Nano‐Interconnected 1D/2D Boron Nitride Hybrid Networks: Unlocking Superior Thermal Conductivity in Electrically Insulating Thermal Interface Nanocomposites Based on Hybrid Thermal Percolation Model

Abstract

Due to its high thermal and low electrical conductivities, boron nitride (BN) has emerged as an optimal filler for thermal interface materials (TIMs) that prevent thermal condensation of nanostructures without causing shutdown due to electron tunneling. The polymer composite based on the BN hybrid strategy can be considered an optimal option as an electrically insulating and heat‐dissipating TIM. However, there is a paucity of systematic experiments and theoretical approaches investigating the optimal content and ratio of BN hybrid fillers, which are key factors in synergistically improving thermal conductivity (TC). In this study, a hybrid thermal percolation model is developed by modifying the Foygel model to investigate the synergistic improvement in systematically measured TC. The model effectively determines the optimal hybrid filler composition and the resultant performance enhancement. Furthermore, the impact of BN surface and interface chemistry is comprehensively analyzed in conjunction with the filler network structure. The highest isotropic TC (10.93 W m⁻¹·K) is achieved by optimizing the formation of nano‐interconnections between the hybrid 1D BN nanotube and 2D hexagonal BN (h‐BN), representing a significant improvement of 1582% and 118% over the TC of pure epoxy and the composite containing the optimized h‐BN network, respectively.

In this research, the synergistic enhancement of thermal conductivity (TC) in composites based on 1D and 2D boron nitride hybrid fillers is systematically investigated, and the mathematical model is proposed to provide a theoretical analysis of the TC enhancement behavior attributed to the formation of nano‐interconnections, an optimal 3D filler network.

1. Introduction

The trend of miniaturization and integration in electronic devices and components has been a response to the needs of consumers.^{[ 1 ]} This trend, however, has the potential to increase the risk of internal heat accumulation during operation, which can lead to device performance degradation and a reduction in lifespan.^{[ 2 ]} Therefore, the heat dissipation properties of thermal interface materials (TIMs) become a crucial factor in determining device performance and lifetime.^{[ 1} , ² , ^{3 ]} Additionally, to mitigate electrical interference between electronic structures with high power density, it is imperative to utilize TIMs based on polymer composites, which possess both exceptional thermal conductivity (TC) and electrical insulation properties.^{[ 2} , ^{4 ]}

Typical conductive polymer composites, which contain carbon or metal fillers and exhibit excellent thermal and electrical conductivity, are not suitable for TIMs that require electrical insulation.^{[ 4} , ^{5 ]} Consequently, various ceramics, such as boron nitride (BN), silicon carbide, aluminum oxide, aluminum nitride, and, zinc oxide, are frequently utilized as fillers for polymer composite‐based TIMs due to their high TC and low electrical conductivity.^{[ 6} , ⁷ , ⁸ , ⁹ , ¹⁰ , ¹¹ , ¹² , ^{13 ]} Notably, BN, a ceramic composed of boron and nitrogen atoms, exhibits low electrical conductivity due to its substantial bandgap of 5.90 eV and high TC, reaching 350 W m⁻¹·K at room temperature.^{[ 7} , ^{14 ]} Consequently, BN is an excellent filler for enhancing the heat dissipation and electrical insulation properties of polymer composite‐based TIMs.

The interfacial thermal resistance (ITR) at the filler‐matrix interface has been identified as a pivotal parameter in determining the TC of polymer composite‐based TIMs.^{[ 15 ]} The reduction of the ITR effect is a critical strategy for enhancing the TC.^{[ 15} , ¹⁶ , ^{17 ]} The formation of the nano‐interconnections has been identified as a promising approach to inducing both stepwise percolation in electrical conduction^{[ 18 ]} and thermal percolation to reduce the ITR effect.^{[ 19} , ²⁰ , ^{21 ]} Various strategies, including high filler content,^{[ 22 ]} segregated^{[ 23 ]} and hybrid^{[ 19} , ²⁴ , ²⁵ , ^{26 ]} networks structures have been employed to induce the nano‐interconnections in polymer composites. However, it should be noted that increasing the filler content and introducing a segregated network have the potential to compromise the mechanical properties of polymer composites.^{[ 22} , ^{23 ]} Therefore, the hybrid strategy may be more suitable for polymer composite‐based TIMs that maintain satisfactory mechanical properties.

The application of polymer composites employing the BN hybrid strategy can be regarded as the optimal option for TIMs, which necessitate both electrical insulation and heat dissipation capabilities. However, systematic experiments and theoretical approaches concerning the optimal content and ratio of hybrid fillers, which are pivotal in synergistically enhancing TC, have seldom been documented. In this study, the synergistic enhancement of TC in composites with 1D and 2D BN hybrid fillers was systematically analyzed based on a hybrid thermal percolation model proposed in this study by modifying the Foygel model. The incorporation of secondary BN nanotubes (BNNTs) resulted in a synergistic improvement in TC due to the formation of nano‐interconnections, and the maximum isotropic TC (10.93 W m⁻¹·K) was achieved at the optimal BNNT content. However, the inclusion of excess BNNT filler beyond the optimum level reduced the synergistic enhancement. Furthermore, the influence of BN surface and interface chemistry was found to differ significantly depending on the filler network structure. This effect was thoroughly analyzed by categorizing the networks into pure hexagonal BN (h‐BN) and hybrid (h‐BN and BNNT) structures, as illustrated in Figure 1 . To investigate the electrical insulation and heat dissipation properties of TIMs, thermal imaging measurements were performed on an electrically conductive circuit. Finally, the performance of the fabricated TIM with the optimized hybrid filler system was tested on an iPhone 15 Pro featuring an A17 Pro (3 nm) chip.

