The Adsorption of H₂ and C₂H₂ on Ge-Doped and Cr-Doped Graphene Structures: A DFT Study

Abstract

In order to find an excellent sensing material for dissolved gases in transformer oil, the adsorption structures of intrinsic graphene (IG), Ge-doped graphene (GeG), and Cr-doped graphene (CrG) to H₂ and C₂H₂ gas molecules were built. It was found that the doping site right above C atom (T) was the most stable structure by studying three potential doping positions of the Ge and Cr atom on the graphene surface. Then, the structural parameters, density of states, and difference state density of these adsorption systems were calculated and analyzed based on the density functional calculations. The results show that the adsorption properties of GeG and CrG systems for H₂ and C₂H₂ are obviously better than the IG system. Furthermore, by comparing the two doping systems, CrG system exhibits more outstanding adsorption performances to H₂ and C₂H₂, especially for C₂H₂ gas. Finally, the highest adsorption energy (−1.436 eV) and the shortest adsorption distance (1.981 Å) indicate that Cr-doped graphene is promising in the field of C₂H₂ gas-sensing detection.

1. Introduction

As one of the main pillars of the current economy, electric energy is gradually accelerating the pace of its intelligent construction, and the scale is also expanding. The oil-immersed transformer, as the key hub of a power system, undertakes the task of power transmission and transformation of the whole power grid, and its operation condition will directly affect the safety of the power network and users [1,2,3,4]. However, insulation faults like partial discharge and partial overheating inevitably exist during oil-immersed transformer long running process [5,6,7,8]. These internal faults can cause the generation of various fault characteristic gases, such as H₂ [9], CH₄ [10], C₂H₂ [11], etc. Therefore, detecting typical dissolved gases have great importance to guarantee the normal operation of a power transformer [12,13,14].

With the discovery of two-dimensional materials, graphene material has captured widespread attention for its excellent performances and considerable applications [15,16,17]. Nevertheless, there is the weak adsorption capacity of the intrinsic graphene to gas molecules, which limits its application in gas-sensing respects [18,19,20,21]. To address this issue, researchers have built new graphene substrates via doping different atoms, such as Pt [22], In [23], Co [24], etc., in which metal atoms with a highly active doped-on graphene surface greatly improves its adsorption properties [25,26]. For instance, Shukri et al. researched the interaction mechanism of NO and CO on Pd-decorated graphene via first-principles study [27]. Zheng et al. analyzed the CO₂ adsorption behavior on doped (B, P, N, Al) graphene by density functional theory (DFT) calculations and indicated that metal doping can be an ideal method to enhance the performances of a graphene-based gas sensor [28]. Gao et al. discussed the structural parameters of an SO₂ molecule on intrinsic graphene and transition metal (Ni, Pd) -doped graphene, suggesting that the latter exhibits stronger adsorption [29]. Hence, metal-doped graphene might be a potential sensing material for detecting oil-dissolved gases.

Chromium (Cr) has received considerable investigation with its high electrical conductivity and excellent ductility as a transition metal (TM) atom [30]. Germanium (Ge) has some interesting electrochemical properties due to its position between metallic and nonmetallic elements [31]. Until now, the two kinds of metal atoms have been designed in different materials by investigators through various methods to achieve excellent properties in diverse fields [32,33,34]. For instance, Zhou et al. exhibited that Cr-decorated graphene could enhance gas adsorption of a formaldehyde (H₂CO) molecule in the aspect of atmospheric environment [35]. Wang et al. found that Cr doping CoFe-layered double hydroxides might improve adsorption property to water and urea molecule in an electro catalytic field [36]. Gecim et al. compared the gas-sensitive properties of methanol on Ge-doped and Ga-doped graphene and signified the more excellent adsorption performance of Ge-doped graphene in terms of methanol gas sensing [37]. However, few pieces of literature have been studied using intrinsic graphene (IG), Ge-doped graphene (GeG), and Cr-doped graphene (CrG) as gas-sensing materials for detecting gases dissolved in transformer oil. Therefore, in this study, the adsorption properties of Ge-doped and Cr-doped graphene are investigated to H₂ and C₂H₂ molecules based on density functional theory (DFT). To analyze and compare the sensing mechanism and adsorption capacity of three kinds of graphene models, their geometric structures, adsorption distances, bond lengths, adsorption energies ($E_{ads}$), charge transfers ($Q_t$), density of states (DOS), and atomic orbitals were calculated. The consequences of research provide theoretical guidance for detection of H₂ and C₂H₂ gas molecules.

