1.. Introduction {#s1}
================

Nowadays, electrical equipment using SF~6~ as the insulation medium occupies a dominant position in the field of medium-voltage (MV) and high-voltage (HV) application. About 80% of the SF~6~ gas produced worldwide is used in HV circuit breakers (GCB) and in gas-insulated switchgear \[[@RSOS181104C1]\]. However, the atmospheric lifetime of SF~6~ is up to 3200 years and its global warming potential (GWP) is 23 500 times than that of CO~2~. Over the past 5 years, the global atmospheric content of SF~6~ has increased by 20% and its atmospheric mole fraction reaches to 7.28 ppq (part(s) per quadrillion) currently corresponding to a radiative forcing of 0.0041 W m^−2^ \[[@RSOS181104C2],[@RSOS181104C3]\]. In addition, SF~4~, SO~2~F~2~, SO~2~, SOF~2~ and other products produced by the decomposition of SF~6~ under long-term operating conditions are toxic substances, which pose a threat to equipment maintenance personnel \[[@RSOS181104C4]\]. With the increasing demand in environmental protection around the world, the carbon emission of power industry has also been strictly limited. Therefore, it is urgent to seek for an environmentally friendly gas as insulation medium for power industry.

At present, scholars have made some achievements on environmentally friendly insulation medium such as perfluorocarbons (PFCs), trifluoroiodomethane (CF~3~I), fluoroketones (FKs), fluoronitriles and their gas mixture \[[@RSOS181104C5]--[@RSOS181104C8]\]. Among them, CF~3~I is a moderately toxic gas and can precipitate iodine element after discharges. Particulate iodine may cause corrosion to the equipment to a certain extent, which limits the application of CF~3~I \[[@RSOS181104C9],[@RSOS181104C10]\]. FKs have a crude formula of the form C*~n~*F~2*n*~O. C~5~F~10~O and C~6~F~10~O are the two main FKs with the liquefaction temperatures of 26.9°C and 49°C under normal pressure and thus need to be used with other gases with lower liquefaction temperature \[[@RSOS181104C11]\]. Fluoronitriles contain CN group in their molecular structure and may produce toxic substances. PFCs mainly include c-C~4~F~8~, C~3~F~8~, C~2~F~6~ and CF~4~. The insulation performance of c-C~4~F~8~ reaches 1.1 times than that of SF~6~, and its GWP value is 8700 \[[@RSOS181104C12]\]. Many scholars have carried out experimental and theoretical research on c-C~4~F~8~ and its gas mixture. It was found that the insulation performance of c-C~4~F~8~/N~2~, c-C~4~F~8~/CO~2~ and c-C~4~F~8~/CF~4~ gas mixture is great, indicating that c-C~4~F~8~ gas mixture has immense potential for use in MV equipment \[[@RSOS181104C12]--[@RSOS181104C14]\].

The internal insulation of the electrical equipment is ageing under normal operating conditions. And it is inevitable to produce a variety of insulation defects, leading to partial discharge (PD) or flashover and decomposition of insulating medium. Thus, the evaluation of the decomposition characteristics of gas-insulated medium is of great significance. Several achievements have been made in the research on the decomposition characteristics of c-C~4~F~8~ under a discharge and local overheating faults. *Li et al*. tested the decomposition products of c-C~4~F~8~/N~2~ gas mixture under PD, spark discharge and arc discharge. They found that CF~4~, C~2~F~6~, C~2~F~4~, C~3~F~8~ and C~3~F~6~ are the main decomposition products \[[@RSOS181104C15]\]. Hayashi *et al.* explored the reaction mechanism of CF~2~ particles produced by c-C~4~F~8~ based on density functional theory (DFT) and revealed the dissociation properties of c-C~4~F~8~ molecules comprehensively \[[@RSOS181104C16]\]. Cobos *et al*. investigated the thermal decomposition characteristics of c-C~4~F~8~ at 1150--2300 K. It is found the decomposition of c-C~4~F~8~ firstly produces two C~2~F~4~ molecules, and C~2~F~4~ can further dissociate producing CF~2~ particles \[[@RSOS181104C17]\].

