Enhanced Thermal Conductivity and Dielectric Properties of Iron Oxide/Polyethylene Nanocomposites Induced by a Magnetic Field

Iron Oxide (Fe3O4) nanoparticles were deposited on the surface of low density polyethylene (LDPE) particles by solvothermal method. A magnetic field was introduced to the preparation of Fe3O4/LDPE composites, and the influences of the magnetic field on thermal conductivity and dielectric properties of composites were investigated systematically. The Fe3O4/LDPE composites treated by a vertical direction magnetic field exhibited a high thermal conductivity and a large dielectric constant at low filler loading. The enhancement of thermal conductivity and dielectric constant is attributed to the formation of ﻿the conductive chains of Fe3O4 in LDPE matrix under the action of the magnetic field, which can effectively enhance the heat flux and interfacial polarization of the Fe3O4/LDPE composites. Moreover, the relatively low dielectric loss and low conductivity achieved are attributed to the low volume fraction of fillers and excellent compatibility between Fe3O4 and LDPE. Of particular note is the dielectric properties of Fe3O4/LDPE composites induced by the magnetic field also retain good stability across a wide temperature range, and this contributes to the stability and lifespan of polymer capacitors. All the above-mentioned properties along with the simplicity and scalability of the preparation for the polymer nanocomposites make them promising for the electronics industry.

at a desired level, because the dielectric strength will decrease with increasing temperature owing to the poor thermal conduction of these dielectric materials. Notably, traditional high dielectric composites would lose their electromechanical stability and displayed a large variation in dielectric constant as well as dielectric loss at a broad temperature range, hindering their reliability and efficiency 14 .
Previous studies have shown that the polymeric composites, which were integrated with high thermal conductivity fillers, such as metal (Cu) 15 , oxide(Al 2 O 3 ) 16 , aluminum nitride (AlN) 17 , carbide(SiC) 18 , and carbon nanotubes 19 , can endow themselves with superior properties. For example, Cu-filled low-density polyethylene (LDPE) composites were studied by Luyt et al. 15 and they found that the thermal conductivity of the composites was 0.35 W m −1 K −1 when the volume fraction of the Cu particles was 7.0 vol.%. Fang et al. 18 prepared different dimensional SiC particles to be filled into LDPE composites, and realized that the thermal conductivity of the composites was 0.37 W m −1 K −1 at 10 vol.% SiC content. High thermal conductivity of the composites usually requires a high volume fraction of fillers, and provision of a low dielectric constant, which is not suitable for use for microelectronics. Additionally, most research has just focused on one single side of thermal conductivity or dielectric property of nanocomposites at room temperature. Few in-depth explorations of the cooperative effect of a large thermal conductivity and a high dielectric constant for polymer materials under broader temperature conditions have been investigated until now, and their influential mechanism is still uncertain. Beyond that, how to improve the thermal conductivity and the dielectric performance of composites at low filler loading is one of the key issues.
The external electric and magnetic field could significantly influence the polymer's molecular arrangement and the conductive particles' distribution of the polymer composites, in the end the microstructure and macro-properties of the composites are influenced [20][21][22] . Hence, in this research, the Fe 3 O 4 -LDPE particles were prepared by solvothermal reaction and then the surface was modified by polydopamine (PDA). On this basis, we treated the Fe 3 23 . Figure 1d shows the SEM morphology of the fractured cross-surface of M-Fe 3 O 4 /LDPE composite at 7 vol.% concentration. It is clearly found that some Fe 3 O 4 particles come into contact with each other and become short chains along the magnetic direction. That is, the distribution of the , and this value is superior to that of many previous reports 15,18,20,[26][27][28] . As shown in Table 1, the thermal conductivity of our composites is larger than that of the high-density polyethylene/fly-ash (HDPE/   To further explore the thermal conductivity behavior of the Fe 3 O 4 /LDPE and M-Fe 3 O 4 /LDPE composites, Maxwell-Eucken's model has been proposed and the comparisons between the experimental and theoretical values were made 30 . Maxwell-Eucken assumes that filler particles are homogeneously distributed in the polymer matrix, non-interacting, and roughly spherical. Fewer filler particles would be covered by the polymer and dispersed in the form of isolated islands in the matrix: where V f is the volume fraction of the filler, and λ c , λ f , and λ p is the thermal conductivity of composites, filler, and matrix, respectively 31,32 . In this paper, the value of λ f and λ p used 6.032 W m −1 K −1 and 0.315 W m −1 K −1 , respectively. Figure 4 gives the comparison between the experimental data and the thermal conductivity predicted by the Maxwell-Eucken's model of the composites. For the Fe 3 O 4 /LDPE composites, Fe 3 O 4 nanoparticles are dispersed randomly in the Fe 3 O 4 /LDPE composites (shown in Fig. 1c), and the theoretical values match well with the experimental data. However, it is interesting to note that the theoretical values of the M-Fe 3 O 4 /LDPE composites are lower than those observed in the experiments. This deviation could be attributed to the easier formation of the thermal conductive net-chain by the interaction of Fe 3 O 4 in the LDPE matrix under the action of the magnetic field.
