# Effect of alignment of h-BN platelets in LDPE disks on the thermal conductivity: Microstructure and modeling

Abdelwahab Boukheit, Christian Garnier, Amèvi Tongne, France Chabert, Belkacem Otazaghine, Aurélie Taguet

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Abdelwahab Boukheit, Christian Garnier, Amèvi Tongne, France Chabert, Belkacem Otazaghine, et al.. Effect of alignment of h-BN platelets in LDPE disks on the thermal conductivity: Microstructure and modeling. FlatChem – Chemistry of Flat Materials, 2026, 55, pp.100989. 10.1016/j flatc.2025.100989. hal-05471529

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# Effect of alignment of h-BN platelets in LDPE disks on the thermal conductivity: Microstructure and modeling

Abdelwahab Boukheit<sup>a</sup>, Christian Garnier<sup>b</sup>, Amèvi Tongne<sup>b</sup>, France Chabert<sup>b</sup>, Belkacem Otazaghine<sup>a</sup>, Aurélie Taguet<sup>a,*</sup>

## ARTICLE INFO

### Keywords:

H-BN platelets

Thermal conductivity

Orientation

Dynamic mechanical analysis

## ABSTRACT

In recent years, hexagonal boron nitride (h-BN) has gained significant attention due to its high thermal conductivity and low electrical conductivity, making it an attractive option for effective heat dissipation in electronic devices. This article specifically explores the impact of unidirectional alignment of h-BN platelets on the thermal conductivity of a low-density polyethylene matrix composite (LDPE/h-BN). The composite materials were fabricated by layering thin films, and various parameters, such as platelet size and film thickness, were systematically investigated. Additionally, dynamic mechanical behavior analysis (DMA) was conducted to assess the influence of incorporating h-BN particles on the dynamic mechanical properties of the composites. The study also involved modeling to enhance our understanding of the correlation between particle orientation and thermal conductivity. Regarding the difference between both h-BN and the use of different dies to elaborate the films, in-plane TC are relatively different because the orientation of the platelets in the final disk is highly influenced by both parameters. This alignment led to a remarkably high thermal conductivity value of 4.25 W/(m·K) with 50 wt% of h-BN 003. The study underscored the critical roles played by particle size and film thickness in achieving optimal thermal conductivity. Notably, this study stands out by avoiding the use of solvents during the composite development process, which sets it apart from approaches generally developed.

## 1. Introduction

Over the past decades, rapid technological advancements in various sectors such as electronics, aerospace, and automotive have led to an increasing demand for high-performance materials [1]. The electrification of various applications, particularly in electronic devices like integrated circuits, transistors, and LEDs, has underscored the critical need for efficient heat dissipation [2–7]. The excessive accumulation of heat in these devices can result in malfunctions, performance degradation, and reduced lifespan [8]. Continued progress in component design has significantly increased computing power and overall device performance, accompanied by component densification due to miniaturization [9–11]. To address the challenges posed by increased heat dissipation requirements in the context of energy and environmental transitions, there is a crucial need to develop new materials. Polymer matrix heat sinks offer advantages such as lightweight, flexibility in shaping, and corrosion resistance [12,13]. Another crucial consideration is electrical

insulation, particularly critical in electronic devices. Few available additives simultaneously possess high thermal conductivity and electrical insulation, both essential for managing heat dissipation in electronic systems. Hexagonal boron nitride (h-BN) stands out due to its unique combination of high thermal conductivity and electrical insulation [14,15]. Additionally, h-BN, as a ceramic material, exhibits exceptional chemical stability, ensuring long-term durability. Its incorporation into a polymer matrix allows for a synergistic combination of advantages, such as low density and mechanical flexibility of polymers, with the excellent thermal conductivity properties of h-BN [13,16–18].

Controlling the orientation of thermally conductive particles in space is an effective way of improving the thermal conductivity (TC) of polymer composites. Numerous studies in literature report the use of different methods for orienting thermally conductive particles, which have led to significant increases in the thermal conductivity of polymer composites [19–22]. Several methods have been developed to obtain this orientation, such as the vertical alignment, the construction of an

<footnote><sup>a</sup> Polymers Composites and Hybrids (PCH), IMT Mines Ales, Ales, France</footnote>

<footnote><sup>b</sup> Université de Toulouse, UTTOP, LGP, Tarbes, France</footnote>

<footnote>* Corresponding author.
E-mail address: aurelie.taguet@mines-ales.fr (A. Taguet).</footnote>
aligned 3D network by freezing/lyophilization or the overlaying of thin composite films in which the particles are aligned in the plane [23–25].

Among recent studies, several authors [26–30] have proposed innovative approaches to enable orientation of h-BN particles, which have led to significant increases in the thermal conductivity of polymer composites. In fact, the improvement in thermal conductivity is essentially in the largest plane of the particles. Anisotropic fillers such as carbon nanotubes, h-BN or graphene have a higher conductivity in their largest dimension. In the case of film development, these particles preferentially orientate themselves in the plane of the films (lie-down) and it is therefore much more difficult to improve the thermal conductivity of composites in the transverse direction called through-plane. Xue et al. [26] have prepared composites based on silicone elastomer (SR) and vertically aligned boron nitride particles (ABN). The ABNs then form preferred vertical conductivity pathways in the SR matrix, with a much higher through-plane thermal conductivity than that of non-oriented SR/BN composites. The through-plane thermal conductivity of SR/ABN at 39.8 vol% filler reached 5.4 W/(m·K), which is around 6.3 and 33 times higher than those of SR/BN and unfilled SR, respectively. Some authors have drawn inspiration from the layered and aligned structure observed in a mille-feuille cake. Chen et al. [31] have prepared thermally conductive flexible polymer nanocomposites via a layer-by-layer evolutionary process. The process involves electrospinning PVA fibers and electrostatic sputtering of BNNS. Thanks to the interparticle connections of the BNNS, the resulting anisotropic PVA/BNNS nanocomposites exhibit a very high in-plane thermal conductivity of 21.4 W/(m·K) for 22.2 vol% BNNS. Kim et al. [27] fabricated epoxy and polyphenylene sulfide (PPS) matrix composites using aligned hexagonal boron nitride and spherical aggregates of these h-BNs [28]. The authors showed that these BN aggregates form more efficient networks for unidirectional transfer.

