# Filler Size Hybridization and Dielectrophoretic Structuring of Soft Polymer Based Thermally Conductive Composites

Omar Zahhaf, Giulia d'Ambrogio, François Grasland, Guilhem Rival, Minh Quyen Le, Pierre-jean Cottinet, Jean-fabien Capsal

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## ► To cite this version:

Omar Zahhaf, Giulia d'Ambrogio, François Grasland, Guilhem Rival, Minh Quyen Le, et al., Filler Size Hybridization and Dielectrophoretic Structuring of Soft Polymer Based Thermally Conductive Composites. Macromolecular Materials and Engineering, In press, 10.1002/mame.202500271. hal-05373230

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RESEARCH ARTICLE

OPEN ACCESS

# Filler Size Hybridization and Dielectrophoretic Structuring of Soft Polymer Based Thermally Conductive Composites

Omar Zahhaf<fnref n="1" /> | Giulia D'Ambrogio<fnref n="1" /> | François Grasland² | Guilhem Rival<fnref n="1" /> | Minh Quyen Le<fnref n="1" /> | Pierre-Jean Cottinet<fnref n="1" /> | Jean-Fabien Capsal<fnref n="1" />

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**Correspondence:** Jean-Fabien Capsal (jean-fabien.capsal@insa-lyon.fr)

**Received:** 4 July 2025 | **Revised:** 21 October 2025 | **Accepted:** 30 October 2025

**Keywords:** dielectrophoretic structuring | filler size hybridization | hybrid composites | thermal conductivity

## ABSTRACT

This study offers a detailed exploration of the dielectrophoretic structuring of filler size hybrid thermally conductive composites, emphasizing the impact of filler size hybridization on the thermal and mechanical properties of PDMS-Al₂O₃ composites. By comparing the performance of monodisperse and hybrid composites, we highlight the advantages of size hybridization in optimizing composite properties. The results indicate significant improvements in thermal conductivity and mechanical stiffness due to enhanced filler packing density and more efficient structuring. Our investigation into various compositions and size ratios reveals optimal thermal properties at specific hybridization levels, suggesting key parameters for superior composite performance. These results demonstrate the advantage of combining size hybridization with dielectrophoretic structuring to design advanced composites for thermal management, while emphasizing the need for future studies to tackle environmental concerns and investigate alternative polymer matrices.

## 1 | Introduction

Newnham's connectivity theory [1] posits that the structural and functional integration of various elements within a system significantly influences its overall behavior and performance. This theory emphasizes the interdependence of components, suggesting that changes in one element can affect the entire system. Newnham argues that understanding these connections is crucial for optimizing design and improving functionality in fields such as materials science and engineering. By analyzing the relationships and interactions among components, researchers can develop more efficient and effective systems. Many studies have investigated the influence of numerous factors on the physical properties of composites structured through dielectrophoresis, specifically, monodisperse composites [2–4]. These

factors included dielectrophoresis parameters, matrix type, and viscosity, as well as filler size. The various findings from these investigations provided valuable insights into the relevance of each factor in the development of high-performing composites with improved properties, well suited for thermal management [5]. Building on the knowledge acquired, this study aims to further investigate thermally conductive composites by exploring the potential of filler size hybridization in enhancing the properties of PDMS-Al₂O₃ composites, particularly in the context of dielectrophoretic structured composites.

Filler size hybrid composites, refer to composite materials containing two or more distinct filler sizes, which can lead to enhanced performance through better filler packing efficiency (i.e., filler packing density) and improved interfacial interactions

[Correction added on 11 November 2025 after first online publication: the article title has been updated in this version.]

This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

© 2025 The Author(s). Macromolecular Materials and Engineering published by Wiley-VCH GmbH

<footnote n="1">¹Univ. Lyon, INSA-Lyon, LGEF, EA682, Villeurbanne, France | ²GETELEC, Buc, France</footnote>
<figure><img src="image_5.png" /><figcaption>**FIGURE 1** | Schematic representation of a filler size hybrid composite. Reprinted from [7].</figcaption></figure>

between the matrix and fillers [6]. Enhancing the filler packing density through size hybridization also leads to lower blend viscosity, which is particularly useful for composite structuring. Furthermore, by combining different filler sizes, it is possible to achieve not only a more optimized filler distribution, but also higher filler contents, which can significantly enhance composite properties such as thermal conductivity, dielectric permittivity, and mechanical performance. This approach is particularly relevant to the development of highly performing thermally conductive composites, as the synergistic effects of filler size hybridization can lead to materials with superior properties compared to their mono-sized counterparts (cf. Figure 1 [7]). For example, regarding thermal conductivity, Choi and Kim reported a maximum value of 3.5 W/m.K for an epoxy composite filled with a bimodal distribution of alumina and aluminum nitride at 58.5 vol%, compared to about 2 W/m.K for a composite containing only monodisperse alumina particles [8]. In contrast, Sui et al. observed a maximum value of around 1 W/m.K in an epoxy composite with a bimodal distribution of alumina particles [9].

While particle size effects and hybrid loading strategies have been reported in various thermally conductive polymer composites, these studies were typically performed without field-induced structuring or at moderate filler loadings in relatively stiff matrices. The present work introduces a synergistic approach that combines binary particle size distributions with dielectrophoretic alignment in a highly compliant PDMS matrix. This combination enables systematic control of particle connectivity and packing while maintaining structural integrity, thereby uncovering design rules for optimizing both thermal and mechanical performance. To our knowledge, such a systematic coupling of hybridization, soft matrices, and dielectrophoretic structuring has not yet been reported. This dual strategy represents the core innovation of this study and is expected to provide new insights into the design of advanced thermal interface materials.