In this paper, the decomposition mechanism of c-C~4~F~8~ and c-C~4~F~8~/N~2~ gas mixture was investigated by the combination of reactive molecular dynamics method and DFT. We built the c-C~4~F~8~ and c-C~4~F~8~/N~2~ models to explore the decomposition process of c-C~4~F~8~ gas mixture under different temperatures. The yield of the main decomposition products, the reaction pathways and enthalpy under different temperatures were also obtained. Relevant results provide guidance for engineering application of c-C~4~F~8~/N~2~ gas mixture.

2.. Methods {#s2}
===========

The development of reactive molecular dynamics method provides an effective way to study the physical and chemical properties of large-scale system (millions of atoms). Reactive force field (ReaxFF) describes bond cleavage and formation based on the bond level, which originates from the distance between two atoms. ReaxFF has been widely used in the field of pyrolysis, combustion and catalysis \[[@RSOS181104C18]--[@RSOS181104C22]\]. The terms of total energy in ReaxFF can be described as the following equation \[[@RSOS181104C23]\]:$$E_{system} = E_{bond} + E_{over} + E_{under} + E_{val} + E_{pen} + E_{tors} + E_{conj} + E_{vdWaals} + E_{Coulomb},$$where *E*~bond~ denotes the bond energy; *E*~over~ and *E*~under~ correspond to the over and under coordinated atom in the energy contribution, respectively; and *E*~val~, *E*~pen~, *E*~tors~, *E*~conj~, *E*~vdwaals~ and *E*~Coulomb~ represent the valence angle term, penalty energy, torsion energy, conjugation effects to energy, non-bonded van der Waals interaction and Coulomb interaction, respectively.

In order to explore the decomposition mechanism of c-C~4~F~8~ and c-C~4~F~8~/N~2~ gas mixture, two periodic cubic models were built (as shown in [figure 1](#RSOS181104F1){ref-type="fig"}). It is reported that the highest allowable pressure of 20%c-C~4~F~8~/80% N~2~ gas mixture at −20°C and −30°C is about 0.35 and 0.2 MPa, respectively \[[@RSOS181104C24]\]. And most MV equipment working at 0.15--0.3 MPa. In order to explore the decomposition mechanism of c-C~4~F~8~/N~2~ mixture at this scale, we built models with 20% c-C~4~F~8~ and 80% N~2~. The width of the c-C~4~F~8~ system is 155 Å, which contains 100 c-C~4~F~8~ molecules with the density about 0.008918 g cm^−3^. The width of c-C~4~F~8~/N~2~ system is 265 Å, which contains 100 c-C~4~F~8~ molecules and 400 N~2~ molecules with the density about 0.00274 g cm^−3^. The above parameters correspond to the actual density of the gas mixture at 0.1 MPa, 25°C. Figure 1.Representative snapshots of c-C~4~F~8~ and c-C~4~F~8~/N~2~ system (light blue for F atom, grey for C atom and dark blue for N atom).

The system was minimized for 5 ps at 5 K using the NVE (keep the number of atoms, volume and potential energy constant) ensemble and then equilibrated with the NVT (keep the number of atoms, volume and temperature constant) ensemble for 10 ps at 1000 K using a time step of 0.1 fs \[[@RSOS181104C22]\]. Then the NVT (keep the number of atoms, volume and temperature constant) molecule dynamics simulations were performed at different temperatures for 1000 ps with the time step of 0.1 fs. The Berendsen thermostat method with a 0.1 ps damping constant was used to control the temperature \[[@RSOS181104C25]\]. All the ReaxFF-MD simulations were carried out using the Amsterdam density functional package, and the force field file is given in the data availability section \[[@RSOS181104C26]\].

In addition, quantum chemistry DFT calculation was performed to obtain the reaction enthalpy of the main decomposition paths at different temperatures \[[@RSOS181104C27]\]. The geometry optimization of the reactants and products for each path is performed using the double numerical atomic orbital augmented by d-polarization (DNP) as the basis set. The exchange--correlation energy is described using the meta-generalized approximation (mGGA-M06 L) function \[[@RSOS181104C28]\]. Geometry optimizations of all the particles were performed using the convergence threshold of 1.0 × 10^−5^ Ha on energy, 0.005 Å on displacement and 0.002 Ha Å^−1^ on gradients. We also did zero-point energy (ZPE) correction and enthalpy correction based on the frequency analysis to obtain more accurate results. All the DFT calculations in this paper were conducted using DMol^3^ package of the Materials studio.

