Study on thermal conductivity of micron BN-nano SiO2 combined modified epoxy resin composites

Epoxy resin has attracted widespread attention in the field of power electronic packaging due to its favorable processing technology, high adhesion, and excellent dielectric properties. The enhancement of thermal conductivity in epoxy resin through the incorporation of diverse particles is a prominent area of interest in the realm of modified insulation materials. In this study, hexagonal boron nitride (h-BN) and silicon dioxide (SiO2) with good thermal conductivity were used as doped fillers to modify epoxy resin (EP). The analysis of experimental results indicated that the thermal conductivity of materials with a total doping amount of 20 wt% and a mass ratio of BN to SiO2 of 70:30 to 60:40 could increase the thermal conductivity by 118.1~126.0%. In contrast to pure EP, the thermal conductivity of composite epoxy resin materials has been significantly enhanced.


Introduction
With the rapid advancement of microelectronic technologies, there are many kinds of electronic packaging materials, including epoxy resins (EP), silicones, and polyurethanes [1,2].Among them, EP is widely used because of its excellent electrical insulation performance, chemical resistance, easy processing, and molding, and is used in the insulation and packaging of electronic components [3][4][5].However, as an amorphous polymer, EP has neither free electrons of metal compounds, nor a large number of lattice vibrations, and the overall thermal conductivity is very poor, usually only 0.17 W•m - 1 •K -1 .Low thermal conductivity increasingly limits the rapid development of epoxy resins in electrical and electronic applications.Therefore, how to maintain the insulation and dielectric properties of epoxy resin itself, while improving its thermal conductivity, so that it can meet the needs of today and tomorrow, is still a huge challenge.
In recent years, the research on the combined modification of epoxy resin by a variety of particles has set off a boom, and scholars at home and abroad have prepared composite insulation materials with excellent performance by doping epoxy resin with nanoparticles.The selected materials usually include alumina (Al 2 O 3 ), boron nitride (BN), silicon dioxide (SiO 2 ), carbon nanotubes, glass fibers, and other materials, and the material scale is micron or nanoscale.Metallic and non-metallic oxide particles usually have high thermal conductivity and excellent insulation and can be mixed uniformly with epoxy resin, which can obtain better electrical properties.BN is considered the most promising candidate, given its excellent mechanical strength, thermal conductivity, and thermal stability [6].Wang et al. [7] added micron-scale h-BN and carbon nanotubes (CNTs) with a diameter of 112 nm and a length of 50 μm to the epoxy matrix and experimentally found that when 1.06 vol% BN-CNT was added, the epoxy nanocomposite adhesive had high electrical and mechanical properties, such as high Young's modulus, thermal stability, and so on.When the filling amount reaches 3.79 vol%, the thermal conductivity reaches its maximum value of 0.46 W•m -1 •K -1 , which is improved compared with pure epoxy resin or only doped BN.The resistivity of SiO 2 is not high, generally at 1015~1016 Ω•cm, but when used as a nanoscale filler, it can show great advantages.Nano-SiO 2 can improve the bonding strength inside the material [8].The molecular structure of nano-SiO 2 is characterized by a three-dimensional chain-like arrangement, with various bonding states of hydroxyl groups and a substantial number of unsaturated residual bonds.These can bond with certain groups of the resin to make the overall molecular structure stronger and greatly improve the hardness and strength of the material on a macroscopic scale.Shen et al. [9] found that 2.5 wt% SiC@SiO 2 composites can improve the thermal conductivity of polymers, but when particles are modified, epoxy resins with different filling amounts and proportions have a greater impact on their properties.Suitable proportioning schemes need to be studied for multi-particle combined modified epoxy resins to greatly improve their insulation.
In this paper, 15 groups of composite epoxy resins with different filling amounts and different proportions were prepared by doping micron h-BN and nano-SiO 2 micro-nanoparticles into the epoxy resin at the same time.By measuring the thermal conductivity of each group, the contribution of the filling amount and the ratio of two particles to the improvement of thermal conductivity and its corresponding microscopic mechanism were analyzed, and how to obtain higher thermal conductivity at lower total filling was discussed.

Material preparation
The experimental preparation method is consistent with what we described before [10].

