Correlations between micro mechanical analyses and
macro-scale mechanical properties of PPS/basalt fiber
composites designed from commingled yarns

CASTRO-CABRERA I., GAUMOND B., CIESLAK, D., GERARD J. F., LIVI S., RUMEAU-DUCHET J.*,
Université Claude Bernard Lyon 1, INSA Lyon, Université Jean Monnet, CNRS UMR 5223, Ingénierie
des Matériaux Polymères F-69621 Cédex, France

Corresponding author: jannick.duchet@insa-lyon.fr
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Abstract

To reduce the environmental impacts of the transportation while enhancing safety and fuel efficiency, the development of lightweight, high-performance composites is imperative. To meet this challenge, polyphenylene sulfide (PPS) composites reinforced with basalt fibers (BF) are investigated with a focus on advanced manufacturing techniques via commingled yarns (CY). In fact, basalt fiber-reinforced polymer composites (FRPCs) are promising candidates across diverse industrial -from automotive to aerospace- owing to their superior mechanical properties and thermal stability. This work bridges the gap between the micro and the macro-mechanical performance of PPS/basalt fiber yarns and their composites by systematically evaluating the key role of fiber-matrix interface. Two different sizing formulations were compared against unsized fiber -one based on polyamide-polyurethane and epoxy-unsaturated polyester. Comprehensive surface characterization including chemical composition analysis, micro-tensile testing, wettability, and morphology assessments, was performed to evaluate micro-scale performance. Pull-out adhesion test quantified improvements in the interfacial shear strength (IFSS) from up to 360% relative to unsized fibers. At the macro-scale, interlaminar shear strength (ILSS) tests established a quantitative relationship with micro-scale phenomena, revealing a 60% enhancement in mechanical performance when using the optimal film former. Lastly Weibull statistical analyses were performed to examine the role of sizing during CY processing on fiber failure distribution, demonstrating the effective protection provided to fibers during processing and distinguishing major differences between sizing formulation. Collectively, these results provide valuable insights for the design of high-performance composites based on basalt fibers and a PPS matrix.

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Keywords: Thermoplastic, composites, Basalt fibers, Interfaces, Sizing, Weibull, Commingled yarns, Adhesion

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Highlights

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* Strong mechanical correlation are established at micro and macro-scale.

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* Fundamental and practical adhesion are interrelated yet distinct due to inherent experimental.

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* Reactive film former enhance stress transfer more effectively than a non-reactive one.

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* Sizing enables improved wettability and structural homogeneity.

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* Weibull statistics proves effective for failures assessment of sized fibers and in commingled processing.

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# 1. Introduction

Nowadays, the development of strategies for materials that address both economic growth and environmental conservation represents a real challenge. To answer these concerns, Industry and Academia have increasingly focused on developing novel and high-performance materials. Among the many strategies being explored, the use of fibers as reinforcement in polymer composite materials stands out as particularly promising. This approach not only meets the demand for superior mechanical performances associated with lightweight materials but also with the improvement of physical properties such as electrical conductivity or thermal and acoustic isolations. Thanks to ongoing research, FRPCs have been developed in various industries, notably in the transportation and energy sectors [1–3].

The polyphenylene sulfide is one of the most popular high-performance and semi-crystalline engineering thermoplastics that offers outstanding thermal stability and chemical resistance to solvents, high stiffness and hardness, dimensional stability, hydrolysis resistance, and low flammability. These advantages make this polymer highly suitable for the design of structural components in industries such as automotive, aircraft, aerospace, electronics, and chemistry [4,5]. However, its high brittleness results in a low impact resistance and elongation at break. To overcome these drawbacks, fiber reinforcements such as carbon, aramid, glass, or basalt are often added [6]. Nevertheless, carbon and glass fibers are the most frequently considered with PPS [7–9].

The list of reinforcement fibers is extensive, each one offering a unique set of advantages and disadvantages. Fibers such as carbon or glass fibers are characterized by high strength and durability. However, despite their attractive properties, these fibers are often associated with high costs and environmental concerns [10]. Basalt fibers (BF), another type of fiber, offer various advantages similar to natural fibers, including renewability [11,12]. In fact, basalt is a natural material formed through the solidification of volcanic rocks. Its composition, which mainly comprises SiO₂ and Al₂O₃, also includes Fe₂O₃, FeO, CaO, and MgO, i.e. a chemical composition quite similar to that of glass fibers [13]. In particular, the FeO and Fe₂O₃ contents play a key role in various physico-mechanical properties, making BF superior to glass fibers in terms of mechanical strength, thermal stability, and chemical resistance [14]. BF are also distinguished by their corrosion resistance, and acoustic isolation [15] [16] [11]. In addition, basalt fibers have already demonstrated their compatibility with many polymer matrices compared with traditional fibers like glass [17].

Research on composites using basalt reinforcement fibers, initially developed for military applications and later extended to public uses, has revealed promising mechanical properties comparable to glass-fiber or carbon fiber-based materials, positioning BF as an interesting alternative. In the literature, research on basalt-reinforced composite polymers based on various matrices is constantly growing. Epoxy-based composites are the most widely cited, valued for their strength, compatibility,
chemical and electrical resistance, and long-term performance [18,19]. Nonetheless, significant research
has also been conducted on thermoplastic matrices such as polypropylene or polyamide [20,21].

Enhancing the interface between the BF and polymer matrix is of considerable interest, Eslami-
Farsani *et al.* [22,23], demonstrated that incorporating silane-modified nanoclays and nano alumina
substantially enhances matrix adhesion, leading to improved flexural, tensile, and quasi-compression
properties in BF-epoxy composites. In the field of high-performance thermoplastics, Xigao-Jiang *et al.*
advanced this approach by tailoring BF surfaces with MXnes structures covalently bonded to silanes
[24], while also promoting in situ growth of ZnO nanoarrays on the basalt surface[25]. The tailored
surfaces effectively optimized load transfer and mechanical performance with poly(phthalation ether
nitrile ketone) matrix (PPENK).

The literature on PPS composites reinforced with BF is constantly growing due to the excellent performances obtained. For example, Kizil *et al.*[26] have investigated the manufacture of hybrid composites combining carbon or basalt fibers with fillers such as zeolite and bentonite. The introduction of 10 wt% of fibers led to an increase in storage modulus of 78% for BF and 152 % for CF. Furthermore, the modulus can be slightly increased by adding zeolite or bentonite fillers (about 5% additional). Guxin-Pan *et al.* [27] highlighted the importance of enhancing interfacial adhesion between basalt fiber modified with γ-APTES and a thermoplastic polyurethane/PPS matrix at different ratios. Aslan *et al.* [28] explored the elaboration of hybrid PPS-basalt fiber-based composites by adding hexagonal boron nitride and graphene nanoplateles to improve mechanical, thermal conductivity, and electrical properties. The authors noted that the ratio of both fillers affects chain mobility, facilitating or delaying PPS crystallization, enhancing stress transfer and ductility, and increasing tensile and flexural strength.

When developing high-performance composite materials, performance not only depends on the
properties of the matrix or fibers but also on the interface between them [29,30]. The interfacial region
comprises a significant domain of the matrix phase, i.e. the interphase, for which properties are different
due to restricted segmental mobilities, transcrystallinity, selective adsorptions, etc [31]. However, the
interfaces are designed to ensure optimum stress transfer and protection of the fibers against aging.
Before the impregnation of fiber by the polymer matrix, sizing is applied as a thin surface layer. This is
mainly made up of organic materials during the manufacturing of fibers. Bare fibers in the industry are
not common since the sizing also aims to protect the fiber during manufacturing. Sizing plays a crucial
role in forming the fiber-polymer interface/interphase providing additional properties to optimize the
processing and performances of the resulting composites. [32,33].

Among the multiple routes to produce FRPC, commingled yarns have gained prominence as a
cost-effective approach. Commingled yarns are hybrid structures in which two different materials, such
as polymers and fibers, are mixed as continuous-filament yarns [34–36]. This method allows for
improved fiber impregnation with a thermoplastic matrix, which typically has high melt viscosity in a
molten state. As a consequence, CY could contribute to reducing impregnation times, and decrease the pressure required for the consolidation step of the processing [34,37]. All these attributes make CY highly attractive for the production of complex-shaped composites. Carbon fibers are widely used as reinforcement fiber in CY when using high-performance thermoplastics such as polyetherimide (PEI) [38], polyether ether ketone (PEEK) [39], or PPS [40]. Glass fibers on CY are frequently found with engineering thermoplastics or commodities such as polyamides [41], polyethylene terephthalate [42] or polypropylene [43]. However, CY as a precursor presents major challenges such as fiber-matrix distribution and process-induced damage of the inorganic fibers [44].

**Figure 1** *Figure 1-a* illustrates an ideal yarn cross-section with all reinforcing fibers perfectly distributed. However, in practice, fiber and matrix distribution is often not homogeneous and distributions such as illustrated in *Figure 1-b* are frequently observed. The initial morphology of the yarn is strongly influenced by the manufacturing processing of yarns. Processes such as powder coating, friction spinning, spreading, stretch breaking, and compressed air are the most commonly used. Among these, the air-jet texturing method stands out as the most popular strategy. This method is versatile and allows produce flexible yarns. In this method, yarns are introduced into a turbulent zone where pressurized air is directly applied parallel to their trajectory, resulting in the development of a filament loop by longitudinal displacement of the filaments [45]. While this approach effectively enhances the uniformity and quality of the composite, it also risks damaging the reinforcing fibers during the process, which can potentially compromise the strength and integrity of the final composite material.

