Dielectric and AC Breakdown Properties of SiO 2 /MMT/LDPE Micro–Nano Composites

: Low-density polyethylene (LDPE) is an important thermoplastic material which can be made into ﬁlms, containers, wires, cables, etc. It is highly valued in the ﬁelds of packaging, medicine, and health, as well as cables. The method of improving the dielectric property of materials by blending LDPE with inorganic particles as ﬁller has been paid much attention by researchers. In this paper, low-density polyethylene is used as the matrix, and montmorillonite (MMT) particles and silica (SiO 2 ) particles are selected as micro and nano ﬁllers, respectively. In changing the order of adding two kinds of particles, a total of ﬁve composite materials were prepared. The crystallization behavior and crystallinity of ﬁve kinds of composites were observed, the ε r and tan δ changes of each material were investigated with frequency and temperature, and the power frequency (50 Hz) AC breakdown performance of materials were measured. The differential scanning calorimetry (DSC) and X-ray diffraction (XRD) results show that the crystallinity of the composites is higher than that of LDPE. Experimental data of dielectric frequency spectra show that the dielectric constants of micro– nano composites and composites with added MMT particles are lower than LDPE, the dielectric loss of composites can be improved by adding MMT particles. The experimental data of dielectric temperature spectra show that the permittivity of SiO 2 -MMT/LDPE is still at a low level under the condition of 20~100 ◦ C. In terms of breakdown ﬁeld strength, the SiO 2 /LDPE composite material increased by about 17% compared with the matrix LDPE, and the breakdown ﬁeld strength of the materials SiO 2 -MMT/LDPE and MMT-SiO 2 /LDPE increased by about 6.8% and 4.6%, respectively.


Introduction
Low-density polyethylene (LDPE) is diffusely employed in many fields, such as wire and cable industry and environmental engineering, because of its outstanding insulation, fine mechanical properties, process performance, and adsorption [1,2].With the rapid economic development of all countries in the world, the cable industry is moving towards high voltage and ultra-high voltage.Therefore, it is very important to enhance the dielectric property of high-voltage insulation materials and d evelop higher-grade high-voltage insulation materials [3].
In the interest of meeting the increasing demand for science and technology progress and the development of society on the insulating electrical properties of polymers, researchers have tried to ameliorate the physicochemical properties of polymers by the method of adding inorganic nano-fillers.A great deal of research work shows that the mixing of nano-fillers and polymer materials could polish up the breakdown field strength [4][5][6], conductivity [7,8], electrical tree resistance, and partial discharge performances [9,10], as well as inhibit the accumulation of space charges [11,12].Nevertheless, the result of the aggregation of nanoparticles in polymers has made achieving good dispersion difficult.Thereby, different researchers have different conclusions.Up to now, the improvement mechanism of added inorganic particles to matrix is still not very clear.For the sake Energies 2021, 14, 1235 2 of 15 of acquisition of maximized dispersion of nanoparticles in polymers, scholars make an attempt to blend micro-and nanoparticles with matrix materials.It is expected that the superior properties of composites will be obtained through the synergistic effect between micro-and nanoparticles.Research shows that the introduction of micron-particles and nanoparticles to matrix materials can not only avoid the agglomeration of nano-particles, but also improve the properties of the matrix materials [13][14][15].At a certain proportion, the adding of the micron particle will highlight unique performances of the nanoparticle to a certain degree.This makes certain performances of micro-nano composites resemblant to nano-composites, and even superior to nano-composites.Ma et al. synthesized micro-nano Co 3 O 4 ceramic materials by liquid phase and calcination method and studied its microstructure and dielectric properties, and found that micro-nano composite materials have more excellent dielectric properties [16].Espinoza-Gonzalez et al. doped CaCu 3 Ti 4 O 12 (CCTO) with ZrO and ZrO 2 as micro-nano fillers, and found the micro-nano composite exhibited lower dielectric loss and a smaller dielectric constant [17].Nazir et al. added micro and nano boron nitride (BN) particles to the matrix ethylene propylene diene monomer (EPDM) by melt blending method.It was found that the composite with 25 wt% micron particles and 5 wt% nanoparticles had good dielectric loss performance; the composite with 29 wt% micron particles and 1% nanoparticles showed low permittivity [18].
Adding nano-SiO 2 particles into LDPE can increase the crystal nucleus density, reduce the spherulite size, and enhance the resistance to partial discharge [19].Montmorillonite (MMT) is a layered silicate mineral with one-dimensional nano-structure.After being organically treated, MMT is introduced into LDPE by melt intercalation method.MMT can scatter and block electrons generated in the discharge process, thus improving the partial discharge resistance of LDPE [20].In this paper, SiO 2 was selected as inorganic nanoparticles, MMT as micron particles, LDPE as polymer matrix, with 1 wt% of added content, LDPE, MMT/LDPE, SiO 2 /LDPE, SiO 2 -MMT/LDPE, and MMT-SiO 2 /LDPE composite materials were prepared by melt blending method.The adding order of micro-nano particles in SiO 2 -MMT/LDPE and MMT-SiO 2 /LDPE was changed.SiO 2 -MMT/LDPE involved adding the SiO 2 particle first and then the MMT particle, while MMT-SiO 2 /LDPE involved adding the MMT particle first and then the SiO 2 particle.The effects of different composite systems and adding order of particles on the crystalline structure, dielectric properties, and AC breakdown properties of the composites were studied.
The research content of the article is a continuation of the research of reference [21].The research results of the conduction current and space charge characteristics of SiO 2 /MMT/ LDPE micro-nano composites are published in reference [21], which concluded that MMT-SiO 2 /LDPE composite materials can well hinder carrier migration and have a strong inhibitory effect on space charges, but many contents could not be perfected because the previous writing and publications are in the COVID-19 epidemic period.In this paper, the polarizing microscope (PLM) experiment and the differential scanning calorimetry (DSC) experiment were supplemented and analyzed, and X-ray diffraction (XRD) experimental results were combined to verify the crystallization behavior and crystallinity of each material.The characteristics of dielectric spectrum and dielectric temperature spectrum of each experimental material were analyzed, and the breakdown field strength characteristics of each composite material were studied.The research done in this paper is a great supplement to the previous research, which can make readers have a more comprehensive understanding of our research work, which has vital function in understanding the mechanism of improving properties of micro and nano composites.