Figure 1.

Schematic of BN‐based epoxy composites in terms of filler network and interfacial structures.

2. Results and Discussion

2.1. Theoretical Approaches

2.1.1. Nan's Model

Lattice mismatch in phonon transmission at the filler‐matrix interface of a composite with randomly dispersed fillers generates the ITR. It has been reported that the ITR is a major obstacle to increasing the TC of polymer composites.^{[ 15 ]} In this study, Nan's model, which takes into account the ITR, was introduced to describe the TC of composites containing BN, which does not induce thermal percolation. TC of composites containing h‐BN or BNNTs using Nan's model ( TC _Nan ) was expressed as follows:^{[ 27 ]}

$$\mathit{T}{\mathit{C}}_{\mathit{Nan}}=\mathit{T}{\mathit{C}}_{\mathit{matrix}}\times \left(\frac{3+{\varphi }_{\mathit{BN}}\times \left({\mathit{\beta }}_{\mathit{x}}+{\mathit{\beta }}_{\mathit{z}}\right)}{3-{\varphi }_{\mathit{BN}}\times {\mathit{\beta }}_{\mathit{x}}}\right)$$ (1)

where,

$${\mathit{\beta }}_{\mathbf{x}}=\frac{\mathbf{2}({\mathbf{K}}_{\mathbf{11}}^{\mathbf{C}}-\mathbf{T}{\mathbf{C}}_{\mathbf{matrix}})}{{\mathbf{K}}_{\mathbf{11}}^{\mathbf{C}}+\mathbf{T}{\mathbf{C}}_{\mathbf{matrix}}},{\mathit{\beta }}_{\mathit{z}}=\frac{{\mathit{K}}_{33}^{\mathit{C}}}{\mathit{T}{\mathit{C}}_{\mathit{matrix}}}-1$$ (2)

where TC _matrix is the TC of the epoxy matrix (0.65 W m⁻¹·K) and ϕ _BN is the volume fraction of h‐BN or BNNT. ${\mathit{K}}_{11}^{\mathit{C}}$ and ${\mathit{K}}_{33}^{\mathit{C}}$ are equivalent TCs for the BN surrounded by the interfacial thermal barrier layer with horizontal and vertical axes of the unit cell, respectively. ${\mathit{K}}_{11}^{\mathit{C}}$ and ${\mathit{K}}_{33}^{\mathit{C}}$ can be written as follows:

$${\mathbf{K}}_{\mathbf{11}}^{\mathbf{C}}=\frac{\mathbf{T}{\mathbf{C}}_{\mathbf{BN}}}{\mathbf{1}+\frac{\mathbf{2}{\mathbf{a}}_{\mathbf{k}}\mathbf{T}{\mathbf{C}}_{\mathbf{BN}}}{\mathbf{hT}{\mathbf{C}}_{\mathbf{matrix}}}},{\mathbf{K}}_{\mathbf{33}}^{\mathbf{C}}=\frac{\mathbf{T}{\mathbf{C}}_{\mathbf{BN}}}{\mathbf{1}+\frac{\mathbf{2}{\mathbf{a}}_{\mathbf{k}}\mathbf{T}{\mathbf{C}}_{\mathbf{BN}}}{\mathbf{dT}{\mathbf{C}}_{\mathbf{matrix}}}},{\mathit{a}}_{\mathit{k}}={\mathit{R}}_{\mathit{ITR}}\times \mathit{T}{\mathit{C}}_{\mathit{matrix}}$$ (3)

where TC _BN and a _k are the TC of h‐BN (300 W m⁻¹·K) or BNNT (300 W m⁻¹·K) and the Kapitza radius (65 nm), respectively. h and d are the thickness (h‐BN of 20 nm and BNNT of 40 nm) and the lateral size (h‐BN of 3 µm and BNNT of 7 µm) of the BN fillers, respectively. R _ITR is the ITR (1 × 10⁻⁷ m²K W⁻¹).^{[ 28 ]}

