QM/MD simulations on the role of SiO₂ in polymeric insulation materials

Abstract

Quantum chemical molecular dynamics (QM/MD) simulations based on a self-consistent charge density functional tight-binding (SCC-DFTB) method on SiO₂ filler in polyethylene (PE) showed that: in the absence of SiO₂, the PE was quickly charged by high-energy electrons, which resulted in C–C or C–H bonds breaking; on the contrary, in the presence of SiO₂ nanoclusters, electron trapping and accumulating were dominated by SiO₂ nanoclusters rather than polyethylene, which made polyethylene be preferentially protected and increased the initial time of electrical treeing. In our calculations, we also observed double electric layers around the SiO₂ nanocluster, in agreement with recent suggestions from experimental observations. Furthermore, compared with some other investigated nanoclusters, SiO₂ was regarded as the most promising candidate attributed to the highest electron affinity. We further observed that once the high-energy electrons were supersaturated in the nanoclusters, the polyethylene chains would be unavoidably charged and C–H bond breaking would occur, which resulted from the interaction between H and O or Si in the nanoclusters. Following that, decomposing and cross-linking of the polyethylene chains were involved in the initial growth of electrical treeing. The current observation can potentially be used in power cable insulation.

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Introduction

Nowadays, polymeric insulation materials, such as cross-linked polyethylene (XLPE), are widely used in high voltage equipment due to the superiority of their electrical performance. However, it is unavoidable that the polymeric materials will become aged, finally resulting in dielectric breakdown. The main reason for dielectric breakdown is attributed to electrical treeing.¹ Significant efforts have been dedicated towards understanding the electrical treeing mechanism and inhibiting electrical treeing formation. Numerous studies have predicted that nano-sized particle fillers, such as SiO₂,^2–6 MgO,^7,8 ZnO,^9–11 Al₂O₃,¹² TiO₂,¹³ C₆₀,^14–17 and PCBM ([6,6]-phenyl-C₆₁-butyric acid methyl ester),^17,18 would be a very promising method in improving the electrical tree resistance and may considerably enhance the transmission efficiency of power grids. Basically, tree initial voltage, tree breakdown voltage, tree initial time, and tree breakdown time are four parameters that have been used to investigate the effectiveness and capabilities of filler to suppress the growth of electrical treeing. Experiments^2–6 have found that silica nanofiller prolonged the tree initiation time and increased the tree breakdown voltage; using MgO^7,8 or TiO₂ (ref. 13) nanoparticles as fillers could increase the tree breakdown time or increase the tree growth time.

Currently, the essential role of nano-composites is explained by the following aspects: the main advantage of using nano-sized particles as a filler was to provide a larger surface area, which is related to the interfacial region of filler and polymer;¹⁹ another superiority is that the surface interaction between polymer and nanoparticles affects the electrical properties of the dielectric material.²⁰ Generally, the behaviour of the nanocomposite material is dominated by the properties of the interfaces of the nanoparticles with its surrounding environment. The interfacial region addition of nanoparticles in a polymer matrix can change some of the structural properties such as local charge, local conductivity distribution, free volume, and charge mobility; also, the charge carriers could be trapped more easily by nanoparticles and these additives could scavenge high-energy electrons, which reduces the accumulated damage in the material and avoids the degradation of polyethylene chains,²¹ thereby increasing the lifetime of the polymer. Moreover, by collision with the nanoparticles, the high-energy electrons will lose energy resulting in the reduction of treeing; nanoparticles can also be responsible for the stability of PE since the PE chains are strongly attracted by the nanoparticle surfaces.

