Sensitivity of SnO2 nanoparticles/reduced graphene oxide hybrid to NO2 gas: a DFT study

The sensitivity of SnO2 nanoparticles/reduced graphene oxide hybrid to NO2 gas is discussed in the present work using density functional theory (DFT). The SnO2 nanoparticle shapes are taken as pyramids, as proved by experiments. The reduced graphene oxide (rGO) edges have oxygen or oxygen-containing functional groups. However, the upper and lower surfaces of rGO are clean, as expected from the oxide reduction procedure. Results show that SnO2 particles are connected at the edges of rGO, making a p-n heterojunction with a reduced agglomeration of SnO2 particles and high gas sensitivity. The DFT results are in good agreement with the experimental characterization of both SnO2 and rGO using energy gap and X-ray photoelectron spectroscopy (XPS) values. Gibbs free energy, enthalpy, and entropy of the various considered reactions are calculated. Results show that the sensitivity of the rGO/SnO2 hybrid to NO2 gas is the result of the interplay of the dissociation and oxidation reactions of NO2 gas. The sensitivity of the rGO/SnO2 hybrid to NO2 increases with temperature until the NO2 dissociation in the air reduces the concentration of NO2.


Introduction
Graphene is a material with high potential applications [1][2][3]. These applications include solar cells [1], light-emitting diodes (LEDs) [2], and many other applications [3]. The same is true for graphene oxide [4]. One contemporary application of graphene or graphene oxide is in gas sensing [5,6]. Graphene is proved to be better than multi-wall carbon nanotubes (MWCNT) in gas sensing [7]. The large surface area of graphene is one of the important features that give graphene superiority in gas sensing operations. This superiority is also kept even after the mixture of graphene with other materials since the mixed materials are dispersed on graphene surfaces or edges that prevent agglomeration [8,9]. Graphene oxide can be activated using materials that remove oxygen-containing functional groups on the surfaces of graphene oxide. Hydrazine is one of these materials that are used as an oxygen scavenger from graphene oxide surface [8]. The resultant material is called reduced graphene oxide (rGO). rGO is an n-type semiconductor [10]. In general, nanomaterials are now playing a vital role in the industry [11][12][13].
Tin oxide is one of the most used materials in gas sensing [14,15]. It is a p-type semiconductor [16]. It has been used practically to detect various gases. The high number of oxygen vacancies in SnO 2 can enhance gas sensing operation by accepting or donating oxygen to the censored gas.
Nitrogen dioxide (NO 2 ) is an important polluting gas that is produced in large quantities due to vehicle engines and from smoking and kerosene heaters [17]. As a result, monitoring NO 2 is of vital importance. The use of graphene or graphene oxide has been suggested several times to build sensors for NO 2 gas [9,18,19]. Adding other sensing materials to graphene or its oxide is a common practice. SnO 2 is one of these materials that improve graphene sensitivity to NO 2 gas [7,[20][21][22]. In addition to SnO 2 , other catalysts such as SnS 2 , Ag, or Pd can also improve the sensitivity of graphene or its oxide [20][21][22].
The use of density functional theory has proved to give valuable information about gas sensing mechanisms, including the various properties of materials used in the sensing operation [23,24]. This includes related electronic structure properties such as the energy gap, vibrational properties of Raman and IR spectroscopy, X-ray photoelectron spectroscopy (XPS), and thermodynamic properties such as Gibbs free energy, enthalpy, and entropy.
In the present work, DFT is used to analyze the gas sensing properties of SnO 2 /rGO hybrid to NO 2 gas. The properties of the different materials used in this work are discussed. The results are compared with experimental findings of the various materials used in the sensing operation. Thermodynamic properties such as Gibbs free energy, enthalpy, and entropy of the various reactions are evaluated to estimate the reaction rates of NO 2 with the sensing materials.