Surface Modification of SiO 2
The nano silica (SiO 2 ) and silane coupling agent (KH570) used to prepare the samples were both from Beijing Deke Daojin Science and Technology (Beijing, China), and the particle size of nano-SiO 2 was 30 nm.SiO 2 particles were treated with coupling agent KH570.Firstly, the SiO 2 powder was dissolved with the mixed solution of anhydrous ethanol and deionized water, and stored in a three-neck boiling flask.Secondly, the ultrasonic wave was used to oscillate for 1 h, silane coupling agent KH570 was added, and heated in a constant temperature water bath.The temperature was set at 80 • C, stirring uniformly at high speed, and applying ultrasonic oscillation for 2 h again.Finally, after filtering, washing, drying, and grinding, the surface-modified SiO 2 particles were obtained.

Organic Treatment of MMT
The montmorillonite (MMT) was purchased from Qinghe Chemical Plant in Zhangjiakou City of China.The particle size of the original MMT was about 40-70 µm, and the cation exchange capacity was 0.9-1.2mol/kg.Firstly, MMT was mixed with weak acid solution in a certain proportion, and then heated in a water bath at 80 • C and stirred at high speed to obtain a uniform MMT suspension.Then, it was centrifuged and purified, and then intercalated with octadecyl trimethyl ammonium chloride solution.The mixture was placed in the water bath again.The temperature was set at 80 • C, and high-speed stirring and ultrasonic treatment were carried out to obtain the MMT with intercalation suspension.The suspension was allowed to stand, then washed with deionized water until no white precipitate appeared after being tested by AgNO 3 solution.After a series of operations such as drying, grinding, and sieving, the intercalated solid MMT particles were obtained.
The MMT particles prepared above were used to prepare the MMT suspension with 95% ethanol solution as solvent in a ratio of 1 g:10 mL, and the solution was stirred at high speed and oscillated by ultrasonic for 3 h with the temperature of 70 • C.After that, the silane coupling agent KH570 was used to modify the surface.The specific operation steps are as follows: In acidic environment with pH value of 3~5, the coupling agent KH570 was pre-hydrolyzed with 95% ethanol aqueous solution.While stirring the MMT suspension, the hydrolyzed KH570 was slowly added into the suspension in three times.After the solution reaction is completed, it should be left to stand for a period of time through the separator funnel.Then, the MMT layer was taken out and dried in an oven under 80 • C for 24 h, and then ground and screened to obtain the organic MMT required in this paper.

Preparation of Composite Materials
Experimental fabrication of materials required for this article is reported in [21].

Crystallization Behavior
The five kinds of materials were soaked in the mixed solution of potassium permanganate and concentrated sulfuric acid with mass fraction of 5% for 5 h to etch the surface of the sample.After that, the samples were cleaned with ultrasonic cleaning apparatus.The microscopic morphology of each sample was detected by LeicaDM2500 polarizing microscope (PLM, Leica Microsystems, Wetzlar, Germany), and the magnification was 500 times.
A DSC-1 differential scanning calorimeter produced by Mettler Toledo company was utilized to measure the crystallization and fusion temperature of each material.The determination condition was nitrogen atmosphere, and the lifting and cooling rates were all 10 • C/min.The temperature selection range was 25~140 • C, and 10~15 mg was weighed for each sample.
The LDPE and composite materials were tested by X-ray diffraction (XRD) using EMPYREAN X-ray diffractometer (Panako, The Netherlands).Cu target was used in the experiment.The tube voltage was 40 kV, the tube current was 30 mA, the experimental scanning speed was 2 • /min, the scanning range was 2θ = 5 • ~50 • , and the X-ray wavelength was 0.154 nm.