Although the presence of nanoparticles or nanoclusters hindering electrical tree propagation in a polymer matrix has been widely observed in experiments, the essence of the obstacle effect is still not clear. Therefore, further research on electrical treeing and its formation mechanism in nanocomposites are urgently required. In this paper, using quantum chemical molecular dynamics (QM/MD) simulations we focused on the effect of SiO₂ nanoclusters on charge redistribution and electron trapping, and investigated the role of SiO₂ as a voltage stabilizer for high-voltage power cable insulation. Furthermore, we discussed the interaction between nanoclusters and polyethylene to explain the critical effect of the interfacial region. The current observation can potentially be used to understand the initiation of the treeing mechanism and improve the performance of power cable insulation.

Computational methodology

A. SCCDFTB method

In the present study, all the electronic structure calculations and nonequilibrium quantum chemical molecular dynamics simulations were carried out by the self-consistent-charge density-functional tight-binding method including van der Waals correction (SCCDFTB-D)²² with the DFTB + program package.²³ DFTB is an approximate density functional theory method based on the tight binding approach, and utilizes an optimized minimal LCAO Slater-type all-valence basis set in combination with a two-center approximation for Hamiltonian matrix elements. The DFTB quantum chemical potential is ideally suited to bridge the gap between reactive force field approaches and first principles density functional theory (DFT) methods. It is several orders of magnitude faster than the latter but in contrast to the former it explicitly includes electronic effects.

All the nonequilibrium MD simulations in this study were performed based on a quantum chemistry method (QM), i.e. the self-consistent charge density functional tight-binding method. The nuclear equations of motion of nuclei were integrated using the Velocity Verlet algorithm²⁴ (Δt = 0.5 fs), and a nuclear temperature of 300 K with the NVT ensemble was maintained via a Nosé–Hoover chain thermostat.²⁵ To achieve convergence a finite electronic temperature approach²⁶ with T_e = 300 K was employed to evaluate the quantum chemical potential on the fly. Standard C–C, C–O, C–H, O–O, O–H, H–H, Si–C, Si–O, Si–H and Si–Si DFTB parameters were selected from the mio-0-1 set which is freely available at http://www.dftb.org.

B. IE, EA, and L.I. definitions

Electron affinity (EA) and ionization potential (IP) are commonly used to evaluate the charge injection abilities,^27–29 and they were defined as follows,

EA_v = E_M − E_M−//M (1)

IP_v = E_M+//M − E_M (2)

EA_a = E_M − E_M− (3)

IP_a = E_M+ − E_M (4)

where the subscripts v and a represented vertical and adiabatic EA and IP, respectively. E_M, E_M+, and E_M− were the energies of neutral, cationic, and anionic molecules. E_M+//M or E_M−//M denoted the single point energies of cationic or anionic molecules based on the geometries of neutral molecules. Otherwise, the mobility of electrons and holes was also dominantly determined by reorganization energy λ.^30,31 A low λ value is necessary for an efficient charge transport process. Generally, reorganization energy is determined by the fast change of the molecular geometry when a charge is added to or removed from a molecule (the intramolecular reorganization energy λ_i) and slow variations in the surrounding medium due to the polarization effects (intermolecular reorganization energy λ_e). The previous reports^32,33 have demonstrated that λ_e is very small and λ_i is dominant in λ. Therefore, in the present study, we focus on the intramolecular reorganization energy λ_i, and the intramolecular reorganization energy for hole/electron transfer is simply defined as follows:

λ_ih = IP_v − HEP (5)

λ_ie = EEP − EA_v (6)

where HEP or EEP represents hole or electron extraction potential, which was the energy difference between M (neutral molecule) and M+ (cationic), based on M+ geometry or the energy difference between M and M− (anionic), based on M− geometry.