2.1.2. Foygel Model

The phonon transfer path formed by the interconnected network in the composite contributes to the induction of thermal percolation.^{[ 19} , ²⁰ , ^{21 ]} The thermal percolation behavior induces the dramatic improvement in the TC exceeding the theoretical TC of the composite in which the ITR was introduced, indicating the transition from an ITR‐dominated heat transfer system to a filler‐to‐filler heat transfer system by forming a thermally percolated filler network. In this study, the TC at filler contents above a certain volume fraction (>21.85 vol%) was evaluated using the Foygel model:^{[ 29 ]}

$$\mathit{T}{\mathit{C}}_{\mathit{foy}}=\mathit{T}{\mathit{C}}_{\mathit{matrix}}\times \mathit{T}{\mathit{C}}_{\mathit{pre}}{\left(\frac{{\varphi }_{\mathit{h}-\mathit{BN}}-{\varphi }_{\mathit{cv}}}{1-{\varphi }_{\mathit{cv}}}\right)}^{\mathit{y}}$$ (4)

$${\mathit{R}}_{\mathit{c}}=\frac{1}{\mathit{T}{\mathit{C}}_{\mathit{pre}}\mathit{L}{{\varphi }_{\mathit{cv}}}^{\mathit{y}}}$$ (5)

where TC _foy and TC _matrix are the TC of the composites and matrix, respectively. TC _pre and y are the pre‐exponential factor (7 W m⁻¹·K in this study) and critical exponent (0.35 in this study), respectively.^{[ 30 ]} ϕ _{h − BN} is the volume fraction of h‐BN. The critical volume fraction (ϕ _cv ) was determined to be 23 vol% in this study. R _c is the contact thermal resistance of the h‐BN network. L is the average length of h‐BNs (3 µm in this study).

2.1.3. Hybrid Thermal Percolation Model

Hybrid thermal percolation model (HTPM) was proposed to describe the thermal behavior of composites containing 1D and 2D BN hybrid fillers. Assuming that the mechanism of thermal percolation generated by the interconnected filler network in the composite was the same as that of nano‐interconnections, the volume fraction of h‐BNs (ϕ _{h − BN} ) and critical volume fraction (ϕ _cv ) of the typical Foygel model were converted to the ratio of 1D filler ( φ ) and the critical ratio of 1D filler ( φ _c , 0.0001 in this study), respectively. The synergistically enhanced TC of the composite ( TC _HTPM ) incorporating h‐BN and BNNT simultaneously was expressed as follows:

$$\mathbf{T}{\mathbf{C}}_{\mathbf{HTPM}}=\mathbf{T}{\mathbf{C}}_{\mathbf{Nan}}+\mathbf{T}{\mathbf{C}}_{\mathbf{pre}}{\left(\frac{\phi -{\phi }_{\mathbf{c}}}{\mathbf{1}-{\phi }_{\mathbf{c}}}\right)}^{\mathbf{z}}(\mathit{\phi }<{\mathit{\phi }}_{\mathit{max}})$$ (6)

$${\mathit{R}}_{\mathit{c}-\mathit{HTPM}}=\frac{1}{\mathit{T}{\mathit{C}}_{\mathit{pre}}\mathit{L}{{\mathit{\phi }}_{\mathit{c}}}^{\mathit{z}}}$$ (7)

where TC _pre , φ , z , and L are the pre‐exponential factor, ratio of the secondary filler to primary filler (volume fraction of secondary filler/volume fraction of total filler), critical exponent (0.31–0.49), and average length of BNNTs (7 µm in this study), respectively. R _{c − HTPM} is contact thermal resistance of the h‐BN and BNNT hybrid network. Parametric studies according to the changes in TC _pre (10–75 W m⁻¹·K) and z (0.31–0.49) are shown in Figure S1 (Supporting Information). φ is known to be a significant parameter determining the synergistic enhancement of TC, and operates within the range of φ _max corresponding to the maximum synergistic effect.

In addition, the reduction in the TC of the composite due to the additional BNNT filler content above the optimal content was predicted by the rule of mixture between the composite with the optimized 3D network of hybrid BN fillers ( TC _max , 3‐component system of epoxy/h‐BN/BNNT) and 2‐component composite of epoxy/BNNT.^{[ 31 ]} The TC corresponding to the reduced synergistic effect ( TC _RSE ) of the composite incorporating the BN hybrid filler was expressed as follows:

$$\begin{array}{ccc}& & \mathit{T}{\mathit{C}}_{\mathit{RSE}}=\left(\frac{1-\mathit{\phi }}{1-{\mathit{\phi }}_{\mathit{max}}}\right)\times \mathit{T}{\mathit{C}}_{\mathit{max}}+\left(\frac{\mathit{\phi }-{\mathit{\phi }}_{\mathit{max}}}{1-{\mathit{\phi }}_{\mathit{max}}}\right)\hfill \\ & & \times \mathit{T}{\mathit{C}}_{\mathit{BNNT}}(\mathrm{upper}\mathrm{boundary})\hfill \end{array}$$ (8)

$$\mathbf{T}{\mathbf{C}}_{\mathbf{RSE}}={\left[\frac{\frac{\mathbf{1}-\phi }{\mathbf{1}-{\phi }_{\mathbf{max}}}}{\mathbf{T}{\mathbf{C}}_{\mathbf{max}}}+\frac{\frac{\phi -{\phi }_{\mathbf{max}}}{\mathbf{1}-{\phi }_{\mathbf{max}}}}{\mathbf{T}{\mathbf{C}}_{\mathbf{BNNT}}}\right]}^{-\mathbf{1}}(\mathrm{lower}\mathrm{boundary})(\mathit{\phi }>{\mathit{\phi }}_{\mathit{max}})$$ (9)

where TC _max represents the TC of epoxy/h‐BN/BNNT at TC _max and TC _BNNT denotes the TC of the epoxy/BNNT composite ( φ = 1).