In this article, we focus specifically on the effect of unidirectional alignment of h-BN platelets on the thermal conductivity of a low-density polyethylene matrix composite (LDPE/h-BN) by using melt mixing processing. The materials were prepared by layering thin films of LDPE/h-BN composite, and various parameters such as h-BN platelets size and film thickness were investigated. Modeling was also carried out to better understand the relationship between particle orientation and thermal conductivity of the LDPE/h-BN composites. This work attempts to make an original contribution to research into thermally conductive polymer composites by focusing solely on the effect of the alignment of thermally conductive particles on the thermal conductivity of the material. In addition, unlike the majority of studies reported in the literature, no solvents were used in this composite development process.

## 2. Materials and methods

### 2.1. Materials

The low-density polyethylene (LDPE) Alcudia PE071 used was supplied by Repsol. For the boron nitride (h-BN) platelets, two different grades were employed CFP003S (noted BN003) and CFP009 (noted BN009) supplied by 3M company, with $D_{50}$ particle size distributions of 2–6 µm and 6–12 µm, respectively (see Fig. 1A and B).

### 2.2. Methods

#### 2.2.1. Preparation of the LDPE/h-BN films by extrusion and calendering

The initial step in the production of LDPE/h-BN composites was extrusion using a twin-screw microcompounder DSM from Xplore Instruments. The whole mixing time was set at 4 min at 190 °C, and the screw speed was maintained at 80 rpm for all formulations. The orientation of h-BN particles in LDPE was achieved through the use of flat dies at the outlet of the microcompounder. This orientation is due to the narrow gap between the die edges, the pressure generated by the rotating screws inside the microcompounder pushing the mixture, and the stretching that the material undergoes at the exit, resulting in the film formation.

The composite obtained is subsequently recovered in the form of a film. The film exiting the die is stretched using an Xplore calender and exposed to compressed air to be cooled. The speed rate went from 2.1 rpm at the beginning of the calendering to 0.43 rpm at the end of the calendering. The dies used for this study had thicknesses of 200 µm and 600 µm, denoted as 02 and 06, respectively. This difference in die opening width consistently resulted in films with different thicknesses.

#### 2.2.2. Stacking of LDPE/h-BN films by thermocompression

The second step in the production of the LDPE/h-BN samples involves stacking the films obtained from the microcompounder, in order to obtain disks for thermal conductivity measurements. To achieve this, the films were cut into small pieces and layered within a mold, as seen in Fig. 1C. The mold was closed and placed into a PEI Lab 800PA heat thermocompression press. The first stage of pressing involved subjecting the loaded mold to a pressure of 115 bars for 30 min at 50 °C. The second stage involved raising the temperature to 120 °C while maintaining the same pressure of 115 bars for 1 h. This process yields a disk with dimensions of 2.5 cm in diameter and 3 mm in thickness Fig. 1D.

#### 2.2.3. Injection procedure

To perform formulations of LDPE/h-BN without orientation of the h-BN particles, composite obtained after microcompounder extrusion were processed into disks using a mini-press from ThermoFisher Scientific (from the platform of the Technological Center of New Aquitaine for Composites and Advanced Materials, CANOE, located in Pau, France). The disks were injected at 190 °C with a mold temperature of 60 °C. The injection pressure and time were 140 bars and 5 s, respectively with a holding time of 20 s. The final disks have the following dimension: 20 mm in diameter and 3.8 mm in thickness.

#### 2.2.4. List of samples

#### 2.2.4.1. Made by thermocompression of LDPE/h-BN films
The samples listed in Table 1 were obtained by the stacking of LDPE films containing 10 to 50 wt% of BN003 and BN009. The films were obtained using microcompounder extrusion via dies 02 and 06. These samples were then used for SEM observation and TC measures by Hot-Disk. The names of the various samples are based on the following structure: "PE - Grade of h-BN - wt% of h-BN - Die thickness - Thermocompression of Films

<figure><img src="image_3.png" /><figcaption>**Fig. 1.** Experimental conditions and materials: SEM Images of h-BN platelets (A) CFP003 with $D_{50}$ of 2–6 µm, and (B) CFP009 with $D_{50}$ of 6–12 µm. Implementation procedure with (C) film stacking step, (D) 25 mm diameter and 3 mm thick disks obtained after thermocompression molding. Schematic representation of the thermal conductivity measured (E) parallel to the plane (in-plane) and through the plane (through-plane) of a composite disk.</figcaption></figure>
<table><caption>**Table 1**
List of the LDPE/h-BN samples produced by thermocompression of LDPE/h-BN films.</caption><thead><tr><td>LDPE-TF</td><td>LDPE-TF</td></tr></thead><tbody><tr><td>PE-BN003-10 %- 02-TF</td><td>PE-BN009-10 %- 02-TF</td></tr><tr><td>PE-BN003-30 %- 02-TF</td><td>PE-BN009-30 %- 02-TF</td></tr><tr><td>PE-BN003-50 %- 02-TF</td><td>PE-BN009-50 %- 02-TF</td></tr><tr><td>PE-BN003-10 %- 06-TF</td><td>PE-BN009-10 %- 06-TF</td></tr><tr><td>PE-BN003-30 %- 06-TF</td><td>PE-BN009-30 %- 06-TF</td></tr><tr><td>PE-BN003-50 %- 06-TF</td><td>PE-BN009-50 %- 06-TF</td></tr></tbody></table>

(TF)".

### 2.2.4.2. Made by thermocompression of LDPE/h-BN pellets.
The samples listed in Table 2 were obtained by thermocompression of LDPE/h-BN pellets, which were previously extruded using a microcompounder without a die, thus not forming films. The names of the various samples are based on the following structure: "PE - Grade of h-BN-wt% of h-BN - Thermocompression of Pellets (TP)".

### 2.2.4.3. Made by injection molding.
The samples listed in Table 3 were obtained by direct injection of pellets obtained by microcompounder extrusion. The names of the various samples are based on the following structure: "PE - Grade of h-BN - wt% of h-BN - Injection (I)".