Theory
DFT at the B3LYP/6-311G** is used in the present work to simulate the structure and different properties of the sensing materials of the SnO 2 /rGO hybrid and their interaction with NO 2 gas. Previous works on SnO 2 surveyed different methods and bases to perform electronic structure calculations such as GGA, LDA, B3LYP, and PBE0 [25]. B3LYP (see reference [26] for the abbreviations) was found to give a bandgap that is more consistent with experimental results. Previous use of B3LYP in gas sensor calculations gave satisfactory results in comparison with experiments [27,28]. The basis 6-311G** reflects the size of molecules and the total number of atoms in the present work. A small number of atoms can give us the freedom to use a more intricate basis, while a large number of atoms can restrict the use of a detailed and complicated basis. Stuttgart/Dresden (SDD) basis is used for heavy Sn atoms that cannot be represented by the 6-311G** basis. Dispersion corrections are important for the present calculations because of the long-range forces between the interacting molecules. GD3BJ dispersion correction version is added [29]. Gaussian 09 molecular facilities program is used to perform present calculations [30]. It is interesting to calculate the calculate basis set superposition error (BSSE) for the system of atoms in Fig. 1a and b, which is of the order of 0.007 atomic units per atom. This number represents the difference between the use of the complete set and the present set. The percentage of HF in B3LYP is 20%. This percentage seems to give an advantage for B3LYP present calculations.
Previous works on SnO 2 relied on the pyramid structure of its surface [24,28,31]. Pyramids on the SnO 2 surface are also confirmed experimentally [27]. Figure 1a shows the pyramid SnO 2 cluster used in the present calculations. The stoichiometry of this cluster (Sn 10 O 16 ) is carefully chosen so that adding more oxygen to this cluster (such as Sn 10 O 17 ) will make the Gibbs free energy of reaction positive, and the cluster will return to the optimum stoichiometry Sn 10 O 16 in a specific reaction rate. This is in agreement with experimental results that SnO 2 has a lot of vacancies [28]. The Sn-O bond length is in the range of 1.9 to 2.1 Å, which is in agreement with the literature [32].
Graphene has a well-known hexagonal honeycomb structure. Coronene (C 24 H 12 ) is used frequently to represent graphene [33][34][35]. However, we use oxygen instead of hydrogen (C 24 O 6 ) to simulate the real existence of oxygen in the air and not the rare hydrogen. A variation of C-C bond length in the range (1.32 to 1.5 Å) according to bond distance from edges is in agreement with the experiment [26]. A lower range for C = O and C-O (1.22 to 1.45 Å) is also in agreement with the experiment [26]. C 24 O 6 (as in Fig. 1b) is called reduced graphene oxide since no oxygen-containing functional groups exist on the surface of this cluster. Practically, the edges of the graphene cluster of atoms are terminated by oxygen, hydroxyl, or oxygen-containing functional groups. The upper and lower surfaces of graphene can also be terminated by oxygen or oxygen-containing groups. However, the functional groups on graphene surfaces can be removed easily, which is not the case for functional groups at the edges. The removal of an OH group by hydrazine (N 2 H 4 ) from the surface and edges of reduced graphene oxide in Fig. 1b can be given by the following reactions (in all the following reactions we use the standard conditions of 25 °C and 1 atm unless mentioned otherwise): ∆G is the Gibbs free energy of the reaction. We can see from the upper two equations that removing the OH functional group from the edge of graphene requires three times the energy required to remove the OH group from the surface. The same is not true for removing oxygen from the surface and edge. Oxygen can be completely removed using hydrazine [8]. The UV radiation can break the OH bond to graphene at the surface only. The energy of a 532 nm (2.331 eV) can break this bond [18] so are the 365 