# Unveiling the Amorphous Phase Contribution to Shear Piezoelectric Properties of Polylactide

Hui Shen, Sébastien Charlon, Cédric Samuel

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Hui Shen, Sébastien Charlon, Cédric Samuel. Unveiling the Amorphous Phase Contribution to Shear Piezoelectric Properties of Polylactide. Macromolecules, 2025, 10.1021/acs.macromol.5c01023. hal-05176283

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# Unveiling the Amorphous Phase Contribution to Shear Piezoelectric Properties of Polylactide

Shen Hui<fnref n="1" />, Charlon Sébastien<fnref n="1" />, Samuel Cédric<fnref n="1" />*

## Table of Content Graphic:

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

**Abstract:** Polylactide (PLA) made from renewable resources represents an interesting alternative to classical ferroelectric fluoropolymers. PLA displays shear piezoelectric properties solely activated by uniaxial orientation and conventional poling treatments are not required. However, moderate piezoelectric coefficients *d*₁₄ of approx. 10 pC/N are reported for oriented PLA films and boosting piezoelectric performances requires in-depth knowledge of process-structure-properties relationships. A predictive 3-phase model was recently proposed but the contribution of the oriented amorphous phase remains quantitatively unknown. This work consequently focuses on shear piezoelectric properties of a fully-amorphous polylactide grade (aPLA) containing 11 – 12% D-content. Extruded aPLA films were submitted to uniaxial stretching experiments by machine-direction orientation (MDO). Amorphous phase orientation (*F*<sub>am</sub>) as a function of the draw ratio was characterized by polarized FTIR and the corresponding piezoelectric response was precisely measured by a contactless voltmeter coupled to a DMA apparatus. In all stretching conditions, the absence of mesophase (< 2%) and cavitation phenomena (iso-volumic stretching) are attested. Amorphous phase orientation increases with the true draw ratio imposed by MDO. Values are consistent with classical deformation theories of rubber networks and deviations at high draw ratios indicate slippage of entanglement points. Stretched aPLA films display *d*₁₄ values up to 2 pC/N with a perfect linear coupling between *F*<sub>am</sub> and *d*₁₄. This result validates the significant contribution of the oriented amorphous phase to the overall piezoelectric performance.

<footnote n="1">¹ IMT Nord Europe, Institut Mines-Télécom, Univ. Lille, Centre for Materials and Processes, Cité scientifique, rue Guglielmo Marconi, BP 20145, F-59653 Villeneuve d'Ascq Cedex, France</footnote>

<footnote>* Corresponding author : cedric.samuel@imt-nord-europe.fr</footnote>
formances of PLA. For the first time, the intrinsic piezoelectricity of the amorphous phase of PLA was found close to 7.2 pC/N by extrapolation. To optimize processing conditions and avoid relaxation phenomena during stretching, additional stretching experiments were performed at various draw rates from 0.01 to 1 s⁻¹. Rouse relaxation modes of aPLA are only active for draw rates below 0.3 s⁻¹ and the orientation factor *F*<sub>am</sub> saturates above this value. Relaxation phenomena are consequently not active in most of MDO conditions. A final discussion is conducted regarding the effect of the optical purity on the amorphous phase contribution. For PLA grades with D-content below 10%, the intrinsic piezoelectricity of the amorphous phase can be considered constant. This study consequently helps refining the current 3-phase model and will be of practical use for further structure-properties analyses on oriented semi-crystalline PLA films.

**Keywords:** Polylactide, Shear Piezoelectricity, Amorphous Phase, Uniaxial Stretching, Orientation.

# 1 Introduction

Piezoelectricity is a unique material property that linearly and reversibly couples the electrical and mechanical states in materials with non-centrosymmetric textures. Based on this unique effect, piezoelectric materials have been used as sensors [1, 2], vibrational energy harvesters [3, 4], ultrasound transducers [5] and precision actuators [6]. Besides, novel applications of piezoelectric materials can be found in tissue regeneration [7], catalysis [8], water treatment [9], wearable sensors [10]. Piezoelectric materials are consequently of strategic importance for many modern applications into the electronic, energy and medical industries.

Compared to piezoelectric ceramics, piezoelectric polymers are flexible and easy to process into complex geometries and shapes [11]. Especially, these flexible piezoelectric materials are suitable for sensing and energy harvesting applications due to their high piezoelectric voltage coefficients [12-14]. Conventional piezoelectric polymers are poly(vinylidene fluoride) (PVDF) and other fluoropolymers. Since piezoelectricity emerges as a result of the elimination of the centrosymmetry in a material, these polar polymers require a poling process to align the dipoles along with the external electric field [15]. After poling, these polymers exhibit *∞m* or *mm2* symmetries depending on whether uniaxial orientation is applied before poling. The poling process requires harsh conditions with electrical fields usually above 1 MV/cm [11]. This step complexifies manufacturing operations. Besides, fluoropolymers rise serious environmental concerns. For instance, the synthesis of fluoropolymers depends on “forever chemicals” that require millennia degradation time [16]. These polymers are also not designed for recycling thus can release hazardous fluorine during post-life handling [17]. Regarding these disadvantages
vantages, more sustainable piezoelectric materials are required. Biopolymers possessing spontaneous shear piezoelectricity upon uniaxial orientation were first reported by Fukada in the 1960s [18, 19]. Among them, poly(L-Lactide) (PLLA or commonly called PLA) has strong shear piezoelectricity [19, 20]. PLA are optically-active polymers and exhibit helical chain configurations when oriented. This situation breaks the mirror plane perpendicular to the stretching direction with an invariant 180° rotational axis perpendicular to the orientational axis [11, 21, 22]. Therefore, uniaxially oriented PLA has the $\infty2$ symmetry that contains only shear piezoelectric coefficients ($d_{25} = -d_{14}$). Poling is excluded and only uniaxial stretching is required for PLA to exhibit piezoelectricity. Compared to poling-induced fluoropolymers, PLA is more biocompatible, biodegradable, and sustainable [2]. The piezoelectric coefficient $d_{14}$ is regularly close to 10 pC/N in many scientific articles [2, 4, 22] which is approximately one third the value of PVDF ($d_{31} = 27$ pC/N) [23]. This value is obtained by uniaxial stretching of PLA films on a tensile bench at 80 °C to draw ratio approx. 4. [23]. Post annealing under tension at 110 °C is also mandatory to increase the crystallinity of oriented PLA films. However, recent investigations by Tajistu et al. indicate that the shear piezoelectric coefficients of PLA can be largely optimized using niche manufacturing techniques such as solid-state extrusion [24], supercritical CO$_2$ treatment [25] and magnetic field orientation [26]. Obviously, PLA represents a serious alternative to PVDF as a green, cheap and easy-to-process piezoelectric material with competitive performances.

The primary research challenge is to understand the origin of shear piezoelectricity of PLA and one can construct structure-property relationships to guide PLA optimization in terms of formations and processing conditions. Initial studies made by Fukada on many oriented biopolymers speculated that both the oriented amorphous and crystalline phases of PLA can contribute to shear piezoelectricity with a very low piezoelectric contribution of the oriented amorphous phase compared to oriented crystals [19, 27]. Fukada proposed a spherical-dispersion model [19], in which the piezoelectric crystals dispense in a non-piezoelectric matrix. Experimental measurements of $d_{14}$ for PLA reveal a linear coupling with the product between the orientation factor of piezoelectric crystals ($F_c$) and the number of piezoelectric crystals ($X_c$). The slope value corresponds to the intrinsic piezoelectricity of such a piezoelectric PLA crystal. Actually it seems that this linear relationship exists only when $F_c \cdot X_c$ is below 0.5, as examined by Lovell et al. [28] and Mat Zin et al. [22]. Those authors clearly demonstrate a saturation for higher $F_c \cdot X_c$ values with a maximal $d_{14}$ value of 10 pC/N. Besides, the intrinsic piezoelectricity of PLA crystals was found between 20 pC/N and 30 pC/N with large deviations when $X_c$ increases up to 50% [19, 29]. New models have been proposed, in particular a three-spring model consisting of piezoelectric crystals surrounded by an amorphous relaxational component connected in series and parallel
lel [22]. This model can capture several features such as piezoelectric relaxations close to the glass transition temperature of PLA but remains of limited interest for formulation and processing optimiza- tions because structural features are not implemented in detail. For instance, upon uniaxial stretching in the rubbery state, it is known that semicrystalline PLA can display various metastable mesophases [30, 31] that originates from the oriented amorphous phase [32]. PLA can also exhibit different crystal pol- ymorphs with different packing, *i.e.* α, α'(also named δ) and β, depending on stretching and post- annealing conditions [33, 34]. Semi-crystalline PLA is also prone to mechanical degradation during uniaxial stretching due to cavitation phenomena [21]. These structural features are absent in previous models and should be captured with their dependency to processing conditions.