In this work, we will systematically investigate the effect of binary size hybridization (i.e., two filler sizes) on the physical properties of both structured and unstructured composites, and compare the performance of “monodisperse” and hybrid composites. This analysis will provide valuable insights into the potential advantages of size hybridization in composite materials and further our understanding of the underlying mechanisms governing their properties. Subsequently, we will dive deeper into the specifics of size hybridization, namely, the composition (i.e., fraction of

smaller fillers, Ω) and the size ratio between the two filler sizes. We will first investigate the influence of composition on the properties of the composites, with a particular emphasis on structured materials. Then, we will examine the impact of size ratio and its correlation to the composition and overall, to the properties of the hybrid composites.

While particle size effects and hybrid loading strategies have been reported in various thermally conductive polymer composites, these studies were typically performed without field-induced structuring or at moderate filler loadings in relatively stiff matrices [8, 10]. The present work combines binary particle size distributions with dielectrophoretic alignment in a highly compliant PDMS host that can accommodate loadings up to 70 vol%. This combination enables systematic control of particle connectivity and packing while maintaining structural integrity, thereby uncovering design rules for optimizing both thermal and mechanical performance. To our knowledge, such a systematic coupling of hybridization, soft matrices, and dielectrophoretic structuring has not yet been reported. Throughout this study, our discussions will primarily focus on the thermal, and mechanical properties of the composites, with a particular emphasis on the structured composites. These investigations will deepen our understanding of the factors affecting the properties of PDMS-Al₂O₃ and will help shed light on the optimal hybridization conditions for achieving highly performing composites with enhanced properties, providing valuable guidance for future research.

## 2 | Materials and Methods

### 2.1 | Materials

Sylgard 527 is a two-part silicone dielectric gel whose formulation offers unique physicochemical properties. These properties make Sylgard 527 a suitable candidate for a wide range of applications, including its use as a polymer matrix for composite materials. Unlike Sylgard 184, Sylgard 527 has a lower mixed viscosity of 0.46 Pa s, with a longer working time of 2 h at 25°C [11]. Upon mixing the two parts in their stoichiometric 1:1 ratio, it cures to a clear material with a density of 0.95 g/cm³ and a relative permittivity of 2.85 at 10 kHz [11]. In terms of mechanical properties, Sylgard 527 has a tensile Young's modulus ranging from 1.5 kPa to 5 kPa, three orders of magnitude lower than its Sylgard 184 counterpart [12, 13]. While extensive research has been conducted on Sylgard 184, few studies have investigated the properties and chemical composition of Sylgard 527. Sylgard 184 and 527 share a similar chemical structure with a difference in the length of base polymer chains. Sylgard 184 has 184 repeating units while Sylgard 527 has 527 repeating units [14]. This difference in length results in varying cross-linking densities and network formation, leading to notable differences in the mechanical properties between the two polymers. However, the exact chemical composition of the curing agents of both Sylgard 184 and 527 remain undisclosed. In this study, Sylgard 527 was used as a polymeric matrix in the preparation of high-filler content composites (≥40 vol%). Its viscoelastic properties, such as its low viscosity and high flexibility, provide an advantage in terms of processing compared to other materials. These properties allow for high filler loading levels, reaching up to 70 vol% for hybrid composites, without
<table><caption>TABLE 1 | Properties of alumina fillers as a function of their size.</caption><thead><tr><th>Size (μm)</th><th>140</th><th>60</th><th>30</th><th>25</th><th>5</th><th>1</th></tr></thead><tbody><tr><td>D10 (μm)</td><td>110</td><td>39</td><td>19</td><td>15</td><td>3</td><td>0.7</td></tr><tr><td>D50 (μm)</td><td>138</td><td>60</td><td>33</td><td>26</td><td>5</td><td>1</td></tr><tr><td>D90 (μm)</td><td>171</td><td>83</td><td>50</td><td>38</td><td>7</td><td>2</td></tr><tr><td>True density at 25°C (g/cm³)</td><td>3.92</td><td>3.81</td><td>3.79</td><td>3.78</td><td>3.74</td><td>3.71</td></tr><tr><td>Spheroidization rate</td><td>96%</td><td>96%</td><td>98%</td><td>97%</td><td>98%</td><td>98%</td></tr></tbody></table>

sacrificing the material's cross-linking capabilities or reducing particle mobility.

To investigate the influence of filler size as well as size hybridization on the properties of thermally conductive composites, spherical alumina fillers with varying sizes were used. The size range of the fillers extended from 1 µm to 140 µm. Table 1 lists some of the relevant properties of the alumina fillers used as a function of their size. It is noteworthy that D50 (respectively, D10, D90) represents the size below which 50 % (respectively, 10 %, 90 %) of the particle population falls. D50 thus represents the median size, marking the point at which half of the particles are finer and half are coarser.

