Effect of the cross-linking agent on the cross-linking degree and electrical properties of cross-linked polyethylene

To study the effect of a cross-linking agent on the cross-linking degree and electrical properties of cross-linked polyethylene, different mass fractions of cross-linked polyethylene and their electrical properties were investigated. The cross-linking degree of cross-linked polyethylene with different mass fractions was tested by the extraction method. The breakdown field strength was tested by DC voltage breakdown tester, and the space charge injection of two kinds of cross-linked polyethylene was tested by Pulsed Electro-Acoustic. In addition, the resistivity was measured with conductivity test. The obtained results show that the crossing degree and breakdown field are the highest when the mass fraction of DCP is 2.5 wt% and BIPB is 1.5 wt%, which is 89.39% and approximately 310 kv mm−1, respectively, while the cross-linking degree and breakdown field are 88.28% and approximately 340 kv mm−1, respectively. At the same time, when DCP is used as the cross-linking agent, the amount of the same cross-linking agent is greater, which leads to more impurities contained in the material and increased space charge accumulation in the material; thus, the breakdown strength is lower than that of BIPB, and the conductivity is higher with the cross linking agent of DCP.


Introduction
Currently, the insulation materials used in power cables mainly include polymers such as polyvinyl chloride (PVC), polyethylene (PE), silicone rubber (SR), polytetrafluoroethylene (PTFE) and cross-linked polyethylene (XLPE) [1][2][3]. Among them, cross-linked polyethylene cable insulation materials have high power transmission, high voltage resistance level, long service life, and low cost [3]. Therefore, high-voltage flexible DC transmission projects that have been put into operation or under construction worldwide basically use cross-linked polyethylene as insulation material for power cables [4,5].
Cross-linked polyethylene (XLPE) is polyethylene cross-linked by various methods. These approaches transform the polyethylene molecule from a linear molecular structure to a three-dimensional network molecular structure and from a thermoplastic to a thermosetting plastic, which improves its heat resistance and mechanical properties and allows it not to melt after heating and maintain the excellent electrical properties of polyethylene [6].
There are five main cross-linking methods for polyethylene: peroxide cross-linking, silane cross-linking, UV cross-linking, salt cross-linking and high-energy radiation cross-linking [7]. Among them, silane cross-linked polyethylene is a polymer that loses the H atom on the tertiary carbon atom (under the action of a free initiator and pyrolysis), which produces free radicals that react with the -CH=CH 2 group of vinyl silane to produce grafted polymers containing a trioxysilyl ester group. During the cross-linking process, the grafted polymers are first hydrolysed in the presence of water to produce silanol, -OH and the adjacent Si-O-H groups to form Si-O-Si bonds, resulting in cross-linking between polymer macromolecules [8]. The method of silane cross-linking has the advantages of simple manufacturing equipment, easy operation and low overall cost. The irradiation cross-linking reaction is a process in which various free radicals are generated after irradiation of the polymer and cross-linked by combining the free radicals with each other to form new bonds. The irradiated cross-linked wire and cable insulation materials have good heat resistance, oil resistance and flame resistance properties. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
However, cross-linked polyethylene produced by silane and radiation cross-linking has a significant crosslink density gradient along the material thickness direction, and the cross-linkage is not uniform, which leads to unstable cross-linked polyethylene properties [9]. In contrast, the cross-linking degree of cross-linked polyethylene formed by cross-linking through the peroxide cross-linking method is more uniform compared to the first two cross-linking methods; therefore, the peroxide cross-linking method is more frequently used in industry to produce cross-linked polyethylene. Currently, the most commonly used peroxide cross-linker is diisopropylbenzene peroxide (DCP) because the decomposition temperature of DCP is lower than the degradation temperature of the polyethylene matrix, which avoids the degradation of polyethylene during crosslinking and effectively prevents the precross-linking phenomenon of cross-linked polyethylene. The crosslinking mechanism of organic peroxides can be divided into three consecutive steps [10], and the cross-linking process of DCP cross-linked polyethylene, as an example, is shown in figure 1.