The Lindemann index (L.I.)³⁴ was employed here to analyze the physical state and the mobility of polyethylene and SiO₂ nanocomposites, and it is defined as below,

where N is the number of atoms in the relevant system, r_ij is the instantaneous distance between atoms i and j, and the brackets denote thermal averaging over a finite interval of time. The Lindemann index has been used on a number of occasions to elucidate the phase-transitions of transition metals and SiO₂ in the context of carbon nanotube or graphene nucleation and growth.^35–39

C. Model

Regarding the calculations of EA, IP, HEP, EEP, and λ, the nanocluster spheres with a radius of 10 Å were prepared by cutting from the bulk structures, as shown in Fig. 1. The total numbers of atoms (∼400) were listed in Table 1. In QM/MD simulations, three models were considered. (1) Four molecules of CH₃(CH₂)₃₈CH₃ with a density of 0.925 g cm⁻³, depicted as PE₄, were set up in a periodic boundary box of 15.9 × 15.9 × 15.9 ų according to the experimental conditions. (2) and (3) To save the simulation time and to provide the appropriate SiO₂ density, two SiO₂ spheres with a radius of 3 Å and 4.5 Å, which are almost the smallest nanoclusters of SiO₂, were inserted into the above PE model. Thus, the SiO₂/PE nanocomposites (C₁₆₀H₃₂₈Si₆O₈ and C₁₆₀H₃₂₈Si₉O₂₂) with a nanocluster content of 11.6 and 21.2 wt%, as model S and model L, were created. Since these two small nanoclusters are prepared by cutting a sphere from the SiO₂ bulk, they do not exactly have 1 : 2 stoichiometric ratios and therefore, in the discussion section SiO₂ is replaced by Si_xO_y to describe the interaction between SiO₂ and PE. The cubic periodic boundary boxes of 16.6 × 16.6 × 16.6 and 17.2 × 17.2 × 17.2 ų were established to keep a constant density of 0.925 g cm⁻³. To evaluate the electron trapping ability of a nanocluster, different numbers of electrons (from 1 to 4) were assumed in the two nanocomposite materials (S and L) and the pure PE systems, named as Sⁿ⁻, Lⁿ⁻, and PEⁿ⁻ (n = 1–4). Three independent trajectories with different initial velocities for each model were performed using randomized initial conditions. These trajectories were denoted as S_mⁿ⁻, L_mⁿ⁻, and PE_mⁿ⁻ (m = 1–3, and n = 0–4).

Fig. 1 The models of nanoparticles for IE and EA estimation. (a) SiO₂; (b) Al₂O₃; (c) Fe₂O₃; (d) TiO₂; (e) CuO; (f) ZnO; (g) C₆₀; (h) C₆₀F; (i) C₅₉N; (j) PCBM.

Table 1 Ionization potentials (IP), electron affinities (EA), hole and electron extraction potentials (HEP and EEP), and internal reorganization energies (λ) (in eV) for the studied complexes. All the nanoparticles are cut as a sphere with a diameter of ∼10 Å from the bulk

	# of atoms	IPv	EAv	IPa	EAa	λih	λie	HEP	EEP
a From ref. 22.b From ref. 23.c From ref. 24.d From ref. 25.
PE4	488	7.14	−3.61	7.12	0.48	0.03	6.94	7.11	2.29
SiO2	342	7.82	6.65	7.80	6.68	0.04	0.04	7.78	6.70
Al2O3	510	6.16	5.11	6.16	5.11	0.02	0.02	6.14	5.12
Fe2O3	418	2.17	1.17	2.16	1.19	0.02	0.02	2.15	1.20
TiO2	404	4.02	2.92	3.99	2.94	0.05	0.04	3.97	2.96
CuO	418	5.00	3.97	4.99	3.98	0.02	0.02	4.98	3.99
ZnO	356	5.66	4.53	5.65	4.56	0.08	0.05	5.58	4.58
C60	60	6.94 (7.60)^a	2.95 (2.67)^b	6.94	2.96	0.01	0.03	6.94	2.97
C60F	61	6.85	3.38	6.83	3.41	0.04	0.07	6.81	3.45
C59N	60	6.19	2.81	6.17	2.83	0.03	0.04	6.16	2.84
PCBM	88	6.66 (7.17)^c	2.93 (2.63)^d	6.59	2.97	0.10	0.07	6.54	3.00