## 2.2 | Composite Elaboration

The preparation of PDMS-Al₂O₃ composites is performed by adding the appropriate amount of alumina filler to the PDMS base (part A). The aim is to ensure that the following sonication process does not cause any local polymerization. Then, the blend is mechanically mixed for 5 min, followed by sonication for 5 min using an ultrasonic probe (Hielscher Ultrasound Technology, UP400S) to disperse any filler aggregation. Subsequently, the curing agent (part B) is added and the blend is further mixed for 5 min using an overhead stirrer. The resulting blend is subjected to room temperature vacuum for 5 min before being mixed once more. This is particularly important when working with high filler content composites where removing entrapped air bubbles decreases their viscosity and thus improves the effectiveness of the mixing process. The resulting homogeneous blend is poured into the bottom part (1) of two identical molds shown in Figure 2. The two bottom parts containing the uncured composite are subjected to room temperature vacuum for 5 min before being sealed by the top part (2). Finally, in order to guarantee a uniform thickness across different samples, both molds are exposed to the same compression force.

The first mold, intended for the fabrication of the 1–3 structured composite according to Newhnam’s connectivity theory [1], is subjected to a high-voltage AC electric field for 1 h at room temperature. The electric field is powered by a high-voltage amplifier (Trek 20/20C, x2000) connected to a waveform generator (Keysight 33210A) that delivers the sinusoidal signal. Both the voltage and current are monitored using an oscilloscope (Keysight DSOX3054A). Subsequently, the temperature is increased to 120°C at a heating rate of 5–10°C/min while maintaining the electric field. Finally, the structured composite is cured at 120°C for 1 h under electric field before being cooled down naturally to room temperature.

Simultaneously, the second mold, intended for the fabrication of the 0-3 unstructured composite, is directly placed at 120°C without applying the electric field. The 0–3 composite is cured at 120°C for 1 h before being cooled down naturally to room temperature.

It is noteworthy that the above-mentioned composite fabrication process is applicable for both Sylgard 184 and Sylgard 527, as well as for various filler types and sizes.

The SEM cross-sections show that the electric-field alignment is effective. The SEM image of the unstructured composite (Figure 2A) reveals a homogeneous dispersion of both small and large particles throughout the matrix, with no significant segregation between particle sizes. In contrast, when the dielectrophoresis process is applied (Figure 2B), mainly the smaller particles are aligned along the electric field direction. The larger particles mainly build the backbone of the chains, while the smaller ones are pulled into the gaps and align with the field. This mixed arrangement lowers the amount of empty space in the composite and strengthens the contacts between fillers. As a result, the material exhibits better thermal transport and mechanical strength.

## 2.3 | Methods

For each composite formulation, four independent samples were prepared and characterized following the same procedure. The values reported in the figures correspond to the mean of these four measurements. Error bars represent the standard deviation and provide an estimate of the experimental variability. This approach ensures that the reported trends in thermal and mechanical properties are statistically supported and not the result of sample-to-sample fluctuations.

Compression tests are widely used characterization methods that provide useful insights into a material’s mechanical behavior when subjected to compressive stress. In this study, experimental uniaxial monotonic compression tests were carried out at ambient temperature using a Shimadzu TCE-N300 testing machine. The composite samples were cut into a circular shape with a diameter of 20 mm and a thickness of 2 mm. The samples were then positioned between two compression plates and subjected to a compressive load in a displacement-controlled mode with a speed of 10 mm/min until reaching 90% strain or the machine’s maximum load of 10 kN. The compressive load and displacement measured were used to calculate the stress and its corresponding strain.
<figure><img src="image_6.png" /><figcaption>**FIGURE 2** | Top: Representation of the molds used in the composite elaboration. (1) Bottom part of the mold where the uncured composite is poured. (2) Top part of the mold to seal the composite. Bottom: SEM images of composites with $k = 140$, $\Omega = 25\%$, and a filler volume fraction of 50%, showing (A) unstructured and (B) dielectrophoretically structured samples.</figcaption></figure>

The measurement of thermal conductivity is of crucial importance to any research study involving thermal conduction. In the current study, the Modified Transient Plane Source (MTPS) method was used to determine the thermal properties (thermal conductivity and effusivity) via the TCi thermal conductivity analyzer (C-therm). The MTPS method is a well-established and widely used technique for measuring thermal properties [15]. Derived from the ISO-standard approved Transient Plane Source (TPS) method, it is based on analysis of the transient temperature response of a material (solid, liquid, powder) to determine its thermal properties.

## 2.4 | Definition of Structuring Efficiency

To quantify the benefit of dielectrophoretic alignment, a structuring efficiency (%) was defined as the relative gain in thermal conductivity of the dielectrophoretic assisted structured composite (1-3 connectivity) compared to the unstructured composites (0-3 composite) at identical filler content and composition

$$ \eta = 100 \times \frac{\lambda_{1-3} - \lambda_{0-3}}{\lambda_{0-3}} \quad (1) $$

here $\lambda_{0-3}$ and $\lambda_{1-3}$ denote the thermal conductivities of the unstructured and structured composites, respectively. This metric allows a direct comparison of how structuring efficiency varies with particle size ratio and hybrid fraction.

## 2.5 | Generality and Limitations of the Approach

The strategies of dielectrophoretic structuring and size hybridization described in this work are not limited to the Sylgard 527/Al₂O₃ system. For dielectrophoretic structuring, the key requirement is a sufficient dielectric contrast between the filler

and matrix, enabling particle polarization and alignment under an electric field. As previously discussed [4], matrices with low viscosity and manageable electrical losses further facilitate successful structuring [16–18]. These criteria allow the extension of the method to a wide range of polymers and fillers.

