Excellent Thermal and Dielectric Properties of Hexagonal Boron Nitride/Phenolic Resin Bulk Composite Material for Heatsink Applications

: In the present paper, we report polymer composites based on phenolic resin ﬁlled with hexagonal boron nitride; hot compression molding coupled with solution-based mixing were used to manufacture the composites. The paper presents experimental results on the physical and physico-chemical properties of the obtained composites: thermal stability in air and argon, dielectric constant and dielectric loss tangent, active electrical resistance, thermal conductivity (mean and anisotropy), and mechanical strength. It is shown that the proposed technique of composite manufacturing, including the application of high-process pressures, makes it possible to obtain materials with high anisotropy of thermal conductivity, extremely high-ﬁller content, and excellent dielectric properties, all of which are very important for prospective highly efﬁcient lightweight heatsink elements for electronic devices. Experimental values of thermal conductivity and dielectric constant were analyzed using known mathematical models. Experimental values for thermal conductivities (up to 18.5 W · m − 1 · K − 1 ) of composites at ﬁller loadings of 65–85 vol.% are signiﬁcantly higher than published data for bulk boron nitride/polymer composites.


Introduction
Intensive growth of transistor-based computer chips in modern technology leads to an exponential increase in heat generation per unit area. Excessive heat generation leads to the formation of local overheated points (so called hotspots) on the surface of the chip, which results in incorrect electronics operation and eventual failure; therefore, it is necessary to create materials with high-thermal conductivity values, including thermal interface materials (TIMs), which can effectively dissipate heat to the environment or active cooling system, such as a radiator, heat pipe, or Peltier element. Air has extremely low-heat conductivity (ca. 0.024 W·m −1 ·K −1 [1]), and even with thorough mechanical finishing, the effective contact area at the chip-radiator interface is only about 1-3% [2]; heat flux is typically distributed ineffectively. Therefore, polymer-based TIMs are required to provide excellent mechanical contact in order to reduce thermal contact resistances between the chip and heatsink [1][2][3][4][5][6][7]. In order to improve heat removal from the surface of the radiator, heat dissipating materials with high-thermal conductivity are required. and functionalization are often used in literature to improve local thermal resistances of the composites [4].
Various surface modifications of boron nitride particles, namely exfoliation in aromatic solvents, such as polysulfide-p-phenylene, poly-p-phenylene-vinylene [34,35], increase contact surface, as well as non-covalent functionalization [36,37], which does not provide PCMs with acceptable thermal properties. For example, functionalization resulted in thermal conductivity increase from 0.3 to 0.35 W·m −1 ·K −1 for PCM with 10% h-BN content [35]. It can be concluded that these types of modification of h-BN particles do not lead to a significant increase in the heat-conducting properties of PCMs.
Heat resistance and thermal properties of phenolic resins (PRs) are superior to most polymers, i.e., for epoxy resins, decomposition is significant already at 430 K, whereas PRs are stable up to 530 K, therefore they are more suitable for manufacturing materials for hightemperature applications. Due to the increased heat and fire resistance, as well as chemical stability, PR-based materials are used in applications that require excellent fire safety properties, i.e., in the production of power supply modules, airspace components, vacuum devices [38,39]. Nevertheless, published data on PR-based, heat-conductive composites, including h-BN/PR-system, are scarce.
Other temperature-resistant polymers, such as polyetheretherketone (PEEK), have a significant disadvantage as compared to PRs; the processing temperatures are much higher, about 340 • C [40], whereas for polyetherketone ketone (PEKK), the temperatures are 320 to 380 • C [41]. In addition, the high-melt viscosity of these thermoplasts is a significant processing disadvantage as compared to PR.
Films based on h-BN are used as TIMs with dielectric properties in electronics. Bulk materials based on h-BN and PRs can be used as materials for heat exchangers and dimensionally stable structures. A lot of research [12][13][14][15] is conducted on bulk heatsink composites.
Dielectric properties of h-BN/PR systems are considered in detail by Ko et al. [42], where electrically insulating properties of PR-based composite and mixture of two heatconducting fillers, h-BN and ZnO, were studied. PR was custom-made; nevertheless, thermal conductivity values were quite low (3.5 W·m −1 ·K −1 in-plane and only ca. 1.1 W·m −1 ·K −1 through-plane at 80 vol.% of filler). The use of PR-based solvent processing makes it possible to achieve high and ultra-high content of the heat-conducting filler in the composite, but post-processing conditions (drying, pre-mixed powder preparation, molding) apparently define the thermophysical characteristics of the resulting material.
In the present paper, the influence of h-BN content on thermal conductivity, thermal stability and electrophysical characteristics (dielectric constant, dielectric loss tangent, electrical conductivity) of hot-pressed compositions of the h-BN/PR composites were studied. Filler concentration correlations of thermal conductivity and dielectric constants were described using known physical models. The adequacy of the isolated medium and effective medium models for the description of h-BN/PR systems was analyzed.