2.2. h‐BN Surface Modification

To investigate the effect of BN surface functional group modifications on TC of the composite, thermal treatment and coupling agent treatment were applied (see the Methods section for detailed procedures). The chemical composition of pristine and surface treated h‐BN are shown in Figure 2 . Following the introduction of ─OH functional groups into h‐BN via thermal treatment, the Fourier transform infrared (FT‐IR) spectrum in Figure 2a exhibited a broad absorption peak around 3201 cm⁻¹, corresponding to the formation of B─OH bonds.^{[ 32} , ^{33 ]} Identical B─N absorption peaks at 1367 cm⁻¹ (B─N stretching vibration) and 794 cm⁻¹ (B─N─B bending vibration) were observed. In comparison with the untreated sample, the peak shift from 794 to 767 cm⁻¹ indicates the introduction of ─OH functional groups, which suggests a modification of the B─N out‐of‐plane structures due to surface functionalization.^{[ 34 ]} In h‐BN functionalized with the silane coupling agent (3‐aminopropyl‐triethoxysilane, APTES), peaks in the range of 1000–1200 cm⁻¹ were observed, corresponding to Si─O─Si and Si─O bonds, respectively.^{[ 35} , ^{36 ]} The X‐ray photoelectron spectroscopy (XPS) survey and deconvoluted spectra of C1s, N1s, B1s, and O1s are shown in Figure 2b–f. The C1s signals observed in all samples may be attributed to the possible presence of airborne adsorbates.^{[ 37} , ³⁸ , ³⁹ , ^{40 ]} As shown in Figure 2e, a significantly enhanced peak at 191.8 eV (B─O) was identified,^{[ 41 ]} indicating the formation of h‐BN–OH. For the fillers functionalized with the silane coupling agent, the O1s peaks at 532.5 eV (Si─O─Si) and 533.4 eV (Si─O) were observed in Figure 2f,^{[ 42 ]} indicating the formation of h‐BN–APTES. Additionally, X‐ray diffraction (XRD) analysis was conducted to verify the functionalization of h‐BN with the silane coupling agent, and the detailed results are provided in Figure S2 (Supporting Information). After the heat treatment, a diffraction peak at 27.9° corresponding to B(OH)₃ on the (010) plane of h‐BN was observed. The disappearance of this peak following APTES treatment confirms that the chemical functionalization effectively modified the surface structure of h‐BN.^{[ 43} , ⁴⁴ , ^{45 ]} Therefore, FT‐IR, XPS, and XRD analyses confirmed that the thermal treatment and silane coupling agent functionalization effectively introduced ─OH and ─O─Si─NH₂ functional groups onto the surface of h‐BN.

Figure 2.

a) FT‐IR spectra, b) XPS survey spectrum, and XPS spectra of c) C1s, d) N1s, e) B1s, and f) O1s for BNNT, raw h‐BN, and surface treated h‐BN fillers.

The functional groups of h‐BN─OH form hydrogen bonds with the hydroxyl and amine groups of the epoxy matrix, enhancing intermolecular interactions that are beneficial for phonon transfer pathways.^{[ 46} , ^{47 ]} In addition, h‐BN–APTES can form covalent bonds with the epoxy matrix via reactions between its reactive amine groups and epoxide rings.^{[ 48 ]} FT‐IR analysis was conducted to investigate the reaction between the amine groups of the silane coupling agent and the epoxy resin, using epoxy resin containing 1, 3, and 5 wt% of APTES. The spectra of the silane‐modified epoxy resin exhibited slight differences compared to the pure epoxy resin. The peaks at 1511 and 1600 cm⁻¹ (aromatic rings of the epoxy resin), at 3055 cm⁻¹ (C─H stretching), 909 cm⁻¹ (C─O stretching), and 826 cm⁻¹ (C─O─C stretching) were observed.^{[ 49} , ^{50 ]} (Details of the FT‐IR analysis results are provided in Figure S3, Supporting Information). The increased C─N bond at 1081 cm⁻¹ indicated that a ring‐opening reaction occurred between the epoxy resin and silane compounds, resulting in effective crosslinking between APTES and the epoxy resin.^{[ 48 ]} Similar results have been reported in other studies on the modification of epoxy resins with APTES.^{[ 49} , ^{51 ]} Therefore, surface‐functionalized h‐BN is expected to exhibit improved interfacial properties with epoxy resins compared to pristine h‐BN.

As shown in the field emission scanning electron microscopy (FE‐SEM) and Cs‐corrected scanning transmission electron microscopy (Cs‐TEM) images in Figure 3 , the average diameter and thickness of raw BNNTs and h‐BNs were measured to be 7 µm and 40 nm, and 3 µm and 20 nm, respectively. In comparison, the heat‐treated h‐BNs exhibited a reduced diameter of 2 µm and a thickness of 10 nm, which was attributed to the partial exfoliation of h‐BNs during the heat treatment process. The aspect ratios of the fillers used in the experiments were presented in Table S1 (Supporting Information).

