the influence of dopants while observing incredibly low chemisorption for CO, O 2 , and CO 2 on bilayer ArGNR.Consequently, Bai et al. [11] executed a computational investigation on B-N doped single-walled CNT that revealed physisorption in the case of NO 2 and NH 3 molecules.Furthermore, Qichao et al. [12] performed an adsorption analysis of NO 2 molecules on Ag-doped graphene but ignored the concept of critical temperature (T C ).Based on the state-ofthe-art research [8], [9], [10], [11], [12], the notion of T C with respect to Graham's Law of diffusion had not been subjected to an experimental investigation of E ads yet.Moreover, a detailed comparison of E ads between monolayer and bilayer with the consecutive effect of doping has not been performed so far.In addition, the effect of variation in the atomic arrangement of doped ArGNR that plays an important role in determining E ads was not demonstrated throughout.Therefore, for the first time, a novel computational modeling of an ArGNR plane having twenty atomic arrangements is performed for an in-depth analysis of the unique ability of monolayer/bilayer to detect the hazardous PM 2.5 contaminants.In succession, H-passivated monolayer/bilayer ArGNR is doped accordingly with a unique configuration of boron (B), phosphorus (P), and BP (adjacent position) in a zigzag orientation with concentrations of 5%, 5%, and 10%, respectively.The placement of dopant in the zigzag direction is taken due to large bandgap variation after the gas adsorption that leads to semiconducting property that will be useful for gas sensing.Following this, the chemisorption is obtained in a consecutive increasing manner for different variants of PM 2.5 contaminants according to the T C that follows Graham's law.As a consequence, BP doped monolayer ArGNR after the adsorption of the gas molecule, has obtained 50% improved chemisorption compared to a bilayer ArGNR.However, this augmentation in chemisorption is accompanied by an increased sensitivity to PM 2.5 contaminants due to the inherent hydrophobic nature of the doped ArGNR [13].
However, current research employs the independent effects of monolayer/bilayer to evaluate the different electronic properties of ArGNR.Typically, bilayer ArGNR can be categorized in AA, AB, and twisted AB patterns depending on the orientation of the surface planes.The fundamental type is the AA bilayer, wherein each C atom in the second layer is positioned directly over the relevant region of the first C sheet.However, in the case of the AB bilayer, some of the C atoms in the upper layer are placed over the hexagonal center of the bottom layer [14].Moreover, in twisted AB configuration, the upper layer is shuffled by some specific angle concerning the lower layer.By introducing a twist angle between the neighbouring graphene layers, a Moiré pattern is formed due to the superposition of the two lattices.This pattern makes the electronic structure of the twisted bilayer graphene system change in a regular way, leading to a number of interesting electronic properties [15].As a result, the suggested gas adsorption on the monolayer/bilayer has a significant impact on the electronic properties of ArGNR.Subsequently, the upcoming sections address the assessors' curiosity in understanding how BP-doped monolayer ArGNR is utilized for PM 2.5 gas sensing applications.
Furthermore, the paper is structured as follows: Section I introduces the hazardous PM 2.5 contaminants and the different stacking's of ArGNR.Further, Section II addresses the modeling and formalism of PM 2.5 contaminant with the substrate.Thereafter, Section III explicates detailed investigations of T C , E B , E ads , Q X , E G , DOS, and LDOS of monolayer/bilayer ArGNR, respectively.Accordingly, the paper is finally concluded in Section IV.

II. MODELLING AND FORMALISM
The industry-standard Virtual Nano Lab (QuantumATK) is used to analyze the atomic structure of monolayer/bilayer ArGNR using the DFT computation [16], [17].This section discusses the computational and structural model for the extraction of parameters that are necessary for sensing CH 4 , NH 3 , and NO 2 contaminants.

A. COMPUTATIONAL ASPECTS
A generalized gradient approximation (GGA) with the Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional approach is used in the LCAO (Linear combination of atomic orbital) calculator for attaining an improved accuracy of DFT (Density Function Theory) [17].It provides a framework for the application of the ab-initio electronic-structure theory and entails the utilization of diverse methodologies and approaches to ascertain distinct electronic parameters, as demonstrated in Table 1.
To enhance the precision of DFT, the approach employs a GGA incorporating the PBE exchange-correlation (XC) functional [18], applied through the LCAO calculator.Moreover, the calculations make use of the Fritz-Haber-Institute (FHI) pseudopotential alongside a double zeta polarized (DZP) basis set.These pseudopotentials serve the purpose of substituting the highly localized core electrons with a simplified, effective potential, enabling more accurate structural computations [19].These pseudopotentials are tailored for representing the valence electrons and generally utilizing the projector augmented-wave (PAW) technique [19], a method that derives pseudopotentials by projecting all-electron wave functions onto a set of localized pseudo-wave functions [20].