<figure><img src="image_1.png" /><figcaption>**Figure 1.** Cross-section of a) an ideal commingled yarn and b) non-homogeneous distributed yarn</figcaption></figure>

The present research aims to bridge the gap between the micro- and macro-scale mechanical performance of PPS/BF yarns and their composites by emphasizing the critical role of fiber-matrix interfaces. Previous works have established that the interface significantly influences overall composite behavior and is largely governed by the interface and the fiber surface *i.e.* the sizing applied during fiber manufacturing. In this study, two different commercial fibers alongside a uniquely sourced batch of unsized fibers are explored to isolate the intrinsic adhesion mechanism of the PPS/BF interface. This eliminates the confounding effects of sizing treatments and avoids the surface damage or alteration caused by desizing procedures. While PPS/BF composites have shown promising properties in existing literature, the use of commingled yarns for their fabrication remains unexplored, and the impact of the

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commingled process on fiber integrity and the resulting composite structure too. This study looks to fill
this gap of information through a comprehensive approach offering valuable insights for the design of
high-performance thermoplastic composites.

## 2. Experimental details

### 2.1 Materials

The basalt fibers B1 and B2 from ISOMATEX Co. are commercially available with two different sizings. The fiber B0, without sizing, was specially and kindly sourced by ISOMATEX Co. The nominal diameters are 9.1 µm for fiber B1 and 9.5 µm for fiber B2.

PPS was supplied from Celanese Co. (Fortron 0320 ®) and was subjected to fiber processing at
The Filament Factory. The nominal diameter of fibers is 25.5 µm.

These materials were used to produce commingled yarns (CY) by Billion Mayor Industry.
Properties of commingled yarns are summarized in Table 1.

<table><caption>Table 1. Properties of commingled yarns</caption><thead><tr><td>Commingled yarn</td><td>Basalt Surface (mm²)</td><td>PPS surface (mm²)</td><td>Weight fraction of reinforcement (%)</td></tr></thead><tbody><tr><td>B1_CY</td><td>0.531</td><td>0.735</td><td>58</td></tr><tr><td>B2_CY</td><td>0.577</td><td>0.733</td><td>60</td></tr></tbody></table>

### 2.2 Manufacturing methods

#### 2.2.1 Micro-composites elaboration

Micro composites were elaborated with a FIMABOND + system (Textechno, Germany). The embedding length was in a range between 70-200 µm [46] at 420 µm.min⁻¹.

The PPS matrix used for the sample was prepared under a nitrogen atmosphere using a 15 g-capacity DSM micro-extruder (Midi 2000 Heerlen, The Netherlands) with co-rotating screws (L/D ratio of 18). The PPS was extruded for about 2 min under shearing at 100-rpm speed at 310 °C. This process was chosen in order to be as close as possible to real conditions, i.e., the thermal story undergone by the PPS filaments in real commingled yarns. BF diameters were determined individually by standard test method for linear density of textile fibers ASTM D1577 option C – vibroscope [47]. The thermal cycle applied for processing, i.e. embedding the filament in the PPS matrix is described in *Errur ! Source du*

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<figure><img src="image_2.png" /></figure>

b)

<figure><img src="image_3.png" /><figcaption>**Figure 2. Sample preparation thermal cycle (a) Micro-composite pull-out sample (b).**</figcaption></figure>

### 2.2.2 Composite elaboration

Unidirectional composite materials were elaborated from commingled yarns by thermocompression process by IPC (Centre Technique Industriel de la Plasturgie et des Composites, France). The yarns were heated from room temperature to 340°C at constant rate of 4 K.min⁻¹. Once the target temperature is reached, the temperature was maintained for 20 min under a pressure of 30 bars. After an isothermal step at 340 °C, the composite was cooled down to room temperature at a rate of 7 K.min⁻¹, with the pressure maintained throughout the cooling step.

## 2.3 Characterization methods

### 2.3.1 FTIR

Fourier Transform Infrared spectra (FTIR) were recorded using a Nicolet IS50 FT-IR spectrometer (Thermo Nicolet) with an attenuated total reflection (ATR) accessory. Samples were analyzed in transmission mode from 4000 to 500 cm⁻¹ (32 scans; resolution 4 cm⁻¹) at room temperature.

### 2.3.2 Sizing content

Thermogravimetric analysis (TGA) was carried out using a TGA 8000 apparatus (Perkin Elmer, USA) from 30 to 700 °C at a heating rate of 10 K.min⁻¹ under 40 mL.min⁻¹ air atmosphere. Initial sample weights (about to 20 mg), were measured prior to testing.

X-ray photoelectron spectroscopy (XPS) was carried out by SERMA Technologies – Laboratoire Sience et Surface. The instrument used was a PHI Quatera SXM. The spectrometer excitation source was the Al K(alpha) line (1486.6 eV). The diameter area size was 200µm, the angle detection of 45°, and the deep of the analysis close to 3nm. The software used for analysing results was Avantage. The chemical composition (expressed in atomic percentage) was determined using integrated peak areas of each element, and peak fitting was made considering a mixed Gaussian-Lorentzian (70-30%) composition.
### 2.3.3 Surface energy

Advancing contact angles were measured using a DCAT 11 tensiometer (Dataphysics, Germany) for the Wilhelmy technique. Three probe solvents (water, ethylene glycol and methylene iodide) were used to determine the surface energy according to Owens-Wendt relation and Young-Dupré equation (1) and (2) [48–50].

$$W_A = \gamma_L (1 + \cos\theta) \qquad (1)$$

$$\gamma_L \times (1 + \cos\theta) = 2 \sqrt{\overline{\gamma_L^d \times \gamma_S^d} + 2 \sqrt{\overline{\gamma_L^{nd} \times \gamma_S^{nd}}}} \qquad (2)$$

where $W_A$ is the reversible work of adhesion, $\gamma_L$ and $\gamma_S$ are the liquid surface tension and the fiber surface energy, respectively. From a thermodynamic perspective, adhesion interactions are characterized by the reversible work of adhesion, which is the energy required to separate a unit area of the adhesive contact.

The total surface energy can be decomposed in dispersive and non-dispersive components, i.e., $\gamma^d$ and $\gamma^{nd}$.

$$\gamma_S = \gamma_S^d + \gamma_S^{nd} \qquad (3)$$

To ensure the test repeatability, five individual fibers were placed onto a circular support FH13. The speed of immersing and retracting fibers in and from the probe liquid was set at 0.01 mm.s⁻¹. The maximal immersed length was 5mm.

### 2.3.4 Fiber/matrix micro-mechanical analysis

Fiber-matrix adhesion can be assessed by performing pull-out tests which measure the force needed to “pull-out” a single fiber embedded in the solid matrix for a given embedded length.

Pull-out tests were done using a FIMAVAT+ system (Textechno, Germany) at room temperature with a constant cross-head speed of 0.1mm.min⁻¹ equipped with a load cell of 210 cN [51].

The common method to quantify the interfacial adhesion is to determine the apparent adhesion strength ($\tau_{app}$). This one is denoted as the average of the interfacial shear strength (IFSS). Although this is the most widely used calculation in literature, it often proves to be insufficient as a reliable interfacial parameter [52]. While looking for more accurate models to characterize the adhesion strength, several approaches have been proposed, including those by Piggott [53], Scheer and Nairn [54], Greszczuk [55], or Peen and Lee [56], depending if stress-based or energy-based approach are considered. In agreement with Zinck et al. [57], studies focusing on the influence of the physico-chemical nature of the components on the interfacial adhesion suggest that the IFSS calculation is inadequate. Therefore, we have chosen to consider two different approaches to analyze the fracture phenomena occurring at the interface, i.e., a critical stress criterion and an energy criterion.
To assess the adhesion phenomena between different fibers and PPS, the Greszczuk model was applied (stress criterion) in order to obtain the maximum interfacial shear stress, $\tau_{max}$, and Peen-Lee model (energetic criterion), leading to obtaining the interfacial toughness $G_{ic}$ [58–60]. Detailed information on these models is provided in the Supporting Information.

### 2.3.5 Single fiber tensile test

The tensile tests on basalt filaments were carried out using a FAVIMAT+ machine (Textechno, Germany) equipped with a 210cN load cell. The testing speed was set at 1 mm.min⁻¹ for a gauge length of 20mm. The diameter of each filament was evaluated by applying the standard test method for linear density of textile fibers ASTM D1577 option C – vibroscope [47]. Statistical analyses were performed from 50 measurements for the BF and 25 measurements for the PPS fibers.

#### 2.3.5.1 Weibull analysis

Research on the effect of size on the ultimate strength has long been studied in engineering. Edmé Mariotte established the concept of the weakest link, focusing on critical points of vulnerability in material structures. Later, Weibull formalized this idea by developing it into a statistical model. He envisioned a chain composed of independent links where the failure of just one link causes the failure of the entire chain.