Diisopropylbenzene peroxide is decomposed in two steps. The first step involves heating to temperature above 130°C; the thermal decomposition of diisopropylbenzene peroxide splits it into isopropylbenzene radicals, which in the presence of monomers can initiate polymerization reactions. In the absence of monomers, isopropylbenzene radicals are prone to further decomposition into phenyl radicals or reconstituted into acetophenone or methyl radicals. Then, the primary radicals (containing isopropyl phenyl radicals, a small amount of phenyl radicals and methyl radicals) react with the macromolecular chain to produce macromolecular chain radicals (j in the formula represents various primary radicals); the macromolecular chain radicals then react with other molecular chains, and the molecular weight keeps increasing. Finally, the chain reaction is terminated, and a three-dimensional mesh structure is finally formed between the polyethylene molecular chains and molecular chains by cross-linking [11].
Polyethylene has improved heat resistance after cross-linking, and the long-term working temperature that can be allowed is increased from 70°C to 90°C [11]. Mechanical properties (such as elongation at break, tensile strength and modulus of elasticity) are also improved to varying degrees [12]. Electrical properties, such as breakdown resistance, have also been improved to varying degrees [13]. Currently, XLPE is widely used in industry. In particular, the cross-linking process of dicumyl peroxide (DCP) has a heavy odour. DCP is a colourless, tasteless, and transparent crystal, but the small molecule products after the decomposition of DCP mainly include acetophenone, which does not easily volatilize and has an odour, which makes the product have a very strong and irritating odour, which pollutes the environment and is harmful to the human body [14]. In addition, the cross-linking effect of DCP is general, and the amount of DCP used in the process of cross-linking of polyethylene is generally between 1% and 3%, which makes it relatively large and easy to cause uneven mixing with the cross-linked polyethylene base material and uneven cross-linking degree, which affects the mechanical properties and electrical property stability of plastic products.
Cross-linking agents can also be used to cross-link polyethylene with bis-tert-butylperoxyisopropylbenzene (BIPB) instead of diisopropyl peroxide. A schematic diagram of the cross-linking process of BIPB cross-linked polyethylene is shown in figure 2.
By comparing the process of cross-linking LDPE with BIPB and DCP, it is observed that the cross-linking agent BIPB has the following main advantages over DCP. (1) The chemical formula of BIPB contains two peroxy bonds, with high cross-linking efficiency and few crosslinking byproducts.
(2) The densification temperature of BIPB and polyethylene is higher than that of DCP by approximately 10°C. The low-density polyethylene matrix has better flowability and densification uniformity.
(3) The cross-linking byproducts produced during the cross-linking process of DCP have an unpleasant odour, and the odour is present in the product for a long time, while BIPB does not have such odour and is called 'odourless DCP' [15].
In this study, DCP and BIPB were used to cross-link low-density polyethylene, and then the cross-linking degree of the polyethylene was measured by the extractive reflux method to compare the cross-linking efficiency of the two cross-linking agents and the cross-linking degree of prepared cross-linked polyethylene. The electrical properties of the cross-linked polyethylene specimens with different degrees of cross-linking were examined, including the DC voltage breakdown test and measurement of the space charge profile, and the influence of the degree of cross-linking on the electrical properties of the cross-linked polyethylene was analysed based on the test results.

Samples and experiments
2.1. Sample preparation First, the LDPE pellets and the cross-linker were mechanically blended using a dense mixing platform of the torque rheometer as follows.
(2) Mechanical blending of LDPE and DCP or BIPB cross-linker using the dense mixing platform of the torque rheometer. The blended composites are removed in blocks, sheared into pellets and prepared for use. (3) A plate vulcanizer was used to thermocompression cross-link LDPE and to prepare the samples. Prepressure and a cross-linking time of 10 min at 180°C and 16 MPa were used to prepare the thermoset sheet composite specimens, which were placed in the specimen bag for backup.
For the cross-linking measurement, a circular specimen with a thickness of 0.15 mm and a length of 12 cm is used for the DC voltage breakdown test at at a ramp rate of 500V s −1 under the environment of 50% relative atmosphere humidity and 32°C in temperature. Figure 3 shows the breakdown strength of insulation measured by the high voltage kit.
A square specimen with a thickness of 0.15 mm and a side length of 11.5 cm is used; for the space charge measurement, a circular specimen with a thickness of 0.3 mm and a diameter of 8 cm is used. The principle of measuring space charge distribution in insulating materials by electroacoustic pulse method is shown in figure 4.