Based on experimental findings, Ben Achour al. proposed that the shear piezoelectric coefficient of PLA *d*₁₄ can be decoupled into three piezoelectric contributions, *i.e.* oriented amorphous phase, ori- ented mesophase and oriented crystal contributions [21]. This three-phase model is an extension of the original model of Fukada using the product between orientation factors and amount of each phase as shown in Equation (1). This model incorporates three specific parameters as the intrinsic piezoelec- tricity for each phase, respectively named *d*₁₄-*am*, *d*₁₄-*meso*, and *d*₁₄-*c*. Using various techniques for precise orientation measurements (in particular polarized infrared spectroscopy), these fundamental parameters were calculated for the mesophase and for α' crystals close to 13 pC/N (*d*₁₄-*meso*) and 18 pC/N (*d*₁₄-*c*), respectively. These values were obtained on extruded PLA films followed by machine- direction orientation (MDO), as an industrial manufacturing technique for piezoelectric biopolymers. This technique is suitable for manufacturing large-scale piezoelectric films with fully-oriented crystals. The impact of the mechanical degradation by cavitation at elevated draw ratios was also clarified and features related to the quality of crystal produced by MDO were discussed. This three-phase model opens a new era for *d*₁₄ predictions and optimizations based on structure-properties relationships. This model should now be applied to a wide range of processing conditions to test its validity in many situa- tions along with the incorporation of new structural features. This model explicitly incorporates an ori- ented amorphous phase with significant piezoelectric properties as recently proved both at nano- and macroscale [21, 35]. An updated application of this model on PLA with various optical purities extrap- olates a maximum *d*₁₄-*am* around 2 pC/N, but the oriented amorphous phase shows no piezoelectricity in a wholly amorphous PLA, which is conflict with shear piezoelectricity [36]. Overall, the precise piezoelectric contribution of the oriented amorphous phase to the overall *d*₁₄ of semi-crystalline PLA films, its evolution with processing conditions and its intrinsic piezoelectricity (*d*₁₄-*am*) remains un- clear.
$$d_{14} = d_{14-am}F_{am}X_{am} + d_{14-meso}F_{meso}X_{meso} + d_{14-c}F_{c}X_{c} \quad (1)$$

with $d_{14}$ the overall shear piezoelectric coefficient of the PLA film, $d_{14-am}$, $d_{14-meso}$, $d_{14-c}$ the intrinsic shear piezoelectricity of the amorphous phase, mesophase and crystals respectively, $F_{am}$, $F_{meso}$, $F_{c}$ the orientation factor of the amorphous phase, mesophase and crystals respectively, $X_{am}$, $X_{meso}$, $X_{c}$ the amount of amorphous phase, mesophase and crystals respectively.

In this context, this study focusses on the shear piezoelectricity of commercially-available and fully-amorphous polylactide grade (aPLA) containing approximately 11.5% of D-content in order to reveal the contribution of the oriented amorphous phase. The extruded film was uniaxially stretched by machine-direction orientation (MDO) close to the glass transition temperature at various draw ratios up to 4. The stretching phase was first analyzed in detailed by dimensional analyses to insure homogenous, isovolumic and uniaxial deformations without cavitation. The absence of strain-induced mesophase and crystallization was also insured by various techniques. Orientation factors were then extracted by polarized FTIR and the piezoelectric response of oriented aPLA films was precisely captured by a contactless voltmeter coupled to a DMA apparatus. The effective contribution of the oriented amorphous phase was revealed without any doubt and, for the first time, the intrinsic piezoelectricity of the amorphous phase was obtained by extrapolation. Several other features were investigated such as the accordance with the deformation theory of rubber networks, the importance of draw rate on relaxation phenomena of the oriented amorphous phase and impact of the optical purity of PLA on amorphous phase piezoelectricity.

# 2 Experimental Section

## 2.1 Materials

Amorphous polylactide (grade Luminy® LX975, hereafter called either aPLA) was kindly supplied by TotalEnergies Corbion. The D-content is approx. 11.55% (Perkin Elmer polarimeter, chloroform as the solvent and under sodium lamp at 589 nm) and the number average molecular weight ($\overline{M_n}$) was found close to 61130 g/mol with a polydispersity index of 1.98 (size exclusion chromatography with tetrahydrofuran as eluant, 1 mL/min, 40 °C). A correction factor of 0.58 was applied according to A. Kowalski [37]. The glass transition onset temperature ($T_g$) is 54.8 °C as determined by differential scanning calorimetry (DSC) at a 10 °C/min rate from the second heating cycle. Another semicrystalline polylactide films (grade NatureWorks® 7000D, D-content 6.4%), which were produced by the extrusion-calendaring-MDO technology, were used for the investigation of optical purity.
## 2.2 Methods

### 2.2.1 Extrusion-calendaring of aPLA films

Pellets of aPLA were transformed into films by extrusion-calendaring as illustrated in **Figure 1**. First, aPLA pellets were dried at 60°C (Maguire LPD30 low-pressure dryer, overnight drying according to the manufacturer's recommendation). Dried pellets were processed on a single-screw extruder (D 40 mm, L/D 25, Kaufman, Germany) equipped with a specific slit die (width 12 cm, gap 300 µm). A screw speed of 10 rpm was used with the following temperature profile was set up (130°C, 200°C, 210°C, 210°C, 210°C and 200°C). Film extrudates were calendared at 50°C with a calendaring speed of 1.5 m/min to obtain aPLA films with controlled dimensions and qualities for further processing (width 8.8 ± 0.1 cm, thickness of around 250.8 ± 13.8 µm).

### 2.2.2 Uniaxial-stretching of aPLA films by machine-direction orientation (MDO)

Extruded aPLA films were uniaxially-stretched by a pilot-scale machine-direction orientation technique (MDO, Collin Techline, Germany) at various draw ratios (**Figure 1**). The upstream and downstream chambers of the MDO machine were both set at 60°C just above the glass transition temperature of aPLA. The upstream rolls were kept at a constant speed of approx. 1 m/min. The downstream rolls operate with increasing speeds from 1.5 to 4 m/min with increments of 0.5 m/min between experiments. In this respect, the apparent draw ratio $\lambda_{app}$ is precisely known as the ratio between downstream to upstream speeds. Films were cooled down instantly and spooled for further analysis.

<figure><img src="image_3.png" /><figcaption>**Figure 1.** Three-step manufacturing strategy for piezoelectric aPLA films. Film extrusion and calendaring in blue and gray respectively. Film orientation by a pilot-scale MDO technique at various draw ratios (highlighted in green). Film orientation by an instrumented lab-scale stretching technique at various draw rates (highlighted in orange).</figcaption></figure>
### 2.2.3 Uniaxial-stretching of aPLA films by an instrumented lab-scale machine

Extruded aPLA films were uniaxially-stretched by an instrumented lab-scale stretching technique (Brueckner Karo® IV, Germany) at various draw rates (Figure 1). Extruded aPLA film were cut into rectangular specimens (length 120 mm and width 100 mm) and clamped into the stretching machine. Films were preheated to 60°C for 2 minutes and stretching experiments were performed at various draw rates from 0.01 to 1 s⁻¹ up to draw ratio 3.5. Films were subsequently quenched to room temperature and removed for further analysis. It can be noticed that force and displacement are recorded throughout the duration of the experiments. Some experiments were also performed with prolonged times at 60°C under clamping after the stretching phase in order to detect relaxation phenomena.