Owing to the Maxwell-Eucken model not matching well with the M-Fe 3 O 4 /LDPE composites, two heat conduction models (parallel and vertical models) were brought forward to judge the heat flow direction in the polymer composites, based on the formation of the thermal conductive net-chain and mutual interaction of particles 33,34 . Considering the crystallinity of the filler and polymer, Agari's model was created based on a hypothesis of homogeneous dispersion of particles in the polymer: where C 1 is the constant, which is related to the crystallinity and crystalline dimension of a polymer, and C 2 is the free factor, which indicates the ability of forming a heat conductive net-chain for fillers. C 2 would significant change due to the increase of the particle filling; therefore, Agari's model should be modified and verified as the following 32,35 : where C p is the formation of the thermal conductive chain free particles, and C f is the reflecting particle formation of the thermal conductivity of difficulty. Table 2 shows the C p and C f for the above two composites. It can be found that the C p of the M-Fe 3 O 4 /LDPE composites did not change significantly compared with the Fe 3 O 4 /LDPE composites. However, the C f of the M-Fe 3 O 4 /LDPE composites was greater than that of the Fe 3 O 4 /LDPE composites. The factor C f related to the ease in forming conductive chains of the filler, that is, the magnetic field shows a strong effect on C f . This also indicates that the external magnetic field could effectively enhance the formation of thermal conductive paths in the LDPE matrix, which is consistent with the results shown in Fig. 1d. In addition, R 2 stands for the fitting degree between the theoretical data and the experimental data. The R 2 value of the M-Fe 3 O 4 /LDPE composites is 0.98522, higher than that of the Fe 3 O 4 /LDPE composites (0.96233), showing that the experimental results for the M-Fe 3 O 4 /LDPE composites had a better fitting effect than the Fe 3 O 4 /LDPE composites. Besides, as shown in Fig. 1d, some changes have taken place in the structure of the LDPE matrix. This phenomenon also indicated that the external magnetic field has some influence on the microstructure of polymer matrix, the similar result has been reported in numerous previous studies [36][37][38]    regarded as a great amount of parallel-connected micro-capacitors, resulting in a greatly enhanced dielectric constant 39,40 . It should be noted that the dielectric properties in our present study is even higher than those of many previous reports 21, 23, 41-43 . For example, as shown in Table 3, the obtained dielectric constant is higher than that of BZT-BCT/PVDF composites containing 24 vol.% BZT-BCT (ɛ = 37.2 at 10 Hz) 41 . Moreover, the amount of filler in the M-Fe 3 O 4 /LDPE composites is smaller than that in other materials described in the literature, and displayed better flexibility. For embedded capacitor applications, the dielectric loss is an essential parameter. The dielectric loss measured at a certain frequency includes polarization loss and conduction loss 44 . The dielectric loss tangent for the M-Fe 3 O 4 /LDPE composites remain below 0.25 at 10 Hz, and the conductivity of the M-Fe 3 O 4 /LDPE composites is also kept at a low value (7 × 10 −11 S/cm). These attributed to the improvement of the interfacial adhesion and compatibility between the filler and the matrix by surface treatment of the PDA, no complete conducting path was formed in the composites (shown in Fig. 1d), resulting in a low dielectric loss and low conductivity of the composites within the acceptable ranges 45 . For example, the achieved dielectric loss and conductivity were found to be significant smaller than that of PEG-Fe 3 O 4 /PVDF composites containing 7.5 vol.% PEG-Fe 3 O 4 fillers 43 .
In addition to the movement of particles under the magnetic field, the dielectric relaxation is also likely to affect the dielectric properties. To clarify the mechanism of the dielectric behaviors of the  (Fig. 6a). However, for the M-Fe 3 O 4 /LDPE composites, it can be seen that M′ decreases with the increasing of   Table 3. Comparison of the dielectric properties of our composites and reported literature materials.