Dielectric Frequency Spectra and Dielectric Temperature Spectra
At ambient temperature, the ε r and tanδ of all samples were tested with frequency f by broadband dielectric/impedance spectrometer (Novocontrol Technologies, Montabaur, Germany), and the test frequency range was 10 −1 Hz~10 6 Hz.For reducing the influence of moisture and residual charge on the test results, it is necessary to short-circuit each experimental material in advance.
The QS30I high-precision high-voltage capacitor bridge (Shanghai Peicheng Electronic Technology Development Co., Ltd., Shanghai, China) and high-low temperature alternating test box (Shanghai Guangpin Test Equipment Manufacturing Co., Ltd., Shanghai, China) were used to test the change of ε r and tanδ with T by three electrode system.The temperature range was 20~100 • C, and the temperature gradient was 10 • C. The pretreatment method of the samples was consistent with the dielectric spectrum.During the time of test, electrodes and samples should be placed in a high and low temperature alternating test chamber and the temperature should be kept constant.

Breakdown Strength
According to the Chinese standard GB/T1408.1-2005,the power frequency AC breakdown performance of each sample was tested by plate-plate electrode, as shown in Figure 1.The diameter and height of the upper electrode were 20 mm and 25 mm, respectively.The diameter and height of the lower electrode were 60 mm and 10 mm, respectively.The edges of the electrodes were rounded and the radius was 2 mm.The sample thickness was 50 µm.In order to prevent residual charge from affecting the test results, it is necessary to short-circuit each sample to be tested before testing the breakdown field strength.In order to prevent the edge discharge of metal electrode, the sample with thickness of 50 µm and electrode should be immersed in cable oil.In the test, 50 Hz alternating current was used, and the voltage was slowly increased at a speed of 1 kV/s until composites were broken down, and the voltage was recorded.By the formula E = U/D, the corresponding power frequency AC breakdown field strength was calculated, where U is the voltage at the breakdown of the sample, D is the thickness of the sample, and E is the breakdown field strength of each sample.was 0.154 nm.

Dielectric Frequency Spectra and Dielectric Temperature Spectra
At ambient temperature, the εr and tanδ of all samples were tested with frequency f by broadband dielectric/impedance spectrometer (Novocontrol Technologies, Montabaur, Germany), and the test frequency range was 10 −1 Hz~10 6 Hz.For reducing the influence of moisture and residual charge on the test results, it is necessary to short-circuit each experimental material in advance.
The QS30I high-precision high-voltage capacitor bridge (Shanghai Peicheng Electronic Technology Development Co., Ltd., Shanghai, China) and high-low temperature alternating test box (Shanghai Guangpin Test Equipment Manufacturing Co., Ltd., Shanghai, China) were used to test the change of εr and tanδ with T by three electrode system.The temperature range was 20~100 °C, and the temperature gradient was 10 °C.The pretreatment method of the samples was consistent with the dielectric spectrum.During the time of test, electrodes and samples should be placed in a high and low temperature alternating test chamber and the temperature should be kept constant.

Breakdown Strength
According to the Chinese standard GB/T1408.1-2005,the power frequency AC breakdown performance of each sample was tested by plate-plate electrode, as shown in Figure 1.The diameter and height of the upper electrode were 20 mm and 25 mm, respectively.The diameter and height of the lower electrode were 60 mm and 10 mm, respectively.The edges of the electrodes were rounded and the radius was 2 mm.The sample thickness was 50 μm.In order to prevent residual charge from affecting the test results, it is necessary to short-circuit each sample to be tested before testing the breakdown field strength.In order to prevent the edge discharge of metal electrode, the sample with thickness of 50 μm and electrode should be immersed in cable oil.In the test, 50 Hz alternating current was used, and the voltage was slowly increased at a speed of 1 kV/s until composites were broken down, and the voltage was recorded.By the formula E = U/D, the corresponding power frequency AC breakdown field strength was calculated, where U is the voltage at the breakdown of the sample, D is the thickness of the sample, and E is the breakdown field strength of each sample.

