Theoretical Study of the Adsorption and Sensing Properties of Cr-Doped SnP₃ Monolayer for Dissolved Characteristic Gases in Oil

Abstract

Dissolved gas analysis (DGA) is a vital method for the online detection of transformer operation state. The adsorption performance of a SnP₃ monolayer modified by transition metal Cr regarding six characteristic gases (CO, C₂H₄, C₂H₂, CH₄, H₂, C₂H₆) dissolved in oil was studied. The study reveals the relevant adsorption and gas-sensing response mechanisms through calculations of the adsorption energy, density of states, differential charge density, energy gap, and recovery time. The results display a considerable increase in the adsorption effect of the Cr-SnP₃ monolayer on six gases. The CO, C₂H₂, and C₂H₄ gases lead to chemical adsorption, and the CH₄, H₂, and C₂H₆ gases lead to physical adsorption. Combined with the recovery time, the Cr-SnP₃ monolayer has a strong adsorption effect on CO and C₂H₂ gases at normal temperatures and even high temperatures, and the adsorption is stable. C₂H₄ gas can be rapidly desorbed from the Cr-SnP₃ monolayer at 398 K. Therefore, the Cr-SnP₃ monolayer can be expected to serve as a CO and C₂H₂ gas adsorbent and a resistive gas sensor for C₂H₄ gas. This research offers a theoretical foundation for the development of the Cr-SnP₃ monolayer in gas-sensitive materials.

1. Introduction

The transformer is the primary component of machinery in a power system; it performs the crucial functions of power transfer, distribution, and the conversion of voltage [1]. The transformer’s regular operation is crucial to the electrical system’s security, reliable operation, and power supply. Over 90% of all transformers are oil-immersed power transformers [2]. Transformer oil is a high-alkane mixture. Under long-term operation, due to pollution, high temperatures, design defects, ageing, and other reasons, hydrocarbons in transformer oil often crack and decompose into CO, C₂H₂, C₂H_4, CH₄, C₂H₄, H₂, C₂H₆, and other gases. These gases are often dissolved in transformer oil, so they are called dissolved fault characteristic gases in transformer oil [3]. Transformer fault types are significantly correlated with the components of the dissolved gas in oil. Therefore, by means of the sensitive identification of dissolved gas components in transformer oil, the internal fault situation and development trends in the transformer can be effectively understood, and then the insulation operation state of the transformer can be scientifically evaluated, which can effectively reduce the incidence of insulation accidents [4].

Two-dimensional (2D) materials have emerged as a popular area of study in the scientific community [5]. The distinctive structural and electrical characteristics of phosphorene and black phosphorene have garnered significant interest [6]. Among them, the phosphides of IV-V compounds, such as SnP₃ [7] and GeP₃ [8], have demonstrated exceptional promise in terms of their optical and electrical qualities [9]. Research in this field provides new possibilities for exploring the potential applications of new materials. The SnP₃ monolayer, a two-dimensional substance, is a layered compound with a triangular space group [10], and has a honeycomb planar structure. Gas molecules are easily adsorbed onto SnP₃ due to its large specific surface area. SnP₃ exhibits semiconductor properties in a single-layer structure. The band gap values obtained with the PBE and HSE06 functions are 0.53 eV and 0.82 eV, respectively [11]. In addition, the SnP₃ monolayer has high carrier mobility [12], and is reportedly a promising material for small gas sensing [13]. Although the intrinsic SnP₃ monolayer has a limited adsorption capacity, its electronic properties can be improved using doping metals [14]. This helps to improve the sensitivity and sensor response of the SnP₃ monolayer [13]. Recently, Cr has attracted increasing attention as a cheap and promising metal catalyst [15]. For example, some scholars have found that 3D transition metal Cr-doped graphene can efficiently adsorb C₂H₂, and the adsorption energy can reach 1.44 eV [16]. Some experts have synthesised Cr-doped SnO₂ nanowires via vapour deposition and found that doping with 1.8% Cr (atomic fraction) can increase the oxygen gas-sensing performance of SnO₂ nanowires by 28% at 250 °C [17]. The doping adsorption of SnP₃ monolayers is less studied, particularly the gas-sensing properties after doping with noble metals [6].