3.. Results and discussion {#s3}
==========================

3.1.. Decomposition rate of c-C~4~F~8~ and c-C~4~F~8~/N~2~ gas mixture {#s3a}
----------------------------------------------------------------------

Local overheating, PD and arc discharge are the common failures in electrical equipment \[[@RSOS181104C29]\]. PD and arc discharge are mostly caused by insulation defects in the devices. And the temperature in the central region of the PD and arc discharge is about 1000 K and 3000--12 000 K, respectively \[[@RSOS181104C30],[@RSOS181104C31]\]. High temperature will lead to the decomposition of insulating medium, producing various free radicals or decomposition products. The generation of decomposition products may affect the insulation performance of the gas-insulated medium and cause threat to the equipment. In this paper, we carried out the reactive molecular dynamics simulations of c-C~4~F~8~ and c-C~4~F~8~/N~2~ system at different temperature conditions to explore its decomposition mechanism.

Figures [2](#RSOS181104F2){ref-type="fig"} and [3](#RSOS181104F3){ref-type="fig"} describe time evolution of c-C~4~F~8~ decomposition in pure c-C~4~F~8~ and c-C~4~F~8~/N~2~ systems and the maximum number of decomposed c-C~4~F~8~ at 2600--3400 K, respectively. It should be noted that in order to allow chemical reactions to be observed on the computational affordable time scale, we enhanced the temperatures to accelerate the simulation process. We have tested and found that c-C~4~F~8~ and c-C~4~F~8~/N~2~ mixture begin to decompose largely at 2600 K ([figure 2](#RSOS181104F2){ref-type="fig"}). The decomposition rate of c-C~4~F~8~ shows an increasing trend with the increase of temperature. The decomposition rate of c-C~4~F~8~ in the pure c-C~4~F~8~ system is significantly accelerated above 3000 K. The final decomposition amount and the decomposition rate of c-C~4~F~8~ in c-C~4~F~8~/N~2~ system are lower than that of pure c-C~4~F~8~ system at the same temperature, which indicates that the decomposition characteristics of c-C~4~F~8~/N~2~ gas mixture is great. For example, only 49 c-C~4~F~8~ decomposed in c-C~4~F~8~/N~2~ system at 3400 K, whereas 59 c-C~4~F~8~ molecules decomposed in c-C~4~F~8~ system under the same condition. In addition, the density of c-C~4~F~8~ system (0.008918 g cm^−3^) is higher than that of c-C~4~F~8~/N~2~ system (0.00274 g cm^−3^). Thus the molecules of c-C~4~F~8~ in the unit volume increase, resulting in the increase of the effective collision number and the intensity of reactions. And the decomposition amount of c-C~4~F~8~ in the c-C~4~F~8~ system is higher than that of c-C~4~F~8~/N~2~ system at the same temperature. Figure 2.Time evolution of c-C~4~F~8~ decomposition at 2600--3400 K. Figure 3.Maximum number of decomposed c-C~4~F~8~ at 2600--3400 K.

[Figure 4](#RSOS181104F4){ref-type="fig"} shows time evolution of potential energy at 2400--3400 K in c-C~4~F~8~ and c-C~4~F~8~/N~2~ system. It can be seen that the potential energy shows an increasing trend in the whole simulation process, indicating that the decomposition process of c-C~4~F~8~ and c-C~4~F~8~/N~2~ gas mixture is endothermic. The total potential energy and its growth rate increases with the increase of temperature. The potential energy of c-C~4~F~8~ system has no obvious change when the ambient temperature is at 2600 K, which is due to the insufficient occurrence of various reactions at this temperature. When the ambient temperature reaches above 3200 K, the potential energy of the system increases rapidly in the time range of 0--400 ps, and exhibits a saturated growth trend after 400 ps. This means the decomposition of c-C~4~F~8~ is concentrated at 0--400 ps. The time evolution of potential energy in c-C~4~F~8~/N~2~ system is basically the same as that of c-C~4~F~8~ system. Figure 4.Time evolution of potential energy at 2400--3400 K in c-C~4~F~8~ system and c-C~4~F~8~/N~2~ system.