## 2.3. Characterizations

### 2.3.1. Microstructure

The microstructure of the composite materials (films and disks) was observed using a Field Emission Scanning Electron Microscope (FEI Quanta 200 FEG) in an environmental scanning electron microscopy (ESEM) mode. The samples were cryofractured in liquid nitrogen, coated with a layer of carbon, and placed under the ESEM. ImageJ was used to convert SEM micrographs into binary images to isolate the h-BN platelets from the LDPE matrix. Quantitative orientation analysis was then performed using the directionality plugin in ImageJ, a standard tool for such analyses. This method calculates the distribution of angles for all the pixels constituting the filler particles, providing robust, statistical parameters to describe the degree of alignment, moving beyond qualitative assessment. Two parameters were calculated: the amount of oriented pixels in a dominant vertical alignment direction (called "amount") and the average angular deviation of local orientations around the main direction which is calculated as the standard deviation of orientation angles, expressed in degrees (called "dispersion").

### 2.3.2. Thermal conductivity

First, the heat capacity (Cp) in J/(g·°C) for pure LDPE and h-BN was measured using a Differential Scanning Calorimeter (DSC) from Perkin Elmer following the "Standard" method with sapphire as the reference.

The density 'ρ' in g/cm³ was determined with a helium pycnometer, specifically the Micromeritics AccuPyc 1330. Each formulation was measured on three different samples (Table 4).

The measurement was performed using the hot-disk method. The two thermal conductivities parallel and perpendicular to the plane (referred to as "in-plane and through-plane TC", respectively) were measured directly Fig. 1E. Measurements were performed on disks, with each sample undergoing five distinct measurements.

<table><caption>**Table 2**
List of the LDPE/h-BN samples produced by thermocompression of LDPE/h-BN pellets.</caption><thead><tr><td>LDPE</td><td>LDPE</td></tr></thead><tbody><tr><td>PE-BN003-10 %-TP</td><td>PE-BN009-10 %-TP</td></tr><tr><td>PE-BN003-30 %-TP</td><td>PE-BN009-30 %-TP</td></tr><tr><td>PE-BN003-50 %-TP</td><td>PE-BN009-50 %-TP</td></tr></tbody></table>

<table><caption>**Table 3**
List of the LDPE/h-BN samples produced by injection of pellets.</caption><thead><tr><td>LDPE</td><td>LDPE</td></tr></thead><tbody><tr><td>PE-BN003-10 %-I</td><td>PE-BN009-10 %-I</td></tr><tr><td>PE-BN003-30 %-I</td><td>PE-BN009-30 %-I</td></tr><tr><td>PE-BN003-50 %-I</td><td>PE-BN009-50 %-I</td></tr></tbody></table>

<table><caption>**Table 4**
Heat capacity (Cp) and density (ρ) values of LDPE and h-BN samples.</caption><thead><tr><td>Samples</td><td>Cp measured by DSC (J/(g·°C) at 25 °C)</td><td>ρ measured by helium pycnometer (g/cm³)</td></tr></thead><tbody><tr><td>LDPE</td><td>2.17</td><td>0.91</td></tr><tr><td>BN003</td><td>0.72</td><td>2.28</td></tr><tr><td>BN009</td><td>0.79</td><td>2.25</td></tr></tbody></table>

### 2.3.2.1. Measurement of through-plane and in-plane TC by the hot-disk method.
The principle of the hot-disk method involves placing a probe between two disks of the same sample. Subsequently, a constant thermal power is applied through this probe, and the temperature variation of the sample is measured. The probe serves both as a heat emitter and a temperature sensor. The variation in the electrical resistance R of the probe during the overall thermal elevation of the system was modeled by Silas E. Gustafsson [32] (Eq. (1)):

$$R = R_0 (1 + \varepsilon \Delta T(\tau)) \quad (1)$$

With: R₀ is the initial electrical resistance of the probe

ε is the thermal resistance coefficient of the probe

ΔT(τ) is an average value of the probe temperature rate.

In the case of using Hot-disk probes, ΔT(τ) is expressed as follows (Equation 2):

$$\Delta T(\tau) = P_0 \left( \frac{3}{\pi^2 r \lambda} \right)^{-1} * F(\tau) \quad (2)$$

With: P₀ the total power delivered by the probe.

r is the radius of the probe.

λ is the thermal conductivity of the sample.

F(τ) the characteristic time-dependent function related to the geometry of the probe.

The user can then calculate the thermal conductivity and diffusivity of the sample and, through an indirect calculation, obtain the thermal capacity and effusivity. The relationship between diffusivity, measurement time, and the radius of the probe corresponds to the characteristic total time τ (Eq. (3)).

$$\tau = \frac{\alpha^* t}{r^2} \quad (3)$$

Where: α is the thermal diffusivity.

t is time.

r is the radius of the probe.

### 2.3.3. Dynamic viscoelastic behavior

The viscoelastic analysis was carried out on samples with parallelepiped geometry of 25 mm length and 10 mm width using the ARES (Advanced Rheometer Expansion System) from Rheometric Scientific, with a controlled-strain. The chosen configuration for this study was a rectangular torsion mode with a fixed strain of 0.1 % at 1 Hz (in the linear viscoelasticity range), imposed by a motor at the lower plate. Each material was tested ranging from room temperature to 110 °C with a temperature ramp of 3 °C/min.
# 3. Results and discussion

## 3.1. Effect of h-BN particle size and shaping process on h-BN orientation

### 3.1.1. Injected samples

The SEM images obtained from the fracture surfaces of injected disks (Fig. 2) show that there is indeed a slight alignment of the h-BN platelets in the plane direction. We believe that this orientation results from the pressure exerted on the particles during the filling of the mold by the material flow [33]. Additionally, there appears to be agglomerates present in this disk. Hence, the use of an injection procedure leads to a certain alignment of the h-BN particles, in the plane of the disk, which can have an influence on the thermal conductivity. However, this procedure also seems to result in the formation of a greater number of agglomerates in the composite than what has been observed with the thermocompression procedure.

### 3.1.2. Observation of h-BN orientation in the thermocompressed films

It is well known that the orientation of the h-BN would play a crucial role on the through-plane and in-plane thermal conductivities. To verify the orientation of h-BN flakes in the LDPE matrix, we observed a film loaded with 50 wt% of the h-BN CFP009 grade, obtained with the 06 die, using a scanning electron microscope (SEM) (Fig. 3).