Therefore, this paper proposes a modification to the doping of single-layer SnP₃ with transition metal Cr. Firstly, the most stable doping structure (Cr-SnP₃) was established. After this, various gas adsorption structures were built. Through geometric optimisation, the most stable Cr-SnP₃ monolayer structure for the absorption of the six gases was determined. Finally, the adsorption properties of Cr-SnP₃ for six gases (CO, C₂H₂, C₂H₄, CH₄, H₂, and C₂H₆) were investigated by analysing the adsorption energy, charge transfer, density of states, differential charge density, energy gap, and recovery time. This finding suggests the prospect of employing Cr-SnP₃ as an absorption material for gases in the transformer oil in gas sensors.

2. Calculation Method and Structural Model

2.1. Parameter Setting

The adsorption behaviour of six gases (CO, C₂H₂, C₂H₄, CH₄, H₂, and C₂H₆) on a Cr-SnP₃ monolayer was simulated. The establishment of all models and the calculations were completed using the DMol3 module of Materials Studio. The optimisation, energy, and related properties of the structure were computed using the PBE. The DNP was selected as the basis set function of the linear combination of atomic orbitals, and the Grimme method in DFT-D dispersion correction was used to correct the influence of the van der Waals force [18]. The gas molecules and transition metals used the all-electron model and DSPP treatments, respectively [19]. The convergence accuracy of SCF was 1.0 × 10⁻⁶, and the DIIS value was set to 6. The Smearing value was 0.005 Ha [20]. The whole system may have magnetic properties because Cr is a transition metal. Therefore, the electron spin was included in the calculation to ensure accuracy.

In this paper, we established a 3 × 3 × 1 single-layer SnP₃ supercell periodic structure which contained 54 P and 18 Sn atoms. The vacuum layer was 20Å. The optimized lattice parameters of the SnP₃ monolayer were a = b = 7.42Å, c = 10.28Å, which are almost consistent with the experimental values (a = b = 7.38Å, c = 10.51Å) [6]. The accuracy of the model was proved.

The intrinsic SnP₃ monolayer was established, and different sites were doped in the folded honeycomb repeat layer. The structure of the intrinsic SnP₃ and four cases are shown in Figure 1; the cases are T_Sn (above the Sn atom), T_P (above the P atom), H₁ (above the centre of the hexagonal ring composed of P and Sn), and H₂ (above the centre of the hexagonal ring composed of P). Finally, the energy of each system after doping was calculated.

The binding energies E_b of different dopant sites can be compared to determine the optimal doped structure, which is described by Equation (1)

$$E_b=E_{\left(Cr\text{-}Sn{P}_3\right)}-E_{\left(Sn{P}_3\right)}-E_{Cr}$$

(1)

where $E_{\left(Cr\text{-}Sn{P}_3\right)}$ is the energy of the system after the Cr doping of SnP₃; $E_{\left(Sn{P}_3\right)}$ and $E_{Cr}$ are the energies of intrinsic SnP₃ and Cr atoms, respectively.

The adsorption energy E_ads was applied to assess the stability of the adsorption system, which is defined by Equation (2)

$$E_{ads}=E_{\left(\mathrm{g}\mathrm{a}\mathrm{s}/\mathrm{C}\mathrm{r}\text{-}\mathrm{S}\mathrm{n}{P}_3\right)}-E_{\left(Cr\text{-}Sn{P}_3\right)}-E_{gas}$$

(2)

where $E_{\left(\mathrm{g}\mathrm{a}\mathrm{s}/\mathrm{C}\mathrm{r}\text{-}\mathrm{S}\mathrm{n}{P}_3\right)}$ is the energy of gas/Cr-SnP₃; $E_{gas}$ is the energy of the gas molecules.