nm (3.397 eV) radiation as in reference [9]. NO 2 gas at low temperatures decomposes to NO and O 2 [36,37] in an endothermic reaction as in the reaction: The decomposition of NO 2 near the surfaces of catalysts affects the ability to sensor NO 2 since it decreases the concentration of the gas near the sensor surface. The rate of decomposition is given by [38]: In the above equation, [NO 2 ] is the concentration of NO 2 gas. C 1 is an empirical coefficient that can be found experimentally. k(T) is the temperature-dependent part: T is the temperature, ∆G a is the Gibbs free energy of activation, and k B is the Boltzmann constant. The same method of Eq. (4) can be used to calculate the reaction Results and discussion Figure 2 shows the HOMO (highest occupied molecular orbital) and LUMO (lowest unoccupied molecular orbital) of both SnO 2 (represented by the Sn 10 O 16 cluster) and the rGO (represented by the C 24 O 6 cluster) and their energy gaps. The experimental energy gap of SnO 2 is 3.6 to 3.92 eV [32,39] which is around our calculated 3.875 eV value. The experimental energy gap of rGO is in the range of 1.00 to 1.69 eV [22]. The present calculated gap of rGO represented by C 24 O 6 is 1.336 eV which is nearly the average of the experimental range. The p-n heterojunction formed between rGO and SnO 2 [40] is the straddling gap since the HOMO, and LUMO energy levels of rGO are within that of SnO 2, as shown in Fig. 2. If the two materials (SnO 2 and rGO) do not interact at all, the final gap should be that of rGO. However, this is not the case. The high affinity of carbon atoms drags oxygen atoms from SnO 2 because of the lower affinity of Sn atoms, as in Fig. 3b. In addition, a bond is formed between carbon and tin atoms. Due to these interactions, the final material is called the rGO/SnO 2 hybrid, which is some kind of a composite at the molecular or nanoscale [41]. The final calculated gap of the rGO/SnO 2 hybrid is 1.534 eV, with the HOMO and LUMO energy levels moved to be higher than that of rGO as in Fig. 2.
Besides the energy gap, calculations of the electronic structure of Sn 10 O 16 and C 24 O 6 clusters and hybrid reveal other quantities such as XPS that match the experimental Although carbon atoms exist only in the C 24 O 6 cluster, the C1s level in the hybrid is wider than that of the C 24 O 6 cluster alone, as in Table 1. Figure 3a shows our initial theoretical arrangement of attaching the SnO 2 cluster (Sn 10 O 16 ) to the rGO cluster (C 24 O 6 ). In this attachment, the base of the SnO 2 pyramid is put on the rGO surface. However, after performing selfconsistent field calculations of the present density functional theory, the SnO 2 cluster is repelled so that the attachment is made between one of the carbon atoms at the edge of rGO and one Sn atom at the edge of SnO 2 as in Fig. 3b. This arrangement is consistent with the above-mentioned high and powerful reactivity of rGO edges with respect to the rGO surface. This is also consistent with experimental findings in field emission scanning electron microscope  . 4 The transition state and the steps of the reaction of rGO/SnO 2 hybrid with NO 2 (FESEM) and scanning electron microscope (SEM) images in which SnO 2 nanoparticles are stacked on rGO sides and edges [8,9]. NO 2 sensitivity is only triggered by its interaction with either rGO or SnO 2 in the rGO/SnO 2 hybrid. This interaction changes the energy gap value that ultimately changes the resistivity of rGO/SnO 2 . The oxidation of the SnO 2 cluster in the rGO/SnO 2 hybrid can be described by the equation: The reaction in the upper equation is endergonic, and we can use Eqs. (4) and (5) to determine the reaction rate. To determine the reaction rate, the Gibbs free energy of activation ∆G a should be determined as in the following reaction: In the above reaction, [C 24 O 6 /Sn 10 O 16 --NO 2 ] ‡ is the transition state. The value of the activation energy (∆G a = − 0.0595 eV) is negative, which means that the formation of the transition state is an exergonic reaction. The steps of this reaction are shown in Fig. 4.