The calculations employ the high-convergence Fermi-Dirac occupancy technique, which characterizes electron distribution within a system at a specified temperature [21], [22].This technique facilitates the determination of occupation numbers for Kohn-Sham (KS) orbitals that are prospective solutions to the non-interacting, single-particle equations, also known as KS equations.These equations underpin the depiction of the system's electronic structure, encompassing factors like band structure and the Mulliken population.The technique is consistently integrated throughout iterations to ensure substantial numerical accuracy, thereby substantially diminishing the requisite number of k-points for calculation convergence [23].Subsequently, the total energy E[n] simulated and obtained from the LCAO computations in the virtual nano lab is depicted as where , and E ext [n] represent the kinetic energy of KS orbitals or electron gas with density n, the exchange-correlation energy, the electrostatic terms, i.e., the Hartree energy and the interaction energy with the pseudopotential ions, and the interaction energy of the electrons in the electrostatic field, respectively.However, for the calculation of adsorption energy, E ads , the total energy of the system, is calculated for both the adsorbed and the separated (molecule and surface) states.The E ads is defined as the difference in total energy between the two states.Accordingly, the simulated energy of the doped/undoped monolayer/bilayer ArGNR with and without the adsorption of a gas molecule is used for the calculation of E ads .Therefore, the E ads of doped/undoped monolayer/bilayer ArGNR is computed as [24] E ads = E (PM 2.5 +ArGNR) − E ArGNR − E PM 2.5 molecule (2) where E PM2.5+ArGNR , E ArGNR, and E PM2.5 molecule are the total energies of the monolayer/bilayer ArGNR with/without the gas adsorption, and energy of PM 2.5 molecule, respectively.The next subsection addresses the structural parameters of ArGNR and PM 2.5 contaminants.

B. STRUCTURAL PARAMETER
The monolayer/bilayer ArGNR has a total equivalent length of 6.67 Å and a C-C bond length of 1.42 Å.Meanwhile, for the bilayer, a 3.71 Å gap is observed between the successive layers of ArGNR.Both structures employ H-passivated edges, with a C-H bond length of 1.09 Å.In accordance, Table 2 demonstrates the respective PM 2.5 bond length and angle.Firstly, the pristine ArGNR structure is optimized without the gas molecule, and the total energy is computed.Subsequently, the gas molecule is purged on the optimized trajectory of different geometries of the ArGNR structure.In each iterative step, it is crucial to meticulously select electronic parameter values associated with the Brillouin Zone, encompassing k-points along the x, y, and z-axes, as well as factors for broadening and density mesh cut-off, as illustrated in Table 1.The principal aim of this selection process is to establish and uphold the utmost stability within the system.In order to ascertain the highest degree of stability, a sequence of self-consistent calculations must be executed with predetermined parameters for stress and force tolerance.The systematic adherence to this procedural framework facilitates the accurate and comprehensive evaluation of the system's behavior throughout the dynamic PM 2.5 adsorption process and its subsequent stages.Finally, using (2), E ads is calculated using the individual energies of PM 2.5 contaminant and pristine ArGNR with and without the adsorption of gas molecules, respectively.Consequently, in order to achieve maximal E ads, a five-atom-width ArGNR (with 20 atoms) with a 2×repeating structure in the z-direction is employed, as shown in Fig. 1.Conclusively, the narrow ArGNRs with fiveatom-width exhibit quantum confinement effects, leading to distinct electronic band structures.These confined states can be engineered to tailor the electronic properties of ArGNRs, making them potential candidates for novel electronic devices.

III. RESULT AND DISCUSSION
This section analyzes the detailed investigation of the impact of critical temperature (T C ), binding energy (E B ), adsorption energy (E ads ), charge transfer (Q X ), band structure (E G ), density of states (DOS), and Local density of states (LDOS) along with comparative justification with respect to E ads .

A. IMPACT OF CRITICAL TEMPERATURE
The impact of critical temperature (T C ) for the evaluation of an ArGNR-based gas sensor can be analyzed by the overall computational procedure displayed in Fig. 2. The monolayer/bilayer ArGNR without the gas molecule is first optimized, and then a gas molecule (CH 4 , NH 3, and NO 2 ) with horizontal orientation is purged on the trajectory of the doped/undoped monolayer/bilayer ArGNR substrate by considering a surface depth of 0.9 Å.Subsequently, a rigorous quantitative analysis was undertaken to assess the intermolecular dynamics within the optimized trajectory depicted in Fig. 3. Afterward, this comprehensive endeavour involved precise quantification of the binding between the adsorbate molecule (CH 4 , NH 3 , and NO 2 ) and the adsorbent (monolayer/bilayer ArGNR).The resulting dataset, encompassing these pivotal adsorbate/adsorbent distances, was meticulously curated and presented in a structured tabular format as detailed in Table 3. Afterward, using the optimized trajectory, the various electronic properties such as Q x , E B , E ads , E G , DOS, and LDOS of both structures are obtained with/without the adsorption of gas molecules.However, different contaminants on ArGNR behave differently with respect to their varying chemical sensitivities and corresponding T C .Hence, it is more convenient to comprehend gas liquefication by Graham's law of diffusion, which primarily states that the diffusion rate of gas (R) is inversely proportional to the square root of its mass (M) and can be formulated as: Using ( 3), the relationship between the molecular weight and corresponding critical temperature (T C ) established for specific PM 2.5 contaminants can be shown in Fig. 4. Commensurably, due to the difference in binding energy between atoms, lighter contaminants diffuse faster, while the heavier one liquefies faster.Using Fig. 4, it can be depicted that the specific PM 2.5 contaminants like CH 4 (T C = 190K) and NH 3 (T C = 405.5K)demonstrate moderate chemisorption because of their lower T C and comparable weights.Furthermore, it can also be discovered that NO 2 (T C = 431.4K)gas is highly chemisorbed on the doped monolayer due to its higher molecular weight and T C .Finally, the E ads of monolayer/bilayer are equated in the response to T C for the specific PM 2.5 contaminants.If the obtained E ads follows the trend of T C , such as higher chemisorption for higher T C and vice-versa, then the design is acceptable, and the structure is promoted that can be further utilized for gas-sensing applications; otherwise, the dopants are once again relocated to the respective alternative site as indicated in Fig. 2.Moreover, Tc is not the sole parameter for determining the adsorption capability of the substrate.However, in the context of gas sensing on an ArGNR substrate, it becomes imperative to thoroughly investigate several other electronic properties.This scrutiny is necessary to comprehend the sensitivity towards specific PM 2.5 contaminants, which will be succinctly described in the subsequent sections.

