# Optimization of structural and poling strategies in piezoelectric elastomer composites for soft sensing applications

Tasnim Missaoui, Xavier P Morelle, Minh Quyen Le, Pierre-Jean Cottinet, Jean-Fabien Capsal, Guilhem Rival

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## ► To cite this version:

Tasnim Missaoui, Xavier P Morelle, Minh Quyen Le, Pierre-Jean Cottinet, Jean-Fabien Capsal, et al. Optimization of structural and poling strategies in piezoelectric elastomer composites for soft sensing applications. Materials & Design, 2026, 262, pp.115457. 10.1016/j.matdes.2026.115457. hal-05450066

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# Optimization of structural and poling strategies in piezoelectric elastomer composites for soft sensing applications

Tasnim Missaoui<sup>a,b</sup>, Xavier P. Morelle<sup>a,c</sup>, Minh Quyen Le<sup>b</sup>, Pierre-Jean Cottinet<sup>b</sup>,
Jean-Fabien Capsal<sup>b,d</sup>, Guilhem Rival<sup>b,* e</sup>

## ARTICLE INFO

### Keywords:

- Biomedical applications

- Dielectrophoresis

- Electromechanical coupling

- Piezoelectric composites

- Structure/properties relationships

## ABSTRACT

Piezoelectric flexible sensors are emerging as key components in medical applications, offering unique electro-mechanical properties for various diagnostic and therapeutic purposes. In this study, ceramic-filled silicone composites were developed as high-performance piezoelectric materials suitable for soft biomedical sensing applications. To enhance their electromechanical response, a multi-parametric design strategy was adopted, combining three approaches: the use of bimodal particle size distribution and the dielectrophoretic alignment of these particles within the matrix, supported by an optimized poling process. Results revealed that composites with an oriented particle distribution, consisting of 25 % of micro-sized particles and 75 % of nano-sized particles exhibited significant improvements in piezoelectric coefficient ($d_{33}$) compared to composites with randomly distributed particles. Additionally, the piezoelectric transverse coefficient ($d_{31}$) was significantly improved under in situ poling conditions, particularly in nano-rich and hybrid systems. These findings underline the potential of combining particle alignment, size hybridization, and poling optimization in enhancing the performance of piezoelectric composites for innovative medical sensor applications.

## 1. Introduction

Flexible sensors have gained significant interest in the biomedical field due to their potential for application in medical diagnostics, human health monitoring, or artificial organ systems [1–3]. Among these, piezoelectric materials are particularly promising in the realm of medical applications where real-time biomechanical feedback is required. Their inherent electromechanical coupling enables them to convert mechanical stimuli into electrical signals and, conversely, to generate mechanical deformation in response to an electric field [4]. This dual functionality makes them ideally suited for integration into medical devices and platforms designed to interface with dynamic physiological environments [5–7].

Recent advancements in piezoelectric biomaterials have led to the development of innovative prosthetic implants, biosensors and scaffolds for tissue regeneration [8,9]. Considering that mechanical pressure arising from external forces or internal physiological processes are critical parameters in diagnosing health conditions and anticipating

injuries, these materials offer opportunities for real-time health monitoring, critical threshold detection and therapeutic interventions.

Piezoelectric materials fall into three main categories: ceramics, polymers, and composites [10,11]. Ceramic materials can be either lead-based (e.g., lead zirconate titanate, PZT) or lead-free (e.g., barium titanate, BaTiO₃ and sodium potassium niobate, KNN). These materials are widely used due to their high piezoelectric coefficient, chemical and thermal stability [12,13]. However, their inherent brittleness and stiffness limit their integration into soft biological environments, and concerns about the cytotoxicity of lead-based ceramics further restrict their biomedical applications. Consequently, piezoelectric polymers have emerged as a more suitable alternative for external use and integration into biological environments. Examples include polyvinylidene fluoride (PVDF) and its copolymers, as well as biodegradable and biocompatible polymers such as poly-lactic acid (PLLA) offer flexibility, biocompatibility, and processability [14,15]. Nonetheless, their electromechanical performance remains significantly lower than that of ceramics.

To address the limitations of bulk ceramics and polymers,

<footnote><sup>a</sup> Laboratoire Ingénierie des Matériaux Polymères, Université Claude Bernard Lyon 1, INSA Lyon, Université Jean Monnet, CNRS UMR 5223, F-69621 Villeurbanne, France</footnote>

<footnote><sup>b</sup> LGEF, INSA-Lyon, UR682, Université de Lyon, F-69621 Villeurbanne, France</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail address: guilhem.rival@insa-lyon.fr (G. Rival).</footnote>
piezoelectric composites, combining both, have emerged as a promising alternative. These composites can successfully combine the high piezoelectric coefficients of ceramic particles with the inherent flexibility of polymers, offering a versatile solution for biomedical applications, notably wearable health devices and implantable medical devices used for health monitoring [16–18].