2. Computation Methods

Density functional calculations between gas molecules and three graphene-based materials were carried out in Dmol3 module of Materials Studio (MS) [38,39,40]. To guarantee the reliability of calculation, the corresponding issues of exchange energy were solved by generalized gradient approximation (GGA) with the functional Perdew–Burke–Ernzerhof (PBE) [41]. In this paper, the further calculation was implemented with the double numerical plus polarization (DNP) to obtain more accurate results [42]. The periodic box conditions (PBC) were employed to describe the 2D structure on the metal-doped graphene surface, and the graphene-based lattice parameters were a = 9.84 Å, b = 9.84 Å, c = 15 Å. The DFT semi-core pseudopotential (DSPP) and the iterative subspace direct inversion (DIIS) were respectively utilized to deal with core electrons and accelerate the convergence of Self-Consistent Field (SCF) charge density [43]. Simultaneously, given the important effect of weak van der Waals interaction in gas molecules, the Grimme (DFT-D2) algorithm was used to correct the dispersion energy [44]. The values of 1 × 10⁻⁵ Ha, 2 × 10⁻³ Ha/Å, and 5 × 10⁻³ Ha were set for energy convergence accuracy, maximum displacement, and stress, respectively. The convergence accuracy of the Self-Consistent Field (SCF) and the k-points of the Brillouin zone were set to 1 × 10⁻⁶ Ha and 6 × 6 × 1. The setting of density of state (DOS) in Dmol3 calculation properties was selected to qualitatively analyze the electronic structure of the material by outputting the charts of the total density of state (TDOS) and partial density of state (PDOS). All of the above calculations were considered Spin polarization effect [45].

The adsorption energy ($E_{ads}$) of gas (H₂ and C₂H₂) on three kinds of graphene-based material is defined in Equation (1).

$$E_{ads}=E_{gas-substrate}-E_{substrate}-E_{gas}$$

(1)

In which, $E_{gas-substrate}$ presents the total energies of gas adsorbed graphene system. $E_{substrate}$ and $E_{gas}$ are the energies of the graphene-based system before gas adsorption and a single gas molecule, respectively [46]. The negative value of $E_{ads}$ shows the spontaneity of reaction and the exothermic process of gas adsorption [47]. Moreover, the change transfer $Q_t$ between the graphene system and gas molecules is defined in Equation (2)

$$Q_t=Q_a-Q_b$$

(2)

where $Q_a$ and $Q_b$ were the number of charges after adsorption carried by the gas and the net carried charge of isolated gas molecule, respectively. The positive value of $Q_t$ represents the charge transfer from gas molecules to the graphene-based system [48].

3. Results and Discussions

3.1. Structures of H₂ and C₂H₂ Molecules and IG

The models of H₂ and C₂H₂ gas molecules were firstly established, and their optimized structures are presented in Figure 1. The bond length of carbon-carbon triple and carbon-hydrogen is 1.211 Å and 1.071 Å in C₂H₂ molecule, respectively. The IG was established with a 4 × 4 × 1 (32 atoms) supercell with the vacuum slab of 20 Å to avoid layer interaction and the slab position of 10 Å to build a two-dimensional graphene monolayer. The models of GeG or CrG were constructed by different sites doping with a Ge or Cr atom. To obtain the steadiest doped structure, the three potential sites of metal-doped graphene structure are discussed, including the doping site right above C atom (T), the hollow site in the positive center of graphene lattice (H), and the bridge site at midpoint the two C atoms (B), which are shown in Figure 2. The binding energy ($E_b$) formula of metal atoms doped on intrinsic graphene is defined as follows: Equation (3) is suitable for calculating the substitution doping of C atoms on the intrinsic graphene [49], and Equation (4) is used to calculate the surface doping of intrinsic graphene [50]. In which, $E_{metal}$, $E_C$, $E_{\mathrm{graphene}}$ and $E_{metal-\mathrm{graphene}}$ are the total energies of the single metal atom, the replaced C atom, the intrinsic graphene, and graphene system after doping metal atom, respectively. Remarkably, the binding energy is only studied from the perspective of the electronic component and the above formulas are applicable to the doping of Ge and Cr metal atoms on the surface of graphene.