The SEM micrograph of the film in Fig. 3.A shows that within the film thickness, there are two different areas regarding the orientation of the h-BN flakes. Indeed, at the edges of the film (Fig. 3.B), the flakes exhibit alignment in the direction of film extrusion through the die, while in the core of the film, it appears that the flakes are oriented in a more random fashion. There are several factors that could explain this difference in flake orientation depending on their position within the LDPE film thickness. When the polymer is pushed through the rectangular die for film shaping, it experiences pressure that can result in two types of flow: laminar flow and/or turbulent flow. Flow velocity and fluid viscosity are key factors influencing the type of flow within the rectangular die. And, the Reynolds number ($R_e$) allows to predict fluid flow patterns, especially if it is a laminar or turbulent flow.

Calculation in the Supporting Information (S.1.) part reveals a $R_e < 1$ regardless of the die used. This is in accordance with the literature [34]. Consequently, the flow around the particles in the die is laminar.

Moreover, it is well known that incompressible laminar viscous Newtonian fluids flowing along a tube (or between plates) exhibit a Poiseuille laminar flow. This flow is characterized by a laminar regime with a maximum velocity at the center of the tube and zero at the walls, forming a parabolic velocity profile [35].

For viscoelastic fluids and especially shear thinning fluid subjected to shear forces, the boundary condition for which the fluid velocity is zero at the pipe wall due to adhesion (no-slip condition) is maintained. Hence, in our case, the melted PE/h-BN blend exhibits a zero velocity at

the wall of the die, and the h-BN platelets have a high tendency to align parallel to the edge of the film.

The random orientation of h-BN platelets observed in the middle of the film can be attributed to several factors, including the interplay between hydrodynamic forces, the viscoelastic behavior of the polymer matrix, and the geometrical characteristics of the particles, such as the concentration of h-BN [36]. Non-spherical particles tend to align in the direction of the flow to reduce the dissipated energy. In our case, the concentration of h-BN platelets is high, and particles can collide during the flow, leading to disturbances in their orientation. Moreover, inter-particle interactions can also play a key role in their orientation in the core of the flow. Additionally, we have to keep in mind that the shear rate is not uniform along the width of the die; it is higher at the edge and lower in the middle. Hence, the viscosity and especially the elastic constituent of the viscosity are different in these two zones.

Fig. 4 illustrates the distribution of smaller-sized h-BN particles (BN003) in films of similar composition to that observed in Fig. 3 (PE-BN003–50 %-06-TF). As in the case of the larger-sized particles (BN009), a similar distribution is observed overall. The particles are aligned at the edges and over most of the film’s thickness. However, in the case of this smaller-sized h-BN grade, the area where particles are randomly oriented (highlighted zones in Fig. 4) is smaller. This difference can be attributed to the difference in surface area between both particles. Indeed, the longest particles (BN009) have lower surface area, then lower surface in contact with the polyethylene matrix and higher probability to collide with each other. This would explain that the longest particles (BN009) are randomly oriented in a larger thickness than smallest ones (BN003).

In the following study, we examined an LDPE/h-BN film with the same composition as the previous one (with h-BN CFP003) but obtained using a finer die, with an opening width of 200 µm (Fig. 5). SEM images revealed that all the particles in the film were aligned within the plane of the film, without any areas showing random particle orientation in the film’s center, as observed previously with the 06 die (Fig. 4). We hypothesize that the presence of a finer die may promote this alignment due to the higher shear rate that occurs in a narrower die [37]. This increased shear rate can contribute to aligning the particles in the same direction as the material flow. This observation suggests that die size can have a significant impact on particle orientation in the film, and, therefore, will have important effects on the final properties of the composite obtained.

Fig. 6 summarizes the influence of the die and size of h-BN on the platelet orientation through the film.

### 3.1.3. Observation of the microstructure of disks obtained by superposition of LDPE/h-BN films

To evaluate the influence of the microstructure differences in LDPE/h-BN composites on thermal conductivity, disks were prepared by

<figure><img src="image_4.png" /><figcaption>Fig. 2. SEM images of the fracture surfaces of injection-molded LDPE/h-BN (CFP003) from pellets loaded with 50 wt% (PE-BN003–50 %-I).</figcaption></figure>
<figure><img src="image_5.png" /><figcaption>Fig. 3. SEM Image of the cryofracture surface of film: PE-BN009-50 %-06.</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>Fig. 4. SEM Images of the fracture surface of PE-BN003-50 %-06, obtained by cryofracture in SE (A) and BSE (B).</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>Fig. 5. SEM Images of the fracture surface of and PE-BN003-50 %-02, obtained by cryofracture in SE (A) and BSE (B).</figcaption></figure>

superimposing films obtained using microcompound ("TF").

Fig. 7 presents the SEM image of the fracture surface of a LDPE/h-BN disk with a 50 wt%, obtained from films made with die 06 and featuring larger particles (BN009). The SEM observation is consistent with the results previously observed for films of same composition, where multiple zones of different orientations are present throughout the thickness of the disk.

In Fig. 8, we can observe SEM images of the fracture surfaces obtained by cryofracture of an LDPE/h-BN disks with 10 wt% loading (die 06, die 02 and BN003), made from thermocompressed pellets PE-

BN003-10 %-TP (Fig. 8A), and from thermocompressed films PE-BN003-10 %-06-TF (Fig. 8B). At sufficient magnification, the h-BN particles can be seen, appearing as white points. As expected, the disks made directly from the pellets exhibited a random orientation of h-BN platelets without any preferred direction, as shown in Fig. 8A. In contrast, the disks made by superimposing LDPE/h-BN films from die 06 exhibited a clear alignment of h-BN platelets in the same direction as that observed in the films (Fig. 8B). This proves that the alignment achieved during the extrusion of LDPE/h-BN films is maintained even after their thermocompression to obtain the disks. Furthermore, unlike
<figure><img src="image_8.png" /><figcaption>Fig. 6. Orientation of platelets based on their sizes and the die used.</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>Fig. 7. SEM image of the fracture surface of PE-BN009-50 %-06-TF sample.</figcaption></figure>

the films observed previously, Fig. 8B does not show areas where h-BN flakes are not aligned (compared to Fig. 5 in the middle part of the film). Although non-aligned particles were observed in the middle of the film for die 06, its significance was reduced in the disk due to thermocompression. It is likely that the film compression process has forced the remaining particles into alignment.