Surface modification.
The particles and coupling agent were added to a sufficient amount of absolute ethanol according to a mass of 20:1, and placed in an ultrasonic dispersion instrument with ultrasonic shaking for 20 min.Then, the suspension after ultrasonic dispersion was heated in a continuous water bath at 50 °C and stirred by an electromagnetic stirrer for 60 minutes to promote the grafting reaction.Then, the reacted suspension is left to stand for some time and washed several times; finally, the slurry obtained after filtration and cleaning is dried, ground, and crushed to obtain particles with surface modification.The surface modification preparation method of micron BN and nano SiO 2 is the same.

Reparation of epoxy resin composites.
The mass ratio of the epoxy resin, the curing agent, and the accelerator is 100:80:0.5,and the mass ratios of BN and SiO 2 are set to 100:0, 90:10, 80:20,  BN/Si60-20 60:40 20wt% 70:30, and 60:40, and the total filling amount of mixed particles added to epoxy resin is set to 5 wt%, 10 wt%, and 20 wt%.Composite epoxy resin materials with different filling amounts and ratios were prepared by electromagnetic stirring, water bath heating, ultrasonic dispersion, vacuum deaeration, high-temperature curing, and other processes.The prepared composite epoxy resin material is shown in Figure 1.The naming and corresponding composition are shown in Table 1.

Thermal performance test principle and experimental system
When different objects touch each other, or when the temperature inside the object is uneven, heat transfer will occur spontaneously.Heat transfer occurs mainly in three ways: heat radiation, heat convection, and heat conduction.Among them, thermal radiation propagates around the object by electromagnetic waves, does not require any medium, and can be transmitted between substances at the speed of light even in a vacuum.Thermal convection mainly occurs in gaseous and liquid objects, and material exchange occurs directly in parts at different temperatures.Since the volume and density of gases and liquids change significantly at different temperatures, gases or liquids at different temperatures will flow and mix under the action of gravity.The adequate flow of gaseous liquids can quickly reduce the overall temperature gap, which is a very efficient method of heat transfer.Heat conduction is the direct transfer of energy from the movement of adjacent material molecules, and it will occur autonomously from the high-temperature object to the low-temperature object, and from the high-temperature region inside the object to the low-temperature region.And for different substances such as metals, metal compounds, graphene, etc., due to their different microstructure, heat conduction performance differences will also be huge.Owing to the abundance of free electrons inside, these materials such as copper tubes, alloy heat mesh, graphene sheets, etc., usually have better thermal conductivity, and usually can be used as a heat conduction medium in the dissipation system, and polymers such as epoxy resin, cross-linked polyethylene usually have poor thermal conductivity, which can be used as an insulating material wrapped in electronic components.The heat generated by the continuous operation of the components will accumulate in these materials, which brings problems such as heat aging.
In solid objects, heat convection cannot be generated, and the efficiency of thermal radiation is very limited, and the main way of heat conduction is heat conduction.When heat conduction occurs inside the object, it results in the spontaneous transfer of heat from a region of higher temperature to one of lower temperature, creating a temperature gradient with successively decreasing temperatures, and each layer is called the isothermal surface.Layers of isothermal surfaces form a temperature gradient, and when the heat is input, the temperature gradient formed by materials with different thermal conductivity is not the same.Therefore, Fourier's law calculates the thermal conductivity of the object according to the heat passed through the object interface and the corresponding temperature gradient, and the formula is as follows: Where J T represents the heat flux density (W•m -2 ), which represents the heat transfer rate in the direction of transmission, that is, in the x direction, on the unit area of the selected cross-section; dT dx represents the temperature gradient; the proportional constant κ of the two represents the heat transport characteristics of the object, that is, the thermal conductivity, also known as the thermal conductivity, in units W•m -1 •K -1 .The symbol implies the transfer of heat from a region of high temperature to a region of low temperature through conduction.
For the same material of isotropic, uniform medium, the thermal conductivity at the same temperature is constant.When temperature changes, the thermal conductivity will also change accordingly, and some materials will change more obviously, such as pure metals and most liquids other than water.Thermal conductivity will decrease with the increase of temperature, and the thermal conductivity of anisotropic materials in different directions will also be different.In addition to thermal conductivity, there is also the thermal diffusion coefficient as a rate to characterize thermal diffusion: Where ρ represents the density of the object in kg•m -3, c is the specific heat capacity of the object in J•kg -1 •K -1 , λ represents the thermal conductivity, in W•m -1 •K -1 , and α represents the thermal diffusivity unit m 2 •s -1 .Therefore, when the density and specific heat capacity of the material are known, the thermal conductivity and thermal diffusion coefficient are directly proportional.
In this paper, the LFA467 laser thermal conductivity analyzer produced by Netzsch, Germany is adopted.The measuring temperature range of this analyzer can support -100 ℃ ~ 500 ℃, the data acquisition rate is up to 2 MHz, and the measuring range of thermal diffusion coefficient is 0.01 mm 2 •s - 1 ~ 2000 mm 2 •s -1 .The measurement range of thermal conductivity is 0.
The device uses the laser pulse of the flash method as the test method, and the principle of this process is illustrated in Figure 2.
The material to be measured needs to be processed to a specified size, placed on a transparent mount (not drawn in the figure), and irradiated with a laser pulse under the material.The laser beam needs to pass through a grating to keep the irradiated area consistent with the material and control the error.Laser pulse irradiation will cause high temperature on the bottom surface of the material, thereby forming a longitudinal temperature gradient, and then the temperature of the top surface can be measured by the infrared probe in a non-contact manner.The temperature gradient of the material can be measured, allowing for the calculation of its thermal conductivity and thermal diffusivity.
Due to the strict requirements of the thermal conduction experiment on the size of the material, the material was processed with fine cutting and grinding processing in this experiment, where the material was unified into rectangular sheets (10 mm × 10 mm), while the thickness and mass were finely measured and the density was calculated.To simulate the long-term operating conditions of the component, the test temperature was selected to be 90 °C.The laser voltage is 250.0V and the pulse width is 0.60 ms.The standard + pulse correction model was used for calculation.Since repeated measurements of the same material have almost no deviation, each material is flashed three times and calculated.3 showed that the thermal conductivity of pure epoxy resin is low at 0.177 W•m -1 •K -1 .After doping, most materials received some improvement.When the doping and packing amount is 5nwt%, the thermal conductivity of the material is slightly enhanced but not obvious, and the thermal conductivity is from 0.171~0.230W•m -1 •K -1 ; when the doping amount is 10 wt%, the results are further improved, and the thermal conductivity distribution is as low as 0.194 W•m -1 •K -1 , up to 0.233 W•m -1 •K -1; when the doping and packing amount was further raised to 20 wt%, the thermal conductivity was qualitatively improved, and the material improvement of BN/Si100 was not obvious, only 0.233 W•m -1 •K -1 , but the thermal conductivity of BN/Si70 and BN/Si60 increased to 0.386 W•m -1 •K -1 and 0.400 W•m -1 •K -1 , respectively, which is 218.1% and 226.0% of the thermal conductivity of the original pure epoxy resin, which means it has been greatly improved compared with the original material.