By optimizing the combination of filler and matrix, composites can be tailored to meet diverse end-user requirements. The remarkable feature of piezoelectric composites lies in the ability to tailor their properties by adjusting the volume fraction, spatial configuration, or distribution of the filler content. A common strategy to enhance the piezoelectric response involves increasing the filler volume fraction [19,20]. However, this approach can alter the composite's mechanical response and impose limitations on its flexibility, as well as adding technical challenges for the fabrication process. An alternative and effective solution is to optimize the arrangement of the phases, referred to as connectivity, which significantly influences the performance of these composites [21]. Among various connectivity patterns, the 1–3 configuration has demonstrated superior piezoelectric properties, as it represents the organization of particles into column-like structure comparing to a 0–3 connectivity in which particles are randomly dispersed. The 1–3 configuration can be obtained using the dielectrophoresis technique, wherein non-uniform electric fields induce the alignment of polarized particles before and during the curing of the polymer matrix, promoting precise control over the spatial distribution and orientation of the ceramic phase, therefore enhancing the piezoelectric properties without overloading the matrix with filler [22–24]. In addition to orienting the filler distribution through dielectrophoresis, some studies have shown that filler surface functionalization could enable an extra gain in piezoelectric response [3,18].

Another approach to further enhance performance involves introducing multimodal particle size or shape distributions to optimize the electric field distribution within the column-like structure, formed through dielectrophoresis [25–27]. Studies have shown that the polydispersity of ceramic particles can improve packing density, which in turn enhances piezoelectric properties. Specifically, carefully selected ratios of particle sizes or shapes can achieve maximum packing density, a condition under which structural and functional properties, such as piezoelectric response, may reach their optimal values [28]. This strategy leverages the synergistic effect of particle size distribution on electric field homogeneity and compaction, ultimately advancing the overall performance of piezocomposites.

In this study, lead free ceramic-filled silicone composites with bimodal particle size distribution, consisting of random and aligned particles within a polymer matrix, were developed through a tailored fabrication process. The main objective being to demonstrate that optimizing the applied design strategies can significantly enhance the piezoelectric response of composites. While this work does not try to out-perform the best performing piezoelectric sensors available today, it focuses on the implementation of advanced techniques to optimize particle arrangement in order to improve the resulting functional properties. These piezoelectric composites are specifically engineered for potential integration into an experimental artificial vascular network model, enabling advanced monitoring of mechanical deformations in artificial arteries.

## 2. Materials and experimental procedures

### 2.1. Materials

This study involves the development of polydimethylsiloxane (PDMS)-based composites with Barium Titanate (BaTiO₃) particles to design materials suitable for use in health monitoring systems. The matrix is a Sylgard 184 silicone elastomer purchased from Dow, Inc., consisting of two parts; the prepolymer and the curing agent with a ratio of 10:1. Two BaTiO₃ particle references with different sizes were used to

investigate the effect of particle size on composite properties. The nano-sized BaTiO₃, averaging 500 nm in diameter and having a density of 5.85 g.cm⁻³, was acquired from Inframat®. The micro-sized BaTiO₃ particles with an average diameter of 2.0 µm and a density of 6.08 g.cm⁻³, was purchased from Sigma Aldrich. Fig. 1 displays the scanning electron microscopy (SEM) images of both particle references, from which particle sizes were quantified using ImageJ software.

It should be noted that apparent clustering of particles on the SEM images is a result of the sample preparation process, involving a mixture of ceramic particles with a solvent followed by the solvent evaporation. This visual effect is therefore attributed to the high ratio of particles in the mixture, rather than an intrinsic tendency of the particles to agglomerate. Hereafter, ceramic particles with a size of 0.5 µm and 2.0 µm will be referred to as n-BT (nano-BT) and µ-BT (micro-BT) respectively.

### 2.2. Preparation procedure of BaTiO₃/PDMS composites

The composites were prepared with a total filler content of 20 vol%. Five formulations were prepared by varying the proportions of large (µ-BT) and small (n-BT) BaTiO₃ particles.

To facilitate the presentation and understanding of the results, a filler composition factor, denoted as Ω, is defined in this study. The factor Ω, as shown in Eq. (1), represents the ratio of the volume fraction of µ-BT to the total filler content, allowing a quantitative characterization of the bimodal particle size distribution.

$$ \Omega (\%) = \frac{\%vol(\mu-BT)}{\%vol(\mu-BT) + \%vol(n-BT)} \times 100 \quad (1) $$

The spatial distribution of particles within the matrix also varies, with two configurations: a random distribution and a column-oriented distribution along the composite's thickness. Thus, a set of 10 samples (Table 1), varying either in filler content or spatial configuration within the matrix, was obtained.

The elaboration process is schematized in Fig. 2. The particles were first mixed with the prepolymer, then dispersed by ultrasonic stirring, using a UP400S Hielscher ultrasonic processor, for better dispersion within the polymer (Fig. 2.a). Subsequently, the curing agent was added to the blend, and the mixture was thoroughly stirred to ensure homogeneity. All steps were carried out at room temperature and the overall process lasted approximately two hours.

The obtained slurry was initially placed in a Memmert vacuum oven at room temperature under its minimum pressure of 9 mbar for a first degassing step. It was then poured into a rectangular 50 mm × 80 mm epoxy mold and subjected to a second degassing step in the vacuum oven under the same conditions, to ensure the complete removal of trapped air brought by the previous mixing and pouring steps.

Following in the composite preparation, the slurry was thermally processed using two different protocols to achieve the previously described filler distributions. For the first protocol, designed to produce a random distribution of ceramic particles, the slurry-filled mold was covered with an epoxy plate and subjected to 100 °C for 3 h.