B. IMPACT OF BINDING ENERGY
The determination of the E B of the doped monolayer and bilayer ArGNR is used to evaluate the substrate stability [25].Firstly, the monolayer and bilayer ArGNR substrate is optimized without any dopants, and corresponding E ArGNR is obtained.Consequently, it is doped individually with the  dopants, and a quantitative value of E (Doped/ArGNR) is obtained.Conjointly, separate energy (E Boron and E Phosphorus ) for each dopant is produced, along with the computational evaluation for the monolayer and bilayer using the first-principle theory [25], [26].Conversely, in order to comprehend the stability of the atoms, the proposed analysis assesses the probability of dopants binding to monolayer/bilayer ArGNR.The determination of binding energy (E B ) of the doped monolayer and bilayer ArGNR is used to evaluate the substrate stability and hence, can be represented as where E b(monolayer) , E dopedArGNR , E ArGNR , E boron , and E phosphorus are the energies of monolayer binding energy, doped/undoped monolayer ArGNR, boron (B), and phosphorus (P), respectively.Consequently, the E B for the bilayer ArGNR is given by where E b(bilayer) , E dopedBilayer-ArGNR , E Bilayer-ArGNR , E boron , and E phosphorus are the energies of bilayer binding energy, doped/undoped bilayer ArGNR, boron (B), and phosphorus (P), respectively.In accordance with ( 4) and ( 5), the E B of monolayer and bilayer ArGNR configurations is determined.
The monolayer ArGNR consists of 20 carbon atoms, while the bilayer ArGNR comprises 40 carbon atoms.The approach for assessing the E B per atom in either a monolayer and bilayer configuration involves dividing the overall binding energy of the monolayer and bilayer ArGNR by the total count of carbon atoms within the monolayer and bilayer ArGNR [27].Table 4 demonstrates the E B of monolayer and bilayer ArGNR (per atom in eV).It indicates that the monolayer ArGNR exhibits higher E B , like 43.60%, 11.16%, and 59% than the AA bilayer ArGNR, 47%, 26.23%, and 59.98%, than the AB bilayer ArGNR, 47.47%, 14.86%, and 61.25%, than the twisted AB bilayer ArGNR, for boron, phosphorus, co-doped boron phosphorus, respectively.Consequently, the BP-doped monolayer ArGNR exhibits a notably higher E B than the bilayer ArGNR, indicating that minimal energy is required to disrupt the dopants' configuration within the ArGNR.As a result of the inherent instability of surface atoms within the BP-doped monolayer, a discernible net force emerges, thereby generating outward-directed residual forces.Hence, during the interaction of ArGNR and the gas molecule, a residual field of force comes into action leading to an enhanced reactivity.Subsequently, in the case of AA, AB, and twisted AB bilayer ArGNR, the lower E B is observed.This could be due to the low intricate interlayer interactions and a weaker Van der Waals forces, than the intralayer interactions within a monolayer ArGNR.As a result, the bilayer ArGNR may have weaker bonding between the layers compared to the monolayer ArGNR.Consequently, the twisted AB and AA bilayer ArGNR likely has a less E B than the AA stacked bilayer ArGNRs, it is due to the disruption of strong π -bonding interactions, the introduction of strain, and differences in the Vander Waals interactions.Furthermore, the electronic properties of monolayer and bilayer ArGNR are strongly influenced by the number of layers.In monolayer ArGNR, the π orbitals of carbon atoms interact strongly with each other, leading to the formation of a continuous π -bonding network.In bilayer ArGNR, the electronic coupling between the layers is reduced, which can result in a weaker E B .Successively, the next sub-section elaborates on a reliable E ads analysis crucial for drawing conclusions about the surface reactivity of monolayer and bilayer ArGNR configuration.