The charge transfer Q_t between the gas molecules and Cr-SnP₃ material is calculated by Equation (3)

$$Q_t=Q_a-Q_b$$

(3)

where Q_a and Q_b denote the net charge of the gas molecules after and before adsorption [21].

2.2. Dissolved Characteristic Gas in Oil

The optimized structure models of dissolved characteristic gases (CO, C₂H₄, C₂H₂, CH₄, H₂, and C₂H₆) in oil are shown in Figure 2.

2.3. Optimised Structural Model of Cr-SnP₃

The four structural parameters of Cr-doped SnP₃ are shown in

Table 1. Structural parameters and η of four doping systems.

System	Eb (eV)	Qt (e)	η (eV)
TP	−3.123	0.087	0.0199
TSn	−4.600	0.210	0.1752
HpSn	−3.653	0.101	0.1414
HP	−4.143	0.151	0.1541

. Through a comparison of the absolute values of binding energy, T_Sn was determined to be the best doping site.

Chemical hardness (η) is an indicator of chemical stability. A higher chemical hardness indicates that the stability of the system is improved [22]. The η is calculated using Equation (4).

$$\eta =(E_{HOMO}-E_{LUMO})/2$$

(4)

The chemical hardness of the four doping sites is shown in Table 1. T_sn corresponds to the maximum chemical hardness, indicating that the system is the most stable. This is consistent with the E_b analysis. The optimal structural model of Cr-SnP₃ is shown in Figure 3.

2.4. The Density of States of the Cr-SnP₃ Monolayer

In order to illustrate the difference in the electronic structure of the SnP₃ crystal plane before and after Cr doping, the density of states (DOS) curves were analysed, as depicted in Figure 4.

The dotted line at 0 eV in Figure 4a represents the Fermi level. The total density of states (TDOS) of Cr-SnP₃ follows a lower-energy path to the left, the shape changes slightly, and the valence band is filled with more electrons. However, the peak value of the TDOS before and after doping is similar, and the overall density of states is still composed of three parts—the conduction band and upper and lower valence bands—which is similar to the density of states of the intrinsic SnP₃. This demonstrates that the crystal energy of SnP₃ is altered by the addition of Cr atoms, but the crystal structure does not change.

The local density of states of Cr-SnP₃ in Figure 4b shows that S-3P, Cr-3d, and Sn-5p have obvious overlapping peaks at −15~5 eV, which suggests that the orbitals are strongly hybridising. As a result, it may be deduced that the Cr atom and SnP₃ can form a stable doping structure.

3. Analysis of Adsorption Results

3.1. Investigation of the Adsorption Properties of Cr-SnP₃ on CO, C₂H₄, C₂H₂, CH₄, H₂, and C₂H₆

Since the gas molecules are placed on the Cr-SnP₃ monolayer in different ways, the article established a variety of gas-monolayer adsorption systems and optimized the different positions so as to obtain the lowest energy-adsorption system. It was finally determined that the most stable adsorption configurations are achieved when gas molecules are adsorbed above the Cr atom. The optimal adsorption models of intrinsic SnP₃ and Cr-SnP₃ for six gases are shown in Figure 5 and Figure 6, respectively. The adsorption parameters are listed in

Table 2. Adsorption parameters of CO, C₂H₄, C₂H₂, CH₄, H₂, and C₂H₆ on SnP₃ and Cr-SnP₃.

System	Eads (eV)	Qt (e)	d (Å)
CO/SnP3	−0.335	0.009	2.849
C2H4/SnP3	−0.584	0.016	3.008
C2H2/SnP3	−1.616	−0.200	2.123
CH4/SnP3	−0.347	−0.020	3.310
H2/SnP3	−0.200	0.0007	2.500
C2H6/SnP3	−0.679	0.005	3.325
CO/Cr-SnP3	−1.643	0.185	1.939 (C-Cr)
C2H4/Cr-SnP3	−1.156	0.141	2.070 (C-Cr)
C2H2/Cr-SnP3	−2.129	0.173	1.896 (C-Cr)
CH4/Cr-SnP3	−0.508	0.106	2.465 (C-Cr)
H2/Cr-SnP3	−0.452	0.093	1.916 (H-Cr)
C2H6/Cr-SnP3	−0.708	0.117	2.254 (C-Cr)

.

