Theoretical study on the tailored side-chain architecture of benzil-like voltage stabilizers for enhanced dielectric strength of cross-linked polyethylene

Abstract

A theoretical investigation on the mechanism of the tailored side-chain architecture of benzil-like voltage stabilizers for enhanced dielectric electrical breakdown strength of cross-linked polyethylene at the atomic and molecular levels is accomplished. The HOMO–LUMO energy gaps, the ionization potentials, and the electron affinities at the ground states of a series of benzil-like molecules are obtained at the B3LYP/6-311+G(d,p) level. The 8 isomerization reactions at the S₀ state, including the harmonic vibration frequencies of the equilibrium geometries and the minimum energy paths (MEP) found using the intrinsic reaction coordinate (IRC) theory, are obtained at the same level. The substituent group effect, functional group effect, and electronic effect of the different heteroatoms (O, N, S) in substituent groups have been evaluated. The results show that benzil-like molecules, which have much smaller HOMO–LUMO energy gaps, much lower ionization potentials, and much larger electron affinities than those of aliphatic chains, can increase the electrical breakdown strength effectively as voltage stabilizers in cross-linked polyethylene. This result is consistent with Jarvid’s suggestions (Journal of Polymer Science, Part B: Polymer Physics, 2014, 52(16): 1047–1054).

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1. Introduction

Cross-linked polyethylene (XLPE) with excellent dielectric properties, heat resistance, and chemical corrosion resistance has become one of the most widely applied insulation materials for high voltage cables up to 500 kV in real applications. The pre-breakdown degradation phenomenon known as electrical treeing initiates at points of high and divergent electric fields and is associated with partial discharges and insulation failure in power cables.^1,2 The initial electron may be created by electrode emission under the local high electric field in XLPE insulated high-voltage cables, such as the inside Schottky effect from insulation, the Schottky effect from the electrode, or collision ionization. The initial electron which gains enough kinetic energy under the electric field in insulation is known as a hot electron. Afterwards, a bound electron is knocked free from an atom through a collision with a hot electron, creating a new carrier. If a chain reaction forms during this process, the carrier concentration increases sharply, resulting in the electron avalanche effect and the loss of insulating properties of the material. This phenomenon is known as electric breakdown. If the electron avalanche mentioned above is limited to a local area, the C–C bond of the polyethylene chain will be attacked, initiating a partial degradation known as electric treeing. Accumulation of the damage can cause dielectric breakdown as soon as an electrical tree channel has bridged and it leads to thorough damage of the insulation matrix. Some organic additives, such as polycyclic aromatic compounds or those with benzophenone-like structures, can serve as so-called voltage stabilizers to effectively increase the resistance to electrical treeing.^3–8 This may be the next solution for XLPE insulating compounds for insulation of power cables exceeding 500 kV. Recently, our research group employed both experimental and computational methods to study the effect of acetophenone as a voltage stabilizer. The addition of acetophenone, a prototypical aromatic ketone compound, leads to a 50% increase in the alternate current (AC) electrical breakdown strength of XLPE.⁹ Using the theoretical studies, we foremost elucidated that keto–enol tautomerism of aromatic carbonyl compounds is one of the important factors for inhibiting initiation and propagation of electrical treeing in polyethylene, and proposed mechanisms for increasing the electrical breakdown strength of XLPE with aromatic carbonyl compounds as voltage stabilizers in 2013.^10–12 However, the compatibility of acetophenone with the XLPE matrix is poor, and it is easy for it to migrate out of the polymeric matrix, leading to worse performance of PE insulation materials. In 2012, a benzil-type compound with a larger alkoxy chain was evaluated as a voltage stabilizer in a super-clean XLPE by Jarvid and his co-workers.⁷ As a result, the electrical treeing inception level was effectively raised, and the compatibility with the PE matrix was also significantly improved. After that, the synthesis and physico-chemical properties of seven benzil-type voltage stabilizers were also reported by Jarvid and his co-workers.⁸ These additives substantially enhance the dielectric strength of the insulating material under high-voltage alternating current conditions. The dielectric strength, 70% higher than the reference XLPE, was improved by the addition of voltage stabilizers with short (methyl) side chains linked to the benzil core via an ester or tertiary amine group.⁸

This inspired us to see that it is essential to investigate the relationship between the electrical character of voltage stabilizers and their molecular structures and the mechanism of PE electrical breakdown strength increments at atomic and molecular levels.¹³ These proposed mechanisms are crucial to understand the molecular functioning of voltage stabilizers in XLPE composites in preventing the degradation of the polymer matrix. In this paper, we aim at providing a systematic investigation on the tailored side-chain architecture of benzil voltage stabilizers for enhanced dielectric strength of XLPE. The behavior of benzil-like molecules in preventing the treeing of XLPE composite materials would be proposed on the basis of the theoretical study, which would be useful for the rational molecular design and synthesis of the desired voltage stabilizers to enhance the transmission efficiency of tomorrow’s power grids in a real commercial application.