The second protocol, which involves the dielectrophoresis process, targeted a composite structure with a 1–3 connectivity. In this case, a voltage amplifier (Ampli HT TREK Tech 20/20) and a waveform generator (Agilent 33220 A) supplied an alternating voltage (AC) with an amplitude of 3 V.µm⁻¹ and a frequency of 1 Hz for 30 min, with the sample initially still held at room temperature. As illustrated in Fig. 2.d, two copper-coated epoxy plates served as electrodes, to apply the electric field during the process. The non-uniform electric field created by the applied alternating voltage interacts with ceramic particles, inducing their polarization.

As a result, the polarized particles experience a dielectrophoretic force that drives them toward regions of higher field intensity. This phenomenon aligns the particles along the field lines, leading to the
<figure><img src="image_4.png" /><figcaption>**Fig. 1.** SEM images and particle size distribution of Barium Titanate particles with an average size of (a) 0.5 µm (b) 2.0 µm. On the right-hand images, the lines are drawn as guides for the eye, while dots are experimental points.</figcaption></figure>

<table><caption>**Table 1**
Filler proportions for composite formulation.</caption><thead><tr><th rowspan="2">Composition Ω (%)</th><th colspan="2">Fraction of ceramic particles (%)</th></tr><tr><th>μ-BT (2.0 μm)</th><th>n-BT (0.5 μm)</th></tr></thead><tbody><tr><td>0</td><td>0</td><td>100</td></tr><tr><td>25</td><td>25</td><td>75</td></tr><tr><td>50</td><td>50</td><td>50</td></tr><tr><td>75</td><td>75</td><td>25</td></tr><tr><td>100</td><td>100</td><td>0</td></tr></tbody></table>

formation of column-like structures oriented in the direction of the applied electric field, that is, along the composite's thickness [29]. The low frequency of 1 Hz ensures sufficient time for particle movement and alignment within the yet uncured polymer matrix. Afterwards, the temperature was gradually increased to 100 °C and maintained for 3 h to cure the slurry. It is worth noting that the parameters related to the dielectrophoresis were chosen following a previous study that optimized this process by varying the AC amplitude and frequency, identifying 3 V.µm⁻¹ and 1 Hz as the most effective combination for enhancing structural anisotropy in BaTiO₃-filled silicone composites [30].

## 2.3. Poling process

To induce macroscopic polarization and activate piezoelectric behavior, BaTiO₃ particles within the composite must undergo a poling process. This procedure entails the application of an external electric field that enables the orientation of internal dipoles of particles along the electric field direction, giving the piezoelectric composite a semi-permanent polarization and piezoelectric properties [31]. During this process, gold electrodes were sputtered on circular samples by means of a Cressington 208 HR sputter coater. Then, coated samples were poled

for 30 min under a direct electric field (DC) with an amplitude of 25 V.µm⁻¹ at 80 °C. Such high temperature was chosen to enhance the mobility of polar domains within the piezoelectric phase [30]. Subsequently, the sample was cooled to room temperature under the same applied electric field to ensure a remanent polarization. As shown in Fig. 3, this process took place in a silicon oil bath to avoid possible dielectric breakdown. Note that the protocol described herein corresponds to the reference procedure, while an optimized and updated version will be proposed and thoroughly described in Section 4.4.

# 3. Characterization techniques

## 3.1. Characterization of piezoelectric effect

After poling, the piezoelectric charge coefficient $d_{33}$ was determined using a Piezometer PM300 commercialized by PiezoTest, Singapore, choosing the very low range values sensitivity mode (i.e. enabling measuring values from 0 to 10 pC/N with an accuracy of ±2 % and ±0.01 pC/N). The working mechanism is referred to as “Berlincourt” method which consist of clamping the sample and subjecting it to a low frequency force. The resulting piezoelectric charge coefficient is directly displayed by the device. In this study, a sinusoidal force of 0.25 N was applied at a frequency of 110 Hz. This force was oriented along the same axis as the alignment direction of the polarized ceramic particles within the composite, enabling the measurement of the longitudinal piezoelectric response.

The influence of composite composition and elaboration process on transverse piezoelectric coefficient $d_{31}$ was investigated as well. Fig. 4 shows a schematic representation of the experimental setup used for this purpose. A picture of the experimental setup can be found in Supplementary Information (Figure SI.1.a). In this case, the gold sputtered samples were cut into rectangular strips with the following dimensions
<figure><img src="image_5.png" /><figcaption>Fig. 2. Illustration of the piezoelectric composite preparation procedure (a) Mixing of composite components (b) Degassing in vacuum oven (c) Curing of random filler distribution composites (d) Curing and structuring of composites.</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>Fig. 3. Schematic presentation of the reference poling procedure.</figcaption></figure>

$$60 \times 10 \times 0.3 \text{ mm}^3.$$

Sample is tightened on one side with a fixed clamp and the other side with a mobile clamp. Both clamps being mounted on a Newport translating table with a motion controller (XPS) and a 10 N force sensor. The

sample was placed between two electrodes screw-fastened to the moving part of the setup and was connected to a charge meter and DEWE® card to record the generated charge during the applied dynamic loading. In this configuration, a triangular waveform was applied to induce cyclic uniaxial nominal strain ranging from 1 % to 15 % were at a 1 Hz frequency. The proportionality between charge output and applied force has been verified in order to be able to determine the transverse piezoelectric coefficient $d_{31}$. Data can be found in Supplementary Information (Figure SI.1.b).