According to Weibull’s law, the probability of failure of a material depends on the size and distribution of these defects. The statistical model relates the probability of failure to parameters such as stress, defect size, and material properties [61,62]. A limitation of Weibull’s model is its reliance on a single type of defect to predict the probability of failure. Such multifaceted behavior has already been documented on glass fibers [63], and commingled fibers [64]. Recognizing this, Beetz et al. [65] proposed a bimodal Weibull distribution. According to this feature, Weibull bimodal probability density statistics was applied in the present work.

$$ 
\begin{aligned}
f_{th}(\sigma, L) &= p \times L \times m_1/\sigma_{01} \times (\sigma/\sigma_{01})^{m_1-1} \times \exp(-L \times (\sigma/\sigma_{01})^{m_1}) + \dots \\
(1-p) \times L \times m_2/\sigma_{02} \times (\sigma/\sigma_{02})^{m_2-1} \times \exp(-L \times (\sigma/\sigma_{02})^{m_2})
\end{aligned} 
\quad (4) 
$$

This relation combines two Weibull Probability Density Function (PDF) weighted by a mixing parameter $p$, where one set of parameters $(\sigma_{01}, m_1)$ accounts for type I defects, and the other $(\sigma_{02}, m_2)$ for type II defects. The fiber length, $L$ is incorporated to adjust the Weibull distribution for variation in component size. In such a description, the two types of defects are assumed to be independent. This relation is summarized in equation (4). The corresponding cumulative density function (CDF) is expressed in equation (5).

$$ P_{th}(\sigma) = 1 - p \times \exp(-L \times (\sigma/\sigma_{01})^{m_1}) - (1-p) \times \exp(-L \times (\sigma/\sigma_{02})^{m_2}) \quad (5) $$
### 2.3.6 Commingled Yarn tensile test

Tensile tests were carried out on yarns using a 2M machine (MTS, France) equipped with a 10kN load cell. To assess quantitative analysis, commingled yarns were mounted with Araldite epoxy clamping in a sandwich between aluminum pieces (20mm x 30mm x 2mm) previously abraded as shown in Figure 3 [Figure 3] [66]. The displacement speed was maintained at 10mm.min⁻¹. To the best of the authors' knowledge, no specific standard for tensile testing of commingled yarn exists in the literature. However, Rocher et al. [44] proposed a protocol to examine the tensile behavior of commingled polypropylene/glass fiber yarns, and their methodology is applied in this study. Specimen designated B1_CY1_model and B2_CY1_model were fabricated for comparison with non-processed yarns.

<figure><img src="image_4.png" /><figcaption>Figure 3. Commingled Yarn tensile test specimen</figcaption></figure>

The tensile strength of the yarns, $\sigma_{xy}$, was determined by dividing the force ($F_{max}$) and composite sectional surface ($S_{BF} + S_{PPS}$):

$$ \sigma_{xy} = F_{max}/(S_{BF} + S_{PPS}) \qquad (6) $$

The tensile strength of basalt fibers ($\sigma_{BF}$) within the commingled yarns was estimated by analyzing the behavior of PPS until the yarn reaches its breaking point (7)

$$ \sigma_{BF} = F_{BF}/S_{BF} = (F_{max} - F_{PPS})/S_{BF} \qquad (7) $$

$$ F_{PPS} = \sigma_{PPS} * S_{PPS} \qquad (8) $$

The dependance of $\varepsilon$ with PPS is given by analyzing a single fiber of PPS under maximal tension.

### 2.3.7 Three-point flexural test

Three-point flexural tests were conducted using a 2M tensile machine (MTS, France) equipped with a 5kN load cell, following the norm ISO 14130 [67]. The standard sample size was 10 x 20 x 2 mm³, obtained from unidirectional composite plates and processed with a computer numerical control (CNC) milling machine.

### 2.3.8 Morphology

Scanning Electron Microscopy (SEM) was performed using a Tescan Vega 3 SEM (TESCAN Ltd.), operating at an accelerating voltage of 10 kV in a vacuum of 9 × 10⁻⁵ mbar, with a beam intensity of 10 and a working distance of approximately 10 mm. Cross-sectional samples were embedded in cold resin

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and then polished for further observation. Fiber samples were fixed with carbon tape. Both types of samples were sputter-coated with a gold layer approximately 10 nm of thickness.

## 3. Results and discussion

### 3.1 The study of the basalt fibers sizing

#### 3.1.1 Sizing nature

The first requirement that arises when studying different fibers mainly concerns the chemical nature as well as the composition of the sizing present on the fiber surface. Accurate determination of the composition of fiber sizing is a quite complex task due to the presence of various components, such as coupling agents, surfactants, lubricants, film formers, and antistatics, among others [68]. Furthermore, most manufacturers consider the composition of fiber sizing to be proprietary, making it difficult to obtain accurate information on its composition. However, chemical analysis techniques, such as infrared studies (FTIR-ATR) can provide valuable information by identifying the functional groups present in sizing. This information discloses to be of interest to infer and understand the behavior of sizing with different polymer matrices. In this study, the sizing of the fibers is commercial and was analyzed using FTIR spectroscopy after Soxhlet extraction with tetrahydrofuran (THF) at 66 °C over a period of 24 hours [69]. The results are reported in Figure 4.

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<figure><img src="image_5.png" /><figcaption>Figure 4. FTIR-ATR characterization of extracted sizing from fibers B1 and B2. Spectra in (a) and (b) correspond to the full spectral range of B1 and B2, respectively. Spectra (c) and (d) display zoomed-in views highlighting characteristics vibrations bands.</figcaption></figure>

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Both sizings display a signal at 1180 cm⁻¹, 1100 cm⁻¹ and at 950 cm⁻¹ indicatives of Si-O-C bonds. These peaks confirm the presence of silanes in sizing formulations [70]. For fiber B1, the presence of N-H bonds (800 cm⁻¹ and at 3333 cm⁻¹), C-N bonds (3333 cm⁻¹), and C=O bonds from amides (1650 cm⁻¹) are observed. Moreover, the vibrations around 1710 and 1220 are typical for the stretching vibration of esters C=O and asymmetric stretching vibration of C-O from N-CO-O. Based on the literature, one can conclude that the main component of B1 fiber sizing, i.e. the film former corresponds to a polyamide and/or polyurethane (PA/PU) [71,72]. The vibration around 800 cm, 920 cm, 950 cm and 1460 cm related to the propyl chain, epoxy, and glycidoxy strongly suggest the presence of 3-glycidoxypropyltrimethoxysilane (GPTMS), a silane frequently employed in industry [73].

In the case of fiber B2, various absorption bands are characteristics of epoxy prepolymers, such as the diglycidyl ether of bisphenol A (DGEBA). These include oxirane bands at 820 and 920 cm⁻¹, the alkyl-aril ether bands at 1038 and 1240 cm⁻¹, and aromatic signals at 1600 and 1510 cm⁻¹ [74,75]. An intense absorption peak at 1720 cm⁻¹, could be originated by carbonyl groups. Lacrampe et al. [76] studied glass fibers treated with unsaturated polyester sizing and observed the presence of v-vibration from fumarate and malate unsaturated at 1640 cm⁻¹ and 880 cm⁻¹ [77], as well as aromatic vibrations at 1040, 1510 and 1600 cm⁻¹. Based on previously reported works, it can be deduced that the film-formers in the B2 fiber formulation are mainly unsaturated polyester (UP) and an epoxy prepolymer. The presence of the (3-glycidoxypropyl)trimethoxysilane (GPTMS) cannot be discarded, as well as the presence of γ-aminopropyltriethoxysilane (γ-APTES), a silane frequently added in sizing formulation [33].

### 3.1.2 Sizing content

TGA was used to evaluate the sizing content present on the BF surface (see Figure 5-a). As can be observed, the weight loss of the B1 reference fiber is estimated to be 2.3 wt% compared to only 1 wt% for the B2 reference fiber. Moreover, two different degradation stages are clearly identified on the derivative curves (DTG) presented in **Figure 5**-b.

The primary weight loss occurred from 220 to 400°C resulting in a total mass loss of 65 and 80 % of the total sizing for the B1 and B2 reference fibers, respectively. These results indicate that the sizing of the BF, including to the lower molar mass components such as surfactants, antistatic agents, and film formers, as well as the organic parts of the coupling agents, begin to decompose from 200 °C. In fact, Thomason et al. [78] reported similar findings on the thermal stability of various sizings applied on glass fibers, showing a significant weight loss from 200 to 300 °C under airflow. This first weight loss was attributed to the thermal decomposition of the film formers. After comparing the thermal stability of sized fibers and commercial emulsion of film formers.

In the case of fiber B2, a more distinct shoulder peak was observed at 300°C, suggesting an additional decomposition. The presence of two distinct decomposition steps supports the assumption

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that two different film formers -epoxy and unsaturated polyester- are present in the sizing formulation. A similar behavior was observed by Peterson *et al.* [74] highlighting that the film formers are often mixtures of different polymers to allow the combination of sized fibers with different types of polymer matrices. Additionally, it is important to be precise about the potential interaction between the oxiranes of epoxies and the hydroxyl groups present on the fibers' surface. Drzal *et al.* [79] highlighted this possibility in carbon fibers-epoxy resins, while Berglund *et al.* [80] suggested a similar interaction on composites made with DGEBA and nano-fibrillated cellulose. Besides, the decomposition temperature of epoxies, such as DGEBA, starts from 270°C [81].

The second weight-loss event, shown in **Figure 5**, occurs above 400°C and corresponds to the breakdown of covalent bonds within the siloxane network formed by the condensed silanes present in the sizing [82,83]. Jenkins [84] confirmed the complete removal of γ-APTES, from glass fibers after heating above 450°C. This hypothesis was supported by XPS analyses which confirm the non-existence of nitrogen at the glass surface.

<figure><img src="image_6.png" /><figcaption>**Figure 5.** Weight loss as a function of temperature (TGA, DTG) from the sizing of basalt fibers, a) thermogravimetric analysis, and b) derivate of weight loss against temperature (heating ramp 10 K·min⁻¹, under airflow).</figcaption></figure>

### 3.1.3 Sizing: coverage, thickness, and reactivity

After the determination of the chemical nature of the sizing as well as the quantification on the fiber surface, a more precise characterization of the fiber surfaces is required to predict the resulting

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fiber-matrix interfaces. This is why, X-ray photoelectron spectroscopy was used as a powerful tool to better understand the composition, reactivity, deposition, and morphology.