Size hybridization, involving the combination of fillers with different sizes, is a general strategy that has been demonstrated to improve composite properties across various material systems. The effectiveness of this approach depends on the ability of smaller particles to fill interstitial spaces between larger ones, increasing packing density and forming efficient conductive networks [19]. This concept has been applied to composites with diverse matrices [20, 21] and fillers [22, 23]. However, limitations exist: achieving uniform dispersion can be challenging, especially at high loadings; and increased surface area of fine fillers may lead to pronounced interfacial effects [24]. Additionally, the optimal ratio of fine to coarse fillers is system-dependent, and excessive fine particles can disrupt network formation and reduce performance. These considerations highlight the need for careful material selection and process optimization when generalizing these strategies to other systems.

# 3 | Results and Discussion

## 3.1 | Improving Thermal Properties from Hybridization and Dielectrophoretic Structuring

In this work, we will explore the impact of size hybridization on the thermal and mechanical properties of PDMS-Al₂O₃ composites, with a particular emphasis on structured composites. Filler size hybridization offers the potential to optimize composite properties by leveraging the increased filler packing density and
<figure><img src="image_7.png" /><figcaption>FIGURE 3 | (A) Thermal conductivity as a function of filler content for structured “monodisperse” and hybrid composites and (B) thermal conductivity of both structured and unstructured “monodisperse” and hybrid composites.</figcaption></figure>

the synergistic effect between different filler sizes. Prior to investigating the parameters of size hybridization, it is important first to better understand the advantages of this approach by conducting a comprehensive analysis of the properties of hybrid composites compared to those of their “monodispersed” counterparts.

Filler size-hybridization can be characterized by two main parameters, namely, the filler size ratio (k) and composition (Ω). In this study, those parameters will be defined mathematically as follows:

$$k = \frac{D_1}{D_2} \quad \text{with } D_1 \ge D_2 \qquad (2)$$

$$\Omega (\%) = \frac{\%vol (D_2)}{\%vol (D_1) + \%vol (D_2)} \quad \text{with } D_1 \ge D_2 \qquad (3)$$

In our investigation, we will compare three composite types across a wide range of filler contents: PDMS-Al₂O₃ 140 µm, PDMS-Al₂O₃ 30 µm, and PDMS-Al₂O₃ hybrid, containing 50 vol% alumina 140 µm and 50 vol% alumina 30 µm (i.e., k ≈ 5, Ω = 50%). The selection of those particular composites is arbitrary, and aims only to highlight the potential benefits of filler size hybridization. All composites are Sylgard 527-based, and all composite structuring will be conducted according to the optimal conditions established previous work [4], namely, an electric field with 4 kV/mm amplitude and 1 Hz frequency. This ensures that our investigation will be built upon the insights gained from previous chapters, and provide a solid foundation for understanding the impact of size hybridization on the properties of the resulting PDMS-Al₂O₃.

To assess the impact of filler size hybridization on the thermal properties of PDMS-Al₂O₃ composites, thermal conductivity measurements were conducted at room temperature for both structured and unstructured “monodisperse” and hybrid composites. A wide range of filler contents were considered for the structured composites. Figure 3A displays the thermal

conductivity as a function of filler content for the considered “monodisperse” and hybrid structured composites. As expected, the results show an increase in thermal conductivity as the filler content increases, regardless of the composite type. The measurements also indicate enhanced thermal conductivity when the filler size increased from 30 to 120 µm. More importantly, the results reveal superior thermal behavior for hybrid composites compared to their “monodisperse” counterparts, with the highest thermal conductivity recorded at 3.2 W/m.K. This improvement is attributed to the higher filler packing density resulting from size hybridization, where smaller particles fill gaps otherwise occupied by the thermally inefficient polymer [7, 25].

Furthermore, the presence of smaller particles helps create more continuous and efficient thermally conductive filler pathways, thus increasing the overall thermal conductivity of the composite [26]. In size-hybridized composites, smaller particles occupy interstitial spaces that would otherwise be filled by polymer. This reduces the length and cross-section of polymer pathways, which are typically associated with high phonon scattering and low thermal conductivity. Although increasing the number of interfaces can introduce additional phonon scattering, the overall effect of higher packing density and improved filler connectivity is a net enhancement of thermal transport. This is especially true in dielectrophoretically structured composites, where field-induced alignment further increases the continuity and efficiency of the thermally conductive network. Recent reviews and experimental studies confirm that the negative effect of more interfaces is usually outweighed by the positive effect of reducing polymer path length, especially when structuring aligns the fillers [27–29]. Higher filler compactness can also lead to lower phonon scattering, particularly in structured composites, which in turn increases overall thermal conductivity. Additionally, higher filler packing density results in lower blend viscosity [30], allowing for more efficient structuring and thus improved thermal properties. As filler content increases, the gap between hybrid composites and “monodisperse” ones widens, reaching up to a 54% and 66% increase in thermal conductivity at 50 vol% compared to PDMS-Al₂O₃ 140 and 30 µm, respectively. This significant
<figure><img src="image_8.png" /><figcaption>**FIGURE 4** | Compressive stress versus strain curves of structured PDMS-Al₂O₃ 30 µm, 140 µm and hybrid composites at 50 vol% filler content.</figcaption></figure>

increase, despite the high filler content, is related to the lower viscosity of uncured hybrid composites, resulting in more efficient structuring. Furthermore, even as viscosity increases with rising filler content, the smaller particles in hybrid composites retain sufficient mobility for particle alignment, leading to a significant enhancement in thermal conductivity. To verify this observation, structured “monodisperse” and hybrid composites were compared to their unstructured equivalents.