## 3.2. Broadband dielectric spectroscopy

The characterization of dielectric properties of the matrix (PDMS) and the developed composites (PDMS/BaTiO$_3$) was done with a Novocontrol Broadband Dielectric 4000 spectrometer consisting of a precision impedance analyzer associated with data acquisition software. Measurements were conducted at room temperature over a wide range of frequencies, from $10^{-1}$ to $10^6$ Hz. The values of complex relative

<figure><img src="image_7.png" /><figcaption>Fig. 4. Illustration of the setup used to measure the electric charge generated under mechanical deformation perpendicular to the direction of polarization.</figcaption></figure>
permittivity $\epsilon_r^*$ are determined from complex impedance $Z^*$ using to the following equation:

$$ \epsilon_r^* = \epsilon_r' - i\epsilon_r'' = \frac{e}{i\omega\epsilon_0SZ'} \quad (2) $$

where e denotes the sample thickness (in m), S is the sample surface (in m²), ω is the angular frequency (in rad/s), ε₀ is the vacuum permittivity (≈ 8.85 × 10⁻¹² F·m⁻¹), and ε' and ε'' are the real and the imaginary parts of the relative permittivity, respectively.

### 3.3. Scanning electron microscopy (SEM)

To determine the average size of the ceramic fillers, a FlexSEM 1000II scanning electron microscope (SEM) was used. BaTiO₃ powder was dispersed in an ethanol solvent, and a small amount of this suspension was carefully placed on a double-sided carbon tape mounted on the SEM support to prepare the sample for imaging. Additionally, SEM observations of composite cross-sections were conducted to assess the alignment and distribution of ceramic fillers within the silicone matrix. For accurate cross-sectional imaging, the samples were cryo-fractured in liquid nitrogen, ensuring clean and straight cuts to preserve the internal structuring of the composite.

## 4. Results and discussion

### 4.1. Microstructural analysis of piezocomposites via SEM

Fig. 5 illustrates cross section SEM pictures of cryo-fractured composites with a filler composition factor of Ω = 50 %, corresponding to an equal ratio of large to small particles, exhibiting 0–3 and 1–3 connectivity. A clear difference can be noticed in the microstructural morphology of each composite based on particles distribution. In Fig. 5, a, the composite with 0–3 connectivity displays well dispersed yet random distribution of ceramic particles. On the other hand, the composite with 1–3 connectivity (Fig. 5.b) illustrates a distinct column-like structure that emerges despite the non-linear spacing between columns. This observation align with previous studies highlighting the impact of dielectrophoresis on the configuration of ceramic fillers in composites [30,32]. It is expected to significantly improve the piezoelectric performance of the composite, which will be explored in detail in the following sections.

### 4.2. Dielectric analysis of PDMS/BaTiO₃ composites

Broadband Dielectric spectroscopy measurements were carried out at room temperature as explained in subsection 3.2 to study the impact of both filler hybridization and orientation on the dielectric properties of the resulting composites. Dielectric loss data (tanδ) can be found in the Supplementary Information (Figure SI.2). All samples were investigated over a frequency range of [10⁻¹ Hz; 10⁶ Hz] under which two main

phenomena can be revealed. The first phenomenon typically occurs at low frequencies, ranging approximately from a few hertz up to several tens of kilohertz, and is associated with electrode and interfacial polarization. It involves the accumulation of charges at the interface between electrodes and the material or between different materials, known as the Maxwell-Wagner-Sillars effect (MWS), which leads to an increase in the real part of the relative permittivity within this frequency range. Higher frequencies are rather associated to polar or orientational polarization during which polar groups attempt to align with the alternating electric field [32,33].

Fig. 6 presents the real part of the relative permittivity ($\epsilon_r'$) of 10 composites varying in composition and filler orientation along with that of the unfilled PDMS matrix, referred to in the graph as PDMS.

A common general pattern with frequency for the evolution of the real part of the relative permittivity ($\epsilon_r'$) can be noticed. For low frequencies, relatively high values of permittivity are measured due to the contributions from interfacial and electrode polarization, where slower polarization mechanisms can follow the applied electric field effectively. As the frequency increases, $\epsilon_r'$ gradually decreases, reflecting the reduced ability of dipoles to align with the more rapidly oscillating field. This trend continues up to 10⁶ Hz, where polarization effects become minimal, stabilizing the permittivity response at lower values.

This behavior is less obvious for unfilled PDMS revealing a rather low and to some extent quite stable $\epsilon_r'$ along the studied frequency range.

<figure><img src="image_8.png" /><figcaption>Fig. 6. Real part of the relative permittivity as a function of frequency of monodisperse and hybrid composites with oriented and random filler distribution, measured at room temperature. The response of the reference unfilled PDMS matrix is shown with black hexagons.</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>Fig. 5. SEM images of the cross-sections of composites with a composition factor Ω = 50 % with (a) 0–3 connectivity (b) 1–3 connectivity. Yellow arrow indicates the direction of the applied electric field along the thickness of the composite.</figcaption></figure>
This stability arises from the lack of polar functional groups in its molecular structure, which limits the material's response to dipolar polarization mechanisms. Its permittivity is rather associated with electronic polarization, a process that only becomes significant at very high frequencies (above $10^6$ Hz). Consequently, unfilled PDMS demonstrates a relatively constant permittivity across the dielectric spectroscopy range considered in this study.