The main atomic elements detected on the sized fiber surfaces are carbon, oxygen and silicon

(*Calculated from Thomason and Dwight model)

**Table 2**

**Table 2**). The presence of carbon and nitrogen elements confirms the presence of the sizing on the basalt surface since those elements are not present in basalt fibers. However, the presence of carbon in bare BF was observed. The low C/Si and the absence of nitrogen suggest that this carbon content may come from pollutants adsorbed on the surface during the storage and packaging of the fibers.

<table><thead><tr><th>Reference</th><th>C</th><th>O</th><th>N</th><th>Si</th><th>Al</th><th>Fe</th><th>Mg</th><th>Zn</th><th>Ca</th><th>C/Si</th><th>(C/O)<sub>during</sub></th><th>Coverage ratio</th><th>Thickness (nm)</th></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>%</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr></thead><tbody><tr><td>B0</td><td>10.6</td><td>60.4</td><td>-</td><td>17.3</td><td>6.5</td><td>1.0</td><td>2.0</td><td>0.2</td><td>1.8</td><td>0.6</td><td>--</td><td>--</td><td>--</td><td>--</td></tr><tr><td>B1</td><td>59.7</td><td>26.7</td><td>3.4</td><td>6.4</td><td>2.2</td><td>--</td><td>0.7</td><td>--</td><td>0.9</td><td>9.3</td><td>7.6</td><td>79%</td><td>189</td><td></td></tr><tr><td>B2</td><td>53.3</td><td>34.9</td><td>1</td><td>6.6</td><td>2.4</td><td>--</td><td>0.9</td><td>--</td><td>0.8</td><td>8.1</td><td>3.3</td><td>80%</td><td>64</td><td></td></tr></tbody></table>

*Calculated from Thomason and Dwight model

<caption>**Table 2.** Atomic elementary composition of BF at the surfaces determined by XPS.</caption>

From elementary composition analysis and knowing the weight of sizing deposited at the surface, calculating the thickness and the fractional surface coverage is possible by applying the Thomason and Dwight model [85]. The results are summarized in *Calculated from Thomason and Dwight model*.

**Table 2**

**Table 2** and the equations applied are described in the Supporting Information. The coverage ratio in both fibers is similar, i.e., close to 80%. However, the sizing of fiber B1, with PA/PU- sizing, is three times thicker than fiber B2, with epoxy-UP-sizing. This result is expected, given the difference in the amount of sizing at the surface determined by TGA.

Thomason and Dwight's research highlighted significant differences in the C/O ratio of reactive and non-reactive (thermoplastic-based sizings). The C/O ratio in thermoplastic-based sizing was much higher than for reactive ones. The trend is confirmed in our study, as the fiber B1 sizing is intended to be designed for a thermoplastic matrix (PA/PU-based), while the fiber B2 sizing is epoxy-based.

A way to understand the reactivity of sizing present on the surface is by analyzing the intricate structure of C 1s of both fibers. High-resolution spectra spanning the range of 278-298 eV were recorded to understand the possible structures on the surface (See **Figure 5**). The deconvolution analysis of these spectra reveals C-C / C-H / C-Si bonds at 284.5 - 284.8 eV, C-O / C-N bonds at 286.4 - 286.8 eV, O- C-C / C=O bonds at 287.8 eV, and O-C-C / C=O bonds at 288.6 - 289.3 eV [86]. The deconvoluted percentage values of these four signals are reported in **Table 3**. The bonds C-O, C-N, or C=O display a higher reactivity compared to the others. Since the percentage of these bonds is more important

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in fiber B2 than in B1, we can suppose that the sizing of B2 (epoxy-UP sizing) will exhibit higher reactivity compared to fiber B1 (PA/PU sizing).

406

407

<figure><img src="image_7.png" /></figure>

<figure><img src="image_8.png" /><figcaption>Figure 6. Deconvolution of C 1s XPS spectra of a) fiber B1, and b) fiber B2.</figcaption></figure>

408

409

410

<table><thead><tr><th>Reference</th><th>C-C / C-H / C-Si<br>284.5 - 284.8 eV</th><th>C-O / C-N<br>286.4 - 286.8 eV</th><th>O-C-C / C=O<br>287.8 eV</th><th>O-C=O<br>288.6 - 289.3 eV</th></tr></thead><tbody><tr><td>B1</td><td>70</td><td>22</td><td>5</td><td>3</td></tr><tr><td>B2</td><td>49</td><td>45</td><td>4</td><td>2</td></tr></tbody></table>

411

<caption>Table 3. Binding energies and intensities (%) of the C1s XPS peaks of basalt fibers B1 and B2.</caption>

412

413

### 3.1.4 Fiber surface energy

An alternative method for accessing surface structure is through surface energy studies. These studies allow to assess crucial surface properties such as wettability, adhesion, or fiber/matrix interactions in composite materials. The surface energy of the different basalt fibers and PPS were determined by applying Owens-Wendt theory [49,50].

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different probe liquids, surface energy, dispersive and non-dispersive components, and work of adhesion between PPS and BF

Experimental contact angle measurements with different probe liquids, surface energy, dispersive and non-dispersive components, and work of adhesion between PPS and BF are reported in Table 4 Table 4.

The reference fiber B0 displays a surface energy value of 57 mN.m⁻¹. This value corresponds to what is reported in the literature for neat basalt fibers and basalt rock: 55 mN.m⁻¹. Other values in the the literature suggest surface energy values closer to neat to glass fibers (74 mN.m⁻¹), the difference might come from manufacturing process of basalt fibers with sodium ion softening water [87,88]. It should be noted that the fibers were analyzed as is from the bobbin especially produced without sizing and they are not exempt from pollution on the surface, as shown in *Calculated from Thomason and Dwight model*

Table 2 Table 2, that might modify the surface energy. After sizing, the surface energy of basalt fibers B1 and B2 is reduced to 40 mN.m⁻¹. The values are close to those of polyamide and polyurethane surface energy (varying between 35 and 45 mN.m⁻¹) [89,90] or to unsaturated polyester (46 mN.m⁻¹) confirming the results previously reported [91]. The thermodynamical adhesion work, Wₐ varies with the sizing nature and it is much lower when unsized BF is used. Indeed, the surface energy of the sized fibers is close to that of PPS which describes an enhanced compatibilization.

<table><caption>Table 4. Experimental contact angle with different probe liquids, surface energy, dispersive and non-dispersive components, and work of adhesion between PPS and BF</caption><thead><tr><th>Fiber</th><th>θ (°)<br>Water</th><th>θ (°)<br>Methylene<br>iodide</th><th>θ (°)<br>Ethylene glycol</th><th>γ (mN.m<sup>-1</sup>)</th><th>γ<sup>d</sup> (mN.m<sup>-1</sup>)</th><th>γ<sup>nd</sup> (mN.m<sup>-1</sup>)</th><th>W<sub>a</sub> (mN.m<sup>-1</sup>)</th></tr></thead><tbody><tr><td>PPS</td><td>78.8 ± 4.3</td><td>31.5 ± 3.1</td><td>----</td><td>47.0</td><td>43.6</td><td>3.4</td><td>----</td></tr><tr><td>B0</td><td>34.5 ± 1.3</td><td>59.0 ± 1.0</td><td>47.5 ± 1.2</td><td>56.5</td><td>10.6</td><td>45.8</td><td>68.0</td></tr><tr><td>B1</td><td>55.5 ± 0.2</td><td>40.2 ± 3.0</td><td>50.1 ± 2.5</td><td>43.2</td><td>22.8</td><td>20.4</td><td>71.7</td></tr><tr><td>B2</td><td>62.9 ± 3.6</td><td>55.1 ± 2.6</td><td>55.2 ± 2.5</td><td>37.3</td><td>18.2</td><td>19.1</td><td>72.5</td></tr></tbody></table>

The combination of FTIR, TGA, XPS, and surface energy analyses offers a comprehensive understanding of the BF surfaces. ATR-FTIR of the soluble part of the sizing allowed us to identify the different chemical compositions of the sizing in the fibers. These analyses also evidence the complexity of these sizing systems given the large number of signatures which makes interpretation difficult. Thermal analysis further quantified the amount of sizing on the fiber surface, which can vary significantly depending on the type of sizing. XPS analyses confirmed the presence of sizing and allowed to estimate a coverage ratio and the thickness of the sizing layer deposited on the fiber surface. The XPS analyses also offer insights into the fiber surface reactivity by examining the intricate structure of the C1s spectrum, expecting a higher reactivity for fiber B2. The sizing can significantly alter the

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fiber polarity and, consequently, its surface energy, making the fibers more or less compatible with the polymer matrix. All these insights are key when designhigh-performance composite materials.

## 3.2 Effect of sizing on the mechanical behavior of fiber and commingled yarns (microscale analysis)

Large differences have been highlighted between the different types of basalt fibers which can be attributed to the nature of the sizing. One of the primary functions of sizing is to protect the fiber before and during the composite manufacturing process. During commingling, fibers are exposed to handlings, different pressures, and temperatures. The key question is how the sizingprotects the fiber before and after the commingled process. To understand this sizing role, micro-mechanical tests were conducted on individual basalt fibers, PPS thermoplastic fibers, and commingled yarn fibers. The main results are summarized in Table 5.