### 2.2.4 Dimensional analysis of stretched a PLA films

A dimensional analysis on aPLA films was performed before and after stretching by MDO to evaluate the true strains. Lines perpendicular to the stretching axis with 5 cm intervals were dotted on initial aPLA films before MDO. Based on the extension of these marks during MDO, true draw ratios $λ_{true}$ and true longitudinal strains $ε_{true longitudinal}$ can be easily calculated with Equation (2). Variations in film width and thickness before and after stretching by MDO were used to calculate true transversal strains $ε_{true transversal}$ and true normal strains $ε_{true normal}$, respectively using Equation (3) and Equation (4). Poisson's ratios in the transverse direction and the normal direction, noted as $ν_{transversal}$ and $ν_{normal}$ respectively, were calculated from Equation (5) and Equation (6). A similar strategy was used for aPLA films stretched by the instrumented lab-scale machine. Here, square grids with 10 mm intervals were imprinted to calculate dimensional changes. In any case, at least 10 measurements were performed to secure accurate values and minimize errors. In the meantime, the density of stretched aPLA films were analyzed by the double weighing method under air and water at 23°C using a high-precision balance (Mettler Toledo XA105, resolution ± 0.01 mg) in order to test hypothesis regarding the stretching phase.

$$ε_{true-longitudinal} = ln(λ_{true}) = ln(\frac{L_{final}}{L_{initial}}) \qquad (2)$$

$$ε_{true-transverse} = ln(\frac{W_{final}}{W_{initial}}) \qquad (3)$$

$$ε_{true-normal} = ln(\frac{t_{final}}{t_{initial}}) \qquad (4)$$
$$ \mathbf{v}_{\text{transverse}} = - \frac{\epsilon_{\text{true transversal}}}{\epsilon_{\text{true longitudinal}}} \qquad (5) $$

$$ \mathbf{v}_{\text{normal}} = - \frac{\epsilon_{\text{true normal}}}{\epsilon_{\text{true longitudinal}}} \qquad (6) $$

with $L_{initial}$ and $L_{final}$ the distance between two successive lines perpendicular to the stretching axis before and after stretching respectively ($L_{initial}$ 5 cm), $W_{initial}$ and $W_{final}$ the width of the films before and after stretching respectively, $t_{initial}$ and $t_{final}$ the thickness of the films before and after stretching respectively.

## 2.3 Characterizations

### 2.3.1 Differential scanning calorimetry (DSC) and Dynamic mechanical analysis (DMA)

The thermal behaviors of stretched aPLA films were analyzed by differential scanning calorimetry (DSC, Mettler Toledo DSC 1, Switzerland) with a classical heat-cool-heat cycle from 25 °C to 220 °C (heating and cooling rates 10 °C/min, nitrogen flow 50 mL/min). Samples of approx. 4 mg were directly cut from stretched aPLA films. The thermal behaviors around the glass transition were particularly analyzed at the first heating scan. The specific heat capacity change $\Delta C_p$ round the glass transition was evaluated at the 1st and the 2nd heating scan. The viscoelastic properties of the stretched aPLA films were analyzed by dynamic mechanical analysis (DMA, Metravib +150 DMA, France) with a single temperature sweep from 30°C to 100°C (heating rate 2°C/min, frequency 10 Hz, constant displacement 0.05 mm). Rectangular specimens were cut from stretched aPLA films within the stretching axis (length 30 mm, width 15 mm). Thicknesses are measured with a caliper. DMA experiments were performed in double-gap shear mode (gap 5 mm) with the shear force applied perpendicular to the stretching axis. Values of the shear storage modulus $G'$ at 30°C and 100°C were recorded as the shear storage modulus in the glass and rubbery state respectively. Temperatures at the peak of the shear loss modulus $G''$ were also recorded which is associated to $\alpha$-relaxation temperature ($T_\alpha$) relating to segmental movements of polymer backbones. Temperatures at the peak of the loss tangent ($T_{tan\delta}$) were determined.

### 2.3.2 Structural analysis of stretched aPLA films by infrared spectroscopy

The structure of stretched aPLA films, in particular the presence of strain-induced mesophase and crystals), was confirmed by Fourier-transform infrared spectroscopy (FTIR, Nicolet iS20 Thermo Scientific™, Germany) in transmission mode at 23°C. Rectangular specimens were cut from stretched aPLA films along the stretching axis. Spectra were collected with 64 scans ranging from 1000 cm⁻¹ to
900 cm⁻¹ at a resolution of 2 cm⁻¹. Automatic baseline corrections were directly performed on Thermo Scientific Omnic™ Specta software. Orientation factors of stretched aPLA films were obtained by polarized FTIR (pFTIR) with the same apparatus, samples and acquisition settings. An extra Thermo Scientific™ KRS.5 polarizer was inserted between the IR beam and the sample. Two spectra were collected, one with the IR light polarized parallel to stretching axis and one with the IR light polarized perpendicular to stretching axis.

### 2.3.3 Piezoelectric measurements

The piezoelectric properties of stretched aPLA films were measured by a contactless voltmeter (Trek 370, USA) coupled to a DMA apparatus (DMA, Metravib +150 DMA, France). Rectangular specimens were cut first from stretched aPLA films at 45° from the stretching axis (length 30 mm, width 15 mm). Incremental static forces from 5 N to 25 N were applied to 45°-cut specimens using the DMA bench in tensile mode (gap 20 mm) and, in the meantime, the open-circuit piezoelectric voltage V as generated by the piezoelectric effect was recorded. This measurement is adapted from previous reference [38]. In this configuration, the piezoelectric voltage constant g₁₄ can be precisely evaluated on stretched aPLA films without electrodes, from the open-circuit piezoelectric voltage V based on the applied static stress σ (or static force F) and geometrical characteristics of the films (thickness t and width W), as shown in Equation (7). To ensure this linear coupling according the piezoelectric voltage effect, V-F plots were performed. Finally, piezoelectric coefficients d₁₄ were calculated with Equation (8) from g₁₄ values obtained at 20 N and according to the dielectric constant εr of 2.5 [23, 39].

$$g_{14} = \frac{4V}{t\sigma} = \frac{4VW}{F} \qquad (7)$$

$$d_{14} = g_{14} \times \epsilon_{r} \qquad (8)$$

## 3 Results and Discussions

### 3.1 Dimensional analysis of the stretching phase by MDO for aPLA extruded films

The stretching phase is of major importance to produce oriented aPLA films by MDO and a deep analysis of this stage was performed in order to extract valuable information such as true strains imposed to aPLA films. As stated above, the MDO process imposes an apparent draw ratio λapp to extruded aPLA films, a value precisely known as the ratio between downstream to upstream roll speeds. Stretchings are performed just above the glass transition temperature of aPLA films in the rubbery state. Stretched aPLA are then cooled down instantly in the downstream stage. True draw ratios λtrue are
known to slightly differ from apparent draw ratios due to process imperfections. In this context, before
stretching experiments, extruded aPLA films are marked with perpendicular lines and their distance
before / after stretching are measured. By this way, true draw ratios λtrue and true strains in the machine
/ longitudinal direction Etrue-longitudinal can be easily calculated. In Figure 2, true draw ratios are plotted
against apparent draw ratio and a linear relationship is observed (R² ≈ 0.99), as a proof that MDO effec-
tively induces film stretching in the longitudinal direction. True draw ratios up to 3.5 are reached. Be-
sides, the dashed line represents an ideal scenario in which the apparent draw ratio equals the true draw
ratio with a slope 1. Nonetheless, experimental data points are below this line with a slope close to 0.8.
Likely reasons are film slippage during stretching and, therefore, λtrue is the most accurate parameter to
quantify the stretching process. In a further dimensional analysis, true stains in the longitudinal, trans-
verse and normal directions, noted as Etrue-longitudinal, Etrue-transverse, and Etrue-normal are compared with
λtrue in the natural logarithm scale (Figure 2). Quantitative values can be also found in Table 1. True
strains in all directions exhibit a linear coupling with the logarithm of λtrue. Both Etrue transverse and Etrue-
normal naturally decrease during the stretching phase due to width and thickness reductions. Of interests,
the slopes for true strains in the transverse and normal directions are similar and their values are ap-
proximately around -0.5. The MDO process not only induces elongation of aPLA films but also results
in similar shrinkage in both transverse and normal directions. The Poisson's ratios Vtransverse and Vnormal
are calculated and tabulated into Table 1. Almost all Poisson's ratios are close to -0.5 for all draw ratio
and the difference between Vtransverse and Vnormal is within 0.02. These elements proves that the stretch-
ing phase during MDO is a pure uniaxial stretching in the elastic rubbery state with no volume varia-
tions and absence of drastic structural variations such as intensive appearance of voids by cavitation
[40]. These later elements are confirmed by density measurements. Indeed, aPLA films has constant
density near 1.25 g/cm³ regardless of the draw ratio. To conclude this section, the MDO process im-
poses nearly-perfect uniaxial stretching at iso-volume in the elastic rubbery state to extruded aPLA
films up to draw ratio of about 3.5 (at least) and without macroscopic mechanical degradation by cavi-
tation mechanisms. Stretched aPLA films are quenched in an oriented state favorable to shear piezoe-
lectricity. It can be noticed that, within the following section, only true draw ratios are considered in-
stead of apparent draw ratio.
<figure><img src="image_4.png" /><figcaption>**Figure 2.** (Left) Relationship between apparent draw ratios $\lambda_{app}$ and true draw ratios $\lambda_{true}$ for aPLA films stretched by MDO. (Right) Relationships between $\ln(\lambda_{true})$, $\varepsilon_{true}$ in the longitudinal direction and $\varepsilon_{true}$ in the transverse / normal directions for aPLA films stretched by MDO.</figcaption></figure>