Characterization Techniques
Particle size distributions of h-BN particles were measured via the laser diffraction technique of aqueous suspensions (6 mg/mL, 15 min. ultrasonication), using SYNC setup with the FLOWSYNC (both Microtrack MRB, Montgomeryville, PA, USA) module for measuring suspensions. Mie theory was used to calculate distributions.
Scanning electron microscopy (SEM) studies were performed using a Thermo Fisher Prisma E instrument (Waltham, MA, USA), operating at 10.0 kV accelerating voltage with no metallization of the samples.
Measurements of thermal conductivities were carried out by steady-state heat flux method at temperature range of 293-303 K (ASTM C5470-17 method) in the direction of the molding axis (through-plane, k z ), as well as in a perpendicular direction (in-plane, k x ).
Thermogravimetric analysis (TGA) was performed on the Jupiter F1 STA unit (TGA/ DSC) (Netzsch, Selb, Germany), using sapphire crucibles and standards; nitrogen (99.999 +%) was used for inert atmosphere, whereas dried air was used as an oxidizing agent; heating rate was 5 K/min in all cases.

Filler Particle Size Distribution
Analysis of the published data showed that, for h-BN-based composites, the higher the initial particle size of the filler, the higher the maximal thermal conductivity in the composite [31,43]. This inverse proportionality between thermal conductivity and particle size can be explained by the fact that h-BN interparticle heat transfer is ballistic in nature, that is, heat transfer between the boundaries of neighboring particles [24] becomes less effective as the relative concentration of the edge atoms increases, whereas the average interparticle contact area decreases. Therefore, no preliminary grinding of the filler was used in the present work.
Particle size distribution for h-BN used in the present study, as determined via laser diffraction, is depicted on Figure 1a. Distribution is clearly bi-modal with only a small fraction of particles having a size above 20 µm. Average particle size of h-BN was 5.3 µm (leftmost peak in Figure 1a).
Results of laser diffraction measurements are further supported by SEM studies. h-BN particles have a typical, layered structure and size in the range of 5-15 µm, which is very similar to natural graphite.

h-BN/PR Composites Manufacturing Technology
The step-by-step scheme for manufacturing h-BN/PR composites is shown in Figure 2. We used the matrix dissolution method in order to obtain ultra-high volumetric filler content (up to 85%), which is extremely important to achieve maximal thermal conductivity values, i.e., values of up to 30.25 W·m −1 ·K −1 , which were achieved in thin oriented composite papers (h-BN-based nanosheets/cellulose nanofibers) at 70 wt.% h-BN loading [44]; similarly, high values were achieved for highly filled PVA-based films by Song et al. [45], but this level of thermal conductivities was never reported for bulk composites, as it is very difficult to achieve particle orientation, i.e., avoiding agglomeration and porosity that lead to significant deterioration of thermal properties. Therefore, most of the published data for bulk composites report modest thermal conductivity values of 0.6-10 W·m −1 K −1 at filler loadings that are typically under 25 vol.% [46]. Results of laser diffraction measurements are further supported by SEM studies. h-BN particles have a typical, layered structure and size in the range of 5-15 μm, which is very similar to natural graphite.