Experimental data analysis. The results of Figure
From the point of view of the filling amount, the increase of the filling amount on the thermal conductivity is not linear, but there is a threshold effect: a low filling amount, such as 5 wt% and 10 wt% can not play a significant effect, and when the filling amount reaches a certain value, such as 20 wt%, thermal conductivity will get a sudden increase.From the perspective of the ratio, the appropriate introduction of nano-SiO 2 can increase the thermal conductivity, and this change can only be seen with a small trend at 5 wt% and 10 wt%, but at 20wt%, gradually increasing the ratio of nano-SiO 2 can achieve an approximately linear increase in thermal conductivity.At 30%-40%, the growth gradually slows down and saturation occurs.The mass ratio of 3:1 is better than 2:2 and 4:0 when ICAMIM-2023 Journal of Physics: Conference Series 2720 (2024) 012009 IOP Publishing doi:10.1088/1742-6596/2720/1/0120096 using micron BN and nano-Al 2 O 3 for combined modification, which is close to the conclusion of researchers [11].It shows that micron BN is still needed as the main force to enhance the thermal conductivity of epoxy resin, and the addition of nano SiO 2 can promote BN's effect, but it cannot maintain high thermal conductivity when nano SiO 2 is the main doping filler.

Discussion of the microscopic mechanism of thermal conductivity.
According to the measurement results of the broadband dielectric analyzer, the real spectrum of the dielectric constant of 15 groups of BN/SiO 2 /EP composite materials was plotted according to different proportions, and the relationship between the spectrum of the real part of the dielectric constant and the filling amount was analyzed.Generally, the dielectric constant real part of pure epoxy resin and each composite epoxy resin material decreased with the increase of frequency, gradually decreasing from 4.2~4.4 to 3.8~4.1,by about 10% with frequency.This is because the epoxy resin is a macromolecular structure, and the polarization process is dominated by dipole polarization.This process takes a certain amount of time, and the higher the applied electric field frequency is, the more difficult it is for the dipole steering rate to keep up with changes in the external electric field.Therefore, in the high-frequency region, the internal electric field of the material gradually weakens with increasing frequency, so the overall dielectric constant continues to decrease.In solid materials, the internal heat conduction process is mainly in the form of energy transfer between the thermal movement of molecules or atoms and the surrounding particles.The amplitude of the thermal motion of the molecules in the micro is relative to the macro temperature, and the higher the temperature of the object is, the faster the molecular and atomic vibration rate and the greater the kinetic energy will be.In solid materials, two types of particles are mainly involved in heat transfer, namely, free electrons that can transfer motion within the material and lattice vibration.The energy in lattice vibration is quantized and each part is called phonon.The two can be calculated superimposed: Where k represents the thermal conductivity of the material, k e represents the thermal conductivity corresponding to the free electron heat conduction, and k p is the thermal conductivity corresponding to the phonon heat conduction.According to the object characteristics of different materials, the size and proportion of k e and k p are greatly different.There are a large number of free electrons in metal materials, the activity space of electrons is large, and the migration rate is higher than that of phonons, so the migration of electrons and the vibration transmission between them play a dominant role, which makes metals have high k e values and thermal conductivity [12].In some crystalline compounds, the constituent atoms can be orderly arranged in the lattice, and the atoms vibrate in their respective crystal positions, thus interacting with the surrounding atoms, which is an approximately elastic process.Therefore, the heat vibration can be transferred to the surrounding area with high efficiency in the form of elastic waves.In this way, the lattice vibration is more obvious, the phonons can gradually diffuse from the direction of decreasing concentration gradient, and the material has a large k p , such as AlN and BN [12], and can also have good thermal conductivity.Materials