The different substituent groups with the heteroatoms O, N and S have been chosen in this study to evaluate the substituent effect, functional group effect, and electronic effect. The role of the voltage stabilizers in increasing the electrical breakdown strength of PE is discussed by focusing on the three effects. The molecular formulae, the names and corresponding abbreviations of the studied molecules are listed in Table 1. In this work, n-hexane (Pe6) is selected as a model molecule of PE; acetophenone (Ap), benzophenone (Bz), and benzil (Ben) are selected as reference molecules.

Table 1 The molecular formulae, molecular names and corresponding abbreviations of studied molecules

Molecular formula	Molecular name	Ab.
	n-Hexane	Pe6
	Acetophenone	Ap
	Benzophenone	Bz
	Benzil	Ben
	4,4′-Dimethoxybenzil	Et1
	4,4′-Dioctyloxybenzil	Et8
	4,4′-Didodecyloxybenzil	Et12
	4,4′-Diacetoxybenzil	Es2
	4,4′-Dioctanoyloxybenzil	Es8
	4,4′-Didodecanoyloxybenzil	Es12
	4,4′-Dicarboxylbenzil	Dc1
	4,4′-Dimethoxycarbonylbenzil	Dc2
	4,4′-Dioctyloxycarbonylbenzil	Dc8
	4,4′-Didodecyloxycarbonylbenzil	Dc12
	4,4′-Diaminocarbonylbenzil	An0
	4,4′-Bis(N-methylaminocarbonyl)benzil	An1
	4,4′-Bis(N-octylaminocarbonyl)benzil	An8
	4,4′-Bis(N-dodecylaminocarbonyl)benzil	An12
	4,4′-Bis(N,N-dimethylaminocarbonyl)benzil	Nc1
	4,4′-Bis(N,N-dioctylaminocarbonyl)benzil	Nc8
	4,4′-Bis(N,N-didodecylaminocarbonyl)benzil	Nc12
	4,4′-Diaminobenzil	Am0
	4,4′-Bis(N,N-dimethylamino)benzil	Am1
	4,4′-Bis(N,N-dioctylamino)benzil	Am8
	4,4′-Bis(N,N-didodecylamino)benzil	Am12
	4,4′-Diacetamidobenzil	Ad2
	4,4′-Dioctanoylamidobenzil	Ad8
	4,4′-Didodecanoylamidobenzil	Ad12
	4,4′-Dithiobenzil	Th0
	4,4′-Dimethylthiobenzil	Th1
	4,4′-Dioctylthiobenzil	Th8
	4,4′-Didodecylthiobenzil	Th12
	4,4′-Diacetylthiobenzil	To2
	4,4′-Dioctanoylthiobenzil	To8
	4,4′-Didodecanoylthiobenzil	To12
	4,4′-Dithioacetylthiobenzil	Tt2
	4,4′-Dithiooctanoylthiobenzil	Tt8
	4,4′-Dithiododecanoylthiobenzil	Tt12
	4,4′-Dithioacetoxybenzil	Oz2
	4,4′-Dithiooctanoyloxybenzil	Oz8
	4,4′-Dithiododecanoyloxybenzil	Oz12

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2. Computational methods

The equilibrium geometries of all the stationary points of the studied molecules at the ground state S₀ were optimized and frequencies were obtained using the B3LYP^14–17 functional with the 6-311+G(d,p) basis set in this work. The B3LYP functional and the 6-311+G(d,p) basis set were confirmed to be suitable for the current study since the computational values of the adiabatic ionization potentials IP(a) and the electron affinities EA(a) at this level are in the most agreement with the corresponding experimental values in our previous paper.¹⁸ Based on these optimized geometries, the energy gaps (E_g) between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), ionization potentials (IPs), and electron affinities (EAs) were obtained. The equilibrium geometries and frequencies of reactants, transition states, and products of 8 isomerization reactions at S₀ were calculated at the same level. The minimum energy path (MEP) was obtained using intrinsic reaction coordinate (IRC) theory with a gradient step-size of 0.05 (amu)^1/2 bohr. Then, the first and second energy derivatives were obtained to calculate the curvature of the reaction path and the generalized vibrational frequencies along the reaction path. The relevant schematic formulae can be defined as follows,