Figure 3B displays the thermal conductivity of both structured and unstructured “monodisperse” and hybrid composites at 50 vol%. The results show a comparable thermal behavior for unstructured composites, where the hybrid sample exhibits a slightly higher thermal conductivity showing a 10% increase over PDMS-Al₂O₃ 30 µm. When compared to their unstructured counterparts, PDMS-Al₂O₃ 30 µm exhibits a 38% increase, PDMS-Al₂O₃ 140 µm an 83% increase, and PDMS-Al₂O₃ hybrid a 106% increase in thermal conductivity. These results highlight not only the advantage of filler size hybridization but also the relevance of combining it with dielectrophoretic structuring.

In practical applications, the composites presented here are designed to function as interlayer joints or thermal interface materials, where they are confined between rigid structural substrates. Under such conditions, the materials are predominantly subjected to compressive stresses, while tensile or peel stresses play only a secondary role. For this reason, compressive properties provide the most relevant measure of their mechanical reliability. Nevertheless, it is worth noting that tensile and interfacial adhesion properties remain important for specific device configurations, for example in applications involving repeated bending or delamination risks. A short discussion of this aspect has therefore been included to place our results in a broader application-oriented context. To assess the mechanical performance of the developed composites, compression tests were conducted at room temperature on both “monodisperse” and hybrid structured composites with 50 vol% filler content. Figure 4 presents the resulting stress-strain curves for the tested materials.

<table><caption>**TABLE 2** | Summary of the estimated compressive moduli for PDMS-Al₂O₃ 30 µm, 140 µm, and hybrid structured composites.</caption><thead><tr><th></th><th><i>E</i><sub>compression</sub><br>(MPa)</th></tr></thead><tbody><tr><td>PDMS-Al<sub>2</sub>O<sub>3</sub> 140 µm</td><td>1.06 ± 0.01</td></tr><tr><td>PDMS-Al<sub>2</sub>O<sub>3</sub> 30 µm</td><td>1.35 ± 0.01</td></tr><tr><td>PDMS-Al<sub>2</sub>O<sub>3</sub> Hybrid</td><td>1.58 ± 0.01</td></tr></tbody></table>

The results indicate that the PDMS-Al₂O₃ 30 µm composite exhibits a stiffer mechanical response than the PDMS-Al₂O₃ 140 µm composite, presenting a lower strain for a given stress. Furthermore, the PDMS-Al₂O₃ hybrid composite displays an even stiffer behavior than its “monodisperse” counterparts, particularly at low strain values. To quantify these differences, linear curve fits at low strain values (i.e., between 15% and 20%) were utilized to estimate the compressive moduli of the tested materials, as summarized in Table 2.

The reported values reveal a higher elastic modulus for the PDMS-Al₂O₃ hybrid composite compared to its “monodisperse” equivalents, with a 17% and 49% increase over PDMS-Al₂O₃ 30 and 140 µm composites, respectively. This behavior may be attributed to the increased filler packing density of the hybrid composite, where dielectrophoresis leads to more efficient filler structuring and better chain-like structure, offering improved resistance to compressive load. As the filler size varies, another phenomenon related to filler-matrix interfaces comes into play. This results in different interfacial bonding strengths between the matrix and fillers, thus altering the overall mechanical behavior of the material. In hybrid composites, where multiple filler sizes are present, both phenomena are involved and compete with each other. In such cases, the influence of the composition (Ω) will help determine which factor is more dominant. This aspect will be discussed in the following section, where the influence of the composition will be investigated.

## 3.2 | Role of Composition (Ω) on Thermal and Mechanical Properties

Understanding the role of composition in hybrid composites is crucial for several reasons. First, the composition can significantly influence the distribution and interaction of the different filler sizes within the PDMS matrix, which in turn affects the overall performance of the composite. Second, an optimized composition could lead to a more prominent synergistic effect between the filler particles, resulting in improved properties compared to composites with a suboptimal composition. Lastly, by studying the impact of composition on the thermal and mechanical properties of hybrid composites, we can gain valuable insights into the mechanisms governing these properties, enabling the development of more effective ways to tailor composite performance. To systematically study the impact of composition on the thermal and mechanical properties of the composites, two hybridization systems were considered: hybrid composites containing alumina 140 and 30 µm (k ≈ 5), and hybrid composites containing alumina 60 and 5 µm (k = 12). A wide range of compositions, varying from 0% to 100%, were investigated
<figure><img src="image_9.png" /><figcaption>**FIGURE 5** | Thermal conductivity as a function of the composition of hybrid composites over different filler contents: (A) PDMS-Al₂O₃ 140 µm and 30 µm (k ≈ 5), (B) PDMS-Al₂O₃ 60 µm and 5 µm (k = 12).</figcaption></figure>

to establish the optimal composition for size hybridization. All composites will be Sylgard 527-based, and the structuring process were conducted according to the optimal conditions, namely, an electric field with 4 kV/mm amplitude and 1 Hz frequency [4]. By analyzing the influence of composition on thermal and mechanical properties, we will deepen our understanding of the underlying mechanisms governing the properties of PDMS-Al₂O₃ composites and provide valuable guidance for the design of high-performing composites with enhanced properties through size hybridization. To assess the thermal properties of the developed composites, thermal conductivity measurements were conducted at room temperature on structured hybrid composites (i.e., *k* ≈ 5 and *k* = 12) over a wide range of filler contents and compositions. As reference points, a comparison was conducted between structured and unstructured composites at a 50 vol% filler content.