Crystalline Morphology
Figure 2 shows the crystalline morphology of each material under PLM after being etched by concentrated sulfuric acid mixed with potassium permanganate.As both the previous writing and the ICHVE 2020 conference were held during the COVID-19 epidemic period, universities were closed, so the crystal cell size of each material was not marked in time [21,22].Now, the epidemic situation in China is well controlled and universities have been opened.We went back to the laboratory and marked the crystal cell size of each composite material, and the statistical distribution of the crystal cell size of each material was calculated; the results are shown in Figure 3. From Figure 2, the crystal of all materials Energies 2021, 14, 1235 5 of 15 are spherical structures.It can be seen from Figure 3 the average and standard deviation of cell size of each sample.In Figures 2 and 3, LDPE has the largest crystal cell size, and the crystal cell size varies, the diameter of crystal cell is about 9~19 µm, and the average size is 12.541 µm.After adding MMT into the matrix, the crystal cell size decreases, the average size is 6.849 m, and the crystal cell spacing decreases to some extent.The crystal cell size of composites with SiO 2 particles is further reduced, with an average diameter of 6.345 µm, and the crystal cell size of SiO 2 /LDPE is uniform, but its crystal cell spacing is larger than that of micro-nano composites SiO 2 -MMT /LDPE and MMT-SiO 2 /LDPE.The crystal cell size and spacing of SiO 2 -MMT/LDPE material prepared by the method of adding SiO 2 particle first and then MMT particle are further reduced.The diameter of the crystal cell is distributed around 4~8 µm, and the average diameter of the cell is 5.341 µm.The internal structure of the material is tight.The crystal size and spacing of MMT-SiO 2 /LDPE material prepared by the method of adding MMT particle first and then SiO 2 particle becomes smaller than the former, and the crystal cell diameter is distributed around 3~7 µm with the average crystal cell diameter as 4.765 µm.The reason why the crystal cell size of MMT-SiO 2 /LDPE is smaller than that of SiO 2 -MMT/LDPE is that the small-sized particle is added first, which makes it easier for the small-sized particles to enter the machine body and play a heterogeneous nucleation role, thus reducing the unit cell size.However, a small-sized particle is added first, and then a large-sized particle is added, which will damage the structure formed by the small-sized particle added first, and weaken the heterogeneous nucleation effect, so the cell size is reduced.

Crystalline Morphology
Figure 2 shows the crystalline morphology of each material under PLM after being etched by concentrated sulfuric acid mixed with potassium permanganate.As both the previous writing and the ICHVE 2020 conference were held during the COVID-19 epidemic period, universities were closed, so the crystal cell size of each material was not marked in time [21,22].Now, the epidemic situation in China is well controlled and universities have been opened.We went back to the laboratory and marked the crystal cell size of each composite material, and the statistical distribution of the crystal cell size of each material was calculated; the results are shown in Figure 3. From Figure 2, the crystal of all materials are spherical structures.It can be seen from Figure 3 the average and standard deviation of cell size of each sample.In Figures 2 and 3, LDPE has the largest crystal cell size, and the crystal cell size varies, the diameter of crystal cell is about 9~19 μm, and the average size is 12.541 μm.After adding MMT into the matrix, the crystal cell size decreases, the average size is 6.849 m, and the crystal cell spacing decreases to some extent.The crystal cell size of composites with SiO2 particles is further reduced, with an average diameter of 6.345 μm, and the crystal cell size of SiO2/LDPE is uniform, but its crystal cell spacing is larger than that of micro-nano composites SiO2-MMT /LDPE and MMT-SiO2/LDPE.The crystal cell size and spacing of SiO2-MMT/LDPE material prepared by the method of adding SiO2 particle first and then MMT particle are further reduced.The diameter of the crystal cell is distributed around 4~8 μm, and the average diameter of the cell is 5.341 μm.The internal structure of the material is tight.The crystal size and spacing of MMT-SiO2/LDPE material prepared by the method of adding MMT particle first and then SiO2 particle becomes smaller than the former, and the crystal cell diameter is distributed around 3~7 μm with the average crystal cell diameter as 4.765 μm.The reason why the crystal cell size of MMT-SiO2/LDPE is smaller than that of SiO2-MMT/LDPE is that the small-sized particle is added first, which makes it easier for the small-sized particles to enter the machine body and play a heterogeneous nucleation role, thus reducing the unit cell size.However, a small-sized particle is added first, and then a large-sized particle is added, which will damage the structure formed by the small-sized particle added first, and weaken the heterogeneous nucleation effect, so the cell size is reduced.

Crystallinity of Composite Materials
This part of the experiment has been given some analysis in reference [22].The experimental results and analysis of XRD, dielectric spectrum, dielectric temperature spectrum, and breakdown in this paper need to be combined with this part of the experiment.In order to make the analysis of this paper more comprehensive, further experimental analysis is given here again.Considering the particles do not contribute to the enthalpy of crystallization, we can obtain the crystallinity of five samples through the calculation of Equation ( 1) [23].
The fusion temperature and crystallinity results of all samples are listed in Table 1.

Crystallinity of Composite Materials
This part of the experiment has been given some analysis in reference [22].The experimental results and analysis of XRD, dielectric spectrum, dielectric temperature spectrum, and breakdown in this paper need to be combined with this part of the experiment.In order to make the analysis of this paper more comprehensive, further experimental analysis is given here again.Considering the particles do not contribute to the enthalpy of crystallization, we can obtain the crystallinity of five samples through the calculation of Equation ( 1) [23].
The fusion temperature and crystallinity results of all samples are listed in Table 1.