<table><caption>**Table 1.** Experimental values for apparent draw ratios $\lambda_{app}$, true draw ratios $\lambda_{true}$, true strains in the longitudinal, transversal and normal directions ($\varepsilon_{true}$) along with respective Poisson's ratio ($\mathbf{v}$) of as-produced aPLA films by MDO.</caption><thead><tr><th>λ<sub>app</sub></th><th>λ<sub>true</sub></th><th>ε<sub>true-longitudinal</sub></th><th>ε<sub>true-transverse</sub></th><th>ε<sub>true-normal</sub></th><th>V<sub>transverse</sub></th><th>V<sub>normal</sub></th></tr></thead><tbody><tr><td>1.5</td><td>1.27±0.01</td><td>0.24±0.01</td><td>-0.12±0.01</td><td>-0.12±0.05</td><td>0.49</td><td>0.49</td></tr><tr><td>2.0</td><td>1.72±0.02</td><td>0.54±0.01</td><td>-0.27±0.01</td><td>-0.27±0.03</td><td>0.49</td><td>0.50</td></tr><tr><td>2.5</td><td>2.03±0.08</td><td>0.71±0.04</td><td>-0.33±0.01</td><td>-0.34±0.06</td><td>0.47</td><td>0.49</td></tr><tr><td>3.0</td><td>2.72±0.12</td><td>1.00±0.04</td><td>-0.48±0.03</td><td>-0.50±0.04</td><td>0.48</td><td>0.50</td></tr><tr><td>3.5</td><td>2.99±0.05</td><td>1.10±0.02</td><td>-0.53±0.02</td><td>-0.56±0.04</td><td>0.48</td><td>0.51</td></tr><tr><td>4.0</td><td>3.49±0.04</td><td>1.25±0.01</td><td>-0.61±0.01</td><td>-0.62±0.08</td><td>0.50</td><td>0.49</td></tr></tbody></table>

## 3.2 Thermal, thermomechanical and spectroscopic analysis of stretched aPLA films

The structure of stretched aPLA films by MDO is of major importance for further analysis of shear piezoelectric properties and their amorphous character particularly need to be confirmed. In this context, aPLA films with various draw ratio were characterized by DSC, DMA and FTIR. The super-
posed first heating thermograms of aPLA films produced at various draw ratio are shown in **Figure 3**.
All of the thermograms contain no cold crystallization exothermic event or endothermic melting peak.
This clearly proves that all aPLA films are highly-amorphous and free from strain-induced crystals
regardless of the draw ratio. Besides, all thermograms show a glass transition phenomenon at approx.
60°C with clear jumps in heat capacity. However, the glass transition temperature remains difficult to
determine with a high precision by DSC due to complex and coupled endothermic events occurring in
the glass transition region. These overlapping events can relate to various phenomenon such as (i) en-
dothermic enthalpy relaxation at the glass transition temperature due to physical aging of aPLA films
for prolonged times below the glass transition temperature [41, 42], (ii) endothermic stress – strain re-
lease at the glass transition temperature of stretched aPLA films[43], and (iii) endothermic melting of
mesophase clusters produced during MDO [32].

The presence of mesophase clusters was subsequently analyzed by FTIR. The superposition of
FTIR absorbance spectra in the range of 972 – 910 cm⁻¹ for previous aPLA films produced at various
draw ratio is shown in **Figure 3**. There are two characteristic absorbance peaks. The strong absorbance
peak at 956 cm⁻¹ corresponds to CH₃ rocking and C-C stretching in the amorphous regions of aPLA
[32]. The decreased intensity of this peak with the elevation of the draw ratio is largely because of the
reduction of thickness according to the Beers-Lambert law. The small absorbance peak at 918 cm⁻¹ is
ascribed to mesophase clusters which originated from oriented amorphous region [32, 44, 45]. Besides,
the absorbance peak at 918 cm⁻¹ exhibits no sign of shifting to 921 cm⁻¹ ascribed to PLA crystals [44,
46]. The amount of mesophase can be calculated from the area or height of the corresponding absorb-
ance peaks at 956 cm⁻¹ and 918 cm⁻¹. The content of mesophase in aPLA films produced by MDO at
various draw ratios is listed in **Table 2**. Mesophase is clearly marginal in aPLA films with content be-
low 2.5%. FTIR analyses consequently confirm that aPLA are highly-amorphous, free from strain-
induced crystals and with a low content of mesophase clusters.
<figure><img src="image_5.png" /><figcaption>**Figure 3.** First heating thermograms (left) and FTIR spectra of aPLA films stretched by MDO at various draw ratios.</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>**Figure 4.** Storage modulus *G*' (left) and loss modulus *G''* (right) as a function of the temperature for aPLA films stretched by MDO at various draw ratios.</figcaption></figure>

Dynamic mechanical analyses were subsequently performed on aPLA films stretched by MDO to identify mechanical parameters of these films (shear moduli *G*, *G''*) and their relaxation temperatures (*T*<sub>α</sub> determined at the maximum *G''* and *T*<sub>tanδ</sub> determined at the *tan*δ peak). Evolution of dynamic shear moduli with temperature for aPLA films stretched by MDO at various draw ratios are displayed
in **Figure 4**. Storage modulus at 30°C and 100°C (G'30°C and G'100°C) are reported into **Table 2** along with relaxation temperatures, mesophase content and changes in heat capacity previously recorded in FTIR and DSC analyses. From a global point of view, dynamic mechanical behaviors of aPLA films stretched by MDO are consistent with a highly-amorphous structure. At temperatures below 55°C, aPLA films naturally are in their glassy state with a shear storage modulus comprised between 850 MPa and 970 MPa. A sharp drop in mechanical properties is observed between 55 and 70°C, a region corresponding to their α-relaxation and glass transition with the activation of long-range cooperative motions. The high drop in mechanical properties by at least 3 decades in a restricted range of temperature attests for highly-amorphous structures in all aPLA films stretched by MDO regardless of the draw ratio, in accordance with previous conclusions by FTIR and DSC. However, apart from this global behavior, some slight but significant modifications are noticed between aPLA films stretched by MDO. All thermomechanical and thermal parameters seem to be constant up to draw ratios of approx. 1.7 – 2. Higher α-relaxation temperatures are observed at elevated draw ratio with an increase from 59°C to 62°C for a draw ratio of 3.5. Simultaneously, the shear storage modulus at 30°C and $\Delta C_p$ slightly drops by approx. 10 – 15 % at these elevated draw ratios. Such phenomena are partly attested for several amorphous polymers such as poly(L-Lactide), poly(carbonate), poly(vinyl acetate) and poly(isobutylmethacrylate) quenched into a highly-oriented state after uniaxial stretching[47-51]. The stretching phase of our aPLA films is carried out at 60°C close to the glass transition in a semi-rubbery state. High draw rates above 1 s⁻¹ are applied and stretched aPLA films at elevated draw ratio are vitrified in the downstream section of the MDO process. A highly-oriented glassy state is consequently favored in these conditions and these out-of-equilibrium glassy states naturally require more time to recover their equilibrium structures compared to unoriented or poorly-oriented glassy states vitrified in similar conditions. This phenomenon is in accordance with α-relaxation and enthalpy relaxation shifted to higher temperatures for aPLA films produced by MDO at elevated true strains. It can be noticed that peak temperatures on $\tan\delta$ curves remain constant with values close to 66 – 67°C suggesting that the structural relaxation of highly-oriented aPLA glasses occur in a restricted temperature range between the α-relaxation temperatures $T_α$ and peak temperatures on $\tan\delta$ curve. Highly-oriented aPLA glasses are also marked by lower mechanical properties and higher heat capacities compared to unoriented glassy states vitrified in similar conditions. Highly-oriented glassy structures produced at elevated draw ratio above 1.7 – 2 subsequently display lower density and higher degree of conformational freedom. It can be speculated that significant modifications of the entanglement density occur during the stretching phase of aPLA films by MDO for draw ratio above 1.7 – 2. It can be here mentioned that the storage
moduli of aPLA films in the rubber state at 100°C also display similar trends and original heat capacities are only recovered in the second DSC heating. The re-entanglement process seems to be a longer process than the structural relaxation process. The equilibrium state of aPLA remains looser even after structural relaxation above the glass transition. Polarized FTIR studies were subsequently performed to quantify the orientation factor of aPLA films produced by MDO at various draw ratios. The agreement with deformation theories of rubber networks was particularly inspected for further analysis of their shear piezoelectric responses.