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Results and discussion

A. EA and IP

The IP⁴⁰ and EA⁴¹ of the additives are correlated with the voltage stability, the electrical treeing, and dielectric strength of the polymeric insulation materials. It has been proven that a high electron affinity of the additives can increase the breakdown field by trapping electrons to delay the formation of an electron avalanche⁴² and the breakdown strength of LDPE (low density polyethylene) films.⁴³ Additionally, experimental and theoretical studies have already identified that high electron affinity and ionization energies were the necessary criteria for efficient electrical tree inhibition.^41,44 Therefore, in this study we calculated the vertical IP (IP_v), adiabatic IP (IP_a), vertical EA (EA_v), and adiabatic EA (EA_a), as well as the hole or electron extraction potentials and internal reorganization energies (HEP or EEP and λ_ih or λ_ie, which are related to the mobility of holes and electrons) of some additive nanoclusters investigated frequently in the experiments, such as fullerenes and their devices (C₆₀, C₆₀F, C₅₉N, PCBM), and some other metal oxides (Al₂O₃, Fe₂O₃, TiO₂, CuO, ZnO). The values are listed in Table 1 and the investigated isolated nanocluster models are shown in Fig. 1. It is obvious that the calculated IP and EA values of C₆₀ and PCBM are very close to the experimental data.^45–48 The IP is underestimated by ∼0.6 eV and the EA is overestimated by 0.3 eV, which further confirms the validity of the DFTB method, while DFTB can save extreme amount of the computational source and time. We also found that the EA and IP values range from 1.0–7.0 and 2.0–8.0 eV, respectively. This suggests that altering the nanoclusters is a possible way to tune the charge transfer properties for these complexes. Among all the investigated nanoclusters, it is obvious that SiO₂ possesses the largest IP, indicating that it is the most difficult hole injection material. On the other hand, SiO₂ has the largest EA, which will contribute to a lower electron-injection barrier. Obviously, the introduction of an electron-injection nanocluster unit to the skeleton of PE would enhance the electron-injection ability. Our calculations indicate that SiO₂ is a promising candidate to reduce electrical treeing due to its high IP and EA. Regarding the λ_ih and λ_ie, all the nanoclusters have comparative values of ∼0.05 eV, indicating a similar hole- and electron-transporting rate and excellent transfer balance. However, for PE, the λ_ih is extremely smaller than λ_ie, demonstrating the better hole-transporting performance for this complex. Since SiO₂ nanoclusters characterized a potential suppression on electrical treeing, QM/MD simulations were performed for these nano-filler composites.

B. PE decomposition mechanism on Si_xO_y nanoparticles

We will initially discuss our QM/MD simulations on the interaction between Si_xO_y nanoclusters and PE. Fig. 2 shows the optimized neutral structures of three models, PE⁰, S⁰, and L⁰. Employing these optimized structures the 60 ps QM/MD simulations were performed. The final snapshots of all trajectories were provided as ESI (Fig. S1–S3†). Since the PE decompositions were similar, here we took four representative trajectories as examples, shown in Fig. 3, to describe the PE decomposing process on Si_xO_y. Three typical procedures can be observed immediately from these figures. First, with the translational and vibrational diffusion of PE and nanoclusters, the O⋯H hydrogen bonds (highlighted in red dashed line) were frequently formed and broken. The same as for S₂²⁻, at 3.12 ps the O started to interact with the H in PE (Fig. 3a) and for L₃⁰, at 3.65 ps two O gradually connected with two neighbor C–H to finally form a four-membered ring (Fig. 3b). These H bonds will lead to an immobilized polymer interface⁴⁹ due to the strong attraction of the polymer chains with the nanocluster surfaces. Second, the H (highlighted in orange) transferred from polymer (–CH₂–) to nanocluster (Si or O) and the –CH– radical was formed, which is the precursor for the branched structures. Although the hydrogen bonds were only observed between O and H due to the higher electronegativity of O and lower electronegativity of Si, H transferring processes from polyethylene to both Si and O took place. For example, for trajectories S₂²⁻, S₁⁴⁻, and S₃⁴⁻, Si–H bonds were formed at 5.62, 8.05, and 6.10 ps, respectively. On the other hand, for L₃⁰, an O–H bond came into being at 15.42 ps, as seen in Fig. 3b. Third, Si–C or O–C bonds were formed, as shown in Fig. 3, highlighted in purple (C) and green (O or Si). Following the H-abstraction reaction, the active –CH– radical was easily saturated by Si–C or O–C bonds. Two trajectories of S₁⁴⁻ and S₃⁴⁻ showed the Si–C formation and one trajectory of L₃⁰ exhibited O–C formation at 52.77, 6.10, and 17.10 ps, respectively.