However, when $BaTiO_3$ fillers are introduced into the matrix, $\epsilon'_r$ increases substantially, regardless of fillers composition. This increase can be attributed to the inherently high permittivity of $BaTiO_3$, often reaching 1000 comparing to 2.7 ~ 3 for PDMS matrix [33,34]. Embedded high-permittivity particles form localized regions with high polarizability, which effectively increases the overall capacity of the composite to store electric energy when an external electric field is applied. Additionally, the dielectric contrast between the polymer matrix and ceramic particles induces interfacial polarization, due to the build-up of charges at their interfaces, which further contributes to an overall increase in the real part of permittivity of the composite [35].

Moreover, beyond the inherent contributions of adding $BaTiO_3$ particles, orienting the particles along the cross-section direction of the composite nearly double its permittivity, as illustrated in Fig. 6. This significant enhancement is even more visualized at 1 kHz in Fig. 7 illustrating the dependence of the real part of relative permittivity on the orientation of fillers in the matrix. This orientation effect likely results from the creation of efficient pathways for electric dipoles, inducing better charge displacement and stronger dipole interactions across the composite. Moreover, The alignment of particles is expected to reduce voids and improve particle packing density along the filler columns which contributes to the enhancement of the composites dielectric response [30,36].

The hypotheses explaining the variations of permittivity can be further corroborated by comparable results reported in previous studies. For instance, D'Ambrogio et al. [30] highlighted an enhancement of the real part of relative permittivity of $BaTiO_3$/PDMS composites compared to unfilled PDMS, attributed to the significant difference in permittivity between the components. Additionally, their study reported that columnar configuration of $BaTiO_3$ particles reduces matrix shielding effect, enabling more efficient interaction with the applied electric field. Also, the dielectric response of 1–3 composites was well fitted with the model proposed by Bowen et al. [37] predicting the dielectric behavior of 1–3 structured composites via dielectrophoresis. According to this model, the dielectric behavior is estimated to be proportional to the ratio of the average particle size to the interparticle distance, which is

<figure><img src="image_10.png" /><figcaption>Fig. 7. Comparison of the real part of relative permittivity at 1 kHz of 0–3 and 1–3 composites with varying particle size fractions.</figcaption></figure>

expected to increase when particles are organized into columns. Similar outcome has been stated for composites featuring columnar filler configurations, such as Zinc oxide (ZnO) particles in a PDMS matrix [38]. In such systems, the columnar arrangement was found to facilitate the formation of continuous dielectric networks, thereby improving the dielectric properties of the composite.

### 4.3. Piezoelectric analysis of $BaTiO_3$/PDMS composites

#### 4.3.1. Direct piezoelectric response

The piezoelectric response of the developed composites was investigated by the determination of the piezoelectric charge coefficient ($d_{33}$) and the piezoelectric voltage coefficient ($g_{33}$). The $d_{33}$ coefficient quantifies the amount of charge generated by the composite under mechanical stress applied in the same direction which is usually compression, and it is expressed in charge per force unit ($pC \cdot N^{-1}$). On the other hand, the $g_{33}$ coefficient represents the electric field produced by unit of mechanical stress ($mV \cdot m \cdot N^{-1}$) reflecting the material's ability to function as a sensor or a voltage generator under stress. It is particularly significant as it combines both piezoelectric and dielectric properties, making it a widely used metric in literature. It is determined as a function of $d_{33}$ and is inversely proportional to the material's relative permittivity, as defined by the following formula:

$$g_{33} = \frac{d_{33}}{\epsilon_0 \times \epsilon'_r} \qquad (3)$$

With $\epsilon_0$ the vacuum permittivity (in $F \cdot m^{-1}$) and $\epsilon'_r$ the relative permittivity of the composite measured at 1 kHz.

#### 4.3.2. Effect of connectivity (0–3 and 1–3)

Fig. 8 illustrates the dependence of the piezoelectric properties on the composition of particles and their distribution within the matrix. Results show that whether the composite is hybrid or monodisperse, the $d_{33}$ increases significantly for composites exhibiting a 1–3 connectivity (Fig. 8.a), with values increasing from two-fold to nearly five-fold, depending on the particle composition. This enhancement is attributed to the optimized organization of ceramic particles into a columnar configuration achieved through dielectrophoresis, promoting an efficient electric field-dipole interaction. In this arrangement, the particles form nearly compact columns, resulting, as discussed in section 4.2, in an optimized electric field distribution across the active piezoelectric phase.

As depicted in Fig. 8.b, the piezoelectric voltage coefficient $g_{33}$ also increases significantly with particle alignment, reaching values up to four times higher than those measured in composites with 0–3 connectivity. This dual improvement in both $d_{33}$ and $g_{33}$ confirms the high impact of filler orientation on the electromechanical performance of $BaTiO_3$/PDMS composites.

Similar trends have been highlighted in literature, particularly for PDMS/$BaTiO_3$ composites, where dielectrophoretic alignment led to a threefold increase of the piezoelectric coefficient up to $8 \cdot pC \cdot N^{-1}$ at 24 vol% filler content. Higher values have been achieved in flexible composites incorporating larger fractions of lead-based ceramic fillers [26,39,40], as well as in rigid systems such as epoxy-based composites, though these improvements often come at the expense of mechanical flexibility [41–43]. Therefore, the piezoelectric performance obtained in the present study is particularly noteworthy given the use of a highly flexible matrix and moderate filler content. This favorable balance between electromechanical functionality and mechanical compliance makes the composites developed here highly suitable for applications requiring soft integration, such as health monitoring of vascular systems.