IP(v) = E⁺(M) − E(M)

IP(a) = E⁺(M⁺) − E(M)

EA(v) = E(M) − E⁻(M)

EA(a) = E(M) − E⁻(M⁻)

where E⁺(M⁺), E⁻(M⁻), and E(M) represent the energies of the cation, anion and neutral species in their lowest energy geometries, respectively; while E⁺(M) and E⁻(M) refer to the energies of the cation and anion species with neutral geometries, respectively; v and a represent vertical energy based on the geometry of the neutral molecule and adiabatic energy from the optimized structure for both the neutral and charged molecule, respectively. A schematic description of geometric coordinate modifications and energy changes is illustrated in Fig. 1. All the electronic structure calculations were performed using the GAUSSIAN09 program package.¹⁹

Fig. 1 Schematic description of geometric coordinate modifications and energy changes.

3. Results and discussion

3.1. Stationary point geometries

The optimized geometric structures of the transition states of 8 isomerization reactions at the B3LYP/6-311+G(d,p) level are presented in Fig. 2. Optimized bond lengths of breaking and forming bonds for the 8 transition states, the corresponding reactant C–H, O–H, and N–H bonds, and the product O–H and S–H bonds, and the calculated harmonic vibrational frequencies corresponding to the stretching modes at the same level are listed in Table 2 with acetophenone as the reference. All the transition states are confirmed to have and only have one imaginary frequency corresponding to the stretching modes of the coupling breaking and forming bonds by normal-mode analysis. The other harmonic vibrational frequencies of the neutral and ionic states of the studied molecules are confirmed to be real by normal-mode analysis. The transition states are abbreviated as TS, and reaction channels are represented as R. In Table 2, it can be seen that in the transition state of the isomerization reaction RDc₁, the lengths of the broken and formed O–H bonds are equal, indicating that the isomerization reaction RDc₁ proceeds via a symmetrical barrier. Other transition state structures of the studied isomerization reactions have a common character, the elongation of the breaking bond is larger than that of the forming bond, and they are all product-like, i.e., those reaction pathways will proceed via “late” transition states, which is consistent with Hammond’s postulate,²⁰ applied for an endothermic reaction.

Fig. 2 Optimized transition state geometric structures of the studied molecules at the B3LYP/6-311+G(d,p) level.

Table 2 Optimized bond lengths (in angstroms) for breaking/forming bonds (L_b/f) for the studied transition states, the equilibrium bond lengths in isolated reactants (L_R) and products (L_p), and calculated frequencies (in cm⁻¹) corresponding to the stretching modes at the B3LYP/6-311+G(d,p) level

Ab.	Molecular formula	LR	Lb/f	Lp	Freq.
Ap		1.089	1.491/1.276	0.963	2175i
Es2		1.088	1.524/1.263	0.964	2099i
Dc1		0.969	1.305/1.305	0.969	1962i
An1		1.007	1.342/1.308	0.969	1932i
Ad2		1.091	1.529/1.245	0.964	2003i
Ad2-1		1.013	1.338/1.308	0.969	1911i
To2		1.094	1.521/1.267	0.966	2112i
Tt2		1.095	1.524/1.666	1.351	1894i
Oz2		1.086	1.523/1.665	1.348	1854i

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3.2. Energies: frontier MOs, IPs and EAs

Both the ionization potentials (IPs) and the electron affinities (EAs) of the molecules are important parameters to characterize their reduction and oxidation abilities, respectively. The calculated values of the vertical and adiabatic IPs, EAs at the B3LYP/6-311+G(d,p) level and the corresponding experimental data²¹ (in brackets) are listed in Table 3, as well as the calculated HOMO–LUMO energy gap (E_g). To clarify quantitatively the influences of different substituent effects on their HOMOs and LUMOs, Pe6, Ap, Bz, and Ben were investigated as reference molecules.