Figure 3.

a) FE‐SEM and b) Cs‐TEM images of BNNT, c) FE‐SEM and d) Cs‐TEM images of h‐BN, and e) FE‐SEM and f) Cs‐TEM images of h‐BN─OH.

2.3. TC of h‐BN Composites

The theoretically predicted TC values based on Nan's equation assuming randomly dispersed fillers are shown as a red dotted line of Figure 4a and Nan's equation accurately predicted the experimentally measured TC values of the composites filled with h‐BN. In addition, the TC values of the composites containing BNNT were well fitted by the Nan's model (Figure S4a, Supporting Information). These results indicated that the h‐BN and BNNT fillers were uniformly dispersed in the epoxy matrix. As the h‐BN content increased from 30 (21.85) to 40 wt% (30.30 vol%), the TC improved significantly, reaching 5.01 W m⁻¹∙K at a filler content of 60 wt% (49.45 vol%). The observed increases were in good agreement with the calculated results based on the Foygel model, as shown by the blue dotted line in Figure 4a, indicating that thermal percolation occurred through the formation of nano‐interconnections resulting from direct contacts between the h‐BN fillers. Therefore, the uniform dispersion of BN fillers was confirmed, and thermal percolation was induced by incorporating a high content of h‐BN fillers.

Figure 4.

TC of composites according to a) the volume fraction of h‐BN fillers (inset image: schematic of nano‐interconnections of h‐BNs), b) the ratio of BNNT in the h‐BN/BNNT hybrid fillers (0< φ <0.25), c) the ratio of BNNT (0< φ < φ _max ) (inset image: schematic of nano‐interconnections of h‐BN/BNNT), d) the comparisons in the TC of composites with BN‐based fillers, e) h‐BN/BNNT composites according to the BNNT ratio ( φ > φ _max ) (inset image: schematic of reduced synergistic effect in h‐BN/BNNT), f) TC of composites with pristine h‐BN and functionalized h‐BN.

2.4. TC of h‐BN/BNNT Hybrid Composites

The TCs of the epoxy/h‐BN/BNNT composites as a function of total filler content and secondary filler ratio ( φ ) are shown in Figure 4b–f. The addition of the secondary filler (BNNT) resulted in a synergistic improvement of the TC, i.e., the composite filled with BN hybrid fillers exhibited a higher TC than the composite containing only the primary filler (h‐BN) at the same total content. Furthermore, as the total BN filler content increased, the proportion of the secondary filler (BNNT) required to achieve the maximum TC value decreased (Figure 4b). Exceeding the optimal secondary filler ratio for the maximum TC resulted in a decrease in the synergistic TC. In addition, the rate of decrease in TC of the hybrid composites increased as the total filler content was increased.

A hybrid thermal percolation model was proposed in this study to theoretically explain the measured TC results. The synergistic increase in the TC of the composites as a function of φ is shown in Figure 4c. The TCs of the composites increased to 6.55 (≈ 908% improvement over pure epoxy resin, φ _max = 0.124), 8.70 (≈ 1238% improvement, φ _max = 0.063) and 10.93 W m⁻¹·K (≈ 1582% improvement, φ _max = 0.013) at filler contents of 30.88, 39.80, and 49.52 vol%, respectively. These results suggest that a higher total filler content was advantageous to effectively form nano‐interconnections and increase TC by replacing only a small amount of the secondary filler. In addition, the results were in good agreement with the theoretical values (dashed‐dotted line) evaluated using the hybrid thermal percolation model (synergistic effect), indicating that an optimized 3D network including the nano‐interconnection effect was formed according to the total BN content (the parametric study using the model is shown in Figure S1, Supporting Information). The R _c of h‐BN network determined based on the Foygel model was 1.20 × 10⁶ KW⁻¹, and the determined R _{c − HTPM} was 2.48 × 10⁵ (30.88 vol%, TC _pre and z are 10 and 0.31, respectively), 2.36 × 10⁵ (39.80 vol%, TC _pre and z are 22 and 0.39, respectively) and 1.74 × 10⁵ (49.52 vol%, TC _pre and z are 75 and 0.49, respectively) KW⁻¹, respectively, indicating that the calculated contact thermal resistance of the hybrid network was significantly reduced compared to that of the h‐BN network, and the contact thermal resistance was lower as the total filler content increased. The R _{c − HTPM} values were found to be similar to the R _c values of BN‐based composites previously reported in Table S2 (Supporting Information).^{[ 52} , ⁵³ , ⁵⁴ , ⁵⁵ , ^{56 ]} Therefore, the TC of the optimized h‐BN/BNNT hybrid composite was higher than the previously reported TC of the composites with h‐BN or BNNT fillers as shown in Figure 4d, Tables S3 ^{[ 57} , ⁵⁸ , ⁵⁹ , ⁶⁰ , ⁶¹ , ⁶² , ⁶³ , ⁶⁴ , ⁶⁵ , ⁶⁶ , ⁶⁷ , ⁶⁸ , ⁶⁹ , ⁷⁰ , ⁷¹ , ⁷² , ⁷³ , ^{74 ]} and S4 (Supporting Information). The most excellent synergistic enhancement in the TC was achieved as shown in Table S5. (Supporting Information)^{[ 68} , ⁷⁴ , ⁷⁵ , ⁷⁶ , ⁷⁷ , ^{78 ]} The comparisons in the TC enhancement of hybrid composites with BNNT loading are shown in Figure S4b (Supporting Information).