Determination of the cross-linking degree of cross-linked polyethylene
The extraction method was used to determine the cross-linking degree of cross-linked polyethylene. The procedure for determining the degree of cross-linking of specimens by the extraction method is as follows.
(1) The press-moulded 0.5 mm thick test piece was cut into 0.5 mm × 0.5 mm size pellets.
(2) Weigh 0.15-0.25 g of the sample into the copper mesh and weigh the mass bit G1 of the copper mesh package.
(3) The copper mesh package was placed in a three-neck flask containing xylene solvent and extracted at 150°C for 6 h at reflux.
(4) The mass of the dried copper mesh package is weighed as G2.  (5) Then, the cross-linking degree (C) of the tested sample can be expressed as: he degree of cross-linking of the cross-linked polyethylene specimens was measured separately by this method.
2.3. Dielectric and electrical properties testing 2.3.1. DC breakdown field strength A DDJ-100 kV voltage breakdown tester was used to measure the DC breakdown field strength of XLPE crosslinked by DCP and XLPE cross-linked by BIPB. Two circular copper electrodes with a diameter of 200 mm were used as the high-voltage electrode and the ground electrode, and silicone oil was used as the medium. The voltage was increased at a linear rate of 1 kV s −1 using a computer program until breakdown occurred on the tested specimens, at which time the voltage data were recorded to derive the breakdown voltage of the XLPE insulation material. A total of 13 test pieces were included, namely, pure LDPE, XLPE/0.5 wt% DCP, XLPE/1.0 wt% DCP, XLPE/1.5 wt% DCP, XLPE/2.0 wt% DCP, XLPE/2.5 wt% DCP, XLPE/3.0 wt% DCP, XLPE/0.3 wt% BIPB, and XLPE. Each specimen was subjected to at least ten DC voltage breakdown tests, the breakdown field strengths of the specimens were obtained from the breakdown voltages and the thicknesses of the specimens, and the Weibull statistical distribution was used to determine the breakdown field strengths of the specimens. The experimental data of the breakdown field strength were processed and analysed by the Weibull statistical distribution.

Space charge
The space charge content and distribution in the samples were measured using the pulsed electroacoustic method (PEA, HEYI-PEA-PT1) [16]. The applied electric field strengths were 10, 20, 30, 40 and 50 kV mm −1 . The same specimen was tested at a certain strength for 30 min for charge injection and another 10 min for decay. In this experiment, the specimen was measured when polyethylene cross-linked by the two cross-linkers reached the maximum cross-linkage.

DC resistance
The DC resistance of the cross-linked polyethylene material is measured using a ZC-90G insulation resistance tester, and then the conductivity is calculated. The diameter of the electrode used in this test is 50 mm, and the data measured by the insulation resistance tester are the electrical resistance (Rv). The resistance of each sample was measured five times, and their average value was taken.