Table 3 The E_g, IPs, and EAs of the studied molecules (in eV) calculated at the B3LYP/6-311+G(d,p) level as well as the corresponding experimental data in brackets

Ab.	Molecular formula	Eg	IP(a)	IP(v)	EA(a)	EA(v)
Pe6		8.76	9.76 (9.97)	10.80	−1.20	−1.21
Ap		5.20	8.95 (9.10 ± 0.10)	9.19	0.33 (0.33)	0.093
Bz		4.90	8.64	8.67	0.73	0.50
Ben		4.23	8.24	8.53	1.53	1.02
Et1		4.22	7.74	7.92	1.31	0.75
Et8		4.22	7.60	7.81	1.28	0.71
Et12		4.22	7.60	7.77	1.28	0.70
Es2		4.20	8.05	8.41	1.70	1.16
Es8		4.20	7.98	8.32	1.68	1.14
Es12		4.20	7.97	8.25	1.68	1.14
Dc1		3.98	8.55	8.87	2.21	1.84
Dc2		4.02	8.39	8.71	2.07	1.69
Dc8		4.02	8.30	8.56	2.04	1.65
Dc12		4.02	8.27	8.43	2.04	1.65
An0		4.08	8.42	8.66	2.05	1.61
An1		4.09	8.31	8.48	1.97	1.53
An8		4.09	8.23	8.33	1.95	1.49
An12		4.09	8.21	8.27	1.95	1.49
Nc1		4.17	8.12	8.18	1.87	1.35
Nc8		4.16	7.78	7.86	1.82	1.29
Nc12		4.16	7.76	7.84	1.82	1.26
Am0		4.11	7.30	7.48	1.11	0.50
Am1		3.86	6.81	6.88	1.02	0.38
Am8		3.81	6.54	6.59	0.94	0.38
Am12		3.77	6.53	6.57	0.94	0.38
Ad2		4.09	7.77	7.99	1.57	1.12
Ad8		4.09	7.76	7.89	1.56	1.10
Ad12		4.09	7.72	7.86	1.56	1.10
Th0		4.01	7.90	7.96	1.70	1.17
Th1		3.82	7.50	7.55	1.64	1.04
Th8		3.80	7.32	7.37	1.64	0.99
Th12		3.80	7.31	7.37	1.64	0.99
To2		4.11	8.00	8.25	1.88	1.38
To8		4.09	7.89	8.11	1.86	1.37
To12		4.09	7.87	8.09	1.86	1.37
Tt2		3.36	7.58	7.66	2.04	1.62
Tt8		3.35	7.44	7.52	2.02	1.59
Tt12		3.32	7.43	7.50	2.02	1.59
Oz2		3.78	7.79	7.90	1.84	1.30
Oz8		3.78	7.66	7.79	1.80	1.29
Oz12		3.77	7.66	7.79	1.80	1.29

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The varied trends of the ionization potentials and electron affinities are similar to those of the negative values of the HOMO and LUMO energies, respectively. Comparing with an aliphatic chain (Pe6), the introduction of carbonyl, phenyl, and heteroatom groups into the molecules is efficacious at decreasing the E_g.¹³ These groups are propitious for electronic dissociation because of their high HOMO energy and hence small ionization potential in terms of Koopmans’ theorem; in addition, they are also favorable for accepting electrons when the molecules possess low LUMO energy and hence large electron affinity energies. For instance, IP(a) (Am₁₂, 6.53 eV) < IP(a) (Ap, 8.95 eV) < IP(a) (Pe, 9.76 eV); EA(a) (Dc₁, 0.73 eV) > EA(a) (Ap, 0.33 eV) > EA(a) (Pe6, −1.20 eV). These benzil-like molecules possess a lower IP(v) than Pe6, so they can give rise to collision ionization before the polyethylene chain has been ionized. This can prevent degradation of the polymer matrix as voltage stabilizers, which is consistent with Jarvid’s suggestion.⁸