Fig. 8C presents SEM images, obtained from films made with die 02 (PE-BN003–10 %-02-TF). Unlike the previous observations, this image shows a more random orientation of particles compared to Fig. 8B performed with die 06. As films prepared from die 02 gave more aligned particles than with die 06, one reason for the randomly oriented particles in the disk of Fig. 8C is that films produced with die 02 have a thinner thickness (Fig. 5), which means that a greater number of layers are superimposed to form the disk. One plausible hypothesis is that the orientation of the platelets may be lost at this stage due to the increased layering.

Fig. 8D&E represents micrographs of Fig. 8 A&B after binarization with ImageJ, respectively. Composites processed with thermocompression of pellets (PE-BN003–10 %-TP) and thermocompression of films (PE-BN003–10 %-06-TP) clearly show differential amounts and dispersion (Table 5). With thermocompression of films, a high amount of platelets are oriented vertically in the image (Fig. 8E) with a low mean angular deviation. Contrarily, with the thermocompression of pellets, a near-zero “amount” reveals randomly oriented platelets with a mean variation of the orientation of platelets at 31.58°. Therefore, this quantitative analysis confirms that our film layering and hot-pressing technique successfully creates a highly aligned h-BN network within the LDPE matrix.

Fig. 9 represents the micrographs of disks prepared in the same manner as in Fig. 8B and C (by thermocompression of films) but using larger BN009 particles. Both samples (PE-BN009–10 %-06-TF and PE-

BN009–10 %-02-TF) seem to have well aligned platelets. However in Fig. 9C, corresponding to the sample loaded with 50 wt% of BN009 (PE-BN009–10 %-06-TF) it is difficult to conclude on the particle alignment, The effect of particle orientation on the thermal conductivity of these composites will be discussed in the following section.

In conclusion, these SEM images validate the effectiveness of this method for aligning h-BN flakes in a single direction within a LDPE polymer matrix. Images of microtomography (in Supporting Information S.2.) reveal absence of microporosity.

## 3.2. Thermal conductivity (TC) of LDPE/h-BN composites

### 3.2.1. Influence of the wt% of h-BN on TC of LDPE/h-BN injected disks

In this section, we study the evolution of thermal conductivity as a function of three factors: the h-BN content, the die thickness (film thickness), and the particle size of h-BN. In Table S.3.A (in the supporting information S.3.), we have compiled the thermal conductivity values of LDPE/h-BN composites (non-oriented particles) with BN003 in proportions of 10, 30, and 50 wt%. Pure LDPE yielded TC values of 0.30 W/(m·K) through-plane and 0.44 W/(m·K) in-plane as measured by the Hot-Disk method. The TC measured by indirect methods (XFA analysis, DSC and pycnometer) gave a value considered as through-plane of 0.31 W/(m·K) (see supporting information S.4.). The two through-plane values of LDPE provided by Hot-disk and XFA devices are close. The significant difference between the in-plane and through-plane thermal conductivity values of pure LDPE measured from Hot-Disk can be attributed to structural variations, macromolecular orientation, and density differences at the microscopic level. The injection process to obtain pure LDPE disks may cause LDPE macromolecules to preferentially orientate in the in-plane direction, resulting in higher thermal conductivity in this direction. Additionally, the core/shell effect in injection can contribute to render thermal conductivity anisotropic in LDPE discs. The introduction of BN003 particles results in an increase in thermal conductivity, especially for in-plane TC. Indeed, at 10 wt% loading, in-plane TC increases from 0.44 to 0.71 W/(m·K), while through-plane TC (Table S.3.A. in the supporting information) keeps constant around 0.30 W/(m·K) at 10 and 30 wt% of h-BN. While increasing the wt% of h-BN (from 10 to 50 %), in-plane TC increases from 0.71 to 2.52 W/(m·K) (Table S.3.A. in the S.I.). Overall, as expected, the introduction of h-BN improves the thermal conductivity of LDPE composites, and the alignment of h-BN particles in the plane of the disk leads to anisotropic TC.

These results are in good agreement with the SEM micrographs observed on injected samples (Fig. 2).

### 3.2.2. Effect of die thickness

In this section, we present the thermal conductivity values of disks obtained by thermocompression of films prepared using two different dies (02 and 06) (Table S.3.B. in the supporting information). The results demonstrate that an increase in the quantity of h-BN leads systematically to an increase in thermal conductivity (both in-plane and through-plane), confirming previous observations made on injection-molded disks.

For Die 02, the results reveal that the in-plane thermal conductivity
<figure><img src="image_10.png" /><figcaption>**Fig. 8.** SEM Images of the fracture surfaces of LDPE/h-BN (CFP003) disks with 10 wt% loading obtained A) from thermocompressed pellets (PE-BN003–10 %-TP), B) from the superposition and thermocompressed films (die 06) (PE-BN003–10 %-06-TF) and C) from superimposed and thermocompressed films (die 02) (PE-BN003–10 %-02-TF), D and E) are the binarized images using ImageJ of SEM images A and B, respectively.</figcaption></figure>

<table><caption>**Table 5**

Quantitative vertical orientation analysis of h-BN platelets in LDPE composites.</caption><thead><tr><td>Sample</td><td>Processing method</td><td>Amount</td><td>Dispersion</td></tr></thead><tbody><tr><td>PE-BN003–10 %-TP</td><td>Thermocompression of pellets</td><td>0.05</td><td>31.58°</td></tr><tr><td>PE-BN003–10 %-06-TF</td><td>Thermocompression of films</td><td>0.32</td><td>1.19°</td></tr></tbody></table>

is slightly lower than the values obtained from injection-molded disks for all percentages of platelets. However, the through-plane thermal conductivity shows higher values compared to injection-molded disks. This phenomenon can be attributed to a loss of alignment during the thermocompression of the films as argued regarding Fig. 8C, compared to injection molded disks (Fig. 2).

On the other hand, the sample produced with Die 06 exhibits an in-plane thermal conductivity of 4.25 W/(m·K). This value is much higher than those obtained for disks obtained by thermocompression of Die 02 films or for disks obtained by injection process. This can be explained by the high particle alignment (as shown previously in Fig. 8B). This particularly interesting result highlights the effect of the structuring of composites during the manufacturing process on their thermal conductivity properties.