C. IMPACT OF ADSORPTION ENERGY
The E ads provide insights into the strength of the interaction between the substrate and different gases, revealing their chemical sensitivities.In the case of monolayer/bilayer ArGNR substrates, the calculation of E ads allows for a comparison of their adsorption capabilities.Consequently, the contaminants are individually purged on each dopant site to compare the adsorption properties.Because the adsorption of the single gas molecule on the ArGNR surface allows us to isolate individual phenomena and interactions, simplifying the system.This simplification is crucial for gaining a deep understanding of the specific electronic properties of the doped/undoped ArGNR substrate during gas adsorption.As a result of having the same atomic size as that of C, B tends to bind to monolayer ArGNR more conveniently and with a very significant amount of E B .It reveals that both B and C atoms are covalently bonded to each other.Further, B doped shows moderate E chemi-ads for both monolayer ArGNR because of its less electronegativity (χ ) in comparison to C. Fascinatingly, because of variations in atomic size, the monolayer/bilayer binds to P atom with a high E B .Considering this fact, the P atom extends far beyond the range of the ArGNR plane due to its comparatively larger radius juxtaposed to the C atom that exerts a net force on the ArGNR surface, which ultimately promotes capturing a wide band of electrons and hence increases the E ads .Due to a higher E B with C atoms, P confirms chemisorption with the ArGNR substrate.Subsequently, from the geometrical perspective, the BP-doped monolayer ArGNR retains a planar form of symmetry.However, the presence of electron-rich P atoms near the periphery of the B atom increases the strength of PM 2.5 molecular adsorptions, as shown in Fig. 5(a).As a consequence, E ads varies according to the elevated T C , the χ of dopants, and the corresponding E B .According to the preceding analysis, the bilayer ArGNR can adopt stacking sequences like AA, AB, and twisted AB with weak Vander Waals binding the consecutive layers.However, the electronic properties of bilayer ArGNR can be altered either by varying the number of layers or by modifying the consequent stacking design throughout.Fig. 5(b)-(d) demonstrates the E ads of different stacking designs such as AA, AB, and twisted AB, wherein the electronegative pollutants such as CH 4 and NH 3 + exhibit moderate chemisorption while the electropositive NO 2 exhibits higher chemisorption, respectively.The B-doped bilayer ArGNR exhibits chemisorption for all the stacking (AA, AB, and twisted AB) because of its extremely low electronegativity than C.However, the specific PM 2.5 molecules like CH 4 and NH 3 + indicate moderate E chemi-ads possessing low T C that results in less E B to form a liquid state.Hence, this complex liquefaction leads to less adsorption phenomenon.Apart from this, the B-doped ArGNR contains holes in the valence band that combines with unpaired electrons of specific PM 2.5 molecules like NO 2 resulting in strong adsorption.Solemnly, the optimal AA stacking indicates chemisorption due to its uniform E B between the subsequent layers.Remarkably, NO 2 is showing higher chemisorption than NH 3 + and CH 4 contaminants as per the T C trend in the AA pattern depicted in Fig. 5(b).Considering a similar scenario, the AB and twisted AB bilayer bind to the P atom with a high E B because of the variation in atomic size and more electronegativity in comparison to the B atom.
Accordingly, the repulsion occurs during the adsorption of CH 4 and NH 3 + molecules on the P dopant site because of the low T C of gas and non-uniform binding forces between the adjacent layers, which ultimately leads to zero adsorption.Furthermore, in the case of the BP co-doped bilayer ArGNR, due to more non-uniformity between the consecutive layer and less T C , the NH 3 + and CH 4 molecules are repelled by the BP-doped ArGNR with a positive value of E ads , indicating the nature of repulsive force leading to instability.Additionally, NO 2 exhibits physisorption because of the weak, non-uniform E B between the layers of P/BP doped AB and twisted AB stacked ArGNR, as demonstrated in Fig. 5(c)-(d).Furthermore, the succeeding sub-section presents the impact of charge transfer (Q X ); this analysis is crucial in analyzing the sensitivity of doped ArGNR substrate for PM 2.5 gas sensing.

D. IMPACT OF CHARGE TRANSFER
The Mulliken population analysis represents a valuable metric for elucidating the net charge distribution within an atom, thereby facilitating in-depth investigations into chemical bonding dynamics.The quantification of charge transfer, denoted as Q X , can be effectively ascertained through the utilization of the Mulliken population formula, as referenced in the literature [8].
Here, Q x , Q a, and Q b represent the charge transfer of the dopant and Mulliken charges of the dopant in ArGNR after and before PM 2.5 adsorptions, respectively.Using (6), the Q x for different variants of ArGNR are calculated, and their corresponding plot is shown in Fig. 6.A positive sign of Q x for different variants of ArGNR are calculated, and their corresponding plot is shown in Fig. 6.It indicates the charge transfer from the PM 2.5 molecules to the ArGNR and vice-versa.It reveals that the adsorbents can interact with contaminants with opposing charges.Conclusively, the charge exchange phenomenon depends on the χ of either dopant and substrate or dopant and contaminants.In the case of B/BP doped monolayer/bilayer, the B site (χ =2.04) possesses lesser electronegativity than the C (χ =2.19) atom and P (χ = 2.55) atom, resulting in electron shortage in all ArGNR designs implying very less amount of Q X for CH 4 and NH + 3 contaminants.Moreover, for the NO 2 molecule, the B/BP doped monolayer/bilayer at the B site that is already very electron deficient results in a significantly less Q X to NO 2 .However, for the P and BP doped (in adjacent positions) monolayer ArGNR, a high amount of Q X (charge gain) is observed for NH + 3 and CH 4 molecules at the electron-rich P site due to its higher electronegativity compared to the C atom, respectively as shown in Fig. 6(a).In defiance, the electron-rich P site of the P/BP monolayer loses lesser electrons to NO 2 compared to the case of the B site resulting in moderate Q X .