$$E_b=E_{metal-\mathrm{graphene}}-E_{metal}-E_{\mathrm{graphene}}+E_C$$

(3)

$$E_b=E_{metal-\mathrm{graphene}}-E_{metal}-E_{\mathrm{graphene}}$$

(4)

3.2. Ge and Cr Doping on Graphene

By comparing the detailed calculated parameters information in

Table 1. The structural parameters of Ge-doped graphene.

Site	${\mathit{d}}_{\mathit{G}\mathit{e}-\mathit{C}}\left(\AA \right)$	${\mathit{E}}_{\mathit{b}}\left(\mathbf{eV}\right)$	Mulliken Charge (e)
GT	1.865	4.725	−0.525
GH	2.119	2.301	0.135
GB	2.279	1.095	0.032

, the most stable structure for Ge-doped graphene is the T site model as shown in Figure 3. After geometry optimization, the Mulliken analysis shows that there is an obvious charge transfer ($-0.525\mathrm{e}$) in G_T doping structure, while the charge transfers in G_H and G_B doping structures are 0.135 e and 0.032 e, respectively. The C atom of graphene and the Ge atom form the C-Ge bond by the shortest length of 1.865 Å in the G_T doping structure, which is much shorter than that in G_H (2.119 Å) and G_B (2.279 Å) doping structures. Remarkably, the larger bind energy of 4.725 eV is consumable to form new Ge-C bonds, because the substitution doping of the T site destroys the internal structure of graphene.

The total density of state (TDOS) and partial density of state (PDOS) of GeG in G_T doping structure are shown in Figure 4. It can be found that the TDOS of the graphene after doping has a distinct rise amplitude near the Fermi level and the new peaks appear near −1 eV. The PDOS (Figure 4b) of each atomic orbital is investigated to further discuss the interaction between graphene and doped-Ge atom. According to the PDOS diagram, the variation of TDOS around the Fermi level is mostly caused by hybridization of C-2p and Ge-4p orbitals. Furthermore, the overlap of C-2p orbital and Ge-4p orbital is evident at −1 eV, manifesting that the doping of Ge atom may be one of the reasons for the appearance of the new peaks of TDOS here. The high peak of Ge-4p orbital around 6 eV indicates the rise of TDOS curve here is mainly contributed by it. Therefore, the Ge atom and graphene have a stable adsorption structure by doped T site.

As shown in

Table 2. The structural parameters of Cr-doped graphene.

Site	${\mathit{d}}_{\mathit{C}\mathit{r}-\mathit{C}}\left(\AA \right)$	${\mathit{E}}_{\mathit{b}}\left(\mathbf{eV}\right)$	Mulliken Charge (e)
GT	1.856	4.732	−0.252
GH	2.111	2.031	0.211
GB	2.442	1.386	0.236

, the parameters of different doping structures are different when a Cr atom approaches the surface of graphene with different sites. The Mulliken charge analyzes electron transfer between Cr and graphene in the three potential doping sites. The doping structures of G_H and G_B show that the Q_t is 0.211 e and 0.236 e, while the charge transfer value in the G_T doping structure is −0.252 e, which is higher than that of other structures. Moreover, the Cr-C bond (1.856 Å) of the G_T doping structure is shortest compared with that of G_H (2.031 Å) and G_B (1.386 Å), but the consumable bind energy (4.732 eV) of the G_T site is larger to form the new Cr-C bonds. The most stable doping configurations obtained by comparing various geometric parameters are depicted in Figure 5.