<table><caption>**Table 5. Micro-mechanical characterization of individual basalt fibers, commingled fibers, and PPS fibers.**</caption><thead><tr><th>Fiber</th><th>E' (GPa)</th><th>σ<sub>r</sub> (GPa)</th><th>D (μm)</th><th>ε<sub>max</sub> (%)</th></tr></thead><tbody><tr><td>B0</td><td>86.2 ± 2.6</td><td>1.4 ± 0.4</td><td>11.8 ± 1.5</td><td>1.9 ± 0.5</td></tr><tr><td>B1</td><td>80.1 ± 1.3</td><td>2.7 ± 0.8</td><td>9.0 ± 1.2</td><td>3.7 ± 1.3</td></tr><tr><td>B1_CY</td><td>77.3 ± 1.5</td><td>2.2 ± 0.8</td><td>9.6 ± 1.1</td><td>3.1 ± 1.4</td></tr><tr><td>B2</td><td>80.7 ± 1.1</td><td>3.1 ± 0.6</td><td>10.2 ± 10.2</td><td>4.2 ± 1.0</td></tr><tr><td>B2_CY</td><td>82.6 ± 1.7</td><td>2.9 ± 0.5</td><td>9.3 ± 0.9</td><td>3.9 ± 0.9</td></tr><tr><td>PPS</td><td>5.7 ± 0.2</td><td>446.2 ± 32.0 (MPa)</td><td>25.6 ± 0.4</td><td>27.3 ± 3.0</td></tr></tbody></table>

For the sized basalt fibers, the Young moduli are slightly different, while an improvement in the tensile strength, $\sigma_R$, is observed for sized fibers compared to the unsized one. The application of sizing enhances fiber durability by minimizing the influence of inherent defects or weak zones along the fibers. This leads to more uniform stress distribution, avoiding basalt fiber premature failure [92,93].

The commingling process has a minimal effect on the moduli. Fiber B2 modulus remains unchanged and fiber B1 modulus is slightly lower. Both fibers keep the same fracture behavior with a slight decrease in performance. Nevertheless, the mechanical properties of commingled fibers are globally given by the inorganic fibers. Conversely, the commingling process seems to negatively affect BF's tensile strength. Hasan *et al.* [94] investigated the effects of changing the commingling process parameters, such as air pressure and temperature, on the mechanical properties of carbon fibers and polyamide 6,6. Their research revealed that high air pressure and heat treatment leads to a slight decrease in tensile and flexural strengths. However, an improvement of tensile strength in the transvers direction (90°) and interlaminar shear strength were observed.

To gain deeper insight into the failure behavior of fibers related to the sizing nature and commingling situation, advanced statistical methods are essential to identify clear patterns. A bimodal

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Weibull statistical analysis provides a precise and detailed understanding of the failure behavior of brittle materials such as basalt fibers. These materials exhibit multiple failure modes, rendering the bimodal Weibull model as a powerful tool for accurately distinguishing the different failure mechanisms.

### 3.2.1 Weibull analysis

To determine whether a bimodal Weibull distribution appropriately describes tensile strength statistics the $ln(ln(1/(1-P)))$ vs $ln(\sigma)$ plot was applied as shown in Figure 7. The slope change is indicative of a multimodal distribution implying that defects of different types govern the failure of basalt fibers. In the region of slope change, a mixed distribution based on both type of defects occurs, while at the extremes of the curve, the distribution is only governed by one type of defects [63].

<figure><img src="image_9.png" /><figcaption>Figure 7. Bimodal Weibull plot of basalt fibers strength.</figcaption></figure>

The parameters of the bimodal Weibull distribution were determined from a conventional least-square method minimizing the sum of squared residuals of failure probability. The results are summarized in Table 6 and the plot of probability density function (PDF) and the cumulative density function (CDF) are plotted in Figure 8.

<table><caption>Table 6. Weibull parameters of different fibers and commingled fibers.</caption><thead><tr><th>Fiber</th><th>P</th><th>σ<sub>01</sub></th><th>σ<sub>02</sub></th><th>m<sub>1</sub></th><th>m<sub>2</sub></th></tr></thead><tbody><tr><td>B0</td><td>0.2</td><td>1.1</td><td>3.5</td><td>27.1</td><td>3.8</td></tr><tr><td>B1</td><td>0.3</td><td>4.4</td><td>5.1</td><td>3.3</td><td>7.3</td></tr><tr><td>B1_CY</td><td>0.3</td><td>2.7</td><td>4.6</td><td>3.0</td><td>6.9</td></tr><tr><td>B2</td><td>0.2</td><td>4.2</td><td>5.2</td><td>20.0</td><td>5.5</td></tr><tr><td>B2_CY</td><td>0.2</td><td>1.1</td><td>3.5</td><td>27.1</td><td>3.8</td></tr></tbody></table>

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<figure><img src="image_10.png" /></figure>

<figure><img src="image_11.png" /></figure>

<figure><img src="image_12.png" /></figure>

<figure><img src="image_13.png" /><figcaption>**Figure 8.** Probability Density Function (PDF) and Cumulative Density Function (CDF) of the tensile strength ($\sigma_R$) for different basalt fibers and their corresponding commingled yarns: (a) and (c) display the PDF and CDF for B1 and B1_CY; (b) and (d) show the PDF and CDF for B2 and B2_CY. B0 is included as a reference in all graphs.</figcaption></figure>

For neat fibers, the bimodal Weibull PDF displays two different maxima at low stresses. The sized fibers highlight these two different fracture phenomena more clearly (See Figure 8 for a and b). This behavior has already been reported by Lissart and Lamon [95] categorizing these two defects as extrinsic and intrinsic flaws. The extrinsic flaws include defects caused by external factors like structural inconsistencies during manufacturing such as variations in diameter, resulting in significant differences in the severity of flaws across the fiber and leading to a wide range of defects. The intrinsic flaws consist of inherent defects along the fiber. They are related to its microstructure, including those on the surface or within the material itself.

Pristine fibers, missing the protective effect of sizing, show reduced durability, evidenced by the PDF maxima at lower stresses. The effect of sizing on tensile strength is observable with the solid lines of Figure 8 for the PDF plot, a shift towards higher stresses of both flaw populations for sized fibers, particularly pronounced for fiber B2.

The dashed curves underscore the commingled process damage for both sized fibers. However, the fiber B1, PA/PU-sized, displays the major changes. When the fibers are commingled, the failure probability shifts to lower stress, and a redistribution of flaws is observed. The results suggest that the commingling process induces severe defects, at lower $\sigma_R$, easily predictable owing to the narrower shape of the distribution. The failure probability for severe defects seems to increase by observing the shift in the PDF, meaning that the amount of surface and volume-located defects increased compared to the sized fiber. Nonetheless, the number of minor defects, at higher $\sigma_R$, is still important. In effect, the commingled processing induces fiber weakening.

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Regarding the behavior of fiber B2 after commingled processes, the tensile strength is significantly less degraded compared to fiber B1. When the fiber is commingled, the severe and minor defects are quite close in terms of probability. From Figure 8, Figure 8-d, it can be suggested that the performance degradation occurred only for minor defects and that no critical failure points were generated by this commingled process.

Overall, the presence of sizing improves the micro-mechanical behavior of interfaces, and the commingled process although it brings many advantages, the generation of damage to the basalt fibers and therefore to the final composite cannot be denied. Nevertheless, the observations on single fibers extracted from commingled yarns can be related to possible damage during extraction from the yarn. To validate these results, tensile tests at a macroscopic scale must be carried out to establish relationships between micro and macroscales.

## 3.3 Micro-mechanical adhesion (fiber-matrix interface)

### 3.3.1 Interfacial Shear Strength: Pull-out test

The characterization of fibers themselves has revealed distinct mechanical behaviors influenced by the chemical nature of sizing. However, the role of interfaces and the effect of the different surface treatments still require further investigation. Fiber-matrix adhesion in composite results from several phenomena such as mechanical interlocking, weak interactions, interdiffusion, electrostatic interactions, and covalent bonding among others. To evaluate the strength of the fiber/matrix interfaces, several micro-mechanical adhesion tests have been developed, including indentation, fragmentation, micro-droplet, debonding, or pull-out test [96]. In order to understand the role and performance of sizing at the micro-scale, pull-out tests were performed on the different available basalt fibers. It's important to note that all experiments attempted to reproduce the same thermal history (see *错! Source du renvoi introuvable. Figure 2*). Any significant change of these parameters could drastically alter the structure of the boundary layer, i.e. affecting the interfacial shear strength such as the formation of different transcrystalline interphases [97,98]. The interface characteristics obtained from the analysis of the

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apparent IFSS, Penn & Lee, and Greszczuk models are summarized in Table 7 and

<figure><img src="image_14.png" /><figcaption>b)</figcaption></figure>

<figure><img src="image_15.png" /><figcaption>c)</figcaption></figure>

<figure><img src="image_16.png" /><figcaption>Figure 9</figcaption></figure>

<table><thead><tr><th rowspan="2">Interface</th><th rowspan="2">#</th><th rowspan="2">τ<sub>app</sub><br>(MPa)</th><th colspan="3">Greszczuk' model</th><th colspan="2">Penn & Lee' model</th></tr><tr><th>τ<sub>max</sub><br>(MPa)</th><th>b<sub>1</sub><br>(m)</th><th>R<sub>1</sub><br>(μm)</th><th>G<sub>ic</sub><br>(J.m<sup>2</sup>)</th><th>R<sub>1</sub>/r<br>(-)</th></tr></thead><tbody><tr><td>PPS/B0</td><td>50</td><td>21.9 ± 5.8</td><td>90</td><td>1.00E-05</td><td>28.1</td><td>23.1</td><td>5.2</td></tr><tr><td>PPS/B1</td><td>30</td><td>40.2 ± 10.3</td><td>147.9</td><td>9.70E-06</td><td>26.6</td><td>64.2</td><td>5.1</td></tr><tr><td>PPS/B2</td><td>25</td><td>52.3 ± 9.8</td><td>202.4</td><td>9.30E-06</td><td>25.7</td><td>106</td><td>5</td></tr></tbody></table>