h-BN/PR Composites Manufacturing Technology
The step-by-step scheme for manufacturing h-BN/PR composites is shown in Figure  2. We used the matrix dissolution method in order to obtain ultra-high volumetric filler content (up to 85%), which is extremely important to achieve maximal thermal conductivity values, i.e., values of up to 30.25 W·m −1 ·K −1 , which were achieved in thin oriented composite papers (h-BN-based nanosheets/cellulose nanofibers) at 70 wt.% h-BN loading [44]; similarly, high values were achieved for highly filled PVA-based films by Song et al. [45], but this level of thermal conductivities was never reported for bulk composites, as it is very difficult to achieve particle orientation, i.e., avoiding agglomeration and porosity that lead to significant deterioration of thermal properties. Therefore, most of the published data for bulk composites report modest thermal conductivity values of 0.6-10 W·m −1 K −1 at filler loadings that are typically under 25 vol.% [46]. We further used vibration grinding to obtain homogeneous powders, which is crucial for high-quality molding. Another advantage of this technique is that the grinding mechanism primarily features shear and interparticle collisions, which ensures that resin is evenly distributed throughout both the mixture (macroscopically) and on particles' surfaces (microscopically, see Figure 1c,d).
As can be readily seen from the sample images on Figure 2, incorrect pressure (too high in this case) leads to visually observable horizontal fractures.
Hot molding is widely used for PR-based composites. In the case of h-BN-based composites, it was shown that the application of pressure is clearly advantageous for thermal conductivity, in order to minimize porosity ( Figure 3a) and ensure strong bonding of the composite (Figure 1c,d). Recently, Moradi et al. [32] showed that by applying only 2 MPa while curing h-BN/epoxy composite, one can increase thermal conductivity twofold. Another consideration in favor of hot molding is moderate particle orientation, sufficient for increased material anisotropy, yet not as high as to prevent effective contacts of layered particles [4,47].
Theoretical density was calculated using the following formula based on the simple rule of mixtures (1): where ρ m -density of matrix (1.20 g/cm 3 ), and ρ f -density of filler (2.10 g/cm 3 ). Porosity φ was calculated using the following Formula (2):