The maximum TC ( TC _max ) of the composites achieved by the nano‐interconnection effect decreased as additional 1D fillers were added, as shown in Figure 4b,e. This reduced trend accelerated as total fillers increased. The TCs of composites with 30.88, 39.80, and 49.52 vol% BN contents were reduced to 4.72, 6.25, and 5.90 at φ = 0.242, 0.160, and 0.063, respectively. The reduced synergistic effect observed after the optimum secondary filler ratio could be due to the inability of the 1D fillers to participate in the formation of nano‐interconnections (Figure 4e), and the effect was well explained by the reduced synergistic effect model.

2.5. Nano‐Interconnection

To confirm the formation of nano‐interconnections inducing thermal percolation and synergistic effects, the morphologies of the fabricated composites were observed, as shown in Figures 5 and S5 (Supporting Information). Uniform filler dispersion was observed in the epoxy composite containing 21.85 vol% h‐BN (Figure 5a), indicating that the process used in this study effectively prevented BN aggregation and facilitated uniform dispersion of fillers within the polymer matrix. On the other hand, as shown in Figure 5b,c and Figure S5a (Supporting Information), direct contacts between h‐BN fillers were observed in the composites with contents above 30.30 vol% h‐BN. In addition, in the Cs‐TEM images of h‐BN composites (Figure 5d,e), nano‐interconnections were observed when the filler content exceeded 30.30 vol% due to contacts between the fillers. Therefore, it was demonstrated that the heat transfer mechanism of the fabricated composites was changed from being dominated by the ITR to being dominated by the nano‐interconnection effect, and the filler‐filler contact was the main structural parameter inducing the thermal percolation behavior of the composite. The FE‐SEM and Cs‐TEM images of the epoxy composite with the 49.52 vol% h‐BN/BNNT hybrid ( φ = 0.013) are shown in Figure 5f,g. Compared to the composite with h‐BN only (Figure 5c), nano‐interconnections of 1D BNNTs located between 2D h‐BNs were clearly observed at low (FE‐SEM, Figure 5f) and high magnifications (Cs‐TEM, Figure 5g), indicating that the thermal percolation generated by the formation of effective phonon transfer pathways (the nano‐interconnections) between the 1D and 2D BN fillers in the composite helped to achieve the maximum TC.

Figure 5.

FE‐SEM images of composites with a) 21.85 vol%, b) 30.30 vol% and c) 49.45 vol% h‐BN. Cs‐TEM images of d) 21.85 vol% and e) 30.30 vol% h‐BN. f) FE‐SEM and g) Cs‐TEM images of composites with 49.52 vol% h‐BN/BNNT ( φ = 0.013). µ‐CT images of composites with h) 30.30 vol% h‐BN and i) 49.52 vol% h‐BN/BNNT ( φ = 0.013).

To observe nano‐interconnections in a large area of the samples, a non‐destructive 3D internal analysis was performed using non‐destructive micro‐computed tomography (µ‐CT) (Figure 5h,i; Figure S5b–d, Supporting Information). As shown in Figure 5h,i, and Figure S5c (Supporting Information), the nano‐interconnections between h‐BNs and h‐BN/BNNT hybrids were observed in samples with dimensions of 1 mm³, which were in good agreement with the results of FE‐SEM and Cs‐TEM (Video S1, Supporting Information). On the other hand, it was confirmed that the excessive 1D fillers at a ratio ( φ = 0.038) greater than that of the optimal secondary filler ( φ _max = 0.013) resulted in the reduced synergistic effect of the BN hybrid composite (Figure S5d, Supporting Information). Therefore, optimized and reduced synergistic effects were identified in the TCs of composites containing 1D and 2D BN fillers.

2.6. TC Based on Interface Engineering

The functional groups in conductive fillers significantly influence the interfacial properties with the polymer matrix.^{[ 79} , ⁸⁰ , ⁸¹ , ^{82 ]} Furthermore, these interfacial properties are critical factors in determining phonon scattering and transfer at interfaces.^{[ 83} , ^{84 ]} It has been reported that functional groups introduced on the surface of BN fillers can significantly improve the TC of composites by reducing the ITR through improved the interfacial properties with the matrix.^{[ 85 ]} Therefore, in this study, the effect of surface functional groups on the TC of composites with the optimal 3D BN network was investigated.