Cross-linking degree
In figure 5, the horizontal coordinates are the contents of the cross-linking agents DCP and BIPB, and the vertical coordinates are the cross-linking degree of the cross-linked polyethylene specimens obtained by their cross-linking, where the square represents cross-linked polyethylene obtained by BIPB cross-linking, and the circular curve is cross-linked polyethylene obtained by DCP cross-linking. By comparison, it can be found that the cross-linking degree of cross-linked polyethylene obtained by DCP cross-linking can reach a maximum of 89.51%, while the cross-linking degree of cross-linked polyethylene obtained by BIPB cross-linking can reach a maximum of 88.28%. However, compared with the cross-linker DCP, the cross-linker BIPB is more efficient, and the cross-linking degree of the cross-linked polyethylene specimens cross-linked by BIPB is greater when the amount used is equal; for example, when they are both used at 1.5 wt%, the cross-linking degree of the crosslinked polyethylene specimens cross-linked by BIPB reaches 88.28%, while the cross-linking degree of the crosslinked polyethylene specimens cross-linked by DCP is only approximately 75%. When the cross-linking degree of cross-linked polyethylene is maximized, the amount of DCP needs to reach 2.5 wt%, while the amount of BIPB only needs 1.5 wt% to make cross-linked polyethylene reach the maximum cross-linking degree. This occurs because the molecular formula of the cross-linker BIPB contains two peroxy bonds, while the crosslinker DCP contains only one peroxy bond; thus, BIPB can produce more free radicals after thermal decomposition. These free radicals can also produce more free radicals through free radical decomposition or free radical recombination, and these free radicals can quickly react with polymer chain segments, thus completing the cross-linking of low-density polyethylene molecular chains. These radicals can quickly react with the polymer chain segments to complete the cross-linking between the LDPE molecular chains.

DC voltage breakdown
The results of DC voltage breakdown tests on uncross-linked linear LDPE specimens, six cross-linked polyethylene specimens cross-linked with different contents of DCP, and six cross-linked polyethylene specimens cross-linked with different contents of BIPB are shown in figure 4. Figure 4(a) shows the Weibull distribution of DC breakdown field strengths of linear LDPE specimens without the cross-linking process and six cross-linked polyethylene specimens with different contents of DCP cross-linking, and figure 4(b) shows the Weibull distribution of DC breakdown field strengths of uncross-linked linear LDPE specimens and six crosslinked polyethylene specimens with different contents of BIPB cross-linking.
From figure 6(a) and table 1, the DC breakdown field strength of uncross-linked linear LDPE specimens is approximately 250 kV mm −1 , while the DC breakdown field strength of cross-linked polyethylene specimens cross-linked with cross-linker DCP is generally greater than that of uncross-linked specimens. Even when the DCP content of cross-linked polyethylene is only 0.5 wt%, the DC breakdown field strength of the specimens increases to approximately 265 kV mm −1 , which is a higher value than that of uncross-linked LDPE specimens. The DC breakdown field strength increased with increasing cross-linker DCP content, which was approximately 280 kV mm −1 at 1.0 wt% DCP, 290 kV mm −1 at 1.5 wt% DCP, and 2.0 wt% DCP. When the DCP content was increased to 2.5 wt%, the DC breakdown field strength reached a maximum of 315 kV mm −1 , but when the DCP content was increased to 3.0 wt%, the DC breakdown field strength decreased to 310 kV mm −1 .
By analysing figure 6(b), we can find the same pattern as above, but the difference between the cross-linked polyethylene specimen cross-linked by BIPB and the cross-linked polyethylene specimen cross-linked by DCP is that at 1.5 wt% BIPB, the DC breakdown field of the specimen reaches 340 kV mm −1 , which is 30 kV mm −1 larger than the DC breakdown field of the specimen cross-linked by DCP at 2.5 wt%. which is approximately 30 kV mm −1 higher than that of the DCP specimen with 2.5 wt%.
By combining the data shown in figure 4 with the relationship between cross-linker content and crosslinking degree in figure 3, it is found that the DC breakdown field of cross-linked polyethylene specimens increases as the cross-linking degree increases, and the change pattern is consistent with the cross-linking degree. When the DCP content of the specimen is 2.5 wt% and the BIPB content is 1.5 wt%, the cross-linked polyethylene reaches the maximum cross-linking degree, and the DC breakdown field intensity of the specimen also reaches the maximum value at this time. This occurs because the cross-linking process of peroxide transforms LDPE from a linear structure to a three-dimensional mesh structure by cross-linking between molecular chains, which greatly improves its dielectric properties and breakdown field strength. When the peroxide content is too high, the decomposition of peroxide produces free radicals that cannot initiate the chain reaction and remain in the specimen, and after cross-linking, too many cross-linking byproducts are produced, including acetophenone, α-methylstyrene and benzyl alcohol, which will affect the breakdown field strength of the specimen to some extent [17,18]. Of note, the DC breakdown voltage of the cross-linked polyethylene specimens cross-linked by BIPB is higher than that of the cross-linked polyethylene specimens cross-linked by DCP on the basis of the maximum cross-linking degree of the specimens, which is due to the high cross-linking efficiency of the BIPB cross-linker, the low dosage and the low content of byproducts.