Spin-polarized total DOS for IG and CrG in G_T doping structure is depicted in Figure 6. As shown in Figure 6a, the TDOS curve of the CrG system is closer to the Fermi level. In addition, the charge density increases significantly in this area. Compared with the TDOS of IG, the eigenstates of both spin-up and spin-down contributions of the TDOS exhibit obviously different near the Fermi level in CrG system, which indicates that the doping of Cr atom changes the non-magnetism of the system. Both alpha-orbital of Cr-3d and Cr-4s orbitals have valley near the Fermi level, while only the beta-orbitals of Cr-3d has peak here, as shown in Figure 6b. Additionally, these obvious asymmetries of spin-up and spin-down densities of states of Cr-3d and Cr-4s orbitals near the Fermi level can further prove that the doping of Cr leads to the change of non-magnetism of system. Moreover, the maximum value of the valence band and the conduction band is mainly affected by Cr-3d orbital. The larger overlap parts of the C-2p orbital, Cr-3d orbital, and Cr-4s orbital are observed around the 0 eV, signifying the close interaction between Cr atom and graphene due to the strong hybridization of these orbitals.

According to the above analysis results, the most stable structures of doped graphene-based materials are doped by T sites, which are C atoms of the graphene structure substituted with Ge or Cr atoms. The metals doping has a strong effect on the electronic structural performances of graphene. Then, the adsorption effects of the three materials of graphene-based to oil-dissolved gas molecules are investigated based on the stable doped structures, especially the adsorption effects of H₂ and C₂H₂ molecules.

3.3. H₂ Adsorbed on IG, GeG, and CrG Systems

The adsorption models of H₂ on intrinsic graphene, Ge-graphene, and Cr-graphene have been established, and the structures after optimization are exhibited in Figure 7. Comparing the three adsorption models, a H₂ molecule tends to vertically close to the surface of IG and GeG systems, to form a stable adsorption structure, while H₂ molecule adsorbs parallelly on Cr atom in CrG system.

Table 3. The geometrical parameters of H₂ adsorption systems.

System	$\mathit{d}$(Å)	${\mathit{E}}_{\mathit{a}\mathit{d}\mathit{s}}\left(\mathbf{eV}\right)$	${\mathit{Q}}_{\mathit{t}}\left(\mathbf{e}\right)$	Mulliken Charge (e)
IG	H-C 3.026	−0.153	−0.012	C −0.014 H −0.006 H −0.006
GeG	Ge-H 2.908	−0.117	−0.010	Ge −0.529 H 0.005 H −0.015
CrG	Cr-H1 2.030 Cr-H2 1.973	−0.390	0.052	Cr −0.317 H 0.107 H −0.055

displays that the adsorption energy of IG, GeG, and CrG systems is −0.153 eV, −0.117 eV, −0.390 eV. The preliminary results display that the adsorption energy of CrG is larger than that of IG and GeG systems, probably because of the doped Cr atom with stronger surface activity. Besides, the adsorption parameters of H₂ molecule have small change in IG and GeG systems. Nevertheless, there are distinct variations of structural parameters in the CrG system, as the adsorption distance is obviously smaller between a H₂ molecule and graphene-based material than that in IG (3.026 Å), and the H₂-adsorbed Cr-graphene exits significant charge transfer (0.052 e). Therefore, these findings suggest that the CrG system is the steadiest adsorption structure to H₂ molecule in metal-doped graphene.