<table><caption>**Table 2.** Mesophase content, α-relaxation temperature $T_α$, peak temperature on tanδ curve ($T_{tanδ}$), shear storage modulus $G'$ and change in heat capacity across the glass transition $ΔC_p$ (1st and 2nd DSC heating) of aPLA films stretched by MDO at various draw ratios.</caption><thead><tr><th>λ<sub>ture</sub></th><th>Mesophase content (%)</th><th>T<sub>α</sub> (°C)</th><th>T<sub>tanδ</sub> (°C)</th><th>G'<sub>30°C</sub> (MPa)</th><th>G'<sub>100°C</sub> (MPa)</th><th>ΔC<sub>p</sub> (J/K.g) 1<sup>st</sup> heating</th><th>ΔC<sub>p</sub> (J/K.g) 2<sup>nd</sup> heating</th></tr></thead><tbody><tr><td>1.00</td><td>0.0</td><td>58.6</td><td>66.7</td><td>967</td><td>0.65</td><td>0.51</td><td>0.51</td></tr><tr><td>1.27</td><td>0.6</td><td>59.2</td><td>66.2</td><td>966</td><td>0.64</td><td>0.50</td><td>0.52</td></tr><tr><td>1.72</td><td>0.4</td><td>58.7</td><td>65.3</td><td>914</td><td>0.63</td><td>0.50</td><td>0.52</td></tr><tr><td>2.03</td><td>0.6</td><td>59.7</td><td>65.9</td><td>871</td><td>0.59</td><td>0.48</td><td>0.52</td></tr><tr><td>2.72</td><td>1.3</td><td>60.1</td><td>65.6</td><td>898</td><td>0.54</td><td>0.46</td><td>0.51</td></tr><tr><td>2.99</td><td>2.0</td><td>60.9</td><td>66.0</td><td>905</td><td>0.52</td><td>0.46</td><td>0.51</td></tr><tr><td>3.49</td><td>2.5</td><td>61.8</td><td>67.0</td><td>862</td><td>0.55</td><td>0.43</td><td>0.52</td></tr></tbody></table>

### 3.3 Impact of draw ratio on the orientation factor of stretched aPLA films

Orientation factor of as-produced aPLA films was analyzed by polarized FTIR between 980 and 900 cm⁻¹, a region of high interest for orientation studies of the amorphous and crystalline phases of
PLA films. Unpolarized FTIR spectra are displayed in **Figure 3** and previously discussed. Polarized FTIR spectra obtained with a KRS-5 polarizer are shown in **Figure 5**, for all aPLA films produced by MDO at various draw ratio. The incident IR light can be polarized either perpendicular or parallel to the MDO stretching direction. For extruded aPLA films, the two spectra are similar with equivalent intensities for the absorption band corresponding to the amorphous phase at 956 cm⁻¹. This clearly at- tests for the absence of orientation in these original aPLA films. The intensity of the absorption band corresponding to the amorphous phase decreases in the perpendicular spectra for stretched aPLA films by MDO. The discrepancy between the two spectra increases with the applied draw ratio and this phe- nomenon indicates an effective orientation of the amorphous phase in aPLA films produced by MDO. The orientation of the amorphous phase increases with the applied draw ratio. The absorption band corresponding to the mesophase at 918 cm⁻¹ rises for draw ratio above 1.72 but its intensity remains marginal, as discussed in the previous section. Besides, no sign of mesophase to crystalline transition is observed as the peak position is stabilized at 918 cm⁻¹. The mesophase absorbance disappears in the perpendicular spectra, indicating a perfect mesophase orientation along the stretching direction, in agreement with its strain-induced formation reported by many authors [44, 52].

The orientation factor of the amorphous phase along the stretching direction ($F_{am}$) is of high im- portance in this study and can be calculated from polarized FTIR spectra using the trichroic ratio for- malism ($D_{tri}$) [40, 53, 54]. The specific calculations for $F_{am}$ within the longitudinal / stretching direc- tion are based on the absorption band at 956 cm⁻¹ using **Equations (9 - 8)**. The intensity of the absorp- tion band with the polarizer parallel to the drawing direction ($A_{am-longitudinal}$) and perpendicular to the drawing direction ($A_{am-transverse}$) are respectively measured. It can be noticed that the intensity of the absorption band in the normal direction ($A_{am-normal}$) cannot be experimentally determined in our FTIR setup but, due to uniaxial stretching, we considered that $A_{am-transverse}$ equals to $A_{am-normal}$ [40] thus reducing **Equation (10)** into **Equation (9)**. Values of $F_{am}$ for aPLA films pro- duced by MDO at various draw ratio are listed in **Table 3**. The orientation factor of the amorphous phase $F_{am}$ increases with the applied draw ratio and a maximal $F_{am}$ value of 0.29 is obtained at the highest draw ratio. This high value is consistent with several studies on uniaxial stretching of PLA[21, 40, 45]. The orientation state of the amorphous phase is consequently controlled by the draw ratio im- posed to aPLA films during the uniaxial stretching phase.

$$F_{am} = \frac{1}{2} \times (D_{tri} - 1) \qquad (9)$$
$$D_{tri} = \frac{3 \times A_{am-longitudinal}}{A_{am-longitudinal} + A_{am-transverse} + A_{am-normal}} \qquad (10)$$

$$D_{tri} = \frac{3 \times A_{am-longitudinal}}{A_{am-longitudinal} + 2 \times A_{am-transverse}} \qquad (11)$$

<figure><img src="image_7.png" /><figcaption>**Figure 5.** Polarized FTIR spectra of aPLA films stretched by MDO at various draw ratios. Incident light polarized perpendicular to the drawing direction (left) and parallel to the drawing direction (right).</figcaption></figure>

<table><caption>**Table 3.** Orientation factor of the amorphous phase ($F_{am}$) and piezoelectric coefficients ($g_{14}$, $d_{14}$) of aPLA films stretched by MDO at various draw ratios.</caption><thead><tr><th>λ<sub>true</sub></th><th>λ<sub>true</sub><sup>2</sup> - λ<sub>true</sub><sup>-1</sup></th><th>F<sub>am</sub></th><th>g<sub>14</sub> (mV.m/V)</th><th>d<sub>14</sub> (pC/N)</th></tr></thead><tbody><tr><td>1.27±0.01</td><td>0.82±0.02</td><td>0.03±0.00</td><td>8.9±2.5</td><td>0.20±0.05</td></tr><tr><td>1.72±0.02</td><td>2.36±0.06</td><td>0.07±0.01</td><td>21±7.3</td><td>0.46±0.16</td></tr><tr><td>2.03±0.08</td><td>3.62±0.31</td><td>0.12±0.01</td><td>42±3.5</td><td>0.92±0.08</td></tr><tr><td>2.72±0.12</td><td>7.02±0.59</td><td>0.19±0.02</td><td>61±5.1</td><td>1.34±0.11</td></tr><tr><td>2.99±0.05</td><td>8.63±0.28</td><td>0.23±0.02</td><td>79±7.3</td><td>1.75±0.16</td></tr><tr><td>3.49±0.04</td><td>11.88±0.25</td><td>0.29±0.03</td><td>91±14</td><td>2.02±0.30</td></tr></tbody></table>

The relationship between $F_{am}$ and $λ_{true}$ is not linear and deformation theories of rubber networks were tested for aPLA films produced by MDO. Amorphous chains of PLA are interlocked and form an
entanglement network with freely-joined Kuhn segments as chain segments between two entanglement points. Based on the affine deformation theory of rubber networks with entanglement points acting as physical crosslinks, the relationship between $F_{am}$ and $\lambda_{true}$ can be expressed by **Equations (10-11)** with $N_k$ the number of freely-joint rigid Kuhn segments between network points (also called Kuhn number), $D_0$ dichroic ratio for perfect chain orientation and $\psi$ the angle between the direction of the vibration transition moment and the polymer chain axis ($\psi$ equals 0 for amorphous PLA chains, thus $D_0$ is 1) [44, 46]. The change of $F_{am}$ is consequently plotted against $\lambda_{true}^2 - \lambda_{true}^{-1}$ in **Figure 6** to evaluate chain orientation upon uniaxial stretching [55].