Space charge
The distribution of space charge inside the cross-linked polyethylene specimens with DCP and BIPB contents of 1.5 wt% under pressurized conditions was measured by the electroacoustic pulse method, and the test results are shown in figure 5 below.   Figure 7 shows the space charge distribution of the cross-linked polyethylene specimens with the same DCP and BIPB content measured by the electroacoustic pulse method, where the applied field strengths are 20 kV mm −1 , with a gradient of 10 kV mm −1 . Figure 7 shows that When the concentrations of DCP and BIPB are the same, the internal space charge of the sample is more when DCP is used as the crosslinking agent.
After cross-linking of linear LDPE with the cross-linking agent DCP, various cross-linking byproducts remain in the polymer, which mainly include methane, 2-phenyl-2-isopropanol, α-methylstyrene, acetophenone and benzyl alcohol. These cross-linking byproducts undergo impurity ionization under high pressure and generate a large space charge [19,20]. In contrast, BIPB has high cross-linking efficiency in the cross-linking process of LDPE, and the content of cross-linking byproducts in the polymer is also lower than that of DCP used as a cross-linking agent. Therefore, the space charge content from ionization of cross-linking byproducts inside the cross-linked polyethylene specimens cross-linked with cross-linker BIPB is lower than that of the cross-linked polyethylene specimens cross-linked with DCP.

DC conductivity
The variation in the DC breakdown field strength can be verified by a DC conductivity test of cross-linked polyethylene. Figure 8 shows the relationship between the content of DCP and BIPB and the DC conductivity of cross-linked polyethylene.
As shown in figure 8, the DC resistivity of cross-linked polyethylene increases with increasing DCP content. The resistivity reaches the maximum value (7.962×10 -14 Ω m) when the DCP content reaches 2.5 wt% but decreases to 7.657×10 −14 Ω m when the DCP content continues to increase to 3 wt%. The variation pattern is also similar for the DC resistivity of cross-linked polyethylene with BIPB as a cross-linking agent. However, it can be seen from the figure that the effect of BIPB on the increase in DC resistivity of nanocomposites is significantly higher than that of DCP on the increase in DC resistivity of nanocomposites. This indicates that the use of different cross-linking agents can effectively increase the DC resistivity of cross-linked polyethylene, and the low cross-linking efficiency and high content of byproducts of DCP cross-linking agents lead to relatively low resistivity and highest DC breakdown field strength at 2.5 wt% DCP and 1.5 wt% BIPB.

Conclusions
The maximum cross-linking degree of cross-linked polyethylene prepared by the two cross-linking agents is approximately the same, but the cross-linking efficiency of BIPB is significantly higher than that of DCP, and only 1.5 wt% of the dosage is needed to make the cross-linked polyethylene reach the maximum cross-linking degree.
(1) The DC breakdown field strength of the cross-linked polyethylene specimens cross-linked by BIPB is greater than that of the specimens cross-linked by the conventional cross-linker DCP.
(2) The internal space charge of the cross-linked polyethylene specimens prepared by BIPB is also reduced when the content is the same compared to the specimens cross-linked by DCP, and the internal space charge of the specimens is similar when the cross-linking degree is similar.
(3) The resistivity of the cross-linked polyethylene-type sample prepared by BIPB is smaller than that of the specimen cross-linked by DCP.

Data availability statement
All data that support the findings of this study are included within the article (and any supplementary files).