# : number of specimens

<caption>Table 7. Summary of pull-out results of systems PPS/BF. Summary of interfacial shear strength (τ<sub>app</sub>) and parameters derived from Greszczuk's and Penn & Lee's micromechanical models for different PPS/basalt fiber interfaces. Tmax is the maximum interfacial shear strength, b<sub>1</sub> is the estimated thickness of the interface, R<sub>1</sub> is the radius subject to stress near the fiber, and G<sub>ic</sub> is the interfacial fracture toughness.</caption>

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<figure><img src="image_17.png" /></figure>

<figure><img src="image_18.png" /></figure>

<figure><img src="image_19.png" /><figcaption>**Figure 9.** IFSS as a function of embedded length (L~e~) of PPS/basalt fibers interfaces: Pull-out analyses applying the shear-lag model, Greszczuk model, and Penn and Lee model for a) bare basalt fiber B0, b) basalt fiber B1 sized with PA/PU, and c) basalt fiber B2 sized with epoxy-UP</figcaption></figure>

The apparent shear strength value of the PPS/bare basalt fiber system is quite close to PPS/bare glass fiber systems (11-22 MPa), likely due to the similarities between both types of fibers regarding surface composition [98–100]. The pristine system, however, exhibits the lowest interfacial shear stress, τmax, and work of fracture, Gic, most likely due to the absence of an engineered surface. The sizing on fiber B1 leads to a notable enhancement of fiber-matrix adhesion given the increase of τmax and Gic, 65% and 180% respectively, compared to the bare fiber/matrix interface. However, the sizing of fiber B2 outperforms that of fiber B1, with a 125% improvement in τapp and 360% for Gic over the pristine fiber system. The results highlight the importance of the sizing to improve interface quality resulting in a relevant stress transfer and a good adhesion [52,101,102]. In our study between PPS and basalt fibers, B2 fibers with a sizing based on epoxy-UP appear to be particularly effective at creating a high
interfacial adhesion between PPS and basalt thanks to a well-built interface/interphase. Although the Greszczuk model and Peen and Lee do not come to the same conclusion regarding adhesion strength, they do show the same trend. The first model is based on the shear stress criterion by determining the interfacial shear strength. The second model is based on an energy criterion, describing the energy needed to propagate a crack along the fiber-matrix interface. Fibers with epoxy-UP sizing led to a more robust interphase than fibers with PA/PU sizing with PPS matrix.

### 3.3.2 *Thermodynamical works of adhesion*

Several works have explored the relationships between the thermodynamical adhesion work ($W_A$) and the adhesion strength of the fiber/matrix interface. The thermodynamical adhesion work, or fundamental adhesion, refers to the break of the interaction (physical or chemical) required to separate a unit area of two contacting dissimilar phases under equilibrium conditions [103]. In contrast, the adhesive strength, or practical adhesion, is based on the same contribution plus several ones as the mechanical properties of the components, and specimen dimensions. These variables make studying and quantifying practical adhesion challenging. This has led to the development of various approaches for assessing adhesive strength. Indeed, some researchers recognize that measuring the practical adhesion can lead to inaccuracies due to factors such as pressure and friction across the interface [104,105].

While fundamental and practical adhesion address different interfacial phenomena, several works have discussed the relationship between both. For instance, the research of Jacobasch *et al.* [106,107], Zhandarov *et al.* [103], or Nardin and Schultz [108,109], have shown a relationship between fundamental and practical adhesion. This trend is also observed in this study. Figure 10Figure 10 displays the shear stress determined from the Peen-Lee model against the work of adhesion determined from the Owens-Wendt theory.

<figure><img src="image_20.png" /><figcaption>Figure 10. Shear stress of Peen-Lee' model as a function of work of adhesion for PPS and BF.</figcaption></figure>

As expected, the results confirm a relationship between the fundamental and practical adhesion. The discrepancy in linearity and in the order of magnitude are anticipated, given the significant

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differences in the experimental procedures. The work of adhesion reflects the wettability of fibers within a polymer matrix, being a thermodynamical reversible process. In contrast, the practical adhesion quantifies the energy required for complete debonding, an irreversible phenomenon. A comparison of these two characterization techniques in **Figure 10** and **Figure 10** clearly shows a difference in the order of magnitude. The change of $G_{ic}$ between the bare fiber and the sized ones are also remarkable. The substantial increase in the energy required to propagate a crack indicates that, in addition to acid-base and hydrogen bonding interactions, covalent bonding likely plays a significant role. Indeed, the works of Gonon *et al.* [110], who demonstrated that even limited functionalization through the introduction of carboxy groups in PPS can markedly enhance the adhesion between the glass fiber and the polymer matrix. A chemical reaction involving $\gamma$-APTES, covalently grafted to glass fibers is proposed. The elevated temperatures applied during the micro composite processing may facilitate the generation of a small amount of these functional groups, promoting the same reaction proposed by Gonon *et al.* Moreover, the lower debonding energy observed for the bare basalt fiber compared to the sized fiber further corroborates this hypothesis.

## 3.4 Macro scale mechanical behavior

### 3.4.1 Composite morphology

After evaluating adhesion at the micro-mechanical scale, analysis at a larger scale is required, i.e. in multi-filament composite materials. Firstly, examining the morphology of the commingled yarn and the composite is crucial to gaining insights into the mechanical behavior at the macro scale. **Figure 11** presents cross-section views of different commingled yarns and their respective composites acquired by SEM. In **Figure 11**-a, the commingled yarns made with fibers B1 which uses PA/PU as film former in their sizing, exhibit a clear separation between the BF and PPS fibers (B1_CY). In contrast, the commingled yarns produced with fibers B2, which include epoxy-UP as film former, show a more homogeneous distribution of basalt and PPS fiber types (B2_CY).

The varying shades of gray in **Figure 11**-b help to elucidate the morphology and the presence of voids. Yarns made with fibers B2 seem to present a lower void content, a crucial parameter in composite fabrication by minimizing the air during manufacturing. Indeed, Thomanny and Ermanni [111] have concluded that composites with low void content can only be obtained from high-quality yarns. The yarns made from fibers B2 appear to align with this trend.

Regarding the composite morphology depicted in **Figure 11**-b, large and numerous voids are not observed. Only small voids between the fibers, known as intra-yarn voids are present. This minimal void content contributes to achieving favorable mechanical properties and durability of the resulting composite. The works of Patou *et al.* [112], have evidenced a significant reduction of mechanical performances for PPS/carbon fiber composites when the void content exceeds 2%.

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The morphology differences observed among the four study cases in Figure 11 Figure 11-b seem to result primarily from variation in fiber sizing rather than the yarn manufacturing process. Composites made with B1 fibers exhibit the classical compacted yarn structure often reported in the literature [64,113]. In contrast, composites made with B2 fibers display a more homogeneous fiber distribution. The surface reactivity of fibers B2, attributed to the epoxy-UP type sizing and evidenced by XPS analysis, plays a veritable asset in promoting enhanced fiber dispersion.

The recorded images and the chemical characterizations underscore the importance of surface
chemistry and its reactivity over processing to achieve optimal composite material morphology. Epoxy-
UP sizing enables a better wetting of fibers by PPS, while PA/PU sizing leads to fibers clustering,
potentially leading to weak spots and uneven load distribution. Mechanical testing of composite
materials could offer further complementary insights to the findings observed at micro-scale.

<figure><img src="image_21.png" /><figcaption>**Figure 11.** SEM cross-sectional views of commingled yarns composed of PPS and basalt fibers with different sizings : (a) BF with PA/PU, (b) BF with epoxy-UP, and their corresponding composites cross-sectional views in (c) and (d), respectively.</figcaption></figure>

3.4.2 Yarn tensile behavior

This study looks to elucidate the mechanical performances aligned with the commingled yarn processing. To achieve this, a comparison of the average fracture strain between CY, CY_model, and the average fracture stresses of both fibers was performed. This approach allows to understand the differences that both fibers might experiment with in the manufacturing process (B1 CY and B2 CY).

While comparing the CY and CY_model, the not-processed samples exhibit the highest fracture stress, indicative of its maximum achievable stress. The same tendency for Young modulus is observed with a decrease of 18% for commingled yarns compared to model yarns. This reduction in modulus might be attributed to a potential misalignment of reinforcement fibers in the commingled yarn or a reduction in the cross-sectional area due to fractured fibers.

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Gras, Anglais (États-Unis)
To go further, the BF tensile strength and the modulus of yarns were estimated by assuming two hypotheses: i) none basalt fibers are fractured before the maximum force, and ii) all basalt fibers are fractured after the maximum force. The relationships (6), (7), and (8), previously discussed were applied, extracting the fiber contribution to determine fiber (filament) behavior. Figure 12Figure 12 summarizes the behavior of extracted fibers and different commingled yarns. The results are in line since the Young modulus value achieved for the CY_model is similar to one obtained at the filament scale (Table 5Table 5 and Table 8Table 8). Additionally, the force changes versus deformation after breakage exhibits a quite similar behavior to monofilament of PPS ($\sigma_{PPS} = f(\epsilon)$), highlighted in yellow in Figure 12Figure 12. Indeed, in figures a) and b) the overlapping of the PPS behavior and the commingled yarn after BF fracture is obvious.