Gibbs free energy, enthalpy, and entropy of a reaction are connected via the relation: ∆H is the change in enthalpy or the enthalpy of reaction. ∆S is the change in entropy, while the term T∆S is the entropy energy of the reaction. As we have seen before in Eq. (5) that Gibbs free energy of activation determines the rate of reaction. The enthalpy of reaction is the heat produced or absorbed in the reaction. The entropy of reaction is usually related to the difference between the number of reacting molecules and the number of product molecules. In Table 2, we listed the different reactions encountered in this work, including their Gibbs free energy, enthalpy, and entropy. We can see from Table 2 that most of the reactions have a higher number of product molecules than the number of (11) ΔG = ΔH − TΔS  Table 2. Reaction number 6 has an equal number of reactants and products and very small entropy energy. Reaction number 7 has the number of products less than the reactants and hence negative entropy energy. The sign of the entropy energy affects the value of Gibbs free energy and the final rate of reaction.
Finally, Fig. 5 summarizes the reactions that take place when NO 2 gas reacts with C 24 O 6 /Sn 10 O 16 cluster hybrid. The first reaction is the dissociation of NO 2 gas to NO and O 2 gases (the upper arrow in Fig. 5). This reaction can take place even before NO 2 reaches the surface of the C 24 O 6 / Sn 10 O 16 cluster, in which the hybrid can be considered a catalyst for the dissociation reaction. Due to this reaction, the concentration of NO 2 decreases as it approaches the C 24 O 6 /Sn 10 O 16 surface (the arrow on the left side of Fig. 5). The remaining NO 2 concentration reacts with both rGO and SnO 2 parts of the rGO/SnO 2 hybrid. At room temperature, the interaction with both rGO and SnO 2 does not change the concentration of NO 2 appreciably. The interaction of NO 2 with rGO takes place only one time, after which the oxygen atom attached to rGO will not be able to escape due to the high Gibbs energy of separation as in reaction number 9 in Table 2. This causes the resistance of the SnO 2 /rGO sensor to increase even after stopping NO 2 gas from flowing. This does not happen for the oxygen connected to the SnO 2 cluster due to negative Gibbs energy of separation of oxygen from SnO 2 as in reaction number 8 in Table 2. The ability of NO 2 gas to oxidize the rGO/SnO 2 hybrid can make it easily distinguished from other gases that mainly reduce oxygen from the sensor, such as NH 3 , CO, acetone, ethanol, methanol gases [8,41].
The sensitivity of the rGO/SnO 2 hybrid increases as we increase the temperature until the temperature reaches between room temperature to 150 °C after which it drops depending on the method of manufacturing and concentration of NO 2 [8,45,46]. However, examining Eqs. (5) and (8), we can see that the reaction rate should increase with temperature. The reason for the drop in sensitivity in high temperatures is that the concentration of NO 2 decreases rapidly in high temperatures due to dissociation before reaching rGO/SnO 2 hybrid surface, as we discussed in Fig. 5.

Conclusions
The interaction of NO 2 gas with rGO/SnO 2 hybrid is analyzed using the DFT method and compared with available experimental findings. The calculated energy gaps and XPS levels are in good agreement with the experiment. DFT calculations show that SnO 2 and rGO are connected by their edges due to the high reactivity of rGO edges with respect to their surface. The energy gap of the rGO/SnO 2 hybrid is in between that of SnO 2 and rGO due to the reaction between them. The present results also show that the sensitivity of the rGO/SnO 2 hybrid to NO 2 is mostly due to SnO 2 interaction with NO 2 gas. The effect of rGO is to distribute SnO 2 nanoparticles evenly on rGO edges and to reduce the agglomeration of SnO 2 . The sensitivity of the rGO/SnO 2 hybrid to NO 2 increases with temperature until the NO 2 dissociation in the air reduces the concentration of NO 2 reaching the surface of rGO/SnO 2 appreciably and decreases the sensitivity. The results are in good agreement with previous experimental findings, including energy gaps and XPS values.