Fig. 2 The optimized geometries of three models. (a) PE⁰; (b) S⁰ (PE₄ + SiO₂ nanocluster with a radius of 3.0 Å) and (c) L⁰ (PE₄ + SiO₂ nanocluster with a radius of 4.5 Å).

Fig. 3 The snapshots of H bond formation between H and O (red dashed line) or H transferring from polymer (CH₂) to nanocluster (Si or O), (a) for trajectory 2 of model S²⁻; (b) for trajectory 3 of model L⁰; (c) for trajectory 1 of model S⁴⁻; (d) for trajectory 3 of model S⁴⁻. The reactive H, Si, and C atoms are highlighted by orange, green, and purple circles.

With regards to the PE decomposition process in pure PE, there was a dramatic difference to the nanocluster-filled composites. In the pure PE model, with the number of trapped electrons increasing, the C–C bonds tended to be broken which is, however, not observed in the above nanocluster-filled composites. Fig. 4a depicts the C–C bond breaking procedure for PE₁¹⁻ (PE₂¹⁻ is similar to PE₁¹⁻). During the 60 ps MD simulations, the C–C bond was continuously wobbling with a C–C distance of ∼2.3 Å, which was elongated by 53.3% compared to the C–C single bond. This C–C bond breaking/elongation was attributed to the repulsion of two negatively charged carbon atoms (−0.41 and 0.40 e), as shown by the red balls in Fig. 4b. This suggests that the C–C bonds were easily activated by the trapped electrons. Fig. 4c describes the average carbon cluster size at 60 ps. It was obvious that for only the pure PE system with one trapped electron (model PE¹⁻), one C₄₀ chain (a total of four C₄₀ chains) decomposing to C₂₄ and C₁₆ is observed. It is noted that for PE₃¹⁻ the broken C–C bond was recovered during the 60 ps MD simulation, however, two C–H bonds were activated, as shown in Fig. 4a (right snapshot). The broken C–H bonds were elongated to 1.87 and 1.85 Å, resulting from the increased repulsive column interaction due to more negatively charged carbon atoms (∼−0.37 e). Consequently, in a pure PE system, without the help of nanoclusters, the redundant electrons were easily localized on certain carbon atoms and gave rise to the breaking of C–C and C–H bonds. Contrarily, in the presence of the Si_xO_y nanoclusters, even with four trapped electrons, there was still no C–C bond disruption and four C₄₀ polyethylene chains were unchanged following the 60 ps MD simulations. It suggests that Si_xO_y filler can redistribute the electrons and prevent the C–C bond from breaking, to further reduce the initial precursor formation of electrical treeing and increase the tree initial time, in agreement with the experimental observation.^2–6

Fig. 4 The snapshots of C–C bond and C–H bond breaking in model PE. The left is for PE₁¹⁻ and the right is for PE₃¹⁻ (the upper inset two figures are enlarged C–H broken structures); (b) Mulliken charge distribution schematics of PE₁¹⁻ and PE₃¹⁻; (c) the averaged carbon cluster size at 60 ps, for all systems. The reactivated C and H atoms are highlighted with purple and orange circles.