On the whole, the decomposition performance of c-C~4~F~8~/N~2~ mixture is better than that of pure c-C~4~F~8~ at the same temperature, which is suitable to use as a gas-insulated medium in the field of MV equipment.

3.2.. Distribution of decomposition products {#s3b}
--------------------------------------------

The distribution of the main decomposition products in the c-C~4~F~8~ and c-C~4~F~8~/N~2~ system is shown in [figure 5](#RSOS181104F5){ref-type="fig"}. It can be found that decomposition of c-C~4~F~8~ mainly produces CF~2~, CF~3~, CF, F, C, C~2~F~4~ and CF~4~. Figure 5.(*a--g*) Time evolution of c-C~4~F~8~ decomposition products at 2600--3400 K.

For the c-C~4~F~8~ system, the yields of CF, F and C show a linear increase trend with the increase of temperature. The two groups of free radicals, CF~2~ and CF~3~ show a saturated growth trend at temperatures below 3200 K. When the temperature is higher than 3200 K, the yield of CF~2~ decreased in the range of 400--1000 ps and the yield of CF~3~ decreased in the range of 600--1000 ps, which is relative to the re-decomposition of CF~2~ and CF~3~ particles at high temperature. The yield of CF~4~ increased significantly at temperatures above 3200 K. The generation of CF~4~ requires the participation of CF~3~, thus the decrease of CF~3~ content is related to the formation of CF~4~. The yield of C~2~F~4~ reached its peak at the beginning of the simulation at 3200 and 3400 K, and then began to decrease. In addition, C atoms are also found during the simulation. It should be noted that particulate carbon is detrimental to the insulation properties of the system.

The yields of the main decomposition particles in the c-C~4~F~8~/N~2~ system are lower than that of pure c-C~4~F~8~ system at the same temperature. The content of CF~2~ shows a saturated growth trend when the temperature is above 3200 K. The generation of CF~3~ begins at 3000 K and its content is relatively low. The time evolution of CF and F radicals is similar to that of c-C~4~F~8~ system. In addition, the yields of C~2~F~4~ and C are much lower than those of pure c-C~4~F~8~ system at the same temperature.

The maximum number of produced decomposition products of c-C~4~F~8~ and c-C~4~F~8~/N~2~ system is shown in figures [6](#RSOS181104F6){ref-type="fig"} and [7](#RSOS181104F7){ref-type="fig"}, respectively. It can be found that the content of F in the C~4~F~8~ system is the highest among all the decomposition products, followed by CF~2~, CF and C. The content of F and CF~2~ is the highest in the c-C~4~F~8~/N~2~ system and the content of CF~3~ is relatively low among all the decomposition products. Figure 6.Maximum number of produced decomposition products of c-C~4~F~8~ at 2600--3400 K (c-C~4~F~8~ system). Figure 7.Maximum number of produced decomposition products of c-C~4~F~8~ at 2600--3400 K (c-C~4~F~8~/N~2~ system).

3.3.. Decomposition mechanism of c-C~4~F~8~ {#s3c}
-------------------------------------------