In the case of optimal AA (with 40 atoms) stacking, the P site in P-doped ArGNR accumulates more electrons owing to the CH 4 and NH + 3 donors due to uniform binding forces between the subsequent layers and increased amount of charge carriers depicted in Fig. 6(b).In response to this, despite having extracting nature of NO 2 molecule, there is a significant increase in charge gain by the AA bilayer ArGNR substrate.In contrast, during the adsorption of NH + 3 at the P site in BP doped, it donates more electrons compared to the CH 4 molecule due to the existence of partial charge, but the presence of electron-deficient 2 Boron atoms results in overall negative Q X .Besides, by virtue of the withdrawing nature of NO 2 , the BP-doped bilayer ArGNR at the P site transfers more charge from the substrate to the NO 2 molecule.Moreover, in AB stacking, the non-uniformity between the successive layers consecutively decreases the transfer compared to AA stacking, wherein all the contaminants behave simultaneously according to their nature demonstrated in Fig. 6(c).However, the AB twisted stacking, the upper layer twists by a certain angle of 5°favoring the requisite inductive effect of NH 3 + donor for the P site, as shown in Fig. 6(d).Therefore, for the NH 3 + molecule, the electron-rich P site in P/BP dopant culminated in more charge gain compared to CH 4 .In addition, the twisting of AB between adjacent layers provides moderate Q X from the P site of P/BP doped ArGNR to NO 2 molecule.Furthermore, the charge transfer concept can be deeply analyzed by considering the electrochemical property of PM 2.5 contaminants, classified as electron acceptors or donors.The CH 4 molecule draws electron density from the neighboring H atoms (less electronegative) towards itself, usually by the resonance effect that results in an electron-donating group.

TABLE 5. Quantitative Analysis of E-k Diagrams
Similarly, a distinct positive charge in NH 3 + results in a better electron-donating group compared to CH 4 due to the presence of partial charge and negative inductive effect (-I).Counterfact, NO 2 behaves as an electron-deficient group, resulting in the formulation of an electron-withdrawing or electronacceptor group.The reason being N has previously exchanged lone pairs with O atoms resulting in the formation of an empty p-orbital by attaching its electrons to O that remain open for electron inclusion.On the other hand, the bilayer ArGNR has more stable surface atoms compared to highly reactive fragile atoms of the monolayer, resulting in a reduced tendency to exchange electrons with gas contaminants and hence leads to limited Q X while it is observed that the BP co-doped monolayer ArGNR renders a good charge transfer, respectively.Conclusively, to clear the ambiguity in investigating the conductivity and sensitivity of monolayer/bilayer ArGNR, another electronic parameter is required for the perfect selection of adsorbate.Therefore, the next sub-section demonstrates the impact of bandgap in monolayer and bilayer ArGNR substrate that is important for analyzing the bandgap variation in the ArGNR substrate with and without the adsorption of the gas molecule.

E. IMPACT OF BAND STRUCTURE
An E-k (Electron-Wave Vector) diagram or energymomentum diagram, also known as an energy-wave vector diagram, is a graphical representation of the relationship between the energy and momentum of electrons in a material [28].As per the quantum electronics, the band structure isolates the lowest unoccupied molecular orbital (LUMO) of the CB from the highest occupied molecular orbital (HOMO) of the VB, and the minimum distance between them is known as the bandgap, E G .Moreover, the sensitivity of a substrate can be determined by altering the E G through the adsorption of contaminants.During the investigation of bandgap for ArGNR, the influence of CH 4 , NH 3 , and NO 2 molecules is predominantly contingent upon their interaction with the ArGNR substrate, depicted in Table 5.
In the case of a pristine monolayer, physisorption, characterized by the Vander Waals force, results in relatively minor variations in the bandgap (E G ). Conversely, moderate chemisorption, involving strong covalent bonding, has been observed in pristine bilayer systems that create highly localized energy states within the bandgap of the bilayer system.The localized states present in the bilayer ArGNR exhibit a heightened capacity for interaction with the existing electronic states.As a consequence of this interaction, there is a notable amplification in the variation of the E G , which nearly induces a shift into a metallic state.It's worth highlighting that the research trajectory has undergone a significant shift due to the exceptionally low E ads .Consequently, the current emphasis of investigation has transitioned towards the realm of doped ArGNR.
Subsequently, when the dopants are introduced, the electronic properties can undergo substantial changes.When monolayer ArGNRs are doped, additional energy levels are introduced near the bandgap or near the VB and CB band edges, depending on the type and concentration of dopants.The dopant atoms or molecules can create localized states that interact with the electronic structure of the monolayer ArGNR, which leads to significant variations in the E G .Consequently, the introduction of separate boron and phosphorus dopants in monolayer ArGNR creates additional energy states within the bandgap that act as charge carriers and contribute to an increased electrical conductivity, leading to a metallic behavior.Furthermore, when the monolayer ArGNR is codoped with BP, the dual effects of these dopants lead to a more complex electronic structure with a potentially larger bandgap variation compared to individual doping.The interaction of these dopant atoms with the adsorbate molecules, such as (CH 4 and NH 3 ), further enhances the electronic modifications in co-doped ArGNRs.This interaction can lead to significant shifts in the electronic states near the Fermi level and, in turn, contribute to the observed bandgap variations in co-doped ArGNRs with −65% for CH 4 molecule and +16% and −68% for NH 3 molecule, at the B and P site of co-doped BP doped monolayer ArGNR respectively.