#### 4.3.3. Effect of the bimodal distribution of particles

The piezoelectric charge coefficient $d_{33}$ for composites with 0–3
<figure><img src="image_11.png" /><figcaption>Fig. 8. (a) Piezoelectric charge coefficient $d_{33}$ (b) Piezoelectric voltage coefficient $g_{33}$ as a function of the particle size distribution for hybrid and monodisperse composites.</figcaption></figure>

connectivity is noted to increase modestly as the volume fraction of larger particles (2.0 µm), represented by Ω(%), increases up to 25 % (Fig. 8.a) but remains low, averaging around 1 pC·N⁻¹. Similar trend is observed for the piezoelectric voltage coefficient $g_{33}$ where a maximum is reached for the same combination with a value around 16 mV·m·N⁻¹.

This behavior can be attributed to the inherent limitations of the 0–3 connectivity. Despite a bimodal distribution, that theoretically enables smaller particles to fill interstitial spaces between larger ones, the particles may remain to some extent isolated by the matrix. As a matter of fact, the random spatial configuration of ceramic particles likely hinders an optimal electromechanical coupling. More specifically, during the $d_{33}$ measurement, the lack of particle alignment would attenuate piezoelectric response to a mechanical stimulus, thereby restricting the effective charge generation.

As previously discussed, composites with 1–3 connectivity exhibit a pronounced enhancement in the piezoelectric charge coefficient compared to their 0–3 connectivity counterparts, and the effect of a bimodal particle composition is even more striking in this aligned spatial configuration. Interestingly, this increase reaches its maximum for Ω = 25 %, as depicted in Fig. 9, with a fivefold increase comparing to random hybrid distribution and up to twofold increase comparing to composites

with monodispersed oriented particle distribution.

This major improvement can be related to an optimized packing density of particles within the polymer matrix, achieved by the bimodal particle size distribution. As illustrated schematically in Fig. 10, introducing particles with a different size into a monodisperse distribution would allow small sized particles to occupy the interstitial voids between larger ones, thereby increasing the overall packing density of the composite [44].

However, this effect is not linear: an optimum ratio of large to small particles exists, at which the packing density reaches a maximum. Beyond this optimum, the packing efficiency decreases due to either insufficient void filling or excessive dominance of one size fraction. Such an optimum packing scenario provides a consistent explanation for the enhanced piezoelectric response observed at Ω = 25 %, since improved packing density along dielectrophoretically aligned ceramic columns facilitates more homogeneous field distribution, more efficient poling and ultimately higher piezoelectric response.

Note that previous studies addressing packing density have focused on granular bulk systems and very highly filled composites. In the case of bimodal distribution, theoretical models stated that the maximum packing density is governed by the shape, size ratio and volume fraction of particles. For instance, discrete element method (DEM) simulations

<figure><img src="image_12.png" /><figcaption>Fig. 9. Comparison of $d_{33}$ of monodisperse and hybrid composites with Ω = 25 %.</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>Fig. 10. Schematic representation of packing density as a function of particle size distribution, illustrating an optimum fraction of large and small particles. In this representation, particles are assumed to be spherical [45].</figcaption></figure>
have shown that ellipsoidal particles with a size ratio higher than 10 achieve optimal packing at a volume fraction of 75/25 % of large-to-small particles. As for spherical particles, an optimum was reached with a size ratio of 2.5 and a volume fraction of 50/50 % of large to small particles. Moreover, the packing density in composites with 81 vol% of magnetic particles in polyphenylene sulfide (PPS), was reached with a size ratio around 30 and a volume fraction of 40/60 % of large to small particles [45–47]. While prior research on granular bulk systems have identified optimal packing densities in bimodal mixtures with mostly large particles, results in this current study on BaTiO₃/PDMS composites with 1–3 connectivity reveal an inverted optimum with 25 % large and 75 % small particles at a 4.4 size ratio. This contrast highlights the decisive role of particle orientation and matrix-mediated electromechanical coupling, which shift the optimal balance beyond what is predicted from purely geometric packing considerations.

Overall, these results underscore the importance of controlling particle size distribution and configuration for an effective design of composite materials. Achieving an optimized balance between particle sizes within a columnar configuration significantly enhances the piezoelectric response of ceramic-filled composites. This improvement is attributed to the synergistic effect of smaller particles filling voids created by larger particles, thereby maximizing packing density, while the columnar arrangement ensures a more efficient and oriented pathway for the electric field.

### 4.3.4. Transverse piezoelectric response

In the same lane, the transverse piezoelectric charge coefficient ($d_{31}$) was investigated for random and oriented ceramic particles at different strain values. This coefficient quantifies the amount of charge generated by the composite under mechanical strain applied in the perpendicular direction to that of the particle’s orientation, and it is expressed in charge per force unit (pC·N⁻¹), and it was estimated as following:

$$d_{31} = \frac{Q/S_{\text{active}}}{F/S} \qquad (4)$$

where Q is the electric charge (in C), F is the applied force (in N), $S_{\text{active}}$ and S denote the gold sputtered surface and the cross-sectional area of the sample respectively (in m²).

It should be noted that this coefficient is often considered more representative for sensor applications where mechanical deformation or vibration occurs perpendicular to the polarization direction.