The proposed decomposition mechanism and reaction enthalpy of c-C~4~F~8~ molecule based on the ReaxFF-MD simulation results are shown in [table 1](#RSOS181104TB1){ref-type="table"} and the relative energy change of c-C~4~F~8~ decomposition process is shown in [figure 8](#RSOS181104F8){ref-type="fig"}. It can be found that the generation of C~2~F~4~ needs to absorb 43.28 kcal mol^−1^, which is more prone to occur than the formation of C~3~F~6~ and CF~2~. C~2~F~4~ can further decompose to two CF~2~ radicals, which needs to absorb 77.93 kcal mol^−1^. As the main decomposition product of c-C~4~F~8~, CF~2~ can also dissociate to produce CF and F or combine with F to generate CF~3~, and these processes need to absorb 97.23 kcal mol^−1^ or release 79.80 kcal mol^−1^, respectively. In addition, the formation of CF~4~ and C~2~F~6~ releases 116.8 and 98.67 kcal mol^−1^, respectively. And the decomposition of CF requires to absorb 111.49 kcal mol^−1^. Table 1.Proposed decomposition mechanism and reaction enthalpy of c-C~4~F~8~.no.reactionenthalpy (kcal mol^−1^)^a^1${c - C_{4}F_{8}}\rightarrow 4{CF_{2}}$198.072${c - C_{4}F_{8}}\rightarrow 2{C_{2}F_{4}}$43.283${c - C_{4}F_{8}}\rightarrow{C_{3}F_{6}} + {CF}_{2}$74.344${CF_{2}}\rightarrow{CF} + F$97.235${CF}\rightarrow C + F$111.496${CF_{2}} + F\rightarrow{CF_{3}}$−79.807${CF_{3}} + F\rightarrow{CF_{4}}$−116.808${2CF_{2}}\rightarrow{C_{2}F_{4}}$−77.939${2CF_{3}}\rightarrow{C_{2}F_{6}}$−98.67[^2] Figure 8.Relative energy change of c-C~4~F~8~ decomposition process.

As shown in [figure 8](#RSOS181104F8){ref-type="fig"}, the various free radicals produced by c-C~4~F~8~ reacting stepwise to form CF~4~ and C~2~F~6~ need to absorb 1.47 and 19.6 kcal mol^−1^, respectively, and the generation of C and F requires to absorb 406.79 kcal mol^−1^. From the thermodynamic point of view, there is a dynamic equilibrium process between the various produced radicals, which ensures the insulation performance of the system to a certain extent.

In order to further analyse the influence of temperature on the main reaction, the enthalpy of each path at 300--3400 K is also calculated (as shown in [figure 9](#RSOS181104F9){ref-type="fig"}). It can be found that the enthalpy of path 1 and path 3 shows a decrease trend with the increase of temperature, which means the decomposition of c-C~4~F~8~ is more likely to occur under high-temperature conditions. The enthalpy of path 2, 4, 5 and 8 does not change with the increase of temperature, thus the ambient temperature has no obvious effect on these reactions. The reaction enthalpy of path 6 and path 9 decreases with the increasing temperature, indicating that the generation of CF~3~ and C~2~F~6~ occurs with more difficulty at high temperature. Figure 9.Enthalpy change of proposed reaction paths at 300--3400 K.

4.. Conclusion {#s4}
==============

In this paper, the decomposition process of c-C~4~F~8~ and c-C~4~F~8~/N~2~ gas mixture were explored based on the ReaxFF molecular dynamics method and DFT. It is found that the decomposition of c-C~4~F~8~ mainly produces CF~2~, F, CF~3~, CF, C, CF~4~ and C~2~F~4~. c-C~4~F~8~ can decompose to C~2~F~4~ by absorbing 43.28 kcal mol^−1^, which is the main decomposition path and this process occurs easily under high temperature. There is a dynamic equilibrium process between the various produced radicals, which ensures the insulation performance of system to a certain extent. The decomposition performance of c-C~4~F~8~/N~2~ gas mixture is better than that of pure c-C~4~F~8~ at the same condition, which is suitable to use as a gas-insulated medium in the field of medium voltage (MV) equipment.

The authors are very grateful to the support by the science and technology project of China Southern Power Grid (no. GZKJXM20170673).

Data accessibility {#s5}
==================

Our data are deposited at Dryad Digital Repository: <http://dx.doi.org/10.5061/dryad.2r984j6> \[[@RSOS181104C32]\].

Authors\' contributions {#s6}
=======================

X.Z. conceived and designed the research; Y.Z., Y.L. and J.T. performed the research and wrote this manuscript while S.X. helped analyse the data.

Competing interests {#s7}
===================

The authors declare no competing interests.

Funding {#s8}
=======

The current work is supported by the science and technology project of China Southern Power Grid (no. GZKJXM20170673).

[^1]: This article has been edited by the Royal Society of Chemistry, including the commissioning, peer review process and editorial aspects up to the point of acceptance.

[^2]: ^a^*T* = 300 K, at mGGA-M06 L level with ZPE correction and enthalpy correction.