At low draw ratio, $F_{am}$ is linear with $\lambda_{true}^2 - \lambda_{true}^{-1}$ with a slope 1/32.5 which corresponds to a $N_k$ value of 6.5. $N_k$ value is known to inversely proportional to the molecular weight. It is worth noticing that the aPLA grade used in this study has $\overline{M}_n$ of 61 kg/mol and the current $N_k$ value is consistent with literature results: $N_k$ is 4 and 6.9 for PLA grades with $\overline{M}_n$ between 120 kg/mol and 3.24 kg/mol, respectively. [46, 56]. These observations validate the affine deformation theory for aPLA films produced by MDO at low draw ratio. Noticeably, starting from draw ratio higher than 2, $F_{am}$ negatively deviates from the previous fit line. It is well-known that, once the draw ratio is above a critical value corresponding to the square root of $N_k$, entanglement points turn into “slip-links” with a reduction of the entanglement density and an increase in the number of monomers into freely-joined Kuhn segments, as proven on many amorphous polymers [57-60]. Based on the previous $N_k$ value of 6.5, the appearance of “slip-links” phenomena should start for critical draw ratio of approx. 2.5 or $\lambda_{true}^2 - \lambda_{true}^{-1}$ of approx. 6. Experimentally, our results are in total accordance with this critical draw ratio (**Figure 6**). Nonetheless, at elevated true draw ratio, the linearity between $F_{am}$ and $\lambda_{true}^2 - \lambda_{true}^{-1}$ still exist with a new fit line with a slope 1/(41.7) indicating an increase Kuhn number from 6.5 to 8.3 due to “slip-links” phenomena (**Figure 6**). Such linearity has been also attested in another system [59]. In this respect, these data validate the reliability of orientation factor $F_{am}$ measured by polarized FTIR for aPLA films produced by MDO on the entire range of draw ratios. The orientation factor $F_{am}$ is primarily controlled by the draw ratio imposed to aPLA films during the uniaxial stretching phase with good accordance to deformation theories of rubber networks. Orientation factor $F_{am}$ can be predicted with a good precision using respective $N_k$ values of 6.5 and 8.3 before and after the critical draw ratio of 2.5. Appearance of “slip-links” phenomena occurs at elevated draw ratio above 2.5 and a link can be made with previous DSC and DMA results. The slight decrease of the shear storage modulus at 30°C and $\Delta C_p$ by approx. 10 – 15 % at elevated draw ratios matches (above the critical draw ratio) with the appearance of “slip-
links” phenomena inducing a reduction of the entanglement density and higher degree of conforma-

$$F_{am} = D_0 \times \frac{1}{5 \times N_k} \times (\lambda_{true}^2 - \lambda_{true}^{-1}) \quad (10)$$

$$D_0 = \frac{2 \cot^2 \psi - 1}{2 \cot^2 \psi + 2} \quad (11)$$

tional freedom in these stretched and highly-oriented glassy aPLA films

<figure><img src="image_8.png" /><figcaption>**Figure 6.** Relationship between the orientation factor of the amorphous phase $F_{am}$ and the draw ratio $(\lambda_{true}^2 - \lambda_{true}^{-1})$ of aPLA films stretched by MDO. Schematic visualization of the Kuhn number $N_k$ and its evolution during stretching by MDO.</figcaption></figure>

## 3.4 Impact of amorphous chain orientation on piezoelectric coefficients

Stretched aPLA films by MDO are quenched in an oriented state favorable to shear piezoelectricity. From previous DSC and FTIR analysis, the amount of mesophase cluster is marginal (below 2.5%) and aPLA films are amorphous at all draw ratios up to 3.5. The situation is consequently ideal to analyze the role of the amorphous phase and its orientation state on resultant shear piezoelectric properties of PLA, an aspect poorly discussed in the specialized literature. The three-phase model displayed in Equation (1) can be greatly simplified into Equation (12) with as-produced aPLA films. Using previous orientation factors $F_{am}$, the validity of the three-phase model with amorphous contribution can be determined together with the intrinsic piezoelectricity of the amorphous phase of PLA. Shear piezoelectric coefficients ($d_{14}$ and $g_{14}$) for aPLA films produced by MDO at various draw ratio are tabulated
in Table 3. Figure 7 clearly validate the linear coupling between $d_{14}$ and $F_{am}$ in our aPLA films. The shear piezoelectric properties of aPLA films can reach significant values up to 2 pC/N at elevated draw ratio or elevated amorphous phase orientation. This value can count for 20% of the recently reported $d_{14}$ values in oriented semicrystalline PLA at elevated draw ratios [22, 28]. In the meantime, piezoelectric voltage coefficients up to 90 mV.m/N are also reported. These values are quite high for an amorphous piezoelectric material and nearly competitive with piezoelectric PVDF films. Piezoelectric aPLA films also remain highly-transparent due to their amorphous character, an effect of good interest for various applications. The slope is an important parameter that represents the intrinsic piezoelectric coefficient for the amorphous phase of PLA ($d_{14-am}$). This value is found close to 7.2 pC/N and seems to be in agreement with previously reported values for the mesophase (13 pC/N) and $\alpha'$-crystals (18 pC/N). Applying this $d_{14-am}$ back to the reference of Ben Achour et. al. [21], the amorphous component can contribute up to 40% in oriented semicrystalline PLA at moderate draw ratios. These findings clearly prove that the contribution of oriented amorphous phase to the overall shear piezoelectricity of PLA films is significant. The 3-phase model with an amorphous contribution is validated and this model can be used with more precision by the future for predictive purposes. For sure, boosting $d_{14}$ of piezoelectric PLA films requires maximizing $F_{am}$ with optimized draw ratio. Further improvement of $d_{14}$ should not only focus on maintaining high amorphous phase orientation in semicrystalline PLA but also increasing the crystal contribution due to its higher impact (by a factor approx. 3).

$$d_{14} = F_{am} \times d_{14-am} \qquad (12)$$

<figure><img src="image_9.png" /><figcaption>Figure 7. Correlation between the orientation factor of the amorphous phase $F_{am}$ and the shear piezoelectric coefficient $d_{14}$ of aPLA films stretched by MDO.</figcaption></figure>
## 3.5 Impact of drawing rate on the piezoelectric coefficients

Upon uniaxial stretching of aPLA films by MDO around the glass transition temperature, a competition between chain orientation and chain relaxation to their original unoriented state can occur [54, 61]. Therefore, the rate of chain relaxation back to unoriented state should be low compared to the rate of stretching in order to favor high orientation factors $F_{am}$ and hence high piezoelectric coefficients $d_{14}$. The draw rate during MDO is known to be quite high and was estimated to approx. $1 - 4 \text{ s}^{-1}$ in our stretching conditions (based on upstream / downstream roll speeds and distances). In this context, the impact of the draw rate on orientation factors $F_{am}$ and piezoelectric coefficients $d_{14}$ of aPLA films was approached in order to detect relaxation phenomena in our MDO conditions. An instrumented lab-scale stretching machine was used for this purpose (Karo IV) to conduct uniaxial stretching experiments on aPLA films with precise draw rates $\dot{\varepsilon}$. Various draw rates were applied between $0.01 \text{ s}^{-1}$ and $1 \text{ s}^{-1}$. A constant draw ratio $\lambda_{app}$ of 3.5 was selected for these experiments and the draw temperature were set to similar conditions than previous MDO experiments.