Fig. 10 summarizes all the TC results on BN003 composites regarding the die thickness influence.

### 3.2.3. Effect of h-BN particle size

As mentioned earlier, two different grades of h-BN were used: grade BN009 has a larger size (6–12 µm) than grade BN003 (2–6 µm). The values reported in Table S.3.C. (in the supporting information S.3.), measured on disks obtained from injection molding also show the influence of the h-BN proportion (10 to 50 wt%) on thermal

conductivities. The introduction of CFP009 h-BN platelets shows a more significant increase in both through-plane and in-plane TC compared to the same formulations with CFP003 platelets. A maximum value of 3.71 W/(m·K) was obtained for 50 wt% of BN009 compared to the value of 2.52 W/(m·K) obtained for CFP003. Hence, as the orientation of platelets in those injected samples is not fully anisotropic with random oriented zones, the length of the platelets plays a key role in the in-plane TC, with larger platelets leading to lower number of interface with the polyethylene matrix (lower interfacial thermal resistance). The improved contact between platelets minimizes the interfacial area with the polymer matrix, thereby limiting heat dissipation and facilitating more efficient thermal transport.

Table S.3.D. (in the supporting information S.3.) displays the thermal conductivity (TC) values of the composites containing BN009 and manufactured using both Die 02 and Die 06. The effect due to orientation is different in these series than with BN003, where a better in-plane TC value of 4.20 W/(m·K) was achieved for 50 wt% with Die 02 compared to 3.71 W/(m·K) for non-aligned h-BN obtained by injection molding (Table S.3.C. in the S.I.) and 3.10 W/(m·K) with Die 06 (Table S.3.D. in the S.I.). The difference in the improvement of thermal conductivity (TC) values can be attributed to the larger particle size of the BN009 grade, which allows for greater contact between particles. This enhancement in TC is primarily due to the orientation and larger particle size of the BN009 grade.

Fig. 11 summarizes all the TC results on BN009 composites regarding the die thickness influence.

### 3.2.4. Summary on the influence of the different parameters and comparison with the literature

In Fig. 12, we compile all the thermal conductivity (TC) values
<figure><img src="image_11.png" /><figcaption>**Fig. 9.** SEM Images of the fracture surfaces of LDPE/h-BN (CFP009) disks with 10 wt% loading obtained A) from the superposition and thermocompressed films (die 06) (PE-BN009–10 %-06-TF) and B) from superimposed and thermocompressed films (die 02) (PE-BN009–10 %-02-TF) and with 50 wt% loading C) from the superposition and thermocompressed films (die 06) (PE-BN009–50 %-06-TF).</figcaption></figure>

obtained by hot-disk method for samples containing the highest amount of h-BN, i.e. 50 wt%. The effect of the die thickness and the h-BN size on in-plane thermal conductivity is demonstrated. Die 06 allows the preservation of alignment of the smallest BN003 platelets after stacking of films since fewer layers are superimposed during disks fabrication.

For composites containing larger platelets (BN009), Die 02 gives higher in-plane thermal conductivity values than Die 06, due to uniform pressure inside the die, promoting better alignment of the platelets compared to Die 06. Furthermore, in thin films, larger platelets have a higher probability of contact, contributing to the improvement in thermal conductivity.

Fig. 13 summarizes these conclusions. In injected samples, the formation of a skin with parallel platelets favors the in-plane TC for both BN003 and BN009, with values in-between the one obtained with thermocompressed films from Die 02 and Die 06. Fig. 13 confirms that the orientation of the h-BN platelets in the final disk are in good agreement with the orientation obtained in the film (Fig. 6) and with the thermal conductivity measurements (Fig. 12).

A comparative analysis reported in the supporting information (S.5.), contextualizes the high thermal conductivity of 4.25 W/(m·K) achieved

in this work at a 50 wt% filler loading via a solvent-free processing route. While some studies utilizing solvent-based alignment techniques report higher absolute conductivity [26,31], they often rely on complex processing or different matrix materials. The value reported in the present work is also competitive with, or exceeds, those from other solvent-free processing methods [19,22], suggesting that the film stacking and thermocompression approach is a promising and practical route for developing thermally conductive composites.

### 3.3. *Dynamic mechanical analysis (DMA) of LDPE/BN003*

In order to assess the dynamic mechanical behavior of the LDPE/BN003 composites, a torsion mode DMA analysis was conducted. Samples containing 10, 30 and 50 wt% of BN003 where analyzed and both samples obtained by thermocompression of pellets (“TP”) and thermocompression of films from Die 06 (“TF”) are reported. This study will enable to analyze the impact of incorporating h-BN particles on the dynamic mechanical properties of our polymers. DMA measures viscoelastic properties and provides information about the molecular mobility of polymer chains. The curves in Fig. 14 showing the evolution
<figure><img src="image_12.png" /><figcaption>Fig. 10. Thermal conductivity values of LDPE/BN003 composite disks obtained by injection and thermocompression of extruded films measured using the Hot Disk method.</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>Fig. 11. Thermal conductivity values of LDPE/BN009 composites with aligned h-BN platelets (film stacking procedure) measured by hot-disk.</figcaption></figure>

of the storage modulus G' and the loss modulus G'' between room temperature and 110 °C are presented. At these temperatures, we are in the rubbery plateau of the polymer as the glass transition temperature is approximately –110 °C. As expected, all the analyzed samples show a decrease in modulus as the temperature increases. By closely examining the storage modulus G' with respect to the processing method and h-BN

concentration, several conclusions can be drawn. The h-BN content has a significant influence on the elastic response, with G' being around 0.30 GPa for 10 wt% and reaching 0.74 GPa for 50 wt%. The effect of the processing method appears to be negligible on both G' and G'' for the same h-BN concentration.

Looking at Fig. 14A,B, all the curves of G' and G'' corresponding to
<figure><img src="image_14.png" /><figcaption>Fig. 12. Thermal conductivity values obtained by hot-disk for samples containing 50 wt% of h-BN.</figcaption></figure>

<figure><img src="image_15.png" /><figcaption>Fig. 13. Schematic summary of the orientation in the disk, of both h-BN grades as a function of the shaping process (injection molding, thermocompression with Die 02 and thermocompression with Die 06).</figcaption></figure>

samples processed by thermocompression of pellets, maintain higher modulus from around 80 °C onwards compared to the samples processed by film stacking. This indicates that materials obtained by direct thermocompression of pellets become stiffer than materials obtained by thermocompression of films at temperatures above approximately 80 °C.