To further investigate the adsorption behavior of H₂ on IG, GeG, and CrG systems, the DOS diagrams of various systems are analyzed. According to the TDOS and PDOS of IG system displayed in Figure 8a,b, the H₂ adsorption has a small influence on the DOS curve due to less hybridization between H-1s orbital and C-2p orbital. Figure 8c,d present the TDOS and PDOS of GeG system. It is found that only the peak near −5 eV changes obviously after H₂ adsorption, while the other distribution of TDOS diagram is almost unchanged in GeG system, and the varied DOS mainly caused by the 1s orbital of H atoms. As for H₂ adsorption, the total DOS of the adsorption system does not change distinctly near the Fermi level in the IG and GeG system. Thus, the introduction of H₂ molecules has little effect on electron properties of intrinsic graphene and Ge-graphene. As the TDOS of CrG depicted in Figure 8e, the curve moves to left overall. Besides, the curve changes obviously around the Fermi level, resulting in the electron transferred easily from valence band to conduction band. Figure 8f shows the H-1s, Cr-4s, and Cr-3d orbitals have considerable overlaps around −9 eV, and H-1s orbital hybridizes slightly with Cr-4s orbital around the Fermi level, indicating that the occurrence of strong interaction between H₂ molecule and Cr-graphene mainly contributes by the hybridization of H-1s and Cr-4s orbitals, while Cr-3d orbital may be main reason for the alpha-spin and beta-spin asymmetry of TDOS. In brief, CrG system shows a stronger adsorption to a H₂ molecule than that of IG and GeG systems, because of the clearly varied DOS of CrG system during the adsorption process.

Figure 9 displays the charge density difference of the CrG system, and the getting and losing of the electron can be seen in the red and blue areas, respectively. H₂ molecule and Cr atom are surrounded by blue and red, respectively, which indicates that Cr atom obtains electrons from the H₂ molecule. This phenomenon further confirms that charges transfer from H₂ molecule to CrG, which is uniform with the results of the Q_t (0.052 e). In addition, a certain amount of interaction exists because of the continuous electron area between H atom and Cr atom.

3.4. C₂H₂ Adsorbed on IG, GeG, and CrG Systems

The adsorption structures of IG, GeG, and CrG systems to C₂H₂ in top and side views are shown in Figure 10, and

Table 4. The geometrical parameters of C₂H₂ adsorption systems.

System	$\mathit{d}$ (Å)	${\mathit{E}}_{\mathit{a}\mathit{d}\mathit{s}}\left(\mathbf{eV}\right)$	${\mathit{Q}}_{\mathit{t}}\left(\mathbf{e}\right)$	Mulliken Charge (e)
IG	H-C 2.548	−0.066	−0.008	CIG 0.024 C −0.092 C −0.092 H 0.096 H 0.096
GeG	Ge-C 2.175 Ge-C 2.208	−0.287	0.063	Ge −0.463 C −0.198 C −0.052 H 0.165 H 0.148
CrG	Cr-C1 1.990 Cr-C2 1.981	−1.436	0.079	Cr −0.317 C −0.137 C 0.018 H 0.095 H 0.103

lists the corresponding adsorption parameters of IG, GeG, and CrG systems to C₂H₂.

For C₂H₂ adsorption on the IG system, the C₂H₂ molecule is far from the graphene surface because of the weak interaction. Table 4 shows that the E_ads and Q_t of the IG system are only −0.066 eV and −0.008 e, which are far smaller than those of GeG and CrG systems. For C₂H₂ adsorption on the GeG system, the C₂H₂ molecule is distinctly deformed after the captured C atom of C₂H₂ molecule by the Ge atom, while C₂H₂ is adsorbed on the top site of the C atom by an H atom in the IG system. It is notable that the C₂H₂ molecule still exhibits a planar configuration after capturing by graphene monolayer, indicating the nonactivation of C₂H₂ molecule during the adsorption. By comparing the adsorption parameters of GeG structures in Table 4, the distance between C atoms of C₂H₂ molecule and Ge-graphene is shorter, which indicates that the C₂H₂ molecule is more likely to be absorbed on Ge-graphene surface by C atom. For C₂H₂ adsorption on Cr-graphene, a C₂H₂ molecule adsorbs on Cr atom with C-Cr bond, and the bond angle of the C₂H₂ molecule changes significantly in the adsorption process. The C-H band was a little elongated from 1.071 Å to 1.089 Å, resulting from the impact of strong adsorption of Cr-C bonds. The adsorption energy of Cr-graphene reaches −1.436 eV, the charge transfer amounts 0.079 e, and the distance is 1.981 Å. Comparing to intrinsic graphene and Ge-graphene, Cr-graphene has the best adsorption energy, largest charge transfer, and shortest distance.