<table><caption>Table 8. Tensile behaviors of commingled yarns (CY) and non-processed yarns (CY_model) with basalt fiber B1 and B2</caption><thead><tr><th rowspan="2"></th><th colspan="2">Commingled Yarn</th><th colspan="2">Basalt fibers</th></tr><tr><th>σ<sub>b</sub> (MPa)</th><th>E' (GPa)</th><th>σ<sub>b</sub> (MPa)</th><th>E' (GPa)</th></tr></thead><tbody><tr><td>B1_CY_model</td><td>539 ± 59</td><td>38 ± 0</td><td>1134 ± 127</td><td>81 ± 2</td></tr><tr><td>B1_CY</td><td>448 ± 78</td><td>32 ± 1</td><td>907 ± 165</td><td>66 ± 1</td></tr><tr><td>B2_CY_model</td><td>736 ± 58</td><td>38 ± 0</td><td>1521 ± 125</td><td>80 ± 1</td></tr><tr><td>B2_CY</td><td>588 ± 39</td><td>33 ± 1</td><td>1171 ± 90</td><td>63 ± 4</td></tr></tbody></table>

<figure><img src="image_22.png" /></figure>

<figure><img src="image_23.png" /></figure>

<figure><img src="image_24.png" /></figure>

<figure><img src="image_25.png" /><figcaption>Figure 12. Force-strain curves of different commingled yarns and their components (basalt fibers and PPS matrix) tested at a tensile speed of 10 mm·min⁻¹. Images a) and b) show modeled commingled yarns (B1_CY_model and B2_CY_model), while images c) and d) present the experimental results for B1_CY and B2_CY, respectively. Each plot includes the corresponding fiber (B1 or B2) and PPS as references.</figcaption></figure>

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For commingled yarns, the calculated BF modulus is comparatively lower, measuring 66 GPa for B1 CY1 and 63 GPa for B2 CY1. Notably, the observed force contribution of PPS did not align with the total measured force after breakage (Figure 12Figure 12-c and d). This indicates that not all reinforcement fibers are fractured after the primary breakage event. The results can be attributed to the nature of commingled yarns, where some fibers are well aligned with the tensile direction and contribute linearly, while others situated in the open zones and off-axis contribute after the primary breakage event.

When comparing the performances of the fiber, the importance of sizing in determining mechanical properties becomes noticeable. The tensile strength for fibers containing epoxy-UP sizing (B2 CY) is more than 30% higher than that of yarns with Polyamide/Polyurethane sizing (B1 CY). The behavior may be explained by the good spreading of the yarns observed in Figure 11Figure 11. Yarns made from fibers B2 display a good spreading while yarns based on fibers B1 exhibit a more limited one. The spreading quality leads to more intimate commingling between basalt fibers and the thermoplastic matrix. This improved interaction likely enhances load transfer during the test.

The mechanical tensile properties further confirm previous observation with single filaments, where the fiber with epoxy-UP sizing, display a higher tensile stress at rupture than fiber with PA/PU as sizing. These observations underscore the complex interaction between material morphology and mechanical behavior in the composites.

### 3.4.3 Interlaminar shear stress analysis (ILSS)

Three-point flexural tests were conducted to evaluate the mechanical performances of interfaces/interphases in composite materials.

The interlaminar shear stress, $\tau$, is given by (9) [114].

$$ \tau = 3P / (4 \times b \times h) \qquad (9) $$

where $P$ is the maximal force applied, $b$ is the width of the sample, and $h$ is the thickness.

The results presented in Table 9 Table 9 illustrate the influence of sizing on the interlaminar shear stress. Indeed, comparing the composites C_B1 CY and C_B2 CY results in a notable enhancement of 62%.

<table><caption>Table 9. Interlaminar shear stresses of composites based on both manufacturing yarn processes and both different fibers.</caption><thead><tr><th>Reference</th><th>N</th><th>m<sub>basalt fiber</sub> (%)</th><th>F<sub>max</sub> (N)</th><th>σ<sub>max</sub> (MPa)</th><th>ILSS (MPa)</th></tr></thead><tbody><tr><td>C_B1 CY</td><td rowspan="2">5</td><td>58</td><td>1133 ± 41</td><td>435.9 ± 14.7</td><td>43.5 ± 1.6</td></tr><tr><td>C_B2 CY</td><td>60</td><td>1844 ± 112</td><td>781.5 ± 53.7</td><td>74.2 ± 4.9</td></tr></tbody></table>

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The ILSS determined for the composite at a nano-scale agrees with the micro-scale, i.e. determined by the pull-out tests. The fiber B2, with a sizing made with epoxy-UP leads to higher mechanical properties of composites than fiber B1 having a sizing made with PA/PU film former.

To go further, a cryofracture of composites was carried out, SEM images are displayed in **Figure 13**. The fracture surface of composite C_B1_CY suggests that the surface of fibers is partially covered by the matrix, while the fracture surface of fiber for composite C_B2_CY displays a higher fiber covering. The fiber-matrix wetting for composite manufactured with fiber B2 is highlighted in fracture zones displaying significant plastic deformation of the matrix at the fiber surface. Gao and Kim [115] have already documented a similar morphology in PEEK/carbon fiber composites, noting that such morphologies are characteristic of highly crystalline samples subjected to shear stress. Under loading, the fracture mechanism occurs within the matrix. This phenomenon suggests that the fiber/matrix interface could transfer higher stress.

<figure><img src="image_26.png" /><figcaption>**Figure 13.** Cryofracture SEM images of composites made from commingled yarns based on fibers B1 a) and fibers B2 b).</figcaption></figure>

## 4. Conclusion

This work presents a comprehensive multiscale investigation of PPS reinforced with basalt fibers to produce composites via a commingled yarn process. The results establish clear relationships between chemical surface treatments, interfacial adhesion, composite morphology, and overall mechanical performance. Initially, detailed chemical characterization using FTIR, TGA, and XPS

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revealed significant differences in the chemical composition, reactive functional groups, and thermal stability of fibers. Contact angle measures further quantified the wettability of fibers, substantially influenced by the surface energy depending on the sizing.

At the micro-scale, pull-out adhesion tests were conducted at the micro-scale to measure the IFSS between the fibers and the PPS matrix. The results demonstrated a remarkable improvement in IFSS up to 125 % when using PA/PU sizing, and a 360% increase with epoxy-UP sizing, both compared to unsized fibers. The improvement confirms that the fiber-matrix interface is critically enhanced by the proper selection of sizing. The results highlight the relationship between thermodynamical and practical adhesion. While good wettability generally predicts good practical adhesion between fibers and polymer matrices, wettability alone may not capture the covalent bonds at the interface; however, the test still provides valuable insights.

At the macro-scale, the ILSS test provided further evidence that the micro-scale adhesion improvements translate to the overall composite performance. The epoxy-UP-based film former sizing yielded an ILSS enhancement of 62% over PA/PU-based film former sizing. This result demonstrates the direct correlation between micro-level interfacial performance and the macroscopic mechanical behavior of the composite.

Morphological analysis revealed the importance of sizing in fiber distribution, particularly in how the basalt fibers open within the composite. Composites fabricated with an epoxy-UP-based sizing displayed a more homogeneous distribution and superior structural integrity compared to the PA/PU-based sizing counterpart.

The Weibull statistical analysis of different fibers assessed the flaw distribution inherent in the fibers. The analysis highlighted severe and minor flaws in fiber, showing that unsized fibers tend to have a higher population of severe defects compared to those sized. The reactive sizing revealed a higher healing effect than the non-reactive sizing. The effect in the different-sized fibers due to the yarn manufacturing is also evidenced. Micro-tensile tests on extracted BF filaments from commingled yarns confirm a decrease in the tensile strength. The results indicate a mechanical degradation caused by the commingling which can be mitigated depending on the sizing. The reactive sizing, the epoxy-UP-based, stands out in the commingling process.

Collectively, the integrated results of this study highlights the essential role of fiber sizing in producing high-performance composite materials. This work provides valuable guidance and establishes a robust multiscale framework that links chemical surface treatments, micro-adhesion, morphological uniformity, and macro-scale mechanical performance when producing PPS/BF materials from commingled yarns.
758 Glossary

759 BF: Basalt fiber

760 CDF: Cumulative density function

761 CY: Commingled yarn

762 FTIR: Fourier transform infrared spectroscopy

763 G<sub>ic</sub>: Interfacial toughness

764 GPTMS: (3-glycidoxypropyl)trimethoxysilane

765 IFSS: Interfacial shear strength

766 ILSS: Interlaminar shear strength

767 PA: Polyamide

768 PDF: Probability density function

769 PPS: Polyphenylene sulfide

770 PU: Polyurethane

771 TGA: Thermogravimetric analysis

772 τ<sub>max</sub>: Maximum interfacial shear stress

773 UP: Unsaturated polyester

774 SEM: Scanning electron microscopy

775 XPS: X-ray photoelectron spectroscopy

776 γ-APTES: γ-aminopropyltriethoxysilane

777

778

779

780

781 Acknowledgements

782 New Hybrid Yarn for. Clothing and Composites

783

784

785 Autor contributions: CRediT

786 CASTRO-CABRERA I.: Writing – original draft, Investigation, Formal analysis, Visualization.

787 GAUMOND B.: Writing – original draft, Investigation, Formal Analysis, Visualization

788 CIESLAK D.: Investigation

789 GERARD J. F.: Writing – review and editing
790 LIVI S.: Writing – review and editing, Supervision, Conceptualization

791 RUMEAU-DUCHET J.: Writing – review and editing, Supervision, Conceptualization, Funding

792 acquisition

793

794

795

796 Bibliography

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1152
1153

1154
1155

1156 Figure 1. Cross-section of a) an ideal commingled yarn and b) non-homogeneous distribution.

1157 Figure 2. Sample preparation thermal cycle (a) Micro-composite pull-out sample (b).
1158 **Figure 3. Commingled Yarn tensile test specimen**

1159 Figure 4. FTIR-ATR spectra of soluble sizing of a) fiber B1 and b) fiber B2.

1160 Figure 5. Weight loss as a function of temperature (TGA, DTG) of the sizing content in fibers references, a) thermogravimetric analysis, and b) derivate of weight loss against temperature (heating ramp 10 K·min⁻¹, Air atmosphere).