In Table 2, the adsorption energy of the six gases is negative, which shows that the adsorption behaviour is a spontaneous exothermic reaction. The E_ads of intrinsic SnP₃ to CO, C₂H₄, CH₄, H₂, and C₂H₆ is relatively small, the charge transfer amount is very weak, and the adsorption distance is far. It is impossible for the five gases to be stably adsorbed on the surface of intrinsic SnP₃. After the modification of SnP₃ by Cr metal, the adsorption parameters increased significantly, and the overall adsorption effect was ideal. The adsorption energies of CO, C₂H₄, and C₂H₂ on Cr-SnP₃ were −1.643, −1.156, and −2.129 eV, respectively, and the corresponding adsorption distances were 1.939, 2.070, and 1.896 Å, respectively. The H-C-C bond angle in C₂H₂ changed from 180° to 142.09°, and the C₂H₄’s H-C-C bond was slightly inclined upward during the surface reaction. It was preliminarily judged that the adsorption of CO, C₂H₄, and C₂H₂ molecules by the Cr-SnP₃ monolayer belonged to chemical adsorption. Generally speaking, the absolute value of the adsorption energy above 0.8 eV was for chemical adsorption. The adsorption energy of CH₄, H₂, and C₂H₆ gases did not reach −0.8 eV, and the adsorption distance was far, with no significant change observed in the bond lengths. Therefore, the three gases’ adsorptions were likely to be physical adsorption.

3.2. Density of State

In this paper, the total density of states (TDOS) and partial density of states (PDOS) of six gas-adsorption systems were studied, as shown in Figure 7.

Figure 7(a1,b1,c1) shows that the TDOS curves slightly shifted to the right after the adsorption of CO, C₂H₄, and C₂H₂ gases by Cr-SnP₃. The PDOS of the three gases shows that this was due to the introduction of gas molecules and that the main contribution was from the C-2P orbitals. The C-2S, C-2P, Cr-3d, and Cr-4S orbitals formed a wide range of orbital overlaps at multiple energy levels in the −15 eV~5 eV interval with multiple overlapping peaks, indicating the existence of interatomic orbital hybridization. This confirms that the interaction between the two is chemical adsorption.

Figure 7d,e shows the curves of the CH₄ and H₂ adsorption systems, respectively. The TDOS curves of Cr-SnP₃ before and after the adsorption of gas almost completely overlap, and the peak value does not change significantly. By observing Figure 7(d2,e2) PDOS, it can be seen that there is only a very small, almost no, overlap of orbital regions. The orbital hybridization effect is very weak, which further indicates that CH₄ and H2 are only physically adsorbed on the surface of Cr-SnP₃.

In Figure 7(f1,f2), the TDOS curves of C₂H₆/Cr-SnP₃ are generally shifted to the right due to the weak orbital hybridization between C and Cr atoms, which leads to a small overlap of PDOS peaks in the range of −15 to −5 eV, but this weak orbital interaction is not sufficient to cause significant charge transfer or significant state changes.