Crystallinity of Composite Materials
This part of the experiment has been given some analysis in reference [22].The experimental results and analysis of XRD, dielectric spectrum, dielectric temperature spectrum, and breakdown in this paper need to be combined with this part of the experiment.In order to make the analysis of this paper more comprehensive, further experimental analysis is given here again.Considering the particles do not contribute to the enthalpy of crystallization, we can obtain the crystallinity of five samples through the calculation of Equation ( 1) [23].
Energies 2021, 14, 1235 8 of 15 The fusion temperature and crystallinity results of all samples are listed in Table 1.
where H 0 = 293.6J/g −1 and w is the particles content in the composites.The increase in the crystallinity of the sample is due to heterogeneous nucleation after doped particles.The heterogeneous nucleation of SiO 2 with smaller particle size is obvious, and the crystallinity of SiO 2 /LDPE material has a larger increase.During the experiment, the addition order of micro-and nanoparticles was changed to research the crystallinity of micro-nano composite materials.According to the order of adding the SiO 2 particle first and then the MMT particle, the crystallinity of SiO 2 -MMT/LDPE composites are weaker than that of the composites with only SiO 2 particles.This is result of the large size of the MMT particles; the addition of MMT particles will squeeze the composite materials crystalline structure of samples, which will change the crystalline structure of the sample.Furthermore, the addition of MMT particles will cause expansion of the original crystal area, and the new structure may increase the hindrance to the movement of molecular chains.According to the order of adding the MMT particle first and then the SiO 2 particle, the crystallinity of MMT-SiO 2 /LDPE composites are weaker than the SiO 2 -MMT/LDPE composites.This is because the size of the MMT particle is larger than the SiO 2 particle.In the preparation of micro-nano composites, small particles added later are harder to squeeze into the matrix than large ones.Simultaneously, the composites filled with particles may add multiple heat conduction channels, which significantly improves the fusion temperature of the material.Experimental data shows that the smaller the particle size, the more significant the improvement of the fusion temperature.When SiO 2 -MMT/LDPE is compared with MMT-SiO 2 /LDPE composite materials, both of them are micro-nano composite materials with two kinds of particles, but the fusion temperature of the former is higher than that of the latter.The reason is that the large-sized MMT particle is added later in the former, and more heat conduction channels will be introduced in composite process than the latter, so that the fusion temperature of SiO 2 -MMT/LDPE composites is high.However, the particles added later will squeeze the original heat conduction channels, resulting in the fusion temperature of micro-nano composites not being as good as that of adding one particle alone.

XRD Analysis of Composite Materials
Figure 4 shows the X-ray diffraction curves of composite materials.From Figure 4, there are two obvious diffraction peaks in each composite, which are 21.35 • and 23.65 • .According to reference [24], these two diffraction peaks correspond to (110) and (200) crystal surfaces, respectively.(3) where  110 ,  200 , and   are diffraction peak integral area of (110) crystal plane, (200) crystal plane, and amorphous scattering diffraction peak integral area, respectively.The XRD parameter calculation results of each sample are listed in Table 2.In Table 2, the crystallinity order of composites is SiO2/LDPE > MMT/LDPE > SiO2-MMT/LDPE > MMT-SiO2/LDPE > LDPE, which is consistent with the DSC test results.From the average grain thickness of each composite, it can be seen that the average grain thickness both of SiO2/LDPE and SiO2-MMT/LDPE composites along the (110) and (200) crystal plane directions have little difference, which indicates that the crystal growth of the two composites is uniform.SiO2-MMT/LDPE composite is the thickest of the average grain thicknesses in terms of both the direction along the (100) crystal plane and the (200) crystal plane, indicating that the addition of large-size MMT particles broaden the crystallization area to a certain extent, and thus increases the average thickness of the grain, which confirms the analysis results of the DSC experiments above.According to Equation (2), the average grain thickness of the composite with different crystal planes can be calculated [25].
where λ is the X-ray wavelength and the value is 0.154 nm; β is half height and width of diffraction peak on diffraction crystal surface; β i is the broadening factor of the instrument; θ is the diffraction angle.According to Equation (3), the crystallinity of each composite material after XRD test is calculated [26].
where I 110 , I 200 , and I A are diffraction peak integral area of (110) crystal plane, (200) crystal plane, and amorphous scattering diffraction peak integral area, respectively.The XRD parameter calculation results of each sample are listed in Table 2. From the average grain thickness of each composite, it can be seen that the average grain thickness both of SiO 2 /LDPE and SiO 2 -MMT/LDPE composites along the (110) and (200) crystal plane directions have little difference, which indicates that the crystal growth of the two composites is uniform.SiO 2 -MMT/LDPE composite is the thickest of the average grain thicknesses in terms of both the direction along the (100) crystal plane and the (200) crystal plane, indicating that the addition of large-size MMT particles broaden the crystallization area to a certain extent, and thus increases the average thickness of the grain, which confirms the analysis results of the DSC experiments above.