The TC values of composites containing BN fillers functionalized with ─OH and ─O─Si─NH₂ groups are shown in Figure 4f and Figure S6 (Supporting Information). In the h‐BN filled composites, the introduction of ─OH and ─O─Si─NH₂ functional groups reduced the ITR and improved phonon transfer, leading to a significant increase in the TC. Specifically, ─O─Si─NH₂, which forms covalent bonds with the epoxy matrix, exhibited a greater improvement in TC than –OH, which forms hydrogen bonds with the epoxy matrix. In contrast, the TC of composites with h‐BN/BNNT hybrid fillers exhibited a pronounced decline upon the introduction of functional groups, indicating that the effect of modifying the hybrid network configuration originated from the exfoliation of h‐BN by the heat treatment outweighed that of enhancing the interfacial properties through the introduction of functional groups. These trends were further supported by Figures S6 and S7 (Supporting Information), which revealed that the optimal BNNT fraction for maximizing TC was modified in the surface‐functionalized h‐BN/BNNT hybrid composites compared to pristine h‐BN/BNNT. Consequently, it can be deduced that constructing a hybrid network with an optimal fraction is more crucial than reducing ITR through the introduction of functional groups. This conclusion is further substantiated by the lower TC values observed outside the optimal hybrid fraction in Figure 4b.

2.7. Application

To apply the fabricated composite to a TIM with electrical insulation properties, the electrical conductivity obtained by measuring the volume resistivity of the sample is summarized in Table S6 (Supporting Information). Little improvement in the electrical conductivity relative to that of the matrix (5.7 × 10⁻¹³ S m⁻¹) was observed regardless of the dimension, content, and optimum ratio of BN, indicating that the fabricated composites were suitable for minimizing electrical interference in electronic components. In this study, an experimental design using an infrared camera, a hot plate (55 °C), and an open circuit of a miniature light bulb (voltage of 3 V) was proposed to simultaneously evaluate the heat dissipation and electrical insulation properties of the fabricated composites, as shown in Figure 6a–h. Commercial carbon‐based compounds (CoolPoly‐E4507, Cool Polymers/Celeanese, RI, USA) showed good heat dissipation performance due to the nanocarbon‐induced high TC, and an LED (red light) was illuminated by electrical conduction (Figure 6b).

Figure 6.

a) Experimental design for heat dissipation and electrical insulation properties, and results of the composites with b) a nanocarbon‐based commercial compound, c) 21.85 vol% h‐BN, d) 30.30 vol% h‐BN, e) 49.45 vol% h‐BN, f) 30.88 vol% h‐BN/BNNT ( φ = 0.124), g) 39.80 vol% h‐BN/BNNT ( φ = 0.063), and h) 49.52 vol% h‐BN/BNNT ( φ = 0.013).

As shown in Figure 6c–h, when composites with h‐BN and h‐BN/BNNT hybrid fillers were applied, excellent heat dissipation performance was observed, which was consistent with the experimental and theoretical TC results shown in Figures 4 and 5, and the LED remained off during the test due to the low electrical conductivity of the BN composite specimens. Therefore, the optimized h‐BN/BNNT hybrid composite developed in this study exhibited suitable thermal and electrical conductivities for use as an electrically insulating TIM. As shown in the thermal images (Figure 7a–d) of a commercial smartphone (iPhone 15 Pro with A17 Pro chip, Apple Inc., CA, USA), the excellent performance of the optimized TIM applied to a 3 nm chipset, which required excellent heat dissipation and electrical insulation properties, was verified (temperature after 20 s of placing the sample on a logic board (≈40 °C)). These results indicate that the BN fillers were ideal for the TIM, which required electrical insulation properties (Video S2, Supporting Information). Furthermore, additional analysis conducted to evaluate the electrical insulation properties of the fabricated composites was presented in Table S7 and Figure S8 (Supporting Information).

Figure 7.

a) Thermal images of (a) the nanocarbon‐based commercial compound and composites incorporating b) 30.88 vol% h‐BN/BNNT ( φ = 0.124), c) 39.80 vol% h‐BN/BNNT ( φ = 0.063), d) 49.52 vol% h‐BN/BNNT ( φ = 0.013) applied to a smartphone with a 3 nm chipset, and e) temperature gradient of composites as a function of time (inset image: temperature enhancement of composite).

3. Conclusion

BN is regarded as an exemplary filler for TIMs, aiding in the prevention of thermal condensation of nanostructures without inducing shutdown due to electron tunnelling. Nevertheless, the nano‐interconnection and optimized synergistic effects stemming from the composition and content of BN hybrid fillers remain to be systematically delineated. In this study, we investigated the optimized synergistic improvement in TC of composites with 1D and 2D BN hybrid fillers and developed a hybrid thermal percolation model to theoretically explain the optimized synergistic improvement. The epoxy composites with 48.90 vol%/0.63 vol% h‐BN/BNNT exhibited the highest TC of 10.93 W m⁻¹·K, representing an increase in TC of 118% and 1582%, respectively, compared to the epoxy composite containing 49.45 vol% h‐BN and pure epoxy resin. The highest TC (10.93 W m⁻¹·K) was obtained at the optimal ratio ( φ ) of the secondary 1D filler due to the synergistic effect of nano‐interconnection formed as a 3D network based on contacts between the h‐BN and BNNT hybrid fillers. The experimentally determined value was in close agreement with the TC of the composites as calculated by applying the hybrid thermal percolation model. Furthermore, the R _c of h‐BN and BNNT hybrid network was quantitatively determined by the hybrid thermal percolation model, thereby validating its efficacy as a predictive and explanatory tool for the synergistic thermal behavior resulting from the formation of nano‐interconnections within a composite with BN hybrid fillers. BN surface treatment exhibited dual effects: it enhanced the TC of h‐BN‐filled composites by improving interfacial properties, but hindered TC improvement in h‐BN/BNNT hybrid composites due to changes in nano‐interconnections and network structures caused by BN morphological modifications. The experimental and theoretical approaches used to determine the TCs of BN hybrid composites provided insight into the design of TIMs with excellent heat dissipation and electrical insulation characteristics.