3.3. Differential Charge Density Analysis

The differential charge density of the CO, C₂H₄, C₂H₂, CH₄, H₂, and C₂H₆ gas molecule adsorption models (red represents electron aggregation; blue represents electron depletion) are shown in Figure 8. The colour map ranges from −0.05 to 0.05 e/Å. This suggests that during the adsorption process, electrons are moved from the gas molecules to the Cr-SnP3 monolayer. In Figure 8a–c, the red electron concentration region of Cr atoms is almost directly connected to the blue electron depletion region of the gas molecules, which demonstrates that the electron exchange between gas molecules and the Cr-SnP₃ monolayer is very close, and the Q_t of the three gases is considerable. Therefore, the interaction between CO, C₂H₂, C₂H₄, and Cr-SnP₃ monolayers is chemical adsorption. The charge transfer of CH₄, H₂, and C₂H₆ in Figure 8d–f is relatively small, so it can be assumed that the interactions between them are dominated by van der Waals forces. Differential charge density analysis verified the adsorption of the Cr-SnP₃ monolayer on six gas molecules (CO, C₂H₄, C₂H₂, CH₄, H₂, and C₂H₆) from the side.

3.4. HOMO-LUMO Energy Gaps

The HOMO, LUMO, and E_g of the intrinsic Cr-SnP₃ and the gas/Cr-SnP₃ system are shown in Figure 9. The energy gap (E_g) can be used to analyse the conductivity of the system [23]. For the resistive gas sensor, the change in conductivity (σ) is an important standard to evaluate the applicability of the sensor when detecting gas [24].

It can be seen from Figure 9 that the energy gap of the C₂H₂ adsorption system almost did not change much, but the energy gap in the CO, C₂H₄, CH₄, H₂, and C₂H₆ adsorption systems decreased significantly, and the reduction ranges were 54.8%, 53.7%, 30%, 43.7%, and 10%, respectively. The E_g of the system decreases after adsorption, suggesting that the system’s conductivity is growing. As the Cr-SnP₃ monolayer has a poor adsorption effect on CH₄, H₂, and C₂H₆, the Cr-SnP₃ monolayer may be employed as a gas-sensitive sensor material for detecting CO and C₂H₄.

3.5. Recovery Time

Recovery time is an important metric that has to be considered in practical gas sensor requirements, as a too-small or too-large recovery time is not ideal for gas sensors [25]. A longer recovery time will make the sensor more difficult to remove [26]. The recovery time τ and the adsorption energy E_ads can be related, and can be calculated by Equation (5).

$$\tau =A^{-1}{e}^{{\displaystyle \frac{{-E}_B}{K_{B}T}}}$$

(5)

where A is the attempt frequency (10¹² s⁻¹); E_B is equal in magnitude to the adsorption energy [25]; K_B is the Boltzmann constant (8.62 × 10⁻⁵ eVK⁻¹); T is the Kelvin temperature.

In this paper, the recovery time of 298 K, 348 K, 398 K, and 448 K at four different temperatures was calculated. The recovery time of six gases is shown in

Table 3. Recovery time of six gases at different temperatures.

Gas	Recovery Time/s
	298 K	348 K	398 K	448 K
CO	5.99 × 1015	5.54 × 1011	5.76 × 108	2.78 × 106
C2H4	3.50 × 107	6.22 × 104	4.96 × 102	11.12
C2H2	1.03 × 1024	6.88 × 1018	9.19 × 1014	9.01 × 1011
CH4	3.87 × 10−4	2.69 × 10−5	2.38 × 10−6	5.44 × 10−7
H2	4.06 × 10−5	3.27 × 10−6	4.97 × 10−7	1.15 × 10−7
C2H6	6.83 × 10−1	1.41 × 10−2	5.59 × 10−4	7.45 × 10−5

. It can be seen that CH₄, H₂, and C₂H₆ have a short recovery time due to their low adsorption energy. The recovery rate is extremely fast in the temperature range of 298 K~448 K, which takes less than 1s. It is verified from the side that the adsorption of CH₄, H₂, and C₂H₆ on the surface of Cr-SnP₃ is extremely unstable. The Cr-SnP₃ monolayer is not appropriate for detecting these three gases, and it is also impossible to achieve the effective removal of these three gases.