A dimensional analysis was first conducted and true draw ratio $\lambda_{true}$ were recalculated from marked lines on the film surface. Data are tabulated in **Table 4** along with the Poisson's ratio in the transversal direction ($\nu_{transverse}$). True draw ratios are slightly lower than apparent draw ratios by approx. 10%, a phenomenon similar to previous MDO experiments that could be linked to stretching imperfections. However, the imposed true draw ratios are constant in all experiments with values comprised between 3.1 and 3.2, values slightly below the maximal true draw ratio of 3.5 for aPLA films stretched by MDO. It can be also noticed that Poisson's ratios in the transversal direction are found close to 0.45 in these lab-scale stretching experiments compared to 0.5 for aPLA films stretched by MDO (**Table 4**). This effect is due to stretching conditions with a fixed width at the clamp ends inducing a more pronounced width reduction in the middle section of aPLA films during stretching. Lab-scale stretching experiments are consequently quite similar to MDO stretching conditions with some minor deviations to perfect uniaxial stretching. Stress – strain curves at 60°C of aPLA films are presented in **Figure 8** with engineering stress against the apparent draw ratio $\lambda_{app}$ at various draw rates. At low draw rates typically $0.01 \text{ s}^{-1}$, the engineering stress smoothly rise with the draw ratio and reached a plateau around 1 MPa at elevated draw ratio. No yielding and strain hardening phenomena are observed at low draw rates. At intermediate draw rates typically $0.05 - 0.1 \text{ s}^{-1}$, similar behaviors are attested in the initial stretching phase of aPLA films with a smooth increase of the engineering stress up to 1.5 – 2 MPa but a strain hardening phenomenon is detected in the final stretching phase. Elevated draw rates typically $0.5 - 1 \text{ s}^{-1}$ are marked by a sharp increase of the engineering stress to 5 – 8 MPa followed by an intense yielding
behavior. The strain hardening phenomena is also detected in the final stretching phase of aPLA films. Interestingly, the strain hardening phenomena always appears for $\lambda_{app}$ above 2 in agreement with the previous critical draw ratio for the appearance of “slip-links” phenomena. The draw rate consequently plays a major role on the uniaxial stretching behavior of aPLA. A clear transition is observed between 0.1 and 0.5 s⁻¹ that probably relates to the relaxation time of entanglement strands (comprising 7 – 8 Kuhn segments) by a Rouse motion. This entanglement time characterizes how long topological constraints imposed by entanglements are active during stretching and is consequently linked to internal stress release during stretching[62, 63]. An entanglement time close to 2 – 10 s for aPLA at 60°C is roughly consistent with the segmental relaxation time of 0.02 s recorded at 58°C on previous DMA analyses (entanglement time ≈ $N_k^2 \times$ segmental time).

<table><caption>**Table 4.** Dimensional data, mesophase content, orientation factors and piezoelectric coefficients of aPLA films stretched at various draw rates. Experiments performed on a lab-scale Karo IV stretching machine. ¹Film stretched at the rate of 1s⁻¹ then relaxed at fixed length for 1800 s.</caption><thead><tr><th>Draw rate (s<sup>-1</sup>)</th><th>λ<sub>true</sub></th><th>V<sub>transversal</sub></th><th>Mesophase (%)</th><th>F<sub>am</sub></th><th>d<sub>14</sub> (pC/N)</th></tr></thead><tbody><tr><td>0.01</td><td>3.28±0.03</td><td>0.45</td><td>1.00</td><td>0.19±0.00</td><td>1.24±0.13</td></tr><tr><td>0.03</td><td>3.24±0.02</td><td>0.45</td><td>1.30</td><td>0.23±0.01</td><td>1.70±0.10</td></tr><tr><td>0.05</td><td>3.18±0.02</td><td>0.46</td><td>1.80</td><td>0.25±0.01</td><td>1.82±0.05</td></tr><tr><td>0.1</td><td>3.11±0.05</td><td>0.45</td><td>1.89</td><td>0.26±0.01</td><td>1.89±0.02</td></tr><tr><td>0.3</td><td>3.18±0.03</td><td>0.44</td><td>1.90</td><td>0.28±0.00</td><td>1.89±0.04</td></tr><tr><td>0.5</td><td>3.15±0.03</td><td>0.46</td><td>2.00</td><td>0.29±0.01</td><td>1.90±0.05</td></tr><tr><td>1</td><td>3.21±0.03</td><td>0.45</td><td>2.20</td><td>0.28±0.01</td><td>2.04±0.14</td></tr><tr><td>1 - R1800<sup>1</sup></td><td>3.17±0.09</td><td>0.46</td><td>1.70</td><td>0.14±0.04</td><td>1.11±0.06</td></tr></tbody></table>
<figure><img src="image_10.png" /><figcaption>**Figure 8.** Stress-strain curves at 60°C and various draw rates for extruded aPLA films. Subsequent evolutions of the orientation factor *F*<sub>am</sub> and piezoelectric constant *d*<sub>14</sub> as a function of the draw rate (up to the maximal draw ratio ≈ 3.2). Experiments performed on a lab-scale Karo IV stretching machine. The values for oriented aPLA films by MDO are mentioned.</figcaption></figure>

The orientation of aPLA films stretched at various draw rate and their subsequent piezoelectric coefficients were naturally checked according to previous methods. Detailed *F*<sub>am</sub> and *d*<sub>14</sub> values at various draw rates are listed in **Table 4** and their evolutions are plotted in **Figure 8**. Mesophase content are also tabulated. At draw rates higher than 0.3 s<sup>-1</sup>, both *F*<sub>am</sub> and *d*<sub>14</sub> display constant values close to 0.25 – 0.28 and 1.9 – 2.0 pC/N respectively. The mesophase content remains below 2% in these stretching conditions. All these values are in agreement with previous ones recorded for aPLA films stretched by MDO and the slight discrepancies are attributed to minor differences in terms of draw ratio (3.2 vs. 3.5 for aPLA films stretched by MDO). A draw rate of 0.3 s<sup>-1</sup> seems to be a critical draw rate value to reach high orientation factors and high piezoelectric coefficients. The orientation factor of aPLA films starts dropping for draw rates below 0.3 s<sup>-1</sup> and significant drop by almost 30% is detected for the lowest draw rate of 0.01 s<sup>-1</sup>. Piezoelectric properties also display a similar trend that reinforce the previous conclusions about the linear coupling between *F*<sub>am</sub> and *d*<sub>14</sub>. These effects indicate the presence of concurrent phenomenon during stretching that restrict the orientation of aPLA films. The
elongation and orientation of aPLA chains during stretching strongly competes with their retraction by
a Rouse motion, an effect controlled by the longest Rouse relaxation mode[62, 63]. The associated re-
traction time is estimated to approx. 600 – 3000 s for aPLA at 60°C based on the previous entangle-
ment time, the aPLA molecular weight (M̄w ≈ 120 kg/mol) and known values for PLA entanglement
density (Me ≈ 5 kg/mol) [64]. A high reduction of the orientation is expected within this timeframe and,
to highlight the importance of the retraction mechanism during stretching, a stress relaxation experi-
ment was conducted for 1800 s at 60°C on a stretched aPLA film at a draw rate of 1 s⁻¹. The stress re-
laxation experiment was also conducted with a fixed length to avoid shrinkage. The orientation factor
and the subsequent piezoelectric coefficient are both reduced by 50% after this relaxation step and the
chain retraction mechanism is significantly active at these timescales, corresponding to draw rates low-
er than 10⁻³ s⁻¹. It can be noticed that a significant orientation is still maintained and a full loss of orien-
tation is only expected extreme timescales at 60°C, i.e. above the disentanglement or reptation time[62,
63]. As a conclusion, the stretching of PLA films by MDO with its inherent high draw rate (estimated
to 4 s⁻¹) is highly beneficial to produce high orientation states and high piezoelectric coefficients.
Compared to conventional stretching techniques using low draw rates, in particular stretching tech-
niques with draw rates below 0.3 s⁻¹, the MDO technique can clearly enhanced piezoelectric perfor-
mances by almost 50 to 30 %. This effect seems related to the deactivation of the retraction mechanism
of aPLA chains at elevated draw rates, an effect of very good interest for future studies on the uniaxial
stretching of semi-crystalline grades PLA by MDO and their subsequent crystallization under orienta-
tion and piezoelectric performances.