Figure 5A,B depicts the thermal conductivity as a function of the composition over different filler contents of both *k* ≈ 5 and *k* = 12 binary-particle systems, respectively.

Figure 5A,B shows the thermal behavior observed in the thermal properties at different volume fraction loadings. First, the structured composites exhibit an increase in their thermal conductivity as the filler content increases, regardless of the size ratio or the composition. This expected result has been observed and addressed in previous sections.

Second, all hybrid composites exhibit equal or higher thermal conductivity than their “monodisperse” counterparts (i.e., Ω = 0% and Ω = 100%). This is in agreement with the results of several studies reported in the literature [26, 31, 32]. The filler size hybridization leads to a higher particle packing density, which reduces the interfacial thermal resistance between fillers and contributes to forming more efficient thermally conductive pathways, thus resulting in higher-performing composites.

Third, and most important, the results suggest that Ω = 25%, corresponding to 25 vol% of smaller size particles, is the opti-

mal composition leading to the highest performing composites, regardless of their filler content or the size ratio. This size ratio is related to a higher filler packing density (i.e., filler packing density) achieved at Ω = 25%, in agreement with the theoretical models describing particle packing density [9, 33, 34]. Similar results were reported in the literature. Choi et al. investigated the thermal conductivity of unstructured epoxy composites with a binary-particle system consisting of alumina and aluminum nitride [8]. In their study, the highest thermal conductivities reported correspond to a composition of Ω = 30%, regardless of the filler content or the filler size ratio.

However, scientific studies reported in the literature investigating structured hybrid composites with binary-filler systems involve fillers with different form factors, such as fibers or whiskers. Thus, to verify that structured hybrid composites with spherical fillers follow a similar thermal behavior as their unstructured counterparts, a comparison between the two structure types was conducted at a 50 vol% filler content over the same range of compositions discussed above. Figure 6A,B presents the thermal conductivity of structured and unstructured composites as a function of their composition for both *k* ≈ 5 and *k* = 12 binary-particle systems, respectively.

The results show the expected increase in thermal conductivity for structured composites compared to their unstructured equivalents. This increase grows larger as the composition approaches the optimal value (i.e., Ω = 25%). Indeed, as the composition converges to the optimal point, the viscosity of the uncured composite decreases, facilitating a more complete and effective structuring process, which consequently results in a greater distinction between structured and unstructured configurations. Overall, both structure types follow similar trends in their thermal conductivities, with the peak value reached at Ω = 25%.

To assess the influence of the composition on the mechanical properties of binary particle size hybrid composites, compression tests were conducted at room temperature on structured PDMS-Al₂O₃ composites with compositions ranging from
<figure><img src="image_10.png" /><figcaption>**FIGURE 6** | Thermal conductivity of structured and unstructured composites as a function of their compositions: (A) PDMS-Al₂O₃ 140 µm and 30 µm (k ≈ 5), (B) PDMS-Al₂O₃ 60 µm and 5 µm (k = 12).</figcaption></figure>

<table><caption>**TABLE 3** | Summary of the estimated elastic moduli of PDMS-Al₂O₃ structured composites with various compositions (Ω).</caption><thead><tr><th></th><th>E<sub>compression</sub><br>(MPa)</th></tr></thead><tbody><tr><td>k ≈ 5 - Ω = 0%</td><td>1.06 ± 0.01</td></tr><tr><td>k ≈ 5 - Ω = 25%</td><td>1.80 ± 0.01</td></tr><tr><td>k ≈ 5 - Ω = 50%</td><td>1.58 ± 0.01</td></tr><tr><td>k ≈ 5 - Ω = 75%</td><td>1.27 ± 0.01</td></tr><tr><td>k ≈ 5 - Ω = 100%</td><td>1.35 ± 0.01</td></tr></tbody></table>

Ω = 0% to Ω = 100% and a size ratio of k ≈ 5.

Table 3 summarizes the estimated elastic moduli of PDMS-Al₂O₃ structured composites with various compositions (Ω). The results highlight a stiffer mechanical behavior in hybrid composites (i.e., Ω ranging from 25% to 75%) compared to the “monodisperse” composite (i.e., Ω = 0%, Ω = 100%). It outlines a stiffer mechanical response as Ω approaches its optimal values (i.e., Ω = 25%) as opposed to other suboptimal compositions. To numerically assess this evolution, linear curve fits at low strain values (i.e., between 15% and 20%) were used to estimate the elastic moduli of the various investigated composites.

Table 3 outlines similarities between the evolution of the elastic modulus and the thermal conductivity as a function of the composition, with a maximum value for Ω = 25%. In agreement with conclusions drawn from previous sections, this behavior might be related to increased filler packing density resulting in denser particle chains that act as stronger load-bearing reinforcements against compressive stress. Furthermore, optimal composition leads to a more effective filler structuring due to a lower viscosity. This may contribute even further to the formation of more efficient structures, thus increasing the stiffness of the composites. Interestingly, a composition of Ω = 75% yields a lower elastic modulus than the “monodisperse” Ω = 100% composite.

This could be related to the fact that such a composition is suboptimal, while simultaneously incorporating larger particles. The resulting mechanical behavior would not sufficiently involve any of the factors contributing to its enhancement (i.e., filler packing density and presence of smaller size fillers).