In the context of bilayer ArGNR, where two layers are involved, this quantization becomes more intricate due to the interplay of these two dimensions of confinement.In the case of phosphorus-doped ArGNR, both AA and AB stacking configurations revealed the presence of strong interlayer interactions and minimal charge transfer with gas molecules that effectively preserve these localized states.This preservation mechanism contributes to an intriguing outcome, an increase in the E G with +2.7% and +13% for CH 4 and NH 3 molecules and +2% and +15% for CH 4 and NH 3 molecules at the AA and AB stacking, respectively.The stable interlayer interactions in these stacking arrangements ensure that the energy levels created by the dopant-adsorbate (CH 4 and NH 3 ) interactions remain distinct, leading to a larger bandgap.Intriguingly, the scenario changes when considering twisted AB stacking; despite the weaker interlayer interactions, the localized electronic states continue to emerge due to the interactions between the dopants and adsorbate molecules (CH 4 and NH 3 ).As charge transfer effects come into play, the localized states become charged, contributing to the partial filling of the bandgap.This intriguing interplay of factors ultimately leads to a decrease in the E G as −2% and −100% at the twisted AB stacking.Following that, the impact of BP-doped bilayer ArGNR doped is examined across different stacking configurations.In instances of AA stacking, the adsorption of CH 4 and NH 3 molecules introduces a distinctive layer separation due to their dimensions and orientations.This separation eventuates in an augmented interlayer distance, culminating in a discernible weakening of interlayer interactions.This phenomenon translates into an amplification of the energy E G by approximately +2% and +38% for CH 4 , and +2% and +40% for NH 3 , respectively.Conversely, in AB stacking, the arrangement of the two layers in a staggered manner weakened van der Waals interactions.This attenuation of interactions further contributes to symmetry disruption, thereby introducing an asymmetry within the electronic distribution.This asymmetry imparts a notable reduction in the E G for the CH 4 molecule, evident by a −14% decrement at both the B and P sites of the BP-doped AB bilayer.Notably, following the adsorption of gas molecules, the E G experiences a substantial −64% and +21% alteration at the B and P sites of the BP-doped AB bilayer, respectively.Moreover, within an AB-twisted bilayer structure, the observed variation in the bandgap of the twisted bilayer ArGNR stems from the intricate interplay between the effects of twisting and doping.Upon the adsorption of CH 4 molecules, a notable consequence emerges in the form of introduced localized states within the E G .These localized states manifest as a partial filling of the E G , resulting in a discernible reduction in size.Specifically, this reduction is quantified at −27% and −16% for the B and P sites of the BP co-doped twisted AB bilayer ArGNR, respectively.Subsequently, the interaction dynamics between NH 3 molecules and the co-doped AB-twisted bilayer present intriguing outcomes like the emergence of energy states within the bandgap due to the inductive effect of the molecule.This influence translates into an increased energy difference between the valence and conduction bands, culminating in a considerable +21% expansion in the energy E G .This phenomenon becomes pronounced at the P site of the BP co-doped bilayer ArGNR.Subsequent to the adsorption of NO 2 molecules onto the surface of doped monolayer and bilayer ArGNRs, a significant interaction occurs between the energy levels of the dopant-induced states and the states induced by NO 2 .Notably, these energy levels align with the VB and CB, respectively, within the material's electronic structure.This alignment of energy levels engenders an intricate overlap, precipitating a profound outcome.Specifically, the E G , an essential characteristic governing the material's electronic behavior, undergoes a conspicuous reduction.As this overlap continues to develop, a critical point is reached where the bandgap effectively vanishes.Consequently, the material transitions into a metallic state and experiences a substantial 100% reduction in its energy gap E G .Moreover, the conductivity of the material increases with a reduced E G after adsorption, resulting in an increased sensitivity and viceversa.Moreover, the next subsection discusses the density of states (DOS) to further investigate the sensitivity of the monolayer and bilayer ArGNR.

F. IMPACT OF DENSITY OF STATES
The Density of states (DOS) is important to analyze the sensitivity and conductivity with respect to the different energy states.It represents the distribution and density of available unoccupied energy states at different energy levels for electrons to occupy [26].In addition, it quantifies the rate of change in the total number of states with respect to the energy given by where N represents the count of electrons possessing energy E within a specified energy range dE.It provides valuable energy levels, the introduction of new states, the broadening or shifting of peaks, and the appearance of new peaks in response to adsorption and the assessment of the device performance for sensing applications.The influence of the adsorption of CH 4 , NH 3 , and NO 2 contaminants on different ArGNR configurations is comprehended by the DOS depicted in Fig. 7.In the context of undoped monolayer ArGNR, the Density of States (DOS) demonstrates distinct peaks representing the VB and CB edges.These peaks are separated by the Energy Gap (E G ), which separates the HOMO from LUMO.The DOS displays a sharp profile near these band edges, indicating a limited number of available electronic states within the bandgap.Prior to molecule adsorption, the energy peaks are positioned at ±20 eV.However, after the adsorption of CH 4 , NH 3 , and NO 2 molecules, the peaks shift to ±75 eV, ±500 eV, and ±0 eV, respectively.It's worth noting that the number of induced states after adsorption is relatively low, prompting a shift in focus towards doped ArGNRs.Upon introducing dopants (e.g., boron and phosphorus) into the monolayer ArGNR, additional energy levels are created within the bandgap or near the band edges before the adsorption as ±60 eV and ±50 eV; after the adsorption, the peaks at B site of B doped monolayer ArGNR are ±110 eV, ±65 eV, ±80 eV for CH 4 , NH 3, and NO 2 , and at P site of P doped monolayer ArGNR is ±130 eV, ±300 eV and ±80 eV for CH 4 , NH 3, and NO 2 , respectively.These dopant-induced energy states contribute to an increased DOS peaks in the bandgap region, which can lead to a significant alteration and appear as localized states within the bandgap.Moreover, when monolayer ArGNRs are co-doped with boron and phosphorus, the DOS becomes more prominent ±40 eV.Subsequently, the presence of both dopants and their interaction with adsorbate molecules (e.g., CH 4 , NH 3 , and NO 2 ) leads to additional energy levels within the bandgap, resulting in multiple peaks at ±100 eV, ±130 eV for CH 4 , ±100 eV, ±70 eV for NH 3 and ±90 eV, ±85 eV for NO 2 at the B and P site of BP doped monolayer ArGNR illustrated in Fig. 7(a).This is due to a redistribution and increment of charge density within the ArGNR after adsorption, indicating that the CH 4 /NH 3 has occupied some energy states with a displacement in peaks and vice-versa.These displacements can manifest as the repositioning of the DOS peaks or the appearance of new peaks and more states at different energies that are previously unoccupied in the DOS, within the bandgap region near the Fermi level, or CB/VB, or throughout the entire energy range.The ArGNR adsorption causes a decrease in the E G , leading to an increase in the DOS and vice-versa.This means that additional electronic states become available for occupation, which can result in an enhanced electronic transition and increased conductivity.