such as graphene and carbon nanoparticles have both a crystal structure and a "large Π bond" composed of many free electrons, both of which can efficiently transfer heat, and the thermal conductivity can usually exceed 2000 W•m -1 •K -1 .The aggregate material is a polymer structure, which is connected by a large number of the same units to form a long chain, and then folded to form a network structure.Therefore, when the heat is transferred in it, a variety of vibration modes will occur, such as stretching vibration, swaying vibration, and torsional vibration.These vibrations are anharmonic coupled vibrations, in which the atoms in the polymer do rotational motion or disordered vibrations near the equilibrium position, and the energy is dispersed to the surrounding groups.This form of vibration travels very fast.Therefore, amorphous polymers such as epoxy resins and polypropylene have very low thermal conductivity.If crystals can be formed inside the polymer, the regular lattice structure can make the polymer have some of the thermal conductivity characteristics of crystal compounds, such as highdensity polyethylene, whose thermal conductivity can reach 0.55 W•m -1 •K -1 , which is significantly higher than that of epoxy resin and polypropylene [13].
When one or more substances are doped in the polymer, the path of heat transfer is changed.This mechanism is usually well explained by the theory of thermal conductivity networks [14].To enhance the thermal conductivity of composite materials, it is necessary to construct a continuous path with low thermal resistance, providing a shortcut for heat transfer.So the heat is mainly propagated along the thermal network, and the ability to build a thermal network plays a crucial role.The content and distribution of the fillers determine the integrity of the thermal conductivity network.When the amount of doping is small, as shown in Figure 4(a), the doped particles will be dispersed in the polymer matrix in isolation, forming a "sea-island" two-phase system.In this way, only the parts with high thermal conductivity in the local area are in a series structure with the epoxy matrix, so an effective thermal conductivity network cannot be formed.This is reflected in the experiment, where the thermal conductivity of 10 wt% doped micron BN composite epoxy resin is only 11.3% higher than that of pure EP.As the filling amount increases, the doping filler can form a through-line thermal conductivity path, and the thermal conductivity network is thus generated.In Figure 4(b), the stacked micron BNS form a thermal conduction channel that is in parallel with the epoxy matrix, so that heat can be transferred quickly between them.This corresponds to the 31.6%increase in the thermal conductivity of the composite epoxy resin at the filling amount of 20 wt% micron BN in the experiment.Generally, continuing to increase the BN content can establish more thermal conductivity channels in the epoxy matrix, form a dense thermal conductivity network, and further improve thermal conductivity [15].On this basis, the introduction of a small amount of nano-SiO 2 can slightly improve the thermal conductivity, as shown in Figure 4(c).The micron BN forms a thermal conduction skeleton, in which dispersed SiO 2 can act as bridges and enhance the efficiency of the thermal conductivity network.This corresponds to a 60.5% and 78.5% increase in the thermal conductivity of BN/Si90 and BN/Si80, respectively, at a filling volume of 20 wt%.When the proportion of SiO 2 is further increased, as shown in Figure 4(d), more nano-SiO2 will disrupt the stacked structure of the layered micron BN, causing the direction of dispersion of some BN particles to change, thereby improving the longitudinal, that is, the thermal conductivity in the direction of measurement.However, the thermal conductivity network still needs micron BN as the skeleton due to the low thermal conductivity of SiO 2 itself, so there is a peak value in the increase of SiO 2 , corresponding to the experimental thermal conductivity of BN/Si70 and BN/Si60 increased by 118.0% and 126.0%, respectively, and there is an obvious saturation effect.In summary, when the filling amount reaches 20 wt%, the addition of SiO 2 can further enhance the thermal conductivity of the composite epoxy resin, resulting in a significant improvement in its overall thermal conductivity.Among them, BN/Si70-20 and BN/Si60-20 materials achieved improved thermal conductivity.