C. Charge redistribution and double electric layer

Obviously, the introduction of Si_xO_y nanoclusters redistributed the Mulliken charge, which is attributed to the different electronegativity of C, H, Si, and O (2.55, 2.20, 3.44, and 1.90). Taking the average Mulliken charge analysis as an example, shown in Fig. 5, all Si_xO_y nanoclusters possessed negative charges from −2 to −1 depending on the different number of trapped electrons (from 0 to 4 e) and the size of Si_xO_y nanocluster fillers. With respect to the Mulliken charge on polyethylene chains (PE) in the nanocomposites (see Fig. 5b), when the nanocomposites were neutral and trapping one electron, the PE in the S or L model were always positively charged by 1 or 2 (red or black curve) and 0.5 or 1 e (green or orange curve). This promised PE can continuously accept electron-injection to reach a stable neutral-close stage, and thereby a longer time was required for charge building up, delaying the electrical treeing initial growth process, and finally increasing the tree initial time, which is consistent with the experimental observation.^2–5 Besides, it is clear that the larger the particle the more negative charge was located on the nanocluster (Fig. 5a S⁰ vs. L⁰ and S¹⁻ vs. L¹⁻), suggesting that the ability of electron trapping and collision was very dependent on the nanocluster size. Larger nanoclusters or higher filler content led to more positively charged polyethylene, indicating that a larger nanocluster or higher filler content can decrease the initiated rate of electrical treeing more significantly, which agrees well with the experimental observations.⁵⁰ On the other hand, with the number of trapped electrons increasing from two to four, in the S model, the polyethylene was gradually negatively charged by −0.5, −1.5, and −3 e, while this was still higher than the charge of the pure PE system without nanocluster filling by 0.5–1 e. Therefore, the Si_xO_y nanoclusters can efficiently accumulate electrons and protect polyethylene from electron trapping and collision. Furthermore, the behavior of Si_xO_y nanoclusters can largely decrease the energy of higher-energy electrons by colliding with and trapping them, and thus, to some extent, the dielectric breakdown was relieved.

Fig. 5 The Mulliken charge as a function of time on (a) Si_xO_y nanoclusters and (b) PE, in a small model with neutral (S⁰), trapping one/two/three/four electrons (S¹⁻/S²⁻/S³⁻/S⁴⁻), and in the large model with neutral and one electron (L⁰ and L¹⁻).

The interface behaviour between the nanoclusters and the polyethylene matrix is important in conductivity, permittivity, and the performance of space charge injection. Based on the interaction zones theory proposed by Lewis,⁵¹ there exists an electric double layer around the nanocluster. In our simulations, we indeed observed the existence of the interface charges between nanoclusters and the polymers, as observed in experimental work.⁵² Fig. 6a and b depicts the averaged RDF (radial distribution function) of Mulliken charge distribution around Si_xO_y nanoclusters for model Sⁿ⁻ (n = 0, 1, 2, 3, 4) and Lⁿ⁻ (n = 0, 1), and the individual charge distribution for each trajectory is shown in Fig. S2.† It is clear that a multi-core model, proposed by Tanaka⁵³ was predicted here. A core-layer, a bound layer, and a free layer were observed in our SiO₂ composite filler. As we know that the nanocluster preferred to trap electrons consequently resulting in the redistribution of charge between nanocluster and the polymer matrix. From Fig. 6a we can see that for the neutral and systems with a small amount of charge trapped (with negative charges of −1 and −2) the positive charge was distributed in the core-layer (1–2 Å from the mass center of the SiO₂ nanocluster) and the negative charge was located in the outer-layer at 2–3 Å. However, once the nanocomposite trapped too many electrons, such as with four electrons, there were two small positive charge layers available at ∼1.8 and 3 Å. On the other hand, two larger negative charge layers were obviously observed with two peaks at 2 and 4 Å. This alternative positive and negative double electronic layer plays a very important role in explaining its impact on the dielectric properties of polymeric insulations. Considering the size effect, the similarity is that the positive core-layer is far away from the mass center with the number of trapped electrons increasing. The difference is that the peak of the core-level in the L model was higher and closer to the mass center than in the S model, suggesting that the larger the nanocluster the higher the ability to trap electrons, which is also consistent with the above Mulliken charge distribution and the experimental result.⁵⁰ We also found several separated small peaks for the large nanocluster system. We can deduce that there are large numbers of local charge domains distributed on the surface of the larger SiO₂ filler sample.