In contrast, bilayer ArGNRs consist of three types, AA, AB, and twisted AB, that exhibit a distinct DOS compared to monolayer ArGNRs due to the presence of an additional layer.The DOS of pristine bilayer ArGNR reflects the interlayer coupling between the two graphene sheets that leads to the formation of new electronic states near the band edges at 40 eV.Subsequently, after the adsorption of the gas molecule, DOS peaks are observed at ±700 eV, ±80 eV, and ±180 eV for CH 4 , NH 3, and NO 2 molecules, respectively.These interlayer interactions cause alterations in the DOS distribution and modify the DOS with large peaks due to more atoms compared to monolayer ArGNRs.Due to less number of states, the dopants are introduced into bilayer ArGNRs; due to this, the DOS can experience additional changes due to the interplay between the dopants and the interlayer coupling.In the context of AA-stacked bilayer ArGNR, the significant interlayer interactions give rise to a noteworthy outcome: the emergence of mini-bands within the electronic band structure.However, there is very lesser variation in the case of individual dopants, upon co-doping it leads to an occurrence of an increased DOS, with values of ±400 eV and ±190 eV observed for CH 4 , ±80 eV, and ±120 eV for NH 3 , and ±100 eV and ±120 eV for NO 2 , at the B and P site of BP co-doped bilayer ArGNR, respectively, as shown in Fig. 7(b).Unlike AA bilayer ArGNR, AB-stacked exhibits a large bandgap variation due to interlayer interactions.This bandgap gives rise to some semiconducting properties in the material that demonstrate the van Hove singularities in their DOS.These singularities occur when the energy levels of the two layers overlap, leading to sharp peaks in the DOS as ±50 eV before the adsorption, and after adsorption, it exhibits ±1200 eV, ±90 eV, and ±950 eV.The van Hove singularities, combined with the presence of a larger E G and the peculiarities of the Bernal stacking, contribute to the peaky nature of the density of states in AB-stacked bilayer graphene nanoribbons, as shown in Fig. 7(c).During the process of co-doping, certain peaks can become more noticeable compared to when only individual dopants are present.This effect can be observed both before and after adsorption.Specifically, for CH 4 adsorption, the peaks at ±100 eV before adsorption become more prominent, and after adsorption, peaks at ±700 eV and ±200 eV are noticeable.Similarly, for NH 3 adsorption, the peaks at ±50 eV and ±250 eV become more pronounced, while for NO 2 adsorption, the peaks at ±100 eV and ±80 eV at the B and P sites of the BP co-doped bilayer ArGNR respectively show increased prominence.Furthermore, in the case of twisted AB-stacked ArGNR, the twist angle between the layers can significantly influence the electronic properties, leading to the emergence of van Hove singularities.These singularities lead to distinct spikes in the Density of States (DOS) due to the overlapping of energy states from the separate layers.This leads to a significant increase in DOS at particular energy levels: ±90 eV prior to adsorption, ±380 eV, ±180 eV for ±CH 4 , ±100 eV and ±1500 eV for NH 3 , and ±90 eV and ±120 eV for NO 2 .These energy spikes occur at both the B and P sites of the BP co-doped AB twisted stacked bilayer ArGNR, as illustrated in Fig. 7(d).In summary, the DOS for doped monolayer ArGNRs exhibits more number states corresponding to the due to localized states induced by the dopants and adsorbate molecules.Subsequently, the DOS for doped bilayer ArGNRs is more pronounced, influenced by the interlayer coupling and the hybridization of electronic states between the two layers, leading to potentially modified DOS distribution.Furthermore, it can be interpreted by the Local density of states (LDOS) in the subsequent section to further investigate the conductivity and sensitivity of the monolayer and bilayer ArGNR.