·100%
(2) ρ experim. being experimental value for bulk density. We further used vibration grinding to obtain homogeneous powders, which is crucial for high-quality molding. Another advantage of this technique is that the grinding mechanism primarily features shear and interparticle collisions, which ensures that resin is evenly distributed throughout both the mixture (macroscopically) and on particles' surfaces (microscopically, see Figure 1c,d).
As can be readily seen from the sample images on Figure 2, incorrect pressure (too high in this case) leads to visually observable horizontal fractures.
Hot molding is widely used for PR-based composites. In the case of h-BN-based composites, it was shown that the application of pressure is clearly advantageous for thermal conductivity, in order to minimize porosity ( Figure 3a) and ensure strong bonding of the composite (Figure 1c,d). Recently, Moradi et al. [32] showed that by applying only 2 MPa while curing h-BN/epoxy composite, one can increase thermal conductivity twofold. Another consideration in favor of hot molding is moderate particle orientation, sufficient for increased material anisotropy, yet not as high as to prevent effective contacts of layered particles [4,47].  Theoretical density was calculated using the following formula based on the simple rule of mixtures (1): where -density of matrix (1.20 g/cm 3 ), and -density of filler (2.10 g/cm 3 ). Porosity was calculated using the following Formula (2): . being experimental value for bulk density. Figure 3a shows the plot of experimental values for bulk density vs. theoretical den-  Figure 3a shows the plot of experimental values for bulk density vs. theoretical density, as defined by Equation (1). It can be readily seen from the data that, in addition to great pressure leading to the formation of cracks in the composite, there is also a threshold value for each filler fraction that allows for manufacturing the composite with minimal porosity (compare the green and orange bars). This fact may be due to increased intrinsic porosity at low molding pressures.
As a result of using significant processing pressures , composites with densities close to theoretical (porosity below 6-7 vol.%) and up to very high-filler loadings (about 75-80 vol.%) were obtained. Increased porosity (above 10 vol.%) is only seen with loadings as high as 85 vol.% (see Figure 3b), which may be attributed to technique's inability to provide sufficient matrix polymer distribution at high-filler fractions. This is very beneficial, as the presence of pores greatly reduces thermal conductivity of the material (see Figure 4a).
. being experimental value for bulk density. Figure 3a shows the plot of experimental values for bulk density vs. theoretical density, as defined by Equation (1). It can be readily seen from the data that, in addition to great pressure leading to the formation of cracks in the composite, there is also a threshold value for each filler fraction that allows for manufacturing the composite with minimal porosity (compare the green and orange bars). This fact may be due to increased intrinsic porosity at low molding pressures.
As a result of using significant processing pressures , composites with densities close to theoretical (porosity below 6-7 vol.%) and up to very high-filler loadings (about 75-80 vol.%) were obtained. Increased porosity (above 10 vol.%) is only seen with loadings as high as 85 vol.% (see Figure 3b), which may be attributed to technique's inability to provide sufficient matrix polymer distribution at high-filler fractions. This is very beneficial, as the presence of pores greatly reduces thermal conductivity of the material (see Figure 4a).  In this work, samples of heat-conducting h-BN/PR composites were obtained with filler loadings in the range of 5 to 85 vol.% and high homogeneity.
Gu et al. [55] described dielectric heat-conducting composite materials, based on boron nitride and polyimide, were obtained by hot pressing. The thermal conductivity of PCM is 0.696 W·m −1 ·K −1 , and the dielectric constant is 3.77 with a mass content of filler of 30%. In the work [56], PCMs based on thiol-epoxy elastomers and micron-sized boron nitride were synthesized by in situ polymerization; a filler of 17.5 wt.% achieved thermal conductivity of 2.4 W·m −1 ·K −1 ; surface activation and the creation of tubes similar to carbon nanotubes based on boron nitride does not lead to a noticeable improvement in the heatconducting properties of the material. In a number of recent works [57,58], PCMs were obtained based on plastics with carbon fillers, such as graphite and graphene; this class of materials does not have the dielectric characteristics necessary for use as heat-dissipating In this work, samples of heat-conducting h-BN/PR composites were obtained with filler loadings in the range of 5 to 85 vol.% and high homogeneity.