Since CH₄, H₂, and C₂H₆ molecules have been repeatedly confirmed to have no good adsorption characteristics on the Cr-SnP₃ monolayer, only the recovery times of CO, C₂H₄, and C₂H₂ are presented. A recovery time histogram of the three gases is shown in Figure 10. Combined with the chart analysis, it was determined that the recovery time of CO and C₂H₂ gases was very long in the temperature range of 298 K~448 K. In the normal temperature environment, the recovery time was as long as several decades, which demonstrates that CO and C₂H₂ may be adsorbed by the Cr-SnP₃ monolayer with excellent effectiveness. Nevertheless, for C₂H₄ gas, the recovery time decreases to 496 s at 398 K and 11.12 s at 448 K, which indicates that the recovery time of the C₂H₄ gas is ideal, so Cr-SnP₃ can be quickly recycled. The conductivity changes greatly, which meets the requirements of actual gas sensors. However, the temperature should not be too high; otherwise, the recovery time is too short to detect C₂H₄. Following a comprehensive analysis, the Cr-SnP₃ monolayer can be considered as an adsorbent for CO and C₂H₂ gases, and it can be used as a resistive gas sensor for C₂H₄ at about 398 K.

3.6. Comparison of Intrinsic and Doped SnP₃ Monolayers for the Adsorption of Dissolved Gases in Six Oils

To further explore the possibility of using SnP₃ monolayers as a gas-sensitive sensor material for application in the power industry, the absolute values of the adsorption energy of SnP₃, Pd-SnP₃ [20], and Cr-SnP₃ monolayers on the six gases are compared. The comparison results are shown in Figure 11. Intrinsic SnP₃ has large adsorption energy only for C₂H₂ and adsorption energy is poor for other gases. The addition of Pd or Cr resulted in a significant increase in the adsorption of six gases, especially CO, C₂H₄, and C₂H₂. It can be observed from the figure that Cr-SnP₃ is better adsorbed compared to Pd-SnP₃. Not only does the Cr-SnP₃ exhibit a stable adsorption capacity for CO and C₂H₂, it has both an adsorption effect and an excellent recovery time for C₂H₄.

Cr and Pd are both transition metals, but Cr is more widely used and has a higher output, making it more readily available. The metal Cr has a significant cost advantage. Therefore, the addition of Cr is an effective means for SnP₃ to adsorb and detect gases.

4. Conclusions

This work offers a comprehensive investigation of the adsorption process of six gases (CO, C₂H_4, C₂H₂, CH₄, H₂, and C₂H₆) on the Cr-SnP₃ monolayer. The conclusions are as follows:

(1)

Compared with the intrinsic SnP₃ monolayer, the adsorption effect of a Cr-SnP₃ monolayer on six dissolved gases (CO, C₂H₄, C₂H₂, CH₄, H₂, and C₂H₆) in oil was significantly enhanced. The growth rates of the adsorption energy were 390.4%, 97.9%, 31.7%, 46.3%, 126.1%, and 4.2%, respectively.

(2)

The adsorption energies of CO, C₂H₄, C₂H₂, CH₄, H₂, and C₂H₆ on the Cr-SnP₃ monolayer are −1.643, −1.156, −2.129, −0.508, −0.452, and −0.708 eV, respectively. The adsorption strengths were C₂H₂ > CO > C₂H₄ > C₂H₆ > CH₄ > H₂. The gas molecules of C₂H₂, CO, and C₂H₄ undergo chemical adsorption, and the gas molecules of C₂H₆, CH₄, and H₂ undergo physical adsorption.

(3)

Considering the energy gap and recovery time, the Cr-SnP₃ monolayer can be considered a high-performance adsorbent for CO and C₂H₂ gases and a resistive gas sensor for C₂H₄.

In conclusion, SnP₃ is a promising gas-sensitive and adsorbent material. We hope that this paper will strongly promote the gas-sensing application of the Cr-SnP₃ and contribute to state-monitoring technology for oil-immersed power equipment in the future. This paper mainly focused on a theoretical study of the ideal case. We will be committed to improving this theoretical research with experimental data in the future.