The transverse piezoelectric response $d_{31}$ was evaluated for composites with oriented (1–3) and randomly (0–3) distributed ceramic particles. The corresponding values under 15 % uniaxial strain are presented in Table 2. A remarkable enhancement is observed for the 1–3 composites, whose $d_{31}$ values are almost systematically five times greater than those of the 0–3 composites. This indicates that, even when the applied strain is perpendicular to the particle alignment direction, the oriented structure promotes dipole activation and charge generation in the transverse direction.

This enhancement can be explained by considering the mechanical and structural anisotropy introduced by particle orientation. When subjected to uniaxial longitudinal strain, the piezoelectric composite encounter lateral compression, considering the near-incompressible

<table><caption>**Table 2**
Transverse piezoelectric charge $d_{31}$ coefficient as a function of the combination and the particle distribution at 15 % applied strain.</caption><thead><tr><th rowspan="2">Composition Ω (%)</th><th colspan="2">d<sub>31</sub> [pC·N<sup>-1</sup>]</th></tr><tr><th>Random distribution</th><th>Columnar oriented distribution</th></tr></thead><tbody><tr><td>0</td><td>0.44</td><td>1.80</td></tr><tr><td>25</td><td>0.22</td><td>1.50</td></tr><tr><td>50</td><td>0.40</td><td>1.76</td></tr><tr><td>75</td><td>0.23</td><td>1.59</td></tr><tr><td>100</td><td>0.30</td><td>1.20</td></tr></tbody></table>

behavior of PDMS matrix (Poisson’s ratio ≈ 0.5 [48]), which can induce an axial stress along the particle alignment direction. This deformation-induced coupling could enhance charge transfer along the aligned ceramic columns, thereby contributing to the observed increase in the transverse response ($d_{31}$).

While the orientation of ceramic particles improves the transverse piezoelectric response, the effect of particle size distribution appears to be less relevant in this loading configuration. Unlike the direct piezoelectric coefficient $d_{33}$ where a bimodal particle size distribution at a ratio of Ω = 25 % led to a significant enhancement in the piezoelectric response, the overall variation of $d_{31}$ values remains rather limited. Moreover, no clear systematic trend can be identified when varying large to small particle ratio. It is worth noting that in the case of $d_{31}$, the electromechanical coupling relies on indirect transverse activation mechanisms, governed by off-diagonal components of the piezoelectric tensor. As a result, increasing the packing density or varying the particle size ratio may improve local packing density but do not introduce additional anisotropic features that would enhance significantly the transverse response.

This behavior reinforces the anisotropic nature of the composites: while particle orientation enhances the $d_{31}$ response compared to random configurations, the piezoelectric activity remains primarily governed by the directionality of the ceramic filler alignment. As such, the $d_{31}$ component remains lower than $d_{33}$ and is less sensitive to microstructural tuning through particle size distribution.

### 4.4. Optimization of poling strategy

The poling process is a critical step in the development of piezoelectric composites, as it aligns the dipoles of the ceramic particles which activate their piezoelectric properties. Conventionally, in the case of contact poling, this alignment is achieved through post-curing poling, wherein a direct electric field is applied to the composite after it has fully cured, typically in an oil bath to enhance electrical insulation and minimize breakdown risks. While effective, this method can be time consuming and may be hindered by the exposure of PDMS composites to silicone oil, which can form an insulating layer on the composite surface, potentially reducing the efficiency of the poling process. To address these limitations, in situ poling presents a promising alternative. This approach aligns the dipoles during the curing process, potentially enhancing processing time efficiency and the resultant piezoelectric performance. In this section, a comparative analysis of post-curing and in situ poling is proposed highlighting their respective impacts on the piezoelectric performance and processing efficiency of ceramic-filled composites. This comparison aims to provide a deeper understanding of how the choice of poling strategy impacts the functional properties of the material.

The in situ poling process implemented in this study involved the simultaneous application of both alternating (AC) and direct (DC) electric fields. The AC field, commonly employed during the dielectrophoresis process, was applied at an amplitude of 3 V·µm⁻¹ for a duration of 30 min at room temperature to orient the ceramic particles. Following this, a DC field typically associated with post-fabrication poling, was superimposed onto the AC field as an offset with an amplitude of 10 V·µm⁻¹. Both electric fields were maintained during the curing cycle to ensure the alignment of dipoles and stabilization of the particle orientation as the composite cured.

Results of the piezoelectric charge coefficient from both poling strategies are presented in Fig. 11. To simplify the analysis, only composites with the particle size distribution yielding the highest piezoelectric charge coefficient (Ω = 25 %) are compared alongside the monodisperse composites containing either nano- or micro-sized particles.

A significant increase in $d_{33}$ is observed when applying the in situ poling protocol with values nearly doubling for all the compositions compared to post-curing poling. Notably, the composite containing the
<figure><img src="image_14.png" /><figcaption>Fig. 11. Comparison of piezoelectric charge coefficient $d_{33}$ for composites with 0–3 and 1–3 connectivity subjected to *in situ* and post-fabrication poling.</figcaption></figure>

bimodal filler distribution (Ω = 25 %) consistently exhibits the highest piezoelectric response, reaching over $10 \text{ pC.N}^{-1}$ with *in situ* poling. This can be attributed to the simultaneous application of alternating (AC) and direct (DC) electric fields during *in situ* processing, which induces a synergistic effect within the uncured composite. The AC field promotes dielectrophoretic alignment of ceramic particles into anisotropic, column-like structures, while the concurrent DC field initiates dipole orientation within these particles. This dual-field approach likely enhances particle–particle and electrode–particle interactions, improving electromechanical connectivity and domain alignment.