Fig. 6 The RDF of averaged Mulliken charge distribution around Si_xO_y nanoparticles from the mass center to radius of 8.5 Å. (a) For model Sⁿ⁻ (n = 0, 1, 2, 3, 4); (b) for model Lⁿ⁻ (n = 0, 1).

D. Mobility of polyethylene

Lindemann indexes (δ) for all systems are shown in Fig. 7 and S3.† It is typically accepted that δ = 0.1 marks the transition between the solid and liquid phases.⁵⁴ Fig. 7 shows that polyethylene rapidly undergoes a solid to liquid-like phase transition upon thermal annealing, as indicated by the rapid increase of δ in all systems. Moreover, the increasing rate of pure PE from 10–60 ps was much faster than that of nanocluster filled systems (see Fig. 7a). This indicates that the mobility and the collision ratio were higher in the pure PE system, making electrical treeing more easily initiated. On the contrary, the smaller δ for the Si_xO_y composite filler indicated a more solid-like character, which stabilized the polyethylene and impeded the chain collision. This immobilized interface agreed with the experimental result.⁴⁹ We also found that the number of trapped electrons can affect the mobility of polyethylene.

Fig. 7 The Lindman index (L.I.) of CH atoms, (a) for PE, Sⁿ⁻, and Lⁿ⁻ (n = 0, 1); (b) for Sⁿ⁻(n = 0, 1, 2, 3, 4).

When the number of trapped electrons is small, for example one or two, the mobility restriction was stronger with a small value of δ. However, once more electrons were trapped in the systems, the mobility of polyethylene was increased, and δ was even larger than in the pure PE systems. This indicates that the ability to trap electrons on the immobilized polymer interface of Si_xO_y was only valid before “electron saturation”. To get a higher dielectric strength, different sized or various other nanoclusters should be characterized.

Conclusions

SiO₂ possessed the highest EA and was identified as an efficient electron-injection materials. In our simulation, we summarized the role of SiO₂: first, SiO₂ can potently collide with the high energy electrons and decrease their energies due to its high electronegativity; second, SiO₂ can efficiently trap the electrons, preventing C–C bonds breaking, and further avoiding the initial precursor growth of electrical treeing; third, Si and O in the SiO₂ nanoclusters can interact with the H in PE by hydrogen bonding, restricting the mobility of PE, which can stabilize PE and decrease the collision ability of PE chains, and then prevent the initial branched structure growth to increase the tree initial time. In this paper, we observed the double electronic layer in the atomic scale, and we hope our observations are helpful to understand the electrical treeing mechanism and can subsequently be used in improving the properties of power cable insulation.

Acknowledgements

The authors thank the National Science Foundation of China (grant No. 51337002, 21203174, 21221061, 21273219), the Natural Science Foundation for Distinguished Young Scholars of Heilongjiang Province (JC201409), and the Natural Science Foundation of Jilin Province (No. 20130522141JH, 20150101012JC). The authors also thank the financial support from the Department of Science and Technology of Sichuan Province. The computational resource is partly supported by the Performance Computing Center of Jilin University, China. We are also grateful to the Computing Center of Jilin Province for essential support.

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Footnote

† Electronic supplementary information (ESI) available: The last snapshots at 60 ps for each trajectory, the RDF of Mulliken charge distribution and the Lindemann index for individual trajectory. See DOI: 10.1039/c5ra19512h

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