Conclusion
In the micron BN-nano SiO 2 composite modified epoxy resin system, micron h-BN acts as the backbone of the thermal conduction network, and its filling amount plays a vital role in improving thermal conductivity.The small filling amount is not enough to bring a significant improvement in thermal conductivity and cannot build a thermal conduction network.When the filling amount is increased to enough (20 wt% and above), the thermal conductivity will be significantly improved; nano-SiO 2 acts as a connection to the thermal conduction network, which further enhances the overall thermal conductivity and achieves the effect of a higher filling amount in a single particle.At the same time, nano-SiO 2 can disrupt the single arrangement of the original micron BN and promote the longitudinal distribution of the heat conduction network.When the micron h-BN content is sufficient, appropriate filling with SiO 2 will further enhance the thermal conductivity.However, as the total filling amount is 20 wt%, and the nano-SiO 2 reaches 30% or more in the doped amount, the thermal conductivity is saturated and the increase rate slows down.In the materials in this experiment, the thermal conductivity of BN/Si70-20 and BN/Si60-20 reached 0.386 W•m -1 •K -1 and 0.4 W•m -1 •K -1 , respectively, compared with pure EP, which is improved by 118.0% and 126.0%, respectively, which effectively improves the thermal conductivity of EP under the condition of lower total fill, and can reduce the occurrence of heat aging.

Figure 1 .
Figure 1.Composite epoxy finished product material.Table 1. Different material names and corresponding components appear in this paper.

Figure 2 .
Figure 2. Measuring principle of LFA 467 thermal conductivity instrument with flash method.

Figure 3 .
Figure 3.The thermal conductivity of composite epoxy resin materials was measured.In solid materials, the internal heat conduction process is mainly in the form of energy transfer between the thermal movement of molecules or atoms and the surrounding particles.The amplitude of the thermal motion of the molecules in the micro is relative to the macro temperature, and the higher the temperature of the object is, the faster the molecular and atomic vibration rate and the greater the kinetic energy will be.In solid materials, two types of particles are mainly involved in heat transfer, namely, free electrons that can transfer motion within the material and lattice vibration.The energy in lattice vibration is quantized and each part is called phonon.The two can be calculated superimposed:

Figure 4 .
Figure 4.The relationship between the spectrum of the real part of the dielectric constant and filling with the ratio at 20 wt% filling: (a) less BN filling, (b) more BN filling, (c) micron BN doped with less nanometer SiO 2 , (d) micron BN doped with more nanometer SiO 2 .In summary, when the filling amount reaches 20 wt%, the addition of SiO 2 can further enhance the thermal conductivity of the composite epoxy resin, resulting in a significant improvement in its overall thermal conductivity.Among them, BN/Si70-20 and BN/Si60-20 materials achieved improved thermal conductivity.

Table 1 .
Different material names and corresponding components appear in this paper.