Dielectric Frequency Spectra of Composite Materials
Two major statements for the change of permittivity exist in composites with certain particles.First, the interaction between particles and composites matrix limits the moving of composite macromolecular chains and reduces the polarization of matrix [27,28].Second, the interfacial polarization would occur in the interface between particles and composites matrix, which will make the value of permittivity rise [29].Figures 5 and 6 show the variation of ε r and t tanδ with f of each sample.In Figures 5 and 6, we can see that LDPE is a non-polar material, the polarization of electron displacement occurs primarily in its interior, and therefore ε r is small.At the same time, it does not vary with the frequency.SiO 2 particles were added into LDPE, and a number of interfaces will be formed.There will be interface polarization in materials, hence ε r and tanδ of SiO 2 /LDPE are higher than LDPE.As the frequency increases, the electrical fields change gradually faster, and the relaxation polarization is too late to keep abreast of the electrical fields.In consequence, polarization establishment is incomplete, and ε r has a downward trend.As stated in the PLM results, MMT/LDPE and MMT-SiO 2 /LDPE have compact structures.Simultaneously, on account of the especially stratified structure of MMT, segment activity and polarization establishment of composite materials are not easy.As a consequence, the value of their dielectric constant is small.The structure of SiO 2 -MMT/LDPE restricts severely the movement of macromolecular chains, and as a result, the ε r and tanδ values of SiO 2 -MMT/LDPE are at low levels in five materials.

Dielectric Frequency Spectra of Composite Materials
Two major statements for the change of permittivity exist in composites with certain particles.First, the interaction between particles and composites matrix limits the moving of composite macromolecular chains and reduces the polarization of matrix [27,28].Second, the interfacial polarization would occur in the interface between particles and composites matrix, which will make the value of permittivity rise [29].Figures 5 and 6 show the variation of εr and t tanδ with f of each sample.In Figures 5 and 6, we can see that LDPE is a non-polar material, the polarization of electron displacement occurs primarily in its interior, and therefore εr is small.At the same time, it does not vary with the frequency.SiO2 particles were added into LDPE, and a number of interfaces will be formed.There will be interface polarization in materials, hence εr and tanδ of SiO2/LDPE are higher than LDPE.As the frequency increases, the electrical fields change gradually faster, and the relaxation polarization is too late to keep abreast of the electrical fields.In consequence, polarization establishment is incomplete, and εr has a downward trend.As stated in the PLM results, MMT/LDPE and MMT-SiO2/LDPE have compact structures.Simultaneously, on account of the especially stratified structure of MMT, segment activity and polarization establishment of composite materials are not easy.As a consequence, the value of their dielectric constant is small.The structure of SiO2-MMT/LDPE restricts severely the movement of macromolecular chains, and as a result, the εr and tanδ values of SiO2-MMT/LDPE are at low levels in five materials.Two major statements for the change of permittivity exist in composites with certain particles.First, the interaction between particles and composites matrix limits the moving of composite macromolecular chains and reduces the polarization of matrix [27,28].Second, the interfacial polarization would occur in the interface between particles and composites matrix, which will make the value of permittivity rise [29].Figures 5 and 6 show the variation of εr and t tanδ with f of each sample.In Figures 5 and 6, we can see that LDPE is a non-polar material, the polarization of electron displacement occurs primarily in its interior, and therefore εr is small.At the same time, it does not vary with the frequency.SiO2 particles were added into LDPE, and a number of interfaces will be formed.There will be interface polarization in materials, hence εr and tanδ of SiO2/LDPE are higher than LDPE.As the frequency increases, the electrical fields change gradually faster, and the relaxation polarization is too late to keep abreast of the electrical fields.In consequence, polarization establishment is incomplete, and εr has a downward trend.As stated in the PLM results, MMT/LDPE and MMT-SiO2/LDPE have compact structures.Simultaneously, on account of the especially stratified structure of MMT, segment activity and polarization establishment of composite materials are not easy.As a consequence, the value of their dielectric constant is small.The structure of SiO2-MMT/LDPE restricts severely the movement of macromolecular chains, and as a result, the εr and tanδ values of SiO2-MMT/LDPE are at low levels in five materials.

Dielectric Temperature Spectra of Composite Materials
Figures 7 and 8 show the changes of ε r and tanδ with T of the five samples, and the test frequency is 50 Hz.It is observed that the dielectric constant of composites reduces with the increment of temperature.This is because of the intensification of molecular thermal motion, which results in directional polarization difficulty.When a micro-nano particle is introduced into the matrix, interface areas will appear, hindering the thermal motion of molecular chains under high temperature, and therefore dielectric constant and loss of composites will raise.Nevertheless, SiO 2 -MMT/LDPE could ruin the original interface areas with adding of small-size fillers first, and then large-size fillers.As a result, interfacial regions have less obstruction to molecular chains' thermal movement under high temperature, and dielectric constant of composites decline accordingly.As the increment of temperature, the loss is chiefly decided by the conductance loss, and tanδ increases along with temperature.Since the main components in MMT are SiO 2 , Al 2 O 3 , and H 2 O, after introducing MMT particles into composites, lots of interfaces formation.Relaxation polarization has a great influence under low temperature and relaxation loss is large.Therefore, the loss of composites with MMT increases first, and then decreases with the temperature rises.