G. IMPACT OF LOCAL DENSITY OF STATES
In the context of the electronic properties and interactions in doped monolayer ArGNRs, the LDOS can be denoted as ρ(r, E), representing the number of electronic states per unit energy, the interval at energy, and position r.For a doped monolayer ArGNR, the LDOS [29] can be expressed as: where i, Ei, i(r), δ represents the index of different electronic states, the energy of the i th state, the wave function of the i th state at position r, and the Dirac delta function, respectively.In the case of undoped ArGNRs and their interaction with molecules, the LDOS at a certain energy level would reflect the density of electronic states available for occupation by electrons or holes.In pristine monolayer/bilayer ArGNRs, the LDOS reflects the characteristic peaks corresponding to the valence conduction band edges, separated by (E G ) that isolates the HOMO from the LUMO.The interaction of molecules like CH 4 , NH 3 , and NO 2 with the ArGNR Substrate-induced localized energy states within the bandgap.These localized states could contribute to the LDOS and influence the electronic band structure near the Fermi level.The LDOS is sharp near the band state, indicating a limited number of available electronic states within the bandgap.Successively, in the context of doped monolayer ArGNRs, the LDOS provides insights into the electronic structure at specific locations within the material.Subsequently, upon introducing dopants such as boron (B) and phosphorus (P) have different valence electron configurations compared to carbon (C), which makes them suitable for introducing localized energy states within the bandgap or near the band edges.Furthermore, in the case of Co-doped monolayer ArGNRs, wherein both boron and phosphorus dopants are introduced simultaneously, the interaction between the dopants can lead to enhanced modifications in the LDOS.In this case, the LDOS is the same at every point or minimum variation in space since the density of available energy states is uniform.This means that the probability of finding an electron with a particular energy remains constant throughout the material.However, when molecules like CH 4 , NH 3 , and NO 2 adhere to a monolayer ArGNR, the LDOS experiences marginal changes for CH 4 and NH 3 molecules.Due to this, the LDOS would be the same at every point in space since the LDOS energy states are homogenous.On the contrary, the covalent bonding formed between the NO 2 molecule and the ArGNR substrate introduces imperfections or other elements that influence the material's electronic structure.This interaction results in defects or deviations that influence the overall electronic behavior of the material, depicted in Fig. 8(a).Subsequently, for a doped bilayer ArGNR, the LDOS can be expressed as where i and σ , E σ i , ψ σ (r,z) i represent the indices of different electronic states and spin orientations, the energy of the i th , σ the wave function of the i th state at position (r, z) within the bilayer, z represents the position in the vertical direction, respectively.In the context of doped bilayer ArGNR, the LDOS exhibits distinctive characteristics based on the stacking arrangement of the bilayer graphene.In the context of AA stacking, the significant interlayer interaction gives rise to mini-bands, which in turn leads to a more even spread of electronic states across space.This phenomenon contributes to an elevated LDOS in the energy spectrum, distinguishing it from alternative stacking configurations, as shown in Fig. 8(b).However, in the presence of gas molecules, the introduction of these molecules results in little more pronounced peak states compared to the monolayer setup.This enhancement in peaky states can be attributed to the complex interplay between the layers in the doped AA stacked bilayer ArGNR.Subsequently, within the AB-stacked configuration, the distinct stacking arrangement gives rise to a major variation in the energy gap.This phenomenon can be attributed to fluctuations in the material's structure, defects, impurities, or other elements that impact its electronic structure.As a consequence, more noticeable peaks in the local density of states (LDOS) are evident before the adsorption of gas molecules, as illustrated in Fig. 8(c).However, after the adsorption molecule, it leads to more homogenous electronic states.Furthermore, the case of twisted AB-stacked bilayer ArGNRs leads to noticeable changes in the Local Density of States (LDOS) profiles.These changes occur due to shifts in the underlying electronic structure.These changes become evident as specific energy levels display reduced LDOS values, indicating the presence of localized electronic states connected to the unique moiré pattern.Consequently, the LDOS varies across the system, giving rise to energy levels referred to as "mobility edges".These energy levels act as boundaries that separate areas where electrons can move more freely from regions with limited mobility.Nevertheless, subsequent to the adsorption process, facilitated by physisorption, a crucial role is played in causing significant changes in the LDOS pattern.These changes manifest as noticeable dips or shifts within the LDOS distribution, as depicted in Fig. 8(d).However, out of all the stacking designs, the AA stacking stands out as a more stable configuration.This is attributed to the robust interlayer interaction and minimal disruption in the structure both before and after the gas molecule's adsorption.

IV. CONCLUSION
This work uncovers a comprehensive first-principles research of specific PM 2.5 contaminants adsorbed on different variants of monolayer/bilayer doped/undoped ArGNR.In light of this, the value of E ads rises as the T C of the PM 2.5 pollutants increases, revealing a solid interaction between the different PM 2.5 molecules and ArGNR.Subsequently, a high charge transfer for Monolayer ArGNR is also obtained, indicating better sensitivity.However, the BP-doped monolayer displays an acceptable remarking semiconducting behaviour after doping and indicates a significant %E g , making it highly suitable for the detection of specific PM 2.5 contaminants.Finally, when compared with the bilayer ArGNR, the BP doped monolayer ArGNR demonstrates chemisorption of −2 eV, −2.95 eV, and −4 eV, with extremely less bandgap variation of −65% to −70% and −100% and a gigantic amount of charge transfer of +0.153 eV, +0.156 eV, and +0.010 eV, and DOS peaks observed the at B site are ±110 eV, ±65 eV, ±80 eV, and at P site is ±130 eV, ±300 eV, and ±80 eV are observed for CH 4 , NH 3, and NO 2, molecule respectively.Thereafter, both the CH 4 and NH 3 molecules exhibit semiconducting characteristics coupled with enhanced sensitivity.In contrast, the NO 2 molecule adopts a metallic attribute due to its robust covalent bonding to the ArGNR.As a result of a comprehensive assessment of all the electronic properties, the BP-doped Monolayer ArGNR is identified as the most efficient in effectively detecting PM 2.5 pollutants.

FIGURE 4 .
FIGURE 4. Relationship between critical temperature and weight of the gas molecule.