Gu et al. [55] described dielectric heat-conducting composite materials, based on boron nitride and polyimide, were obtained by hot pressing. The thermal conductivity of PCM is 0.696 W·m −1 ·K −1 , and the dielectric constant is 3.77 with a mass content of filler of 30%. In the work [56], PCMs based on thiol-epoxy elastomers and micron-sized boron nitride were synthesized by in situ polymerization; a filler of 17.5 wt.% achieved thermal conductivity of 2.4 W·m −1 ·K −1 ; surface activation and the creation of tubes similar to carbon nanotubes based on boron nitride does not lead to a noticeable improvement in the heat-conducting properties of the material. In a number of recent works [57,58], PCMs were obtained based on plastics with carbon fillers, such as graphite and graphene; this class of materials does not have the dielectric characteristics necessary for use as heat-dissipating components in microelectronics [59]. PCMs based on polydopamine and boron nitride with a filler content of 17.5 wt % were obtained, and thermal conductivity of 2.4 W·m −1 ·K −1 was achieved.
Nevertheless, despite the wide scatter of the data obtained and insufficient thermal properties of most of the obtained PCMs, in a number of works, researchers were able to manufacture PCMs with high-thermal conductivity; for example, in the work by Novokshonova et al. [60], thermal conductivity of 27.6 W·m −1 ·K −1 was achieved at a filler content of 95 wt %. The thermal conductivity value of 12.5 W·m −1 ·K −1 was reported at a filler content of 65 wt % [61]. PCM, based on cellulose fibers and boron nitride nanotubes, achieved a thermal conductivity of 22 W·m −1 ·K −1 [37].
As can be readily seen from Figure 4a, all composites demonstrated significant anisotropy of thermal conductivity, which may be due to preferential orientation of filler particles. In-plane thermal conductivity k x reaches very high values of 18.5 W·m −1 ·K −1 at 75 vol.%, and the k x /k z ratio is 1.5-2.2 (for 5 and 85 vol.%, respectively). Anisotropy makes it possible to create a predefined structure for preferential heat removal in the heatsink system. We further used effective thermal conductivity k eff , defined by simple averaging over three main axes of a transverse-orthotropic body (3), as a figure of merit for thermal conductivity: Experimental values were compared with three models that are most suitable for describing thermal conductivity in polymer composites. Thermal conductivity of pure h-BN was taken to be 100 W·m −1 ·K −1 (taking into account possible local contact resistances), whereas thermal conductivity of the PR was 0.25 W·m −1 ·K −1 [42]. Thermal conductivity of composites is a property that is difficult to describe adequately, since there may be substantial differences in the properties of components, i.e., 400 times in this case.
Historically, the first group of models used an approximation of the isolated medium [62], that is, particles of heat-conducting filler are considered as non-interacting homogeneous spheres in a homogeneous polymer medium. These models have a high accuracy for regularly shaped particles at low filler content (less than 20-30 vol.%), and account for small differences in the thermal conductivity of the matrix and filler. The first proposed model to use this approximation was the Maxwell-Eucken model [62] (4): k m -thermal conductivity of matrix, k f -thermal conductivity of filler, V f -filler volume content. It is clearly seen from Figure 4b-f that this model provides significantly lower estimates and is not adequate in all of the studied concentration range, which might indicate that interparticle interactions and property differences play their significant role, even at lower filler loadings (see Figure 4b).
Second, more modern groups of models use effective medium approximation (EMA); the first model of this type was proposed by Bruggeman (5) [63,64]. It is applicable in the case of particles with complex shapes, for example, layered structures, fibers, etc.; its main advantage is that interparticle contacts can be taken into account. In addition, it has been reported to provide a higher accuracy, even beyond the percolation threshold.
For the reported data, the Bruggeman model is much more accurate than Maxwell-Eucken (4) at lower and medium loadings (up to 30 vol.%, see Figure 4b), but provides significant overestimates at higher concentrations (Figure 4c,d). Apparently, local contact thermal resistances (with possible re-agglomeration) dominate at higher concentrations, and should also be taken into account.
In addition to the Bruggeman model, the semi-empirical Agari-Uno model (6) is widely used to describe composites based on metal particles, graphite, and ceramics [65,66]. It accurately describes the thermal conductivity of materials with high-and ultra-high filler content, including highly anisotropic fillers. We set the empirical coefficients as C 1 = 0.7, C 2 = 1 as the best fit through zero and 100 vol.% points: log The Agari-Uno model seems to best describe experimental data (see Figure 4d-f), but definitive structural conclusions cannot be drawn from it, except that C 2 ≥ 1 means that the filler is very prone to forming conduction paths throughout polymer matrix in this particular system, and conductivity is defined not by polymer crystallization and orientation in the presence of filler, but by the formation and structure of these conductive paths. It can be seen that deviations are greatest in the middle of concentration range (20-60 vol.%,) above the percolation threshold but before the dominating influence of the filler thermal conductivity.

