Theoretical study on the grafting reaction of maleimide containing 2-hydroxy-benzophenone onto polyethylene

A theoretical study on the multi-channel hydrogen addition of maleimide containing 2-hydroxy-benzophenone onto polyethylene in ultra-violet (UV) radiation cross-linking process was carried out using density functional theory (DFT) method at the B3LYP/6–311 + G(d,p) level. The energetic information and the minimum energy path (MEP) are calculated for nine reaction channels. The electrophilic addition reactions at two positions in the target molecule (maleimide containing 2-hydroxy-benzophenone) were investigated, which are on the C atom of C = C groups and on the O atom of C = O groups. Frontier molecular orbitals (MOs) and natural bond orbital (NBO) charge population of the target molecule have been analyzed in detail. As a result, the reaction site of C in C = C group is more active than the site of O in C = O groups. The target molecule can be used as a multi-functional additive candidate. The predicted mechanism may provide a theoretical basis for the real application of cross-linked polyethylene (XLPE) high-voltage insulation cables.


Introduction
XLPE insulation cables have broad application prospects in high-voltage and ultra-high-voltage fields due to the superiority of their electrical performance [1]. The insulation material is one of the most important issues for restricting the fast development of polymeric high-voltage direct current (HVDC) cables in the near future. The electrical treeing and the space charge accumulation leads to a decreasing service behavior of in-service XLPE cables [2][3][4][5]. Hence, a voltage stabilizer and a space charge inhibitor are needed to increase the electric breakdown strength and inhibit space charge accumulation in the polyethylene (PE) insulation materials. Voltage stabilizers can effectively improve the electrical treeing resistance, which usually have a polycyclic aromatic hydrocarbons structure [6][7][8][9][10][11]. Our group proposes a guiding criterion using the electron affinity and the reaction potential barrier heights to identify the high efficiency of the voltage stabilizers [5][6][7]. And it is reported that polar molecules (such as maleic anhydride) can be grafted to the polymer chains with the aim of inducing deep traps and reducing the accumulation of space charge [12,13]. Our group also proposes a guiding criterion using the reaction potential barrier heights to identify high efficiency of the space charge inhibitor [14,15].
Compared with the traditional dicumyl peroxide (DCP) cross-linking technology, ultra-violet (UV) radiation crosslinking technology has become a candidate because of its advantages such as fast processing speed, small radiation area, energy-saving efficiency, and insensitivity to heat. And theoretical studies [16,17] also show that the reaction energy barrier of hydrogen abstraction on the PE chain by benzophenone (BP) is 0.17 eV in the UV radiation crosslinking process, which is 0.08 eV lower than 0.25 eV for the hydrogen abstraction on the PE chain by the cumyl peroxide (CP) radical in DCP cross-linking process. This indicates that UV radiation cross-linking process has the advantage of replacing traditional DCP process for XLPE production.
Recently, Kim's group [18] reported the reaction conditions and photo-stabilization effects of the synthesized novel UV absorber (abbreviated as AB, a benzoic acid derivative containing maleimide group and 2-hydroxy-benzophenone group). As an effective light stabilizer, the UV absorber is widely used to assimilate UV light with short wavelength (200-400 nm) and convert it into harmless form. This gives us an inspiration, can the AB be used as a multi-functional additive to improve the voltage stabilization and space charge inhibition property of insulation materials? The molecular structure of the AB is presented in Fig. 1. The name and abbreviation of the studied molecules are listed in Table 1. We expect the carbonyl group or benzene in AB molecule to act as deep traps to inhibit space charge, and meanwhile, it can be used as a voltage stabilizer to improve electrical tree resistance capability. The addition of the multi-functional AB in the system would decrease the amount of additive, reducing the introduction of chemical impurities; thus, the electronic conductivity of the materials will reduce.
In this paper, 4-methylheptane (Pe) was selected as a model molecule of PE; we further clarify and verify the  Clarifying the reaction mechanism is beneficial to optimize the cross-linking process of UV radiation and promote the development of high-voltage cable insulation materials.