From Table 3, it is obvious that the introduction of carbonyl and phenyl groups in Bz and Ben molecules can decrease the values of E_g compared with Ap, because their conjugated system extends. The π–π–π and π–π–π–π conjugated systems are formed in Bz and Ben, respectively, resulting in the electronegativity of C in the phenyl ring (sp²) being larger than that in the alkyl group (sp³). Therefore, the abilities of π-electron delocalization and electron trapping are stronger than those of Ap (π–π). Bz and Ben molecules possess lower barriers to accepting electrons because of their low LUMO energy levels. For Bz, as the two benzene rings link to a carbonyl group directly, the steric hindrance is big, causing the two benzene rings to not be planar, and not providing the optimal π-orbital overlap. For Ben, as the two benzene rings link with different carbonyls, the steric hindrance decreases evidently, the degree of coplanarity increases, and the conjugation effect is increased, so E_g (Ben) < E_g (Bz). It can be seen that the contribution of the carbonyl group is larger in decreasing the E_g and increasing the EA in the Ben molecule than that of the phenyl group, because the electron withdrawing inductive effect of the carbonyl group is stronger than that of the phenyl group. Thus, E_g (Ben) < E_g (Bz) < E_g (Ap); EA(a) (Ap, 0.33 eV) < EA(a) (Bz, 0.73 eV) < EA(a) (Ben, 1.53 eV). The EA of benzil-like molecules increases gradually when –Z, , and groups are linked to the para-position of Ben, so they are in the order EA(–Z) < EA() < EA(), where Z = OH, OR, NH₂, NHR, NR₂, SH, and SR; Z′ = O and NH. EA(Dc₁) is the largest.

Comparing with Ap (π–π conjugated system), not only a π–π–π–π conjugated system between carbonyl groups and benzene rings is formed in Et and Am, but also a p–π conjugated system is formed, as the electron-donating groups –OR or –NR₂ are linked to the benzene ring, stretching the conjugated system. It can be concluded that the E_g decreases, for example E_g (Et₁₂, 4.22 eV) < E_g (Ap, 5.20 eV); E_g (Am₁₂, 3.77) < E_g (Ap). The calculated results have been well explained by Jarvid, Englund, and their co-workers^2,7,8 that the introduction of a carbonyl or alkoxy group into benzophenone molecules is an exciting molecular design because they can effectively decrease the E_g value and increase the compatibility with polymer matrices. The energy of electronic transition becomes smaller as the E_g decreases. In addition, the –OR or –NR₂ groups in Et or Am exhibit inductive electron-donating effects, which makes the electron densities of the benzene ring larger than those of Ben, resulting in the weaker ability to accept electrons. For instance, EA(a) (Et₁₂, 1.28 eV) < EA(a) (Ben, 1.53 eV) and EA(a) (Am₁₂, 0.94 eV) < EA(a) (Ben). There are two carbonyl groups in Ben, and one carbonyl group in Bz. The electron density in the benzene ring in Bz is larger than that of Ben, so EA (Bz, 0.73 eV) < EA (Ben). The E_g decreases evidently with the increasing conjugated effect, the N in the amino group is the best one that conjugated with a benzene ring among the studied molecules, thus E_g (Ad) < E_g (Es); E_g (Am) < E_g (Et).

From Table 3, the results indicate that the introduction of electron-withdrawing groups (Z = OH, OR, NH₂, NHR, and NR₂) can increase the ability of accepting electrons, and the EA increases markedly. For example, EA(a) (Ben, 1.53 eV) < EA(a) (Dc₁, 2.21 eV); EA(a) (Ben) < EA(a) (An₀). When –SR, , and groups are linked to the para-position of Ben, the E_g of the benzil-like molecules decreases and the EA increases gradually. Because the radius of the S atom is larger than that of the O atom, the space of delocalization has expanded. Thus, EA(a) (Th) < EA(a) (To) ≈ EA(a) (Oz) < EA(a) (Tt).

3.3. Energetics

The reaction enthalpies at 298 K (ΔH⁰₂₉₈) and the potential barrier heights (ΔE^TS) with zero-point energy (ZPE) corrections for the 8 isomerization reactions obtained based on the electronic structure calculations at the B3LYP/6-311+G(d,p) level are listed in Table 4. The calculated ΔE^TS of acetophenone at the B3LYP/6-311+G(d,p) level is 62.31 kcal mol⁻¹, which has been reported in our previous paper.¹¹ The mechanisms have been firstly proposed on the basis of our theoretical results^10,11 that voltage stabilizers can trap hot electrons, facilitate electronic transition, and restore the aliphatic cation radical. In addition, keto–enol and valence bond isomerization is suggested to occur when acetophenone is used as a voltage stabilizer.