### 3.3 | Role of Size Ratio (k) on Thermal and Mechanical Properties

In this section, we will focus on the influence of the size ratio and its correlation with the composition on the thermal and mechanical properties of PDMS-Al₂O₃ composites, with a particular emphasis on structured composites. Size hybridization is most effective when the disparity in size between the particles is significant enough that smaller particles can settle into the interstitial spaces between larger ones without displacing them. Thus, the size ratio is a crucial aspect to study, as it can significantly influence the distribution and interaction of different filler sizes within the PDMS matrix, and ultimately affect the overall performance of the composite. By understanding the impact of the size ratio on these properties, we can gain valuable insights into the mechanisms governing the behavior of hybrid composites and further optimize their performance.

To systematically study the effect of this parameter, four size ratios ranging from k = 2 to k = 140 were considered, each investigated over different compositions ranging from Ω = 0% to Ω = 100%. For an accurate and representative comparison, all size ratios share the same larger size particles (i.e., 140 µm), acting as the backbone of the composite structure.

The primary objective is to uncover the optimal size ratio, as well as its optimal composition, in order to maximize composite properties. By examining the relationship between the size ratio and composition, we aim to provide a comprehensive understanding of their combined influence on the thermal and mechanical properties of PDMS-Al₂O₃ composites. This investigation will not only deepen our understanding of the underlying
<figure><img src="image_11.png" /><figcaption>**FIGURE 7** | Thermal conductivity of structured hybrid composites as a function of their composition for the various considered size ratios (k).</figcaption></figure>

mechanisms governing the properties of hybrid composites but also offer valuable guidance for the design of more complex and high-performing systems such as ternary size hybridization. To investigate the influence of size ratio on the thermal performance of hybrid composites, thermal conductivity measurements were conducted at room temperature on PDMS-Al₂O₃ structured composites, with a binary-filler system covering a wide range of particle size ratios and compositions. As a reference point, the best-performing size ratio was compared to its unstructured counterpart over the considered composition range. Figure 7 presents the thermal conductivity of structured composites as a function of the composition (Ω), for the various considered size ratios (k).

First, hybrid structured composites exhibit enhanced thermal conductivity compared to their monodisperse counterparts (i.e., Ω = 0% and Ω = 100%) As previously discussed, this is due to the higher packing density of hybrid composites, which enables the formation of more efficient thermally conductive pathways. Additionally, hybrid composites exhibit a lower viscosity, facilitating enhanced dielectrophoretic structuring and, consequently, leading to higher thermal conductivity. Furthermore, the findings emphasize the optimal compositions for each size ratio. As discussed in the previous section, for a size ratio of *k* = 5 and higher, the peak values of thermal conductivity are achieved at a composition of Ω = 25%, while a size ratio of *k* = 2 demonstrates optimal performance at a composition of Ω = 50%. This is related to the fact that the maximum filler packing density in every binary system is achieved at different compositions depending on the considered size ratio.

Lastly, at their respective optimal composition, binary-filler systems exhibit higher thermal conductivities as their size ratio increases, with *k* = 140 achieving up to 4.1 W/m.K, the highest value documented in this study. Indeed, as the size ratio increases, the maximum packing density attainable within that binary-filler system also increases. This enhancement yields more efficient thermal pathways, superior heat transfer, and ultimately improved thermal conductivity. A higher packing density further

results in a lower blend viscosity, higher particle mobility, and more complete filler structuring.

For a more comprehensive illustration of the impact of size ratio on the thermal properties of structured hybrid composites, Figure 8A presents the thermal conductivity as a function of size ratio, evaluated specifically at the optimal composition.

The thermal conductivity exhibits an initial rapid increase, from *k* = 1 to *k* = 5, followed by a more gradual evolution at high size ratios that appears to approach saturation. As previously discussed, this trend is also observed in the evolution of filler-packing density of binary systems as a function of their size ratio [35]. The filler-packing density greatly influences the filler distribution within the matrix as well as the viscosity of the uncured blend, leading to enhanced composite performance. It is noteworthy that exploring even larger size ratios (i.e., micrometric and nanometric fillers) may prove insightful, as it could uncover potential drawbacks associated with from such configurations, such as increased interfacial phonon scattering, where an excessive size ratio might become counterproductive.

Figure 8B depicts the thermal conductivity of both structured and unstructured composites as a function of their composition for a binary-filler system of *k* = 140 size ratio. The results show the expected increase in thermal conductivity for structured composites compared to their unstructured counterparts, regardless of their respective compositions. Additionally, the findings outline a similar behavior between the two structure types as a function of the composition. Due to improved filler packing density, the unstructured composites also appear to favor a Ω = 25% composition, as it yields higher thermal conductivity. However, this increase at the optimal composition is less prominent compared to the one exhibited by structured composites. This may be related to the decrease in blend viscosity, as it does not play any significant positive role in the case of unstructured composites. Thus, besides increased packing density, filler hybridization confers additional advantages to structured composites, as it enhances their structuring potential, and by extension, their overall properties.

Figure 9 reveals a pronounced dependence of the structuring efficiency on the fraction of smaller particles. When no hybridization is applied (Ω = 0%), the alignment already enhances the thermal conductivity by roughly 80%. Introducing a moderate amount of fine particles strongly amplifies this effect, with η reaching its maximum at Ω ≈ 25%, where the improvement exceeds 160%. Beyond this optimum, the efficiency decreases steadily with increasing Ω, falling to about 15% at Ω = 100%.