Computational methods
In this work, the geometry optimizations and frequency calculations of all the stationary points on the ground state S 0 or the triplet state T 1 were carried out by DFT method [19] at the B3LYP [20][21][22][23] functional level with the 6-311 + G(d,p) basis set. The B3LYP//6-311 + G(d,p) levels were confirmed to be suitable for the current study because the computational values of the adiabatic ionization potentials IP(a) and the electron affinities EA(a) at this level are in very good agreement with the corresponding experimental values in the Supplementary information 1. The minimum energy path (MEP) is calculated at the same level and obtained by the intrinsic reaction coordinate (IRC) theory. The gradient step is 0.05 (amu) 1/2 Bohr. Based on these electronic structure calculations, we obtain the values of E g , IP(a), and EA(a), respectively. E g refers to the energy gaps between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), IP(a) refers to the adiabatic ionization potentials, and EA(a) refers to the adiabatic electron affinities. Based on the optimized geometries of the triplet state, we calculate the lowest triplet excitation energies of the studied molecules by the time-dependent density functional theory (TDDFT) method [24,25], which is the vertical excitation single-point energy. The natural charge population was analyzed by the natural bond orbital (NBO) method [26]. All the electronic structure calculations were performed by using the GAUSSIAN09 program package [27].

Results and discussion
The calculated lowest triplet excitation energies (T 1 ) of AB (0.10 eV) in this work is much lower than that of the photoinitiator BP (0.73 eV) [15] at the B3LYP/6-311 + G(d,p) level by the TDDFT method [24,25]. In the process of UV radiation, BP will be excited from S 0 to its singlet excited state S 1 (n, π*) and, after, to its triplet excited state T 1 (n, π*) through inter-system crossing (ISC). According to the sensitization rule, AB molecule will be sensitized to its T 1 state by BP because the excitation energy of T 1 state is 0.63 eV lower than that of BP. That is to say, the T 1 state BP quenches by the S 0 state AB, forming the T 1 state AB and the S 0 state BP. AB can be grafted onto the PE chain, which consists of two fragments, 4-(2,5-dioxo-2,5-dihyro-pyrrol-1-yl)-benzoic acid (A fragment) and 2,4-dihydroxybenzophenone (B fragment) [18]. We calculated the key structural parameters of the reactions between the molecule AB and the model compound Pe that are listed in Table 2. At the same time, the relevant data of the two fragments A and B are also listed in Table 2. The computed E g , IP(a)s, and EA(a)s of studied molecules are listed in Table 3, and their NBO calculation results are listed in Table 4.