1163 Figure 6. Deconvolution of C 1s XPS spectra of a) fiber B1, and b) fiber B2.

1164 Figure 7. Bimodal Weibull plot of basalt fibers strength.

1165 Figure 8. Probability density function (PDF) and cumulative density function (CDF) of different basalt fibers, commingled yarns CY (a and c),

1167 Figure 9. Summary of pull-out results applying the apparent IFSS, Peen and Lee, and Greszczuk model for a) fiber pristine B0, b) fiber with PA sizing B1, and c) fiber with Epoxy-UP sizing B2.

1169 Figure 10. Shearing stress as function of adhesion work for PPS and BF.

1170 Figure 11. Cross-sectional view of commingled yarns with PPS and: (a) BF sized with PA/PU, (b) BF sized with Epoxy-UP, and their corresponding composites (c) and (d)

1172 Figure 12. Force-strain plots of different commingled yarns.

1173 Figure 13. Cryofracture SEM images of composites made from commingled yarns based on fibers B1 a) and fibers B2 b).

1175

1176 Table 1. Properties of commingled yarns provided by Billon Mayor Industry.

1179 Table 2. The elementary composition of BF at the surface determined by XPS analysis.

1180 Table 3. Positions and intensities (%) of the C1s sub-peaks of basalt fibers B1 and B2.

1181 Table 4. Experimental contact angle measurements with different probe solvents, surface energy, dispersive and non-dispersive components, and work of adhesion between PPS and BF

1183 Table 5. Micro-mechanical characterization of basalt fibers, commingled fibers, and PPS.

1184 Table 6. Weibull parameters of different fibers and commingled fibers.

1185 Table 7. Summary of pull-out results of systems PPS/BF.

1186 Table 8. Summary of tensile test results of commingled yarns (CY1) and non-processed yarns (CY1_model) with basalt fiber B1 and B2

1188 Table 9. interlaminar shear stresses obtained for both manufacturing yarn processes and both different fibers.

1190

1191
1192 Appendix A. Supporting information

1193 Fiber matrix adhesion

1194 • Apparent Interfacial Stress Strength, IFSS (shear stress criterion)

1195 The Apparent IFSS (a) considers a uniform distribution of shear stress along the fiber. This model is

1196 widely used due to its simplicity.

1197 $\tau_{app} = \frac{F_{max}}{2\pi r_f l_e}$ (a)

1198 where $\tau_{app}$ is the apparent shear stress, $F_{max}$ denotes the maximal force, $r_f$ is the fiber ratio, and $l_e$ indicates

1199 the embedded length.

1200 • Greszczuk model (shear stress criterion)

1201 Greszczuk model is a shear stress criterion, stating that the interface failure occurs when the shear stress

1202 reaches a limit value (b). Furthermore, the shear stress varies along the fiber, reeling the “shear lag”

1203 theory. This assumes that the shear stresses on the fiber and the tensile stresses on the matrix are

1204 negligible compared to the tensile stress within the fiber and the shear stress on the matrix ($\tau_f \ll$

1205 $\sigma_f$; $\sigma_m \ll \tau_m$). The model does not consider friction or Poisson effect, or residual stress.

1206 $\tau(x) = \frac{F\alpha}{2\pi r_f} [\coth(\alpha l_e) \cosh(\alpha x) - \sin(\alpha x)]$ (b)

1207 $\alpha = \sqrt{\frac{2G_i}{r_f E_f b_i}}$ (c)

1208 $b_i = r_f \ln(\frac{R}{r_i})$ (d)

1209 Where $F$ is the tensile force and $\alpha$ a geometry factor. The parameter $b_i$ is defined as the thickness around

1210 the fiber, or the interface, and this is the zone that experiments the shear stress. The parameter $G_i$ is the

1211 interfacial fracture toughness, assumed equal to the matrix shear modulus ($E_m$), and $E_f$ is the young

1212 modulus of fiber and $R_i$ is the radius subject to stress near the fiber.

1213 Greszczuk’s model allows to obtain the maximum interfacial shear strength when the embedded

1214 length is equal to zero (e). The expression comes as follows:

1215 $\tau(x) = \tau(0) = \frac{F\alpha}{2\pi r_f} [\coth(\alpha l_e)]$ (e)

1216
1217 • Peen-Lee model (energy criterion)
1218 Peen-Lee model is an energy-base criterion that considers a pre-existing or initiated crack of length l at the interface (f). The model determines the energy necessary to propagate the failure and cause complete debonding. It enables the determination of fracture energy Gic from the following relationship:

$$1221 \qquad F(max) = \frac{2\pi r_f \sqrt{r_f G_{ic} E_f}}{\sqrt{1 + \left(\frac{1}{\sinh(n \frac{l_e}{r_f})}\right)^2}} \qquad (f)$$

$$1222 \qquad n = \sqrt{\frac{E_m}{E_f(1+\nu_m)\ln\left(\frac{R}{r_f}\right)}} \qquad (g)$$

1223 XPS analysis

1225 The thickness of sizing e is given by equation (h), which, in turn, depends on the coverage ratio, f, determined from equations (i), (j), (k), (l), and the ratio C/Si and O/Si measured by 1226 XPS (Table 2). The sizing content (m_e and m_f) was obtained from TGA results. The density of fiber and 1227 sizing, ρ_f = 2.62 g.cm⁻¹ and ρ_e=1.2 g.cm⁻¹, are given by the supplier and the ratio of fiber, r_f, was 1228 determined by Vibroscope method. 1229

$$1230 \qquad e = (r_f * m_e * \rho) / (2 * \rho_e m_f * f) \qquad (h)$$

$$1231 \qquad N_c = f * x * \rho_e * P(e, d) * [N_a / (16 + 14x)] \qquad (i)$$

1232 From the hypothesis of (i)

$$1233 \qquad x = (N_c / N_o)_{sizing} \qquad (j)$$

$$1234 \qquad N_o = f * \rho_e * P(e, d) * [N_a/(16 + 14x)] + f * \rho_f * (1-P) * [2 * N_a / 60] + (1-f) * \rho_f * [2 * N_a / 60] \qquad (k)$$

$$1235 \qquad N_{Si} = f * k * \rho_f * (1 - P) * [N_a/60] + (1 - f) * k * \rho_f * [N_a / 60] \qquad (l)$$

$$1236 \qquad 1 - P = \exp(-e/d); \quad d = 3\lambda \sin(\theta) \qquad (m)$$

1237 The following relations summarized the methodology applied to determine the sizing thickness 1238 according to the Thomason and Dwing model.

1239 From equation (i):

$$1240 \qquad x = 16N_c / (f * \rho_e * P(e, d) * N_a - 14N_c) \qquad (n)$$

$$1241 \qquad x = 16(N_c / N_{Si})_{experimental} * N_{Si, theo} / (f * \rho_e * P(e, d) * N_a - 14 * (N_c / N_{Si})_{experimental} * N_{Si, theo}) \qquad (o)$$

$$1242 \qquad x = (16 * (N_c / N_{Si})_{experimental} * N_{Si, theo}) / f * \rho_e * P(e, d) * N_a - 14 * (N_c / N_{Si})_{experimental} * N_{Si, theo} \qquad (p)$$

1243 The coverage ratio, f, was determined numerically by applying the conditions (q) and (r) from 1244 equations (i), (k), and (l), and the experimental data recorded.
1245 $(N_c/N_{Si})_{theo} = (N_c/N_{Si})_{experimental}$ (q)

1246 $(N_o/N_{Si})_{theo} = (N_o/N_{Si})_{experimental}$ (r)

1247
1248 Where *d* is the nominal deep analysis, *e* is the thickness of sizing, *λ* the mean free path of inelastic electrons, *f* is the coverage ratio, *N*<sub>C</sub>, the number of Carbon, *N*<sub>Si</sub>, the number of Silicon, *N*<sub>o</sub>, the number of Oxygens issue of the sizing layer by XPS, and *Na* is the Avogadro's Number. The weight of fibers and sizing were determined by TGA analysis, *m*<sub>f</sub> and *m*<sub>e</sub>. The density of fiber and sizing, ρ<sub>f</sub> = 2.62 g.cm⁻³ and ρ<sub>e</sub>=1.2 g.cm⁻³, are given by the supplier<fnref n="1" />.

1253

<footnote n="1">¹ ISOMATEX S.A., "Product information and technical data sheet - FILAVA," 2019</footnote>