**3.6 Impact of optical purity on piezoelectric coefficients of amorphous films**

The impact of the optical purity on piezoelectric properties of amorphous PLA films was finally
checked to enable transposition of previous results to any commercial PLA grades. The intrinsic piezo-
electric coefficient for the amorphous phase of PLA (d<sub>14-am</sub>) was previously found close to 7.2 pC/N
for an aPLA grade with a D-content of 11.55 %. The optical purity of PLA is expected to modify this
value. For instance, piezoelectric properties should vanish for a random copolymer with 50% L-
Lactide and 50% D-Lactide due to a total break of the material symmetry even in the oriented state.
Based on previous results, the intrinsic piezoelectric coefficient for the amorphous phase of PLA can
be roughly estimated to 9 pC/N for PLA with pure L-lactide units. To test this hypothesis, additional
tests were performed and various results from the previous literature were treated according to our
methods. The focus was placed on commercial PLA grades with D-content ranging from 2% to 10%
and their piezoelectric films produced by MDO at low draw ratio to avoid excessive production of
mesophase. A commercial grade of PLA with a D-content of 6.4 % was selected and submitted to extrusion – MDO trials in similar conditions than previously depicted. The draw ratio was limited to approx. 2.2 with this grade. Mesophase content, amorphous phase orientation factor $F_{am}$, and the subsequent piezoelectric coefficient $d_{14}$ are listed in Table 5. These values are also tabulated from other PLA grades with a reduced D-content down to 2% by extracting and reprocessing valuable data from literature [21]. All $d_{14}$ values are plotted against $F_{am}$ in Figure 9 to estimate whether optical purity impacts the piezoelectricity of oriented and amorphous PLA films. Piezoelectric coefficients $d_{14}$ are slightly above the previous fit line obtained with the highly-amorphous aPLA grade and a fit line corresponding to an intrinsic coefficient of the amorphous phase $d_{14-am}$ close to 9 pC/N is included into Figure 9. These elements suggest a small impact of the optical purity on the intrinsic coefficient of the amorphous phase that potentially rise to approx. 9 pC/N for PLA grade with low D-content. However, taking into a small but significant production of mesophase even at low draw ratio with tested PLA grades (Table 5), this conclusion cannot be totally proven with a high certitude. The mesophase production is estimated to 5 – 9 % with these PLA grades and up to 9 % in certain conditions. A high deviation is expected and clearly attested with such elevated mesophase content. Subtraction of the mesophase contribution from these experimental piezoelectric coefficients is possible with the three-phase model and all values fall in the previous fit line with an intrinsic coefficient of the amorphous phase $d_{14-am}$ of 7.2 pC/N. The main experimental uncertainty is linked to the mesophase orientation that cannot be estimated with a high precision from available data. As a conclusion, the optical purity should modify the intrinsic piezoelectric contribution of amorphous phase. Such slight modifications of the piezoelectric activity are attested for commercial PLA grades with low D-content and their piezoelectric films produced by MDO at low draw ratio. Taking into account experimental precision, one can conclude that a $d_{14-am}$ value in the range 7 – 8 pC/N can be applied to all commercial PLA grades.

<table><caption>**Table 5.** Mesophase content, orientation factor of the amorphous phase $F_{am}$ and measured shear piezoelectric coefficients $d_{14}$ for various commercial grades of PLA with different optical purities. Oriented films at low draw ratio by extrusion – MDO. Data taken from Ben Achour et al.[21]</caption><thead><tr><td>D-Content (%)</td><td>λ<sub>app</sub></td><td>Mesophase (%)</td><td>F<sub>am</sub></td><td>d<sub>14</sub> (pC/N)</td></tr></thead><tbody><tr><td>6.4</td><td>1</td><td>6</td><td>0.01±0.02</td><td>0.11±0.04</td></tr><tr><td>6.4</td><td>2.2</td><td>6</td><td>0.17±0.01</td><td>1.42±0.25</td></tr><tr><td>4</td><td>2</td><td>4</td><td>0.06</td><td>0.69±0.11</td></tr></tbody></table>
<table><tr><td>4</td><td>3</td><td>6</td><td>0.21</td><td>1.78±0.12</td></tr><tr><td>2</td><td>2</td><td>5</td><td>0.09</td><td>0.90±0.14</td></tr><tr><td>2</td><td>3</td><td>9</td><td>0.23</td><td>2.69±0.23</td></tr></table>

<figure><img src="image_11.png" /><figcaption>**Figure 9.** Evolution of the shear piezoelectric coefficients *d*<sub>14</sub> with the orientation factor of the amorphous phase *F*<sub>am</sub> for various commercial grades of PLA with different optical purities. Oriented films at low draw ratio by extrusion – MDO. Data taken from [21].</figcaption></figure>

## 4 Conclusions

In this study, a high D-content aPLA grade was chosen to unveil the contribution of the oriented amorphous to the piezoelectric performances of PLA and the intrinsic piezoelectric constant of the amorphous phase was approached. Uniaxially-stretched and oriented aPLA films were produced by an industrially-relevant extrusion – MDO process. True draw ratios (*λ*<sub>true</sub>) of the films were thoroughly measured along with several structural analyses such as DSC, DMA, FTIR, polarized FTIR. Dimensional analysis on as-produced aPLA films revealed that films underwent a quasi-pure iso-volumetric uniaxial stretching without mechanical degradation by formation of voids and cavitation up to draw ratio 3.5 at least. Oriented mesophase was detected in trace amount on uniaxially-stretched aPLA (up to 2.5%) and all analyses attested for an amorphous character of these aPLA films at all draw ratios. Extrusion – MDO clearly produced oriented amorphous films with high orientation factors *F*<sub>am</sub> up to 0.29. With these regards, *F*<sub>am</sub> is proportional to *λ*<sub>true</sub><sup>2</sup> *λ*<sub>true</sub><sup>-1</sup> at low draw ratios in accordance with the affine
deformation theory of rubbery networks with a Kuhn number between entanglement $N_k$ consistent with
several studies. The current system exhibited fixed chain entanglement points at low draw ratios but
"slip-links" appear once $\lambda_{true}$ was beyond $\sqrt{N_k}$, of approx. 2.5. The evolution of "slip-link" was also
linked to thermal and mechanical variations of stretched aPLA films and could be explained by reduc-
tion of the entanglement density and elevated conformational freedom in highly oriented aPLA films.
Measured $d_{14}$ values exhibited a linear coupling with the increase of $F_{am}$. Because of the amorphous
character, the intrinsic piezoelectric coefficient of the oriented amorphous phase $d_{14-am}$ was extrapolat-
ed by the slope value to 7.2 pC/N according to the simplified "3-phase" model. Unprecedentedly, oriented
aPLA films in this study could exhibit a $d_{14}$ value of 2 pC/N, which accounted for 20% of the regularly
reported $d_{14}$ values. Clearly oriented amorphous is indispensable for the shear piezoelectricity of
polylactide. Complementary lab-scale stretching experiments at various stretching rates proved that the
MDO process is highly-efficient in inducing high $F_{am}$ value due to limited chain relaxation phenomena.
Validity of $d_{14-am}$ within commercial polylactide grades was also proved by cross-referring other pub-
lished values or experimental data. Further work to maximize $d_{14}$ in polylactide can be based on the "3
phase" prediction model. While MDO is effective to maximize the amorphous piezoelectric contribu-
tion, it should be combined with other technology, for example, post-stretching annealing, to alter the
crystalline phase as this phase has a triple piezoelectric contribution than the amorphous part.

Funding and acknowledgements

Authors gratefully acknowledge the National Research Agency (ANR) for funding this work (ANR
JCJC 2021, GENEPI project, grant number ANR-21-CE06-0003, https://anr.fr/Projet-ANR-21-CE06-
0003). CS and SC acknowledge both International Campus on Safety and Intermodality in Transporta-
tion (CISIT, France) and Hauts-de-France Region (France) for their contributions to funding extrusion
equipment and important characterization tools (DSC, DMA, FTIR). CS and SC acknowledge
TotalEnergies Corbion and specifically Dr. Gerrit Gobuis du Sart for supporting this study with rele-
vant material selection and supply. CS, SC and HS acknowledge Mrs. Adeline Marin and Prof. Valérie
Gaucher from University of Lille (UMET Laboratory) for their important experimental contributions to
lab-scale stretching experiments. CS, SC and HS acknowledge Prof. Philippe Zinck, Dr. Florine
Nonque, UCCS (polarimétrie et SEC) ainsi que Maxence Epinat - Plateforme SEC de l'université.

Data availability

Raw and treated data of this study are are openly available in Zenodo
(https://zenodo.org/records/15237061). It includes extrusion conditions, MDO conditions, stretching /
dimensional analyses, DSC analyses, DMA analyses, FTIR (non-polarized and polarized) analyses and shear piezoelectric properties. These data are also available upon reasonable request to the authors.

## Author contributions

Methodology HS – CS – SC, Investigations HS, Formal analysis and validation HS – CS – SC, Writing and original draft preparation HS, Reviewing and editing CS – SC, Supervision CS – SC, Funding acquisition CS. All authors have read and agreed to the published version of the manuscript.

## Conflict of interest

The authors declare no conflict of interest. The funders had no role (i) in the design of the study, (ii) in the collection, analyses, or interpretation of data, (iii) in the writing of the manuscript and (iv) in the decision to publish the results.

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