Table 4 The reaction enthalpies at 298 K (ΔH⁰₂₉₈), the potential barrier heights TS (ΔE^TS) with zero-point energy (ZPE) corrections for the studied reactions calculated on S₀ states at the B3LYP/6-311+G(d,p) level (in kcal mol⁻¹)

	Reaction equation	ΔE^TS + ZPE	ΔH^0298
RAp		62.31	13.81
REs2		71.53	26.38
RDc1		32.76	0.01
RAn1		44.07	16.35
RAd2		64.38	25.74
RAd2-1		37.16	8.05
RTo2		67.66	21.86
RTt2		54.89	9.75
ROz2		57.24	13.84

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The 8 isomerization reactions have energy barriers of both the forward and reverse reactions. Comparing RAp with RDc₁, the –CH₃ in the acetyl group of Ap has been replaced by –OH. The H in the –OH of the Dc₁ molecule is more active than that in –CH₃ due to the larger electronegativity of O than of C. Therefore, the H in –OH dissociates more easily and leads to a more facile carboxyl isomerization reaction with lower energy barriers. In addition, when –CH₃ is replaced by –OH, it exhibits an inductive electron withdrawing effect and electron donating conjugated effect at the same time, while the latter is stronger than the former, resulting in a good electron donating effect at last. This further facilitates the transfer of π electrons to the O in –C=O, which in turn exerts a stronger attraction to the H in the acetyl group, and thus the isomerization reaction occurs in an easier fashion. Similarly, when –CH₃ is replaced by –NHR, its isomerization reaction energy barriers are lower than that of Ap. The electronegativity is in the order C < N < O, and the corresponding reaction activity of the H atom is in the order –CH < –NH < –OH, too. The above results indicate that the studied aromatic carbonyl and carboxyl molecules can undergo isomerization reactions, absorbing and transferring the energy of hot electrons when hot electrons are injected into the polyethylene compound. A lesser amount of energy (about 32.76–71.53 kcal mol⁻¹) is needed to complete the isomerization reaction, which is much lower than that of the carbon–carbon single bond energy (the average bond energy is 82.95 kcal mol⁻¹) in XLPE. It means that if the isomerization reaction energy barrier of any molecule is higher than 82.95 kcal mol⁻¹, the reaction process is not competitive to the C–C bond breaking, and then those molecules cannot be used as voltage stabilizer adulterated to XLPE material. In principle, the studied benzil-like molecules could be effective as voltage stabilizers for increasing the breakdown strength of insulating XLPE materials.

4. Conclusion

Comparing with aliphatic compounds, we conjecture that the studied benzil-like molecules with heteroatom (O, N and S) groups as voltage stabilizers can: (1) effectively improve the ability of trapping hot electrons (larger electronegativity) and decrease the kinetic energy of the hot electrons (so as to not have enough energy to break the C–C bonds of polyethylene and prevent degradation of the polymer matrix); (2) obtain the energy of hot electrons and dissipate it through isomerization reactions (the energies of isomerization reactions are lower than that of C–C single bond breakdown in XLPE; (3) prevent the hot electrons from bombarding the C–C bonds of the XLPE matrix and electronic transition (lower HOMO–LUMO energy gaps); and (4) transform the XLPE aliphatic cation to a relatively stable aromatic cation and restore the partially injured aliphatic cation to prevent the degradation of the insulation matrix (as aromatic cations possess much stronger abilities of π-electron delocalization than aliphatic cations).

With the increase in electronegativity of the substituent group, the value of EA increases, the hot electron in the XLPE insulated material has been bound, and benzil-like molecules can not only decrease electronic mobility, but also reduce electronic conductance when they are used as voltage stabilizers. This is favorable for improving the insulating properties of the material. At the same time, the probabilities of electronic collision ionization and C–C bond cleavages are also decreased. In this way, benzil-like molecules can effectively inhibit the initiation and propagation of polyethylene electrical treeing and simultaneously strengthen the alternate electric breakdown that polyethylene can endure. From the macro-point of view, as a consequence, the insulating XLPE material exhibits an elevated AC breakdown strength. With the increase in the conjugation effect, the value of the E_g decreases. Further work to account for reaction energy barriers, enthalpies and products of the isomerization of negative molecular ions under electron injection, together with the following electronic transfer, as well as electronic mobility and interface energy etc. of benzil-like molecules as voltage stabilizers in XLPE is under way.

Acknowledgements

We thank Professor Tierui Zhang (Key Laboratory of Photochemical Conversion and Optoelectronic Materials, Technical Institute of Physics and Chemistry (TIPC), Chinese Academy of Sciences (CAS), Beijing 100190, China) for his fruitful discussions and for checking the English. This work is supported by the National Basic Research Program of China (2012CB723308), the National Natural Science Foundation of China (51337002 and 50977019), the Doctoral Foundation by the Ministry of Education of China (20112303110005), the Science Foundation for Distinguished Young Scholar of Heilongjiang Province (JC201206).

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