Stationary point geometries and NBO charge population
The optimized structures of the reactants, transition states, and products on S 0 or T 1 states for nine channels were obtained. The standard coordination of the TSs for every channel is given in the Supplementary information 2. The schematic diagram of reaction progress of the studied nine channels is shown in Fig. 2.
Four sites on the AB molecule can undergo H addition reactions with Pe, one is electrophilic addition reaction of the 4-position hydrogen in Pe to C of C = C group and the other three are electrophilic addition reaction of the 4-position hydrogen in Pe to O of C = O groups (the three sites are carbonyl in amide, ester carbonyl, and ketone carbonyl, respectively). The natural charge density (− 0.14e) on site 1 in AB molecule given in Table 4 is lower than that of others.
The maleimide structure in Fig. 1, the N atom, and the carbonyl group C = O form p-π conjugate, and N atom exhibits a strong electron-donating conjugation effect, which increases the electron cloud density on the carbonyl group C = O, and the π electron cloud shifts from C to O, which increases the amount of negative charge on O of C = O (site 2). As a result, the density of the electron cloud on the C = C double bond decreases significantly. The electrophilic addition reaction of C = C group in the AB molecule would be easier than that of C = O groups. For the three addition channels on the O of C = O groups in the AB molecule, the natural charge density on site 2 (− 0.33e) > site 4 (− 0.25e) > site 3 (− 0.17e). As a result, site 2 shows higher reactivity; the reaction potential barrier heights of AB on site 2 would be lower than those of the other two reaction sites 3 and 4.
The calculated imaginary frequencies of nine transition states, the optimized bond lengths for breaking and forming bonds, and the corresponding chemical reaction equations are listed in Table 2. The normal mode analysis confirms that all transition states present a single imaginary frequency which corresponds to the stretching mode of Table 2 Optimized bond lengths of breaking/forming bonds for transition state, reactants, and products (in angstrom), together with the calculated breaking/forming bond frequencies (in cm −1 ), the reaction energy barrier (ΔG ≠ ), and reaction Gibbs free energies ΔG 0 (in eV), as well as the abbreviation of transition state (ab.)   coupling fracture and bond formation. In TSA-1 and TAB-1 structures, it can be seen that the breaking bonds C-H increase by 18.27% and 18.09% compared with the equilibrium bond length in Pe; the forming bonds C-H stretch by 32.18% and 32.36% over the equilibrium bond lengths in isolated A and AB, respectively. The elongation of the breaking bond is smaller than that of the corresponding forming bond, in the case of the three electrophilic addition reaction channels of TSB, TSAB-2, and TSA-2, similar features can be drawn, which indicates that the abovementioned electrophilic addition reactions are all reaction-like; i.e., the five reaction channels will proceed via "early" transition states. It is consistent with Hammond's postulate [28], for an exothermic reaction. Table 3 lists the adiabatic IP (a), EA (a) and the corresponding experimental data [29], as well as the calculated HOMO-LUMO gap (E g ) and the value of BP for reference. Compared with Pe, the other molecules in Table 3 all have π bonds. π bond has higher HOMO and lower  Fig. 2 The schematic diagram of reaction progress of the studied nine channels LUMO compared with σ bond, so the E g value is relatively lower. Moreover, as the conjugated system increases, the gap between the HOMO and the LUMO keeps narrowing. Therefore, the order of E g values is AB < A < B < MAM < BP < Aa < Pe, and AB has the lowest E g value. The σ electrons are in the sp n hybrid orbits, which are close to the nucleus. The σ electrons cannot dissociate easily, as they are firmly attracted by the nucleus. While the π electrons are in the p orbitals, which are far from the nucleus, they are easier to dissociate than the σ electrons. In a conjugated system, the degree of delocalization of π electrons will increase with the enlarging of the conjugated system, and the degree of being bounded by the nucleus will be lower, so it is easier for π electrons to dissociate from the system. It is reported that compounds containing conjugated aromatic structure are suitable to act as voltage stabilizers [16,17]. The IP values in Table 3 of BP, Aa, AB, A, and B are all smaller than Pe, while the IP value of MAM is the highest. The analysis shows that the proportion of heteroatoms in MAM's conjugated chain is 3/7(4 C atoms,1 N atom, and 2 O atoms), which is higher than that of the other conjugated molecules. Compared with C atoms, heteroatoms have the greater electronegativity, so the electrons in MAM are not easy to emit. At the same time, the greater the proportion of electronegative atoms in the molecule is, the easier it is to accept the hot electrons. MAM contains relatively more heteroatoms, so its EA value (1.35 eV) is relatively large, much larger than Pe. It is reported that MAM can be used as space charge inhibitor [14,15]. On the other hand, our researches show that when the conjugated system in the molecule gets larger, its accepting hot electrons' ability gets higher as well, and it is much easier for the larger conjugated system to disperse the accepted hot electrons, so the EA value becomes higher; this regularity can be seen in Table 3 also. Considering the above two factors, the EA value of AB is the largest.