Dielectric Temperature Spectra of Composite Materials
Figures 7 and 8 show the changes of εr and tanδ with T of the five samples, and the test frequency is 50 Hz.It is observed that the dielectric constant of composites reduces with the increment of temperature.This is because of the intensification of molecular thermal motion, which results in directional polarization difficulty.When a micro-nano particle is introduced into the matrix, interface areas will appear, hindering the thermal motion of molecular chains under high temperature, and therefore dielectric constant and loss of composites will raise.Nevertheless, SiO2-MMT/LDPE could ruin the original interface areas with adding of small-size fillers first, and then large-size fillers.As a result, interfacial regions have less obstruction to molecular chains' thermal movement under high temperature, and dielectric constant of composites decline accordingly.As the increment of temperature, the loss is chiefly decided by the conductance loss, and tanδ increases along with temperature.Since the main components in MMT are SiO2, Al2O3, and H2O, after introducing MMT particles into composites, lots of interfaces formation.Relaxation polarization has a great influence under low temperature and relaxation loss is large.Therefore, the loss of composites with MMT increases first, and then decreases with the temperature rises.test frequency is 50 Hz.It is observed that the dielectric constant of composites reduces with the increment of temperature.This is because of the intensification of molecular thermal motion, which results in directional polarization difficulty.When a micro-nano particle is introduced into the matrix, interface areas will appear, hindering the thermal motion of molecular chains under high temperature, and therefore dielectric constant and loss of composites will raise.Nevertheless, SiO2-MMT/LDPE could ruin the original interface areas with adding of small-size fillers first, and then large-size fillers.As a result, interfacial regions have less obstruction to molecular chains' thermal movement under high temperature, and dielectric constant of composites decline accordingly.As the increment of temperature, the loss is chiefly decided by the conductance loss, and tanδ increases along with temperature.Since the main components in MMT are SiO2, Al2O3, and H2O, after introducing MMT particles into composites, lots of interfaces formation.Relaxation polarization has a great influence under low temperature and relaxation loss is large.Therefore, the loss of composites with MMT increases first, and then decreases with the temperature rises.

Breakdown Field Strength
The breakdown test data of each composite material are processed by two-parameter Weibull distribution [30,31].The relationship between the cumulative breakdown probability P(E) and the breakdown electric field intensity E is: In Equation ( 4), E 0 is the standard breakdown field strength when the cumulative breakdown probability is 63.2%; β is the shape parameter, which characterizes the dispersion of breakdown data.
The Weibull distribution analysis of breakdown field strength data of each sample measured by the experimental device in Figure 1 was analyzed by MINITAB software; 15 samples were measured for each material, and the results are shown in Figure 9.
persion of breakdown data.
The Weibull distribution analysis of breakdown field strength data of each sample measured by the experimental device in Figure 1 was analyzed by MINITAB software; 15 samples were measured for each material, and the results are shown in Figure 9.
The logarithm of both sides of Equation ( 4) are taken at the same time, and then simplified to get: The breakdown field strength  0 can be calculated by Equation ( 5).The characteristic breakdown field strength values of each sample are shown in Table 3.   represents the degree of data dispersion.The smaller the value, the more dispersed the data.From Table 3, it can be seen that the  values of each material are greater than 1.At present, regarding the mechanism by which inorganic particles improve the break- The breakdown field strength E 0 can be calculated by Equation (5).The characteristic breakdown field strength values of each sample are shown in Table 3. β represents the degree of data dispersion.The smaller the value, the more dispersed the data.From Table 3, it can be seen that the β values of each material are greater than 1.At present, regarding the mechanism by which inorganic particles improve the breakdown strength of polymer insulating dielectrics, scholars at home and abroad have basically reached a certain consensus.Lewis et al. proposed that the interface is the main factor determining the electrical properties of nano-dielectrics, and an interface charged layer will form between particles and polyethylene matrix; the interface effect will improve the dielectric properties of the dielectric [32].
From the PLM experiment and dielectric spectrum analysis, it serves to show that the addition of micron MMT particle will impede the movement of molecular chains and inhibit the migration of carriers, which will weaken the collision of electrons on the macromolecular chains to a certain extent, and lead to the improvement of the breakdown performance of MMT/LDPE composite materials.However, due to the weak interface between micron particles and matrix, the breakdown performance is not significantly improved.
The addition of nano-SiO 2 particles will form an independent interface domain in the polyethylene matrix, which will affect the space charge transport and improve the breakdown field strength.By mixing and ultrasonic treatment of the twin-screw extruder, nano-SiO 2 particles can obtain better uniform dispersion [33,34], which are easy to form more interface domains.In the previous study [21], it was proved that the addition of SiO 2 particles will introduce deep traps into the matrix LDPE.Under the action of the electric field, the charge cannot be trapped and is limited on the surface of dielectric materials.Moreover, the structure formed by SiO 2 /LDPE composite materials has a certain blocking effect on carrier migration, thereby reducing the energy accumulation of electrons and weakening its impact on macromolecular chains, thus improving the impact breakdown field strength by about 17% [35].
For SiO 2 -MMT/LDPE and MMT-SiO 2 /LDPE, due to the introduction of two kinds of particles, a great many interfaces are introduced into the matrix, so the breakdown field strength is increased by about 6.8% and 4.6%, respectively.However, due to the introduction of micron particles that will form part of the weak interface with the matrix, the breakdown field strength of them is lower than SiO 2 /LDPE.When MMT-SiO 2 /LDPE is compared with SiO 2 -MMT/LDPE, according to the PLM experimental results, the MMT-SiO 2 /LDPE composite materials formed by adding large-sized MMT particle first and then small-sized SiO 2 particle have a compact crystal structure, and the crystallinity is small from the crystallinity results of DSC and XRD.This will increase the free volume of the materials, increase the chance of electron collisions, and decrease the breakdown field strength.At the same time, according to DSC experiment and analysis, the heat dissipation of MMT-SiO 2 /LDPE composite materials is worse than that of SiO 2 -MMT/LDPE, so MMT-SiO 2 /LDPE easily accumulates heat inside the materials, which improves the probability of thermal breakdown of the materials.Therefore, the breakdown field strength of MMT-SiO 2 /LDPE is about 2% lower than that of SiO 2 -MMT/LDPE.