This phenomenon can be explained by differences in the microstructure of the samples, and especially the orientation of the platelets, which significantly impact their mechanical properties. Two key factors might contribute to this: it was shown previously that the orientation of h-BN platelets was not the same for disks obtained by thermocompression of pellets or films (obtained from different dies). This must have a high influence on the dynamic mechanical properties, such as on thermal conductivity. Thermocompressed pellets should give more randomly oriented platelets than thermocompressed films. And this

random orientation favors higher G' and G'' above 80 °C when solicitation is a torsion mode.

Another explanation can be that samples obtained from thermocompressed films lead to higher porosity and lower density than samples obtained from thermocompressed pellets. As X-ray tomography stated (S.I.2) that there is no microscopic porosity in disks obtained from stacked films. This discrepancy suggests that the porosity might exist on a nanometric scale.

The loss factor (tan δ, which is the G''/G' ratio) (Fig. 14C) shows a broad peak between 20 and 90 °C, depending on the wt% of h-BN. This interval is within the rubbery domain, so the observed peak does not correspond to the α transition, which is the mechanical manifestation of the glass transition. These peaks, therefore, have a different origin that needs to be identified. One hypothesis is due to an increase in inter-
<figure><img src="image_16.png" /><figcaption>Fig. 14. Evolution of a) storage modulus G', b) loss modulus G", and c) loss angle tan δ for LDPE/ BN003 composites obtained by direct thermocompression of pellets ("TP") or by film stacking (with Die 06) ("TF").</figcaption></figure>

particle friction (particle-particle) with temperature, resulting in a G" value increasing compared to G', leading to an increase in tan δ. This peak appears around 68 °C for the sample obtained by thermocompression of films ("TF") with 50 wt% h-BN loaded films and at 85 °C for the sample obtained by thermocompression of pellets (with also 50 wt% h-BN). It is also present for lower concentrations, but its size is largely reduced. Starting from 110 °C, the material begins to flow. Indeed, the melting temperature of pure LDPE has been measured at 114 °C for the peak determined by DSC (fig. S.6. in the supporting information). The presence of h-BN platelets stiffens the material at any concentration, and the bars remain intact after the tests.

## 3.4. Modeling of heat transfer

### 3.4.1. Methodology

The thermal measurements in the previous section provide information on the orientation of the platelets into the disks. Numerical simulation of heat transfer is an essential tool to access the heat diffusion through the thickness of the sample and better understand the thermal gradients generated during heat diffusion in a heterogeneous material. Furthermore, while the thermal properties of each phase are known, the thermal interfacial resistance is not known, and there is very little data available in the literature [38,39]. Moreover, measurements of interfacial resistance at the nanoscale present significant experimental challenges. These techniques, described in this review [38] are not mature and difficult to carry out. However, as mentioned by Chen et al. [40] interfacial thermal resistance plays a significant role in heat transfer at

various scales. In our study, the interface resistance between the polymer matrix and h-BN platelets could be responsible for the low thermal conductivity measured in the composites.

Our approach aims to determine the homogenized thermal conductivity of the composites through a numerical simulation without taking into account the interfacial thermal resistance to quantify its influence on the composite's conductivity. The numerical model is developed using the "Heat transfer" module of the commercial finite element software Abaqus.

The heat equation governing the problem is given by Eq. (4).

$$ \mathrm{div}(k\overline{\nabla T}) + \dot{q} = \rho C_p \frac{\partial T}{\partial t} \qquad (4) $$

Where: k is the thermal conductivity, T is the temperature, $\dot{q}$ is the heat source term, $\rho$ is the density and $C_p$ is the heat capacity. The term $\mathrm{div}(k\overline{\nabla T})$ corresponds to heat diffusion, while the term $(\rho C_p \frac{\partial T}{\partial t})$ corresponds to the transient thermal regime.

In our study, the heat source term was considered as zero because no internal volumetric energy is generated. All the geometric modeling, physical modeling, and post-processing operations were automated using Python macros.

### 3.4.2. Geometric modeling

The h-BN particles are represented by disks with a thickness of $e_p = 0.46\mu$m and a radius of $r_p = 3\mu$m. The Disks are anisotropically dispersed in the z direction, and isotropically dispersed in the x and y
directions. Representative Elementary Volume (REV) of the composite measures 2.76 × 27 × 27µm and consists of 33 vol% of particles (50 wt %) with their positions generated randomly without overlapping (Fig. 15a). The rest of the volume is occupied by the LDPE polymer.

Since the interfacial thermal resistances are not considered, the particles are merged together, and the portions extending beyond the Representative Elementary Volume (REV) are trimmed, as shown in Fig. 15b. The other portion of the REV represented by the LDPE polymer is depicted in Fig. 15c.

The mesh of the entire structure is shown in Fig. 16A. Due to the complexity of the geometry, it is meshed using quadratic tetrahedral elements known as DC3D10 elements in Abaqus. In total, 138628 elements and 200,275 nodes were generated.

### 3.4.3. Physical modeling

The properties of the two materials are provided in the supporting information (S.7) [40].

The thermal properties of the materials are considered isotropic-transverse. Therefore, for each of the two materials, two thermal conductivities are required: the first represents the thermal properties for in-plane conduction (x and y directions), while the second corresponds to the through-plane thermal behavior (z direction). The transient thermal study is conducted in 3D conduction. The boundary conditions, as shown in Fig. 16B, are related to the z-direction, but the approach is similar for the other directions. A surface power density of $P = 10^7$ W/m² is imposed on the “inlet” irradiated face, and a specified temperature $T_{outlet} = 25$ °C is applied to the “outlet” face. The thermal conductivity of the composite is determined by the applied Fourier’s law in Eq. (5).

$$ \lambda = \frac{P L}{T_{\text{inlet}} - T_{\text{outlet}}} \qquad (5) $$

Where L represents the length of the composite in the considered direction, and $T_{inlet}$ is the average temperature of the inlet face calculated using a post-processing macro.

The other faces of the composite are adiabatic, meaning they do not exchange heat with the external environment. The simulations are conducted for all three directions in steady-state conditions. The computing machine used is a laptop with a 1.8 GHz processor, 1 processor core.