Fe 3 O 4 content (Fig. 6b), and increases with frequency; this behavior is similar to other polymer composites containing conducting fillers 48,49 . As shown in Fig. 6c and d, compared with the Fe 3 O 4 /LDPE composites, obvious interfacial polarization relaxation peaks occur for the M-Fe 3 O 4 /LDPE composites when the Fe 3 O 4 content is higher than 1.9 vol.%. Moreover, the relaxation strength of the composites decreases with the increase of Fe 3 O 4 loading, and the relaxation peak moved toward higher frequency as the Fe 3 O 4 content increased. The inter-particle distance would decrease as the volume fraction of the Fe 3 O 4 increased, and as a result, the probability of Fe 3 O 4 nanoparticles coming into contact increased because of the external magnetic field. As shown in Fig. 1d, some Fe 3 O 4 particles come into contact with each other and become short chains along the direction of the magnetic field, which leads to a higher possibility for the charge carriers to accumulate on the interface between Fe 3 O 4 and LDPE, the polarization and dielectric response are greatly enhanced under the electric field 22 . Therefore, a high dielectric constant of M-Fe 3 O 4 /LDPE composites is achieved at a low volume fraction. For polymer capacitors, it is essential that the dielectric properties of the composites retain excellent stability across a wide temperature range 11, 14 . In this research, the temperature dependence of the dielectric constant and dissipation factor of the Fe 3 O 4 /LDPE and M-Fe 3 O 4 /LDPE composites at 10 Hz are given in Fig. 7. It can be found that a minor variation in dielectric constant of the M-Fe 3 O 4 /LDPE composites occurs with the increasing of temperature. The M-Fe 3 O 4 /LDPE composites at 7.0 vol.% Fe 3 O 4 concentration display the largest dielectric constant (>51) across the whole temperature ranges. However, for the Fe 3 O 4 /LDPE composites, an obvious increasing trend occurred when the temperature was over 100 °C. Concurrently, the dissipation factor of the M-Fe 3 O 4 / LDPE composites at 10 Hz also remained at a slightly low value and maintained good stability across the whole temperature range, but an appreciable change has been observed in the Fe 3 O 4 /LDPE composites at 7.0 vol.% concentration. It is also evident that, of the dielectric assessed, the M-Fe 3 O 4 /LDPE composites offer a stable dielectric constant and dissipation factor at high temperature. This is attributed to the fact that the higher thermal conductivity of the M-Fe 3 O 4 /LDPE composites can effectively depress the dielectric loss and conductivity. It also indicates that the magnetic field could largely enhance the dielectric-temperature stability of the Fe 3 O 4 /LDPE composites across broad temperature range. There is an undoubtable benefit to the use of Fe 3 O 4 /LDPE composites across a wider temperature range in electronics.
In our present study, Fe 3 O 4 nanoparticles adopted a directional arrangement along the direction of the magnetic field, and formed a conductive network in the LDPE matrix under the action of a magnetic field, resulting in greatly enhanced thermal conductivity. Moreover, the interfacial polarization of the Fe 3 O 4 /LDPE composites is effectively enhanced under magnetic field treatment, and the maximum dielectric constant of the composites reaches 51 at 7.0 vol.% concentration. Additionally, the low volume fraction of the fillers and the excellent compatibility of the Fe 3 O 4 nanoparticles and LDPE matrix, resulted in a relatively low dielectric loss (0.25) and a low conductivity (7 × 10 −11 S/cm). Moreover, the dielectric properties of the M-Fe 3 O 4 /LDPE composites retain

Conclusion
In summary, Fe 3 O 4 -deposited LDPE hybrid particles were prepared by a solvothermal reaction, and the corresponding Fe 3 O 4 /LDPE composites were also prepared. SEM images show that Fe 3 O 4 nanoparticles were embedded in the LDPE matrix without agglomeration and defects. The magnetic field enhanced the probability of forming Fe 3 O 4 conductive chains, which can effectively enhance the heat flux and interfacial polarization of Fe 3 O 4 /LDPE composites. The Fe 3 O 4 /LDPE composites induced by the magnetic field exhibited higher thermal conductivity and a higher dielectric constant in comparison with the Fe 3 O 4 /LDPE composites at the same filler content. Moreover, the relatively low dielectric loss and low conductivity are attributed to the low filler content and the improvement compatibility of the Fe 3 O 4 nanoparticles and LDPE matrix by the surfactant treatment of the PDA. The low filler content leads to good mechanical properties and material processibility. Additionally, the dielectric properties of the M-Fe 3 O 4 /LDPE composites also retain good stability across a wide temperature range, due to the high thermal conductivity of the Fe 3 O 4 /LDPE composites induced by the magnetic field. This work establishes a facile, yet efficient approach to synthesize polymer materials with high thermal conductivity and high dielectric properties in order to make them suitable candidates for use in the electronics industry.  Characterization. The morphology of the Fe 3 O 4 -LDPE particles and the microstructure of the LDPE composites were observed using SEM (Quanta 200 FEI). The phase compositions of the Fe 3 O 4 /LDPE composites were analyzed using XRD (Empyrean), using Cu Kα radiation at 40 kV and 40 mA. The thermal diffusivity (α) and specific heat (C) were measured on the disk samples with an LFA447 light flash system (NETZSCH, Selb, Germany) at 25 °C. The thermal conductivity was calculated by λ = αCρ, in which ρ is the density of the Fe 3 O 4 / LDPE composite. Prior to performing dielectric measurements, a layer of Al paste (diameter 25 mm) was evaporated on both surfaces to serve as electrodes. Dielectric measurements were employed across a frequency range from 10 to 10 6 Hz and a temperature range of −10 °C to 105 °C using a broad frequency dielectric spectrometer (Novocontrol Alpha-A).