Conclusions
From PLM experiment, DSC experiment, and XRD experiment results, it can be seen that the introduction of micro-and nanoparticles together will make the internal structure of the materials more compact than the matrix.The adding method of first small and then large can more effectively limit the molecular chains activity than the composite materials prepared by adding large first and then small.The addition of a variety of particles will destroy the original crystal structure, which makes the crystallinity of materials added with varieties of particles slightly lower than materials added with a single particle.The addition method of first small and then large will expand the crystallization region of the composites, and the crystallinity is higher than that of the composite materials prepared by first large and then small addition method.
From the experimental results of dielectric spectrum, it can be seen that the addition of micro-and nanoparticles will make the materials structure more compact, resulting in serious restriction of molecular chain motion, difficulty in establishing partial polarization, and a decrease in the dielectric constant and loss to a certain extent.Among them, the effect of adding small particles first and then large particles is better.
From the experimental results of dielectric temperature spectrum, it can be seen that with the change of temperature, the original interface area may be destroyed by the addition method of first small and then large, and the interface area is not bound enough to the thermal motion of molecules, so the dielectric constant will decrease.
From the experimental results of AC breakdown field strength, it can be seen that the interface effect is the main factor affecting the breakdown performance of composite materials.By adding nano-SiO 2 particles alone in LDPE, the breakdown field strength is greatly increased by about 17%.Adding micro-and nanoparticles into LDPE at the same time will introduce a large number of interfaces into the matrix, which will also improve the breakdown field strength of micro-nano composite materials.The lifting amplitude of SiO 2 -MMT/LDPE composite materials is about 6.8%, and that of MMT-SiO 2 /LDPE composite materials is about 4.6%.

Figure 3 .
Figure 3. Statistical distribution of crystal cell size of each sample.

Figure 3 .
Figure 3. Statistical distribution of crystal cell size of each sample.

Figure 3 .
Figure 3. Statistical distribution of crystal cell size of each sample.

Figure 5 .
Figure 5. Curves of εr with respect to f.

Figure 6 .
Figure 6.Curves of tanδ with respect to f.

Figure 5 .
Figure 5. Curves of ε r with respect to f.

Figure 5 .
Figure 5. Curves of εr with respect to f.

Figure 6 .
Figure 6.Curves of tanδ with respect to f.

Figure 6 .
Figure 6.Curves of tanδ with respect to f.

Figure 7 .
Figure 7. Curves of εr with respect to T.

Figure 8 .
Figure 8. Curves of tanδ with respect to T.

Figure 7 .
Figure 7. Curves of ε r with respect to T.

Figure 7 .
Figure 7. Curves of εr with respect to T.

Figure 8 .
Figure 8. Curves of tanδ with respect to T.

Figure 8 .
Figure 8. Curves of tanδ with respect to T.

Figure 9 .
Figure 9. Weibull curve of breakdown field strength of each sample.

Figure 9 .
Figure 9. Weibull curve of breakdown field strength of each sample.The logarithm of both sides of Equation (4) are taken at the same time, and then simplified to get: ln[−ln(1 − P)] = β(lnE − lnE 0 )(5)

Table 1 .
Fusion peaks and crystallinity of samples.

Table 2 .
XRD parameters of each sample.

Table 2 .
XRD parameters of each sample.

Table 3 .
Characteristic breakdown field strength of each sample.

Table 3 .
Characteristic breakdown field strength of each sample.