The temperature fields on the three directions (x, y and z) are shown in Fig. 16C,D,E. It can be observed that the temperature is not uniform on the inlet faces, in contrast to the outlet faces where a temperature of 25 °C was imposed. The maximum temperatures are localized in the polymer areas, as evident in images of Fig. 16C,D,E where the morphology of the h-BN grain particles is clearly visible. Based on the average temperature of the faces, the conductivities are evaluated. The average temperatures of the inlet faces in the z, x, and y directions are 73 °C, 68 °C, and 93 °C, respectively. This results in conductivities of 0.58 W/(m.K), 6.23 W/(m.K), and 3.9 W/(m.K) for the respective directions. All the calculation data and the results of the numerical and experimental conductivities are presented in Table 6.

Firstly, we can observe a similar influence of the direction (x, y and z) on both experimental and simulated thermal conductivity values. Modeling allows to dissociate x and y directions that gives different values of thermal conductivities (6.23 and 3.95 W/(m.K), respectively)

whereas experimental values using hot disk measurements and the Silas E. Gustafsson model gives an average value in both directions. An average value of numerical TC in the x and y directions would give a higher value (5.09 W/(m.K) obtained with the law of mixture) than the experimental ones obtained for well-aligned h-BN particle-composites (PE-BN003-50 %-06-TF and PE-BN009-50 %-02-TF).

In the z direction, the simulated value is also higher than experimental ones. All simulated values higher than experimental ones might be explained by the presence of an interfacial thermal resistance in the composite that reduces the experimental values. Moreover, when we compare the simulated conductivity value in the x direction, the significant difference from the y direction indicates that the random distribution of particles has favored conductivity in the x direction at the expense of the y direction. We can conclude that the presence of interfacial thermal resistance reduces the thermal conductivity by approximately 20 %.

## 4. Conclusion

Thermal conductivity depends heavily on the shaping process (injection, thermocompression from films or pellets). This study has highlighted the importance of the alignment of h-BN platelets in improving the in-plane thermal conductivity of LDPE/h-BN composites. It was also observed that particle size and film thickness play a crucial role in the achieved orientation of the platelets and thermal conductivity. In the films, the Poiseuille effect was observed, with particles aligning at the film edges, while in the middle, they showed a more random orientation due to higher flow velocity and lower viscosity. However, small boron nitride platelets were less affected by this flow difference due to their high specific surface area and greater contact with the matrix, preventing them from moving randomly in films. For the smallest platelets (BN003), the high orientation is not preserved in the disks obtained from thermocompressed films obtained from Die 02 due to a high number of films. And this has an influence on the final in-plane TC. Maximum in-plane TC value of 4.20 and 4.25 W/(m.K) were achieved for composites containing larger platelets (BN009) combined with extruder Die 02 and for shorter platelets (BN003) combined with extruder Die 06, respectively. Alignment of the platelets led to a higher probability of contact with each other, further enhancing thermal conductivity. In general, it is possible to determine favorable compositions to achieve better thermal conductivity based on particle size. The results of dynamic torsion tests showed that materials obtained by direct pellets granule thermocompression had G' and G'' modules similar to those obtained by thermocompression of films. However, materials obtained by direct thermocompression of granules were stiffer beyond 80 °C than those obtained by film thermocompression, regardless of the h-BN content.

### CRediT authorship contribution statement

**Abdelwahab Boukheit:** Writing – original draft, Methodology, Formal analysis, Data curation. **Christian Garnier:** Writing – review & editing, Validation, Supervision, Formal analysis, Data curation. **Amèvi Tongne:** Writing – review & editing, Validation, Supervision, Methodology, Formal analysis, Data curation. **France Chabert:** Writing –

<figure><img src="image_17.png" /><figcaption>Fig. 15. (a) h-BN particles randomly generated; (b) Merged and cut particles, (c) LDPE polymer geometry.</figcaption></figure>
<figure><img src="image_18.png" /><figcaption>Fig. 16. (A) Meshing of the composite. (B) Boundary conditions. (C, D, E) Temperature fields in °C in the different directions.</figcaption></figure>

<table><caption>**Table 6**

Results of numerical and experimental conductivity calculations.</caption><thead><tr><th></th><th>Outlet T<br>(°C)</th><th>Inlet T<br>(°C)</th><th>Surface thermal power (W/<br>m²)</th><th>Length L<br>(µm)</th><th>Numerical<br>TC<br>(W/(m.K))</th><th>Experimental TC for PE-BN003-50<br>%-06-TF<br>(W/(m.K))</th><th>Experimental TC for PE-BN009-50<br>%-02-TF<br>(W/(m.K))</th></tr></thead><tbody><tr><td>z</td><td>25</td><td>73</td><td>10<sup>7</sup></td><td>2.76</td><td>0.58</td><td>0.34</td><td>0.50</td></tr><tr><td>x</td><td>25</td><td>68</td><td>10<sup>7</sup></td><td>27</td><td>6.23</td><td>4.25</td><td>4.20</td></tr><tr><td>y</td><td>25</td><td>93</td><td>10<sup>7</sup></td><td>27</td><td>3.95</td><td></td><td></td></tr></tbody></table>

review & editing, Validation, Supervision, Resources, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. Belkacem Oztazaghine: Writing – review & editing, Validation, Supervision, Methodology, Formal analysis, Data curation. Aurélie Taguet: Writing – review & editing, Visualization, Validation, Supervision, Resources, Project administration, Methodology, Investigation, Funding acquisition, Data curation, Conceptualization.

### Declaration of competing interest

The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: Région Occitanie, France. Aurelie TAGUET reports financial support was provided by Engineering College Ales Polymers Composites and Hybrids. Aurelie Taguet reports a relationship with Engineering College Ales Polymers Composites and Hybrids that includes: funding grants. If there are other authors, they declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

### Acknowledgement

The authors would like to thank the region of Occitanie for the financial support of this work and Jean Claude Roux (IMT Mines Ales) for the SEM images and Guillaume Morel (UTTOP) for the supervision for the Hot Disk measurement.

## Appendix A. Supplementary data

Supplementary data to this article can be found online at https://doi.org/10.1016/j flatc.2025.100989.

### Data availability

Data will be made available on request.

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