Thermogravimetric Analysis and Thermal Stability
Thermogravimetric method is widely used to evaluate degradation temperatures of polymer-based compounds. We used a temperature range of 300-1250 K for each composition and then estimated its degradation temperature as corresponding to a 2% weight loss. Figure 5a shows concentration curves for as-defined degradation temperature. While degradation temperatures monotonously increase with filler loading, stability in the air for low and medium loadings is surprisingly even and slightly higher than in the inert atmosphere at 75 and 85 vol.% stability in the air However, decreases may be attributed to increased porosity. In any case, for high-filler loadings, temperature stability reaches 600-800 K, which makes these composites suitable for power electronics and applications with substantial fire safety requirements. 60 vol.%,) above the percolation threshold but before the dominating influence of the filler thermal conductivity.

Thermogravimetric Analysis and Thermal Stability
Thermogravimetric method is widely used to evaluate degradation temperatures of polymer-based compounds. We used a temperature range of 300-1250 K for each composition and then estimated its degradation temperature as corresponding to a 2% weight loss. Figure 5a shows concentration curves for as-defined degradation temperature. While degradation temperatures monotonously increase with filler loading, stability in the air for low and medium loadings is surprisingly even and slightly higher than in the inert atmosphere at 75 and 85 vol.% stability in the air However, decreases may be attributed to increased porosity. In any case, for high-filler loadings, temperature stability reaches 600-800 K, which makes these composites suitable for power electronics and applications with substantial fire safety requirements.  Figure 5b compares the thermogravimetric curves in the air, argon 5 and 85 vol.% composites. It can be readily seen that the 85 vol.% h-BN composite is far more thermally stable; therefore, it is highly desirable to use composites with higher filler content for hightemperature applications. Therefore, it is obvious that this technology for obtaining PCM h-BN/PRs makes it possible to obtain TIM with an operating temperature of at least 480 K.