4. Experimental Section

Materials

A mixture of epoxy resin and a curing agent was used as the matrix. h‐BN with a mean particle size of 3 µm, a mean thickness of 20 nm, and a purity of 99% was used as the primary filler to improve the TC of epoxy composites, and a BNNT with a mean length and diameter of 7 µm and 40 nm, respectively, was selected as the secondary filler. Specific information on the materials used can be found in S1.1 (Supporting Information).

BN Functionalization

The raw h‐BN was thermally treated at 1000 °C in a tubular electric furnace to functionalize the surface with ─OH groups (h‐BN–OH). The h‐BN in an alumina mold was heated at a rate of 5 °C min⁻¹ under atmospheric conditions without a chemical catalyst, and after reaching 1000 °C, the temperature was maintained for 7 h to achieve oxidation. 0.15 g of APTES (3 wt% by weight of the filler) was mixed with 500 mL of ethyl alcohol and hydrolyzed at a temperature of 60 °C for 30 min. The mixture was adjusted to slightly acidic (pH 4–5) with 37% hydrochloric acid. 5 g of h‐BN─OH was added and stirred at 80 °C for 6 h. Additionally, the mixture was filtered through a 0.2 µm polytetrafluoroethylene filter and dried at 80 °C to prepare the fillers functionalized with ─Si─NH₂ groups (h‐BN–APTES). Specific information on the surface treatment is provided in S1.2 (Supporting Information).

Composite Fabrication

The hardener and epoxy resin were premixed in a weight ratio of 9:100 using a Thinky mixer at 2000 rpm for 2 min. The raw or surface treated h‐BN and BNNT powders dried at 80 °C for 24 h were added to the premix and then mixed at 2000 rpm for 2 min using the same equipment to uniformly disperse the fillers. As shown in Figure S9 (Supporting Information), the mixture was poured into a metal mold (25 × 25 × 2 mm³) and pressed at 80 °C and 15 MPa for 1 h using a hot press. The compositions of the composites are summarized in Table S8 (Supporting Information). Specific information on the mechanical mixer and hot press is given in S1.3 (Supporting Information).

Characterization

To analyze the surface functionality of the BN fillers, FT‐IR spectra of the fillers were obtained and recorded in the wavelength range from 4000 to 400 cm⁻¹. In addition, XPS was performed using an Al X‐ray source with a power of 72 W under a pressure of 5 × 10⁻⁹ mbar. XRD patterns were obtained using a diffractometer equipped with Cu Kα radiation, operated at 40 kV and 30 mA. Data were collected over a 2θ range of 5–80° with a scan rate of 2 min⁻¹. The isotropic TC of the composites was measured using a TC analyzer based on ISO 22007‐2. The composites frozen in liquid nitrogen were fractured, and the fracture surfaces of the composites were coated with Pt for 180 s under vacuum using a coating machine. FE‐SEM was used at a voltage of 10 kV to observe the morphology of the filler and the fracture surface. In addition, high magnification observation of the filler morphology and composites was performed using Cs‐TEM. The composite was transferred to a grid after being milled by a focused ion beam and observed at a voltage of 80 kV.

µ‐CT was performed to confirm the 3D structure within the large area (≈1 mm³) in the composite samples. The original images obtained by X‐ray irradiation (10 kV) were reconstructed into 2D images and then converted into 3D images using software. The electrical conductivity of the prepared composites was evaluated by inverting the volume resistivity measured with an ultrahigh resistivity meter. The thermal dissipation characteristics for TIM applications were observed using an infrared (IR) thermal camera with a resolution of 0.04 K. After placing the fabricated composites between the disconnected miniature light bulb circuits on a hot plate at 55 °C, the on/off status of the light bulb and the surface temperature of the samples were observed after 20 s. To evaluate the electrical insulation properties, the AC breakdown strength of the composites was measured in accordance with ASTM D149 using specimens of (50 × 50 × 2) mm³, and the voltage was applied at a rate of 4000 V s⁻¹. The relative permittivity (ε′) of the fabricated composites was measured in the frequency range of 10¹–10⁵ Hz using a broadband dielectric spectrometer. Specific information on the equipment used can be found in S1.4 (Supporting Information).

Conflict of Interest

The authors declare no conflict of interest.

Supporting information

Supporting Information

Supplemental Video 1

Supplemental Video 2

Jang S. Y., Jang J., Yoo G. Y., et al. “Nano‐Interconnected 1D/2D Boron Nitride Hybrid Networks: Unlocking Superior Thermal Conductivity in Electrically Insulating Thermal Interface Nanocomposites Based on Hybrid Thermal Percolation Model.” Small Methods 9, no. 9 (2025): 2500453. 10.1002/smtd.202500453

Data Availability Statement

The data supporting the findings of this study are available in the Supporting Information of this article.