The dependence of the optimal fine-particle fraction on the size ratio is consistent with binary packing models and discrete element simulations. Classical [30, 33, 34, 36] predicts that the fine fraction required to maximize packing decreases as the size ratio increases. Our results follow this trend: for moderate ratios (k ≈ 2), the optimum occurs near Ω ≈ 50%, while for larger ratios (k ≥ 5) the optimum shifts toward Ω ≈ 25%. The agreement indicates that the observed thermal conductivity enhancements originate primarily from geometrical packing effects, complemented by the field-induced anisotropy that further improves contact density along the structuring direction. The origin of the optimum around
<figure><img src="image_12.png" /><figcaption>**FIGURE 8** | (A) Thermal conductivity as a function of size ratio for structured hybrid composites with a composition of Ω = 25% and a filler loading level of 50 vol%. (k = 1 corresponds to the larger-sized monodisperse composite, Ω = 0%) (B) Thermal conductivity as a function of composition of both structured and unstructured composites with a size ratio of 140 and a filler content of 50 vol%.</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>**FIGURE 9** | Structuring efficiency (η) of dielectrophoretically aligned composites as a function of the fine-particle fraction (Ω) at a total filler loading of 50 vol% and a particle size ratio of k = 140.</figcaption></figure>

Ω ≈ 25% for k ≥ 5 can be rationalized by considering the formation of a percolative thermal network. At this composition, small particles efficiently occupy the interstitial voids between larger ones, maximizing the packing density and contact number. As a result, both the number of thermally conductive pathways and the mechanical load transfer between fillers are enhanced. For higher Ω values, excessive fine particles hinder alignment and increase interfacial resistance, while for lower Ω values the voids remain unfilled, reducing network connectivity. This network-based view provides a quantitative structural rationale for the experimentally observed optima in thermal conductivity.

This behavior indicates that a limited addition of smaller particles effectively fills the voids between larger ones, thereby improving packing density and enhancing the continuity of the thermally

<table><caption>**TABLE 4** | Summary of the estimated compression moduli of hybrid composites with various size ratios (k).</caption><thead><tr><th></th><th>E<sub>compression</sub><br>(MPa)</th></tr></thead><tbody><tr><td>k ≈ 2 - Ω = 25%</td><td>2.9 ± 0.01</td></tr><tr><td>k ≈ 5 - Ω = 25%</td><td>1.8 ± 0.01</td></tr><tr><td>k = 28 - Ω = 25%</td><td>3.2 ± 0.01</td></tr><tr><td>k = 140 - Ω = 25%</td><td>1.5 ± 0.01</td></tr></tbody></table>

conductive network under dielectrophoretic alignment. However, excessive amounts of fine particles tend to disrupt the chain-like structures formed by the larger fillers and introduce additional interfaces, which diminish the benefits of alignment. The resulting bell-shaped trend highlights the critical role of particle size distribution in maximizing the synergy between hybridization and field-induced structuring.

To assess the influence of size ratio on the mechanical properties of hybrid structured composites, compression tests were conducted on binary-filler systems with size ratios ranging from 2 to 140, specifically at their optimal composition. Results suggest no clear visual trend regarding the mechanical behavior of hybrid structured composites as a function of their size ratio. In order to numerically compare the various analyzed composites, linear curve fits at low strain values (i.e., between 15% and 20%) were utilized to estimate the elastic moduli of those composites, as summarized in Table 4.

The findings reveal an inconclusive trend of the elastic modulus as a function of the size ratio, where the highest value is recorded at k = 28, while the lower value is reported for k = 140. It is important to note that characterizing the influence of the size ratio (k) is less straightforward than that of filler composition (Ω). Indeed, unlike the filler composition (Ω), the
size ratio (k) involves various systems composed of diverse
particles sizes potentially exhibiting different interactions and
bonding strengths with the polymer matrix. Furthermore, the
fixed composition at which the size ratio is being investigated
might also play a role in the outcome, as these two parameters
are closely interconnected. Ideally, following the conclusions
reached in previous sections, the elastic modulus of structured
hybrid composites should increase with the increasing size
ratio, as the filler packing density increases and the viscosity
decreases, leading to the formation of denser and more efficient
structures. Moreover, higher size ratios are also composed of
smaller size fillers, which promotes stronger interfacial bond-
ing with the matrix, further increasing the stiffness of the
composite.

4 | Conclusions

This study thoroughly investigated the dielectrophoretic struc-
turing of hybrid thermally conductive composites, highlighting
the influence of filler size hybridization on the thermal, and
mechanical properties of PDMS-Al₂O₃ composites. The results
demonstrate significant advantages in terms of filler packing den-
sity, thermal conductivity, and mechanical properties of hybrid
structured composites compared to their monodisperse counter-
parts. The thermal conductivity of hybrid composites showed
a significant increase, up to 66%, compared to monodisperse
PDMS-Al₂O₃. This improvement is attributed to increased filler
packing density and more efficient structuring. The mechanical
performance of hybrid composites exhibits a stiffer response
under high compressive loads due to better filler structuring.
The study also revealed that the optimal composition, with 25
vol% smaller particles, provides the best thermal properties.
The findings underscore the potential of size hybridization and
dielectrophoretic structuring in developing advanced composite
materials for thermal management, with future research needed
to address environmental challenges and explore alternative
polymeric matrices.

Acknowledgements

This study was funded by the ANRT under grant number Cifre
n°2019/1046 and supported by the Carnot Institute I@L.

Conflicts of Interest

The authors declare no conflicts of interest.

Data Availability Statement

The data that support the findings of this study are available from the
corresponding author upon reasonable request.

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