Dielectric Properties
Frequency range 1 KHz to 1 MHz was used for εr and tan δ measurements; 1 MHz  Figure 5b compares the thermogravimetric curves in the air, argon 5 and 85 vol.% composites. It can be readily seen that the 85 vol.% h-BN composite is far more thermally stable; therefore, it is highly desirable to use composites with higher filler content for high-temperature applications. Therefore, it is obvious that this technology for obtaining PCM h-BN/PRs makes it possible to obtain TIM with an operating temperature of at least 480 K.

Dielectric Properties
Frequency range 1 KHz to 1 MHz was used for ε r and tan δ measurements; 1 MHz was taken as the reference frequency for concentration correlations. Figure 6a shows that ε r values vary in the range from 4.2 to 5.5 and even slightly decrease at higher loadings. This is explained by the fact that boron nitride has an extremely low dielectric constant: ε r, h-BN in the plane of the particle is 6 to 6.5, in the through-plane direction 2.8 to 3.8; whereas for the PR, ε r is in the range of 3.5-4.5 [17,19,67]. In addition, composite ε r value also depends on the boundary and contact phenomena, as well as porosity. As can be seen, at such close values for the filler and matrix, ε r appears to be following the simple rule of mixtures (Figure 6a). Maxwell-Garnett isolated media model for dielectric constant (7) [68] matches experimental data only slightly better.
ε f , ε m -dielectric constants for filler and matrix respectively.
that tan δ at 1 MHz varies with filler loading from 0.015 to 0.055, which corresponds to an angle change from 0.8 to 3.2, showing a slight minimum at 50 vol.%, which may once again be linked with an increased influence of contact phenomena and porosity at higher filler loadings. The low value of tan δ and weak frequency dependence are important for dielectrics used in high-frequency applications, i.e., 5G. On the other hand, tan δ is a structurally dependent property, especially for composites, so its relatively low values for a given polymer may be used as a sign of well-structured dielectric material. Figure 6d shows the tan δ-frequency plot for the 30 vol.% composite. From 20 KHz upwards, tan δ is almost constant (around 0.05). Through analyzing the plots, we can conclude that, in the entire range of filler loadings, both εr and tan δ values meet the requirements usually posed on industrial dielectrics (ε ~2 to 8, tan δ < 10 −1 ), although the scatter in the experimental data is significant. The current study was not able to measure the anisotropy of the dielectric properties; therefore, it is logical to assume that, on the one hand, concentration correlations should generally follow the same trends as for thermal conductivity due to orientation of the filler particles, but on the other hand, one should not expect significant differences for axial and radial directions, as εr for h-BN and PR are very close, as can be readily seen from Figure 6a.
It should also be noted that the studied range frequency plots for the real part of εr and tan δ behave symbatically. Although further research might clarify the nature of refraction and reflection properties in the studied composites, one can qualitatively state that in the h-BN/PR system at low frequencies, the well-known Kramers-Kronig dispersion equations take hold, and the system shows no non-linear effects [69].
Much research has been carried out to implement h-BN-based materials and nanostructures in nanoelectronic devices [70]. In the present case, used frequencies were too low to establish any significant electronic effects, which is due to the wide bandgap in h-BN. Nevertheless, the assessment of near-optical and THz frequency areas might reveal potentially interesting effects for the system under study. Figure 6b demonstrates that ε r ranges from 4.6 to 5.6 at 30 vol.% filler content for frequencies of 8-1000 KHz; therefore, the frequency plot is highly stable. Figure 5c shows that tan δ at 1 MHz varies with filler loading from 0.015 to 0.055, which corresponds to an angle change from 0.8 to 3.2, showing a slight minimum at 50 vol.%, which may once again be linked with an increased influence of contact phenomena and porosity at higher filler loadings. The low value of tan δ and weak frequency dependence are important for dielectrics used in high-frequency applications, i.e., 5G. On the other hand, tan δ is a structurally dependent property, especially for composites, so its relatively low values for a given polymer may be used as a sign of well-structured dielectric material. Figure 6d shows the tan δ-frequency plot for the 30 vol.% composite. From 20 KHz upwards, tan δ is almost constant (around 0.05). Through analyzing the plots, we can conclude that, in the entire range of filler loadings, both ε r and tan δ values meet the requirements usually posed on industrial dielectrics (ε~2 to 8, tan δ < 10 −1 ), although the scatter in the experimental data is significant. The current study was not able to measure the anisotropy of the dielectric properties; therefore, it is logical to assume that, on the one hand, concentration correlations should generally follow the same trends as for thermal conductivity due to orientation of the filler particles, but on the other hand, one should not expect significant differences for axial and radial directions, as ε r for h-BN and PR are very close, as can be readily seen from Figure 6a.
It should also be noted that the studied range frequency plots for the real part of ε r and tan δ behave symbatically. Although further research might clarify the nature of refraction and reflection properties in the studied composites, one can qualitatively state that in the h-BN/PR system at low frequencies, the well-known Kramers-Kronig dispersion equations take hold, and the system shows no non-linear effects [69].
Much research has been carried out to implement h-BN-based materials and nanostructures in nanoelectronic devices [70]. In the present case, used frequencies were too low to establish any significant electronic effects, which is due to the wide bandgap in h-BN. Nevertheless, the assessment of near-optical and THz frequency areas might reveal potentially interesting effects for the system under study.
Evaluation of specific electrical resistance and electrical conductivity was performed using the 2-probe technique and a teraohmmeter. Figure 7 shows that all h-BN/PR composites have sufficient electrical resistance (>>10 MΩ·cm), so all of them are sufficiently reliable dielectrics to ensure static discharge or short circuit safety. Evaluation of specific electrical resistance and electrical conductivity was performed using the 2-probe technique and a teraohmmeter. Figure 7 shows that all h-BN/PR composites have sufficient electrical resistance (>>10 MΩ·cm), so all of them are sufficiently reliable dielectrics to ensure static discharge or short circuit safety. The plots show the constant increase of electrical resistivity with increased filler loading, again supporting the need to use composities above 40 vol.% filler content, in order to achieve higher level of both thermal and electrical properties.