In conclusion, considering the energy and structures of IG, GeG, and CrG adsorption systems, the adsorption of C₂H₂ molecule on the intrinsic graphene and Ge-graphene is relatively weaker, while Cr-graphene exhibits strong adsorption capacity owing to the huge adsorption energy (−1.436 eV). Furthermore, CrG system should be the most stable structure due to the excellent adsorption properties.

The TDOS and PDOS distributions for C₂H₂ system are displayed in Figure 11. It can be found that the two TDOS (Figure 11a) curves are overlapped near the Fermi level and the PDOS (Figure 11b) diagram of H-1s and C-2p orbitals are hardly hybridized in this area, implying the weak interaction between the C₂H₂ molecule and intrinsic graphene and the few charge transfers of adsorption. For the GeG system depicted in Figure 11c, the overall curve of the DOS is clearly closer to Fermi level after C₂H₂ molecule adsorption, suggesting the notable change of charge density and the easy transfer of electron distribution from valence to conduction band. Figure 11d displays that the overlapping peaks of H-1s, C-2p, Ge-4s, and Ge-4p orbitals appear near the Fermi level, manifesting the strong hybridization of these orbitals. Besides, the high amplitudes of C-2p orbital of C₂H₂ near −7 eV, −3 eV, and 3 eV imply that the appearance of the new peak of TDOS at these place may be caused by C₂H₂ adsorption. Figure 11e shows that the TDOS of CrG system goes from asymmetric to symmetric in the spin up and spin down channels at some energies, indicating that the C₂H₂ adsorption turns magnetic Cr-graphene into a non-magnetic system. From Figure 11f, the 2p orbital of C atom, the 3d and 4s orbitals of Cr atom have a large range of strong overlap at −2 eV to −4 eV, and the PDOS diagram of H-1s, C-2p, Cr-3d, and Cr-4s orbitals basically overlap from −7 eV to −9 eV, signifying the occurrence of strong hybridization.

By analyzing the charge density difference as shown in Figure 12, the electron transfer mechanism of GeG and CrG system is researched. Figure 12a shows the obvious contact of the electron occurrence region between the C₂H₂ molecule and Ge atom, which infers a strong interaction between them because of a certain amount of transferred electron. A direct continuous electron region is found in Figure 12b, indicating that part of electron transfers between C and H atoms. In addition, the Cr atom is surrounded distinctly by red areas, while the C atom of C₂H₂ is surrounded by blue areas. This phenomenon suggests that a mass of electrons transfer from the C₂H₂ molecule to CrG system. The findings show that a strong chemical interaction appears between C₂H₂ and CrG, and results in the appearance of a new Cr-C bond. The above conclusions are uniform with the consequences of the Mulliken analysis.

4. Conclusions

In this paper, the adsorption abilities of IG, GeG, and CrG systems towards two oil-dissolved gases (H₂ and C₂H₂) were investigated via a detailed DFT study. The most stable structure was explored by studying structural and electronic properties of various adsorption models. The adsorption energy, charge transfer, density of state, and other structural parameters have been employed to discuss the adsorption mechanism. It is found that both Ge doping and Cr doping by T site have most stable doping structure through researching three typical doping structures. By constructing and optimizing different adsorption models of gas molecules to IG, GeG, and CrG systems, H₂ closes to Ge and Cr atom through H atom, but C atom of C₂H₂ directly adsorbs above Ge and Cr atom. The adsorption energies of H₂ and C₂H₂ molecules absorbed on GeG system are −0.117 eV and −0.287 eV, and those of the CrG system are −0.390 eV and −1.436 eV, respectively. The results show that CrG system has strong adsorption abilities to H₂ and C₂H₂ molecules, while GeG system is relatively weaker. For CrG system, the charge transfer value of Cr-graphene to C₂H₂ (0.079 e) is distinctly higher than that of H₂ (0.052 e), confirming that the interaction between C₂H₂ molecule and Cr-graphene is stronger. In addition, the strong hybridization between atomic orbitals results in the more excellent adsorption performances of CrG to C₂H₂. Therefore, the Cr-graphene is expected to be an ideal gas-sensing material for detecting C₂H₂ gas.