While this phenomenon has been rarely addressed in literature, a few studies investigated the *in situ* poling in rigid systems. For instance, an improvement of the piezoelectric response of PZT/epoxy composites was reported, when undergoing *in situ* poling [49]. This was attributed to higher electrical conductivity and permittivity of the uncured epoxy matrix, compared to its cured counterpart leading to a higher poling efficiency. Moreover, combining dielectrophoresis and poling was noted to reduce interparticle distance while improving polymer chain orientation, thereby intensifying the local field acting on each ceramic particle. This structural refinement directly contributed to higher dipole activation and improved $d_{33}$ values.

To assess the effect of *in situ* poling on the transverse piezoelectric coefficient, results at 1 % and 15 % uniaxial strain are illustrated in Fig. 12. An even more dramatic enhancement in $d_{31}$ is observed for all the *in situ* poled composites with 1–3 connectivity. This increase, which mirrors the behavior observed for $d_{33}$, suggests an optimized local electric field distribution and dipole activation along off-axis direction as well.

Interestingly, composites with monodisperse large particle distribution (Ω = 0 %) and hybrid combination (Ω = 25 %) exhibit the highest $d_{31}$ with a value reaching $16 \text{ pC.N}^{-1}$ under 1 % strain and values up to $20 \text{ pC.N}^{-1}$ under 15 % strain. This specific behavior likely stems from a more favorable microstructural evolution from the uncured state of the particle–matrix mixture. While post-curing poling showed limited impact of particle size and hybrid composition on $d_{31}$, possibly due to the inherent off-axis nature of the electromechanical coupling, *in situ* poling introduces a different response. The slurry allows ceramic particles to realign and reorganize under the simultaneous application of AC and DC fields. Nano-sized fillers, due to their high surface area, respond more efficiently to these fields, forming denser, more uniform particle networks with reduced interparticle spacing. This enhanced structural organization promotes better lateral stress transfer and local field intensification, thereby enabling more effective dipole activation in the transverse direction. Hence, under *in situ* conditions, composition and filler morphology regain a central role in governing the optimization of the transverse piezoelectric response ($d_{31}$).

These results suggest that poling at the early stages of matrix cross-linking and during structural alignment remains an effective route to enhance the electromechanical properties of soft flexible composites.

## 5. Conclusion

This study underscores the development of ceramic-filled silicone composites tailored for biomedical applications as flexible piezoelectric sensors, through the combined optimization of filler composition, their spatial distribution and *in situ* poling strategy. By leveraging a bimodal particle size distribution, Ω = 25 % alongside dielectrophoretic alignment, a significant improvement of the direct piezoelectric response was achieved. This effect was further amplified when polarization was applied *in-situ*, during the uncured state of the matrix, revealing a synergistic interaction between structural orientation and dipole activation.

Interestingly, the transverse piezoelectric response also exhibited a dramatic enhancement under *in situ* poling, particularly in nano-rich and hybrid filler systems. These results suggest that dynamic particle alignment during matrix cross-linking not only reinforces axial charge

<figure><img src="image_15.png" /><figcaption>Fig. 12. Comparison of transverse piezoelectric coefficient $d_{31}$ for composite with 0–3 and 1–3 connectivity subjected to *in situ* and post-curing poling (a) 1 % of uniaxial strain (b) 15 % of uniaxial strain.</figcaption></figure>
transfer pathways but also enables efficient lateral dipole activation, likely through reduced interparticle spacing and improved local electric field coupling. The differential impact of composition and alignment on d33 and d31 further highlights the anisotropic nature of electromechanical interactions in such flexible composites.

These findings offer a comprehensive strategy to tune both axial and transverse piezoelectric response in soft composite materials, an essential step toward broadening the functional versatility of flexible piezoelectric sensors. The enhanced performance demonstrated under multi-directional strain provides a promising foundation for more sensitive integration of piezoelectric composites into next-generation diagnostic and therapeutic platforms, particularly within soft and dynamically deformable systems involving complex mechanical stimuli and large strain amplitude.

## CRediT authorship contribution statement

**Tasnim Missaoui:** Writing – original draft, Visualization, Validation, Methodology, Investigation, Conceptualization. **Xavier P. Morelle:** Writing – review & editing, Supervision, Project administration, Methodology, Investigation, Funding acquisition, Conceptualization. **Minh Quyen Le:** Writing – review & editing, Methodology, Conceptualization. **Pierre-Jean Cottinet:** Writing – review & editing, Methodology, Conceptualization. **Jean-Fabien Capsal:** Writing – review & editing, Methodology, Conceptualization. **Guilhem Rival:** Writing – review & editing, Supervision, Project administration, Methodology, Investigation, Funding acquisition, Conceptualization.

## Funding

This work was carried out as part of the MIMIMed@Lyon project financially supported by the Institut Carnot Ingénierie@Lyon, labelled by the French National Research Agency.

## Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

## Appendix A. Supplementary data

Supplementary data to this article can be found online at https://doi.org/10.1016/j.matdes.2026.115457.

## Data availability

Data will be made available on request.

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