Mechanical Properties
Composites for heatsink application should withstand mechanical stress in order to be machined into finned radiators, heat exchangers, etc. Generally, the accepted level of mechanical strength for the material to be processed by most machining techniques (cutting, milling cutting, drilling, polishing) is over 20 MPa. Stress-strain curves at compression for several filler loadings are depicted in Figure 8. The plots show the constant increase of electrical resistivity with increased filler loading, again supporting the need to use composities above 40 vol.% filler content, in order to achieve higher level of both thermal and electrical properties.

Mechanical Properties
Composites for heatsink application should withstand mechanical stress in order to be machined into finned radiators, heat exchangers, etc. Generally, the accepted level of mechanical strength for the material to be processed by most machining techniques (cutting, milling cutting, drilling, polishing) is over 20 MPa. Stress-strain curves at compression for several filler loadings are depicted in Figure 8.

Mechanical Properties
Composites for heatsink application should withstand mechanical stress in order to be machined into finned radiators, heat exchangers, etc. Generally, the accepted level of mechanical strength for the material to be processed by most machining techniques (cutting, milling cutting, drilling, polishing) is over 20 MPa. Stress-strain curves at compression for several filler loadings are depicted in Figure 8. As can be readily seen from the data, all composites as well as neat PR, demonstrate fragile behavior during compression. Introducing ceramic filler leads to a decreased ultimate deformation (increased brittleness) of the material and also increased rigidity (as indicated by Young's modulus). The overall effect is that the compressive strength of the composites under study, decreased almost steadily with an increase in the filler loading, indicating a dominant effect of the former factor. Nevertheless, even at a very-high filler loading (65 vol.%), the ultimate compressive strength was above 40 MPa, which is more than enough for the material to be machined into complex-shaped heatsink articles. A sharp decrease at 85 vol.% filler loading may once again be linked with increased porosity. As can be readily seen from the data, all composites as well as neat PR, demonstrate fragile behavior during compression. Introducing ceramic filler leads to a decreased ultimate deformation (increased brittleness) of the material and also increased rigidity (as indicated by Young's modulus). The overall effect is that the compressive strength of the composites under study, decreased almost steadily with an increase in the filler loading, indicating a dominant effect of the former factor. Nevertheless, even at a very-high filler loading (65 vol.%), the ultimate compressive strength was above 40 MPa, which is more than enough for the material to be machined into complex-shaped heatsink articles. A sharp decrease at 85 vol.% filler loading may once again be linked with increased porosity.
It should also be noted that Young's modulus of composites, throughout all the studied concentrations, was close to that of neat resin, which, in this case, should mean that composite mechanics in the elastic region are primarily defined by the matrix. The layered filler particles apparently do not contribute to the stiffness of the composite at low strains and influence mechanics at higher deformations due to porosity and its resistance to crack propagation.

Conclusions
h-BN/PR composites were obtained in a wide range of component ratios via solution mixing, vibrational milling and hot-compression molding. The thermal conductivity of the obtained materials varied in the range from 0.63 to 18.5 W·m −1 ·K −1 at filler loadings of 5 to 85 vol.%, respectively. Increased porosity is only significant above 80 vol.% loading, so the proposed technology is quite effective for manufacturing composites with extremely high filler loadings. The percolation threshold is not very pronounced, but lies in the range 25-30 vol.%. Reported data on thermal conductivity is significantly higher than published values for bulk BN/polymer composites, which can be explained by both high-filler loading and advantages of the proposed technology. This fact can be attributed to resin curing under pressure, ensuring the optimal level of adhession on the matrix-filler interface, optimal filler particle size, as well as two-step mixing that enabled homogeneous dispersion of the filler.
Several models were considered to describe thermal conductivity in h-BN/PR composites. An isolated medium model is inadequate in this particular case, whereas the effective medium (Bruggeman) model, although hugely overestimates at higher concentrations, may be used as an approximation at concentrations up to 30 vol.%. The best fitting was achieved with the Agari-Uno model, using parameters of C 1 = 0.7 and C 2 = 1.0. Therefore, composite behavior, in this case, is best distributed with a mixed series-parallel model with filler particles prone to the formation of percolation-type networks.
Thermogravimetric analysis provided the evaluation of short-term degradation stability; it is sufficient for the use of manufactured composites in high-temperature power electronics (over 480 K). As thermal stability significantly improves with an increase of filler loading, it is very important for prospective applications to develop stable technologies for manufacturing materials with over 50 vol.% of h-BN.
The dielectric constant ranged from 5.6 to 4.2 for 85 and 5 vol.% respectively. As the difference in component values for ε r is not very large, Maxwell-Garnett model, which is based on an isolated medium approximation, describes the obtained experimental values with high accuracy (but so does the rule of mixtures). Dielectric loss tangent tan δ values are also small (0.015 to 0.055) and weakly frequency-dependent, at least in the 20 KHz-1 MHz range. Specific active resistance of the materials ranged from 17 to 140 MΩ. It is concluded that reported composites are applicable as dielectric heatsink materials for electronics. Mechanical properties (compression strength over 40 MPa at 65 vol.% h-BN) of the composites are sufficient for the manufacturing of complex-shaped articles via most conventional machining techniques.
Taking into account the excellent dielectric properties of the obtained h-BN/PR composites, the high-thermal stability both in inert and oxidative atmospheres, controlled anisotropy of thermal conductivity, as well as its high absolute values and relatively low density, shows that reported composites are promising for the application as components of heat-removal systems in electronic engineering and microelectronics. Composites may also be used to manufacture independent heat-dissipating elements (various heat exchangers), since they can be machined into complex shapes. Current research suggests that it is generally feasible to achieve even higher filler loadings in h-BN/polymer composites, as filler content above 60 vol.% enables to drastically increase thermal conductivity, thermal stability, and dielectric properties.

Data Availability Statement:
The data presented in this study are available on request from the corresponding author.