Frontier MOs and energetics
As a voltage stabilizer, it needs to have an excellent ability to receive hot electrons, AB molecule has it; at the same time, the imine structure in AB has the capability of space charge suppression. Therefore, it is ideal to select the AB molecule as a multi-functional additive to improve the electric breakdown strength and inhibit the generation of space charge. We focus on the potential energy surface of the reaction between AB molecule and Pe in the following study.
The reaction energy barrier (ΔG ≠ ) and the reaction Gibbs free energy (ΔG 0 ) for the nine reaction channels are also listed in Table 2. AB can be sensitized by photoinitiator BP mentioned above. It can be seen that AB, A, and B can be grafted to the Pe chain by UV radiation; moreover, AB can be grafted to the Pe chain through four sites. From the data in Table 2, we can also discover that the order of reaction potential barrier (ΔG ≠ ) of four sites in AB isΔG ≠ site1 (0.89 eV) < ΔG ≠ site2 (1.24 eV) < ΔG ≠ site4 (1.96 eV) < ΔG ≠ site3 (2.05 eV). As for the reaction on site 1, it has the lowest reaction potential barrier among the four reaction channels.
For the three electrophilic addition reactions of the 4-position hydrogen in Pe to C of C = O groups (carbonyl in amide, ester carbonyl, and ketone carbonyl), the reaction potential barrier on site 3 of AB is 2.05 eV, which is the highest among the four reaction sites. Site 2 has the lowest reaction potential barrier (1.24 eV) and the lowest Gibbs free energy (ΔG 0 = − 0.01 eV). The reaction channel of site 2 is more advantageous than the other channels in thermodynamics and kinetics. In Table 2, we can see that the reaction potential barrier of the grafting of AB on site 3 is higher than that on site 2 and site 4; this is consistent with the results of natural charge population discussed above (see Table 4). It can be deduced that with the increasing of charge density of the C = O double bond, the reaction potential barrier of electrophilic addition reaction decreases. In other words, when the charge density of the C = O double bond in the molecule decreases, the electrophilic hydrogen addition reaction will become more and more difficult.
Comparing the addition reaction on C of C = C group with that on O of C = O group in AB, it can be seen from Table 2 Table 4 exactly illustrates the problem. In experimental study, AB can be grafted onto the PE chain [18]. According to our computed results, the electrophilic addition reaction of the 4-position hydrogen in Pe to C of C = C group is the dominant reaction channel. AB can be used as a potential multi-functional additive of XLPE insulation material. In addition, as aryl cation in AB molecule possesses strong ability of π electron delocalization than that of alkyl cation PE, aromatic molecule AB is chosen as an additive added in XLPE composite material, which can restore alkyl cation radical from transforming the alkyl cation radical to relatively stable aryl cation radical.

Conclusions
The multiple-channel addition reaction mechanism of hydrogen in polyethylene to four sites on AB molecule has been investigated. The electrophilic addition reaction of the 4-position hydrogen in Pe to C of C = C group is more likely to occur than that of the 4-position hydrogen in Pe to O of C = O groups. As a multi-functional additive, AB molecule can be grafted onto the PE chain by UV radiation to avoid migration. As a UV absorber, AB molecule can play roles as a voltage stabilizer and a space electron inhibitor, improve the electronic breakdown strength of PE insulating materials, and inhibit the generation and accumulation of space charges. The use of multi-functional AB molecule in the material system will reduce the amount of additives and the introduction of chemical impurities and improve the electronic conductivity of insulating materials.
Author contribution We declare that this work was done by the authors named in this article, and all liabilities pertaining to claims relating to the content of this article will be borne by the authors. In addition, a declaration of the role of each author is mentioned as follows: Prof Hui Zhang carried out the geometry optimizations, participated in data analysis, and drafted the manuscript; Dr Chi Deng carried out the calculation of stationary points and frequency analysis; Dr Xia Du carried out the calculation of charger density and the statistical analysis and collected field data; Prof Yan Shang participated in the analysis of the results; Prof Hong Zhao, Xuan Wang, and Baozhong Han designed the study; Prof Zesheng Li helped perform the analysis with constructive discussions. All authors read and approved the final manuscript.
Funding This work is supported by the National Natural Science Foundation of China (51337002) and Key Project of the Joint Fund for Regional Innovation and Development of National Natural Science Foundation of China (U20A2030).

Data availability
The standard coordination of the TSs for every channel is given in the Supplementary information.

Code availability
The study was carried out on the basis of Gaussian 09, Revision A.01.