# New insights on the crystal structure of P(VDF-co-TrFE) copolymer (55/45 mol%) and influence on the high piezoelectric response

Melanie Girardot, Jean-Francois Tahon, Joel Lyskawa, Sophie Barrau

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Melanie Girardot, Jean-Francois Tahon, Joel Lyskawa, Sophie Barrau. New insights on the crystal structure of P(VDF-co-TrFE) copolymer (55/45 mol%) and influence on the high piezoelectric response. Polymer, 2025, Polymer, 325, pp.128317. 10.1016/j.polymer.2025.128317. hal-05014979

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Submitted on 1 Apr 2025

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# New insights on the crystal structure of P(VDF-co-TrFE) copolymer (55/45 mol%) and influence on the high piezoelectric response

Mélanie Girardot*, Jean-François Tahon, Joël Lyskawa, Sophie Barrau

Univ. Lille, Sciences et Technologies, CNRS, Centrale Lille, INRAE, UMR 8207, Unité Matériaux Et Transformations (UMET), F-59655, Villeneuve D'Ascq, France

## ARTICLE INFO

### Keywords:

P(VDF-co-TrFE)

55/45 copolymer

WAXS

Crystal structure

Piezoelectric coefficient

## ABSTRACT

Copolymers of vinylidene fluoride (VDF) and trifluoroethylene (TrFE), P(VDF-co-TrFE), exhibit remarkable electroactive properties. More precisely, the copolymers with a molar fraction of VDF between 49 % and 55 % present high piezoelectric properties. However, the literature on P(VDF-co-TrFE) with this composition range is limited, and there are divergences regarding the attribution of crystal phases, unlike the copolymers containing around 70 %–80 % of VDF, which have been extensively studied. In this study, wide-angle X-ray scattering (WAXS) experiments were conducted on a 55/45 P(VDF-co-TrFE) film to gain a better understanding of its crystal structure in correlation to its high piezoelectric properties. For comparison, a 80/20 P(VDF-co-TrFE) film is used as a reference. The results reveal that 55/45 P(VDF-co-TrFE) is mainly composed of two defective ferroelectric (DFE) phases, unlike 80/20 P(VDF-co-TrFE), which contains a mixture of a small fraction of DFE phase and a high fraction of ferroelectric (FE) phases. The stretching of 55/45 copolymer film induces the transformation of DFE phases to FE phase to obtain a structure very similar to that of the unstretched 80/20 copolymer. After poling, the unstretched 55/45 P(VDF-co-TrFE) film exhibits a high piezoelectric coefficient $d_{33}$ of –41 pC/N, compared to more classical values of –22 pC/N for both the stretched 55/45 P(VDF-co-TrFE) and the unstretched 80/20 P(VDF-co-TrFE). This result is mainly explained by the exclusive presence of DFE phases in the unstretched 55/45 P(VDF-co-TrFE), which have greater mobility and then a better ability to polarize compared to the FE phase. This study thus highlights the importance of the DFE phase presence impacted by the film elaboration process in achieving a high piezoelectric coefficient in copolymers. This investigation contributes to a better understanding of the relationships between elaboration, structure and properties of P(VDF-co-TrFE) films, which is a key issue for the design of advanced electroactive organic devices.

## 1. Introduction

Poly(vinylidene fluoride) (PVDF) has garnered significant attention over the past fifty years due to its unique combination of ferroelectric and piezoelectric properties, coupled with ductile mechanical characteristics. These distinctive properties have led to numerous applications, particularly in the field of sensor and actuator devices and technologies [1]. The optimization of PVDF's properties is highly dependent on the structure and conformation of its crystal phase. PVDF exhibits multiple crystal phases, such as α, β, γ, δ and ε phases [2–4]. The α phase is the most dominant and stable phase, presenting a non-polar nature with macromolecular chains adopting TGTG' conformations. In contrast, the β phase stands out as the most polar phase, characterized by macromolecular chains in TTTT (all-trans) conformation, endowing PVDF with the best piezoelectric properties. The β phase can be induced from

the α phase through mechanical stretching [5–7] or by using specific solvents [8,9]. However, in many cases, a blend of α and β crystal phases is obtained [10]. To address this issue, an alternative approach involves the copolymerization of VDF with another fluoromonomer such as trifluoroethylene (TrFE) to obtain the P(VDF-co-TrFE) copolymer which crystallize directly in an electroactive crystal phase [11,12].

In the 1980s, Tashiro et al. demonstrated that the crystal structure of the P(VDF-co-TrFE) copolymer is influenced by both the molar fraction of VDF and the temperature [12,13]. Indeed, for copolymers with approximately 70–80 mol% of VDF, the crystal phase presenting macromolecular chains in an all-trans (TTTT) conformation, is similar to the orthorhombic β phase of PVDF and is known as LT (Low Temperature) [12] or FE (Ferroelectric) [14–16] phase. When these copolymers are heated at a temperature above the Curie transition temperature, the macromolecular chains undergo a conformational change, adopting a

<footnote>* Corresponding author.</footnote>

<footnote>E-mail address: sophie.barrau@univ-lille.fr (S. Barrau).</footnote>
dynamically disordered TGTG' conformation. The associated crystal structure is hexagonal [17,18] and is known as HT (High Temperature) [12] or PE (Paraelectric) [14–16] phase. In 2016, Bargain et al. demonstrated that, in addition to the ferroelectric phase, a second phase may emerge upon cooling from the paraelectric phase. This phase called the DFE (Defective Ferroelectric) phase, crystallizes with macromolecular chains predominantly in trans conformations but with the presence of gauche conformation defects [19]. Tashiro et al. [13] have reported that the FE (or low temperature) phase can be obtained from the DFE (or cooled) phase by stretching or by poling.

For copolymers with approximately 50–60 mol% of VDF, multiple interpretations exist regarding the identification of the crystal phases. Tashiro et al. conducted a study on film of P(VDF-co-TrFE) with a molar ratio 55/45 and made by solvent casting [13,20]. After cooling from the paraelectric phase, the copolymer presented a unique crystal phase named the CL (cooled) phase. This phase is considered to be an intermediate phase between a ferroelectric and paraelectric phase due to the main presence of trans conformations in the macromolecular chains but with some gauche conformations. Simultaneously, Lovinger et al. investigated the crystal structure of P(VDF-co-TrFE) films with a molar ratio of 52/48, prepared by compression molding at 180 °C and cooled to room temperature [21]. They showed the copolymer presented a mixture of trans-planar disordered and 3/1-helical phases, each phase exhibiting hexagonal packing. Both Tashiro and Lovinger demonstrated that it is possible to achieve a single ferroelectric phase (FE) with an all-trans conformation in these polymers from the application of an electric field or from uniaxial stretching. More recently, in 2018, Liu et al. investigated the structure of P(VDF-co-TrFE) films with a VDF molar fraction ranging from 49 % to 55 %. The films were prepared by solvent casting and subsequently annealed at 130 °C [22]. The authors demonstrated a competition between a trans-planar and 3/1 helical phase along the same macromolecular chain [23]. Particularly, they showed that P(VDF-co-TrFE) copolymers with VDF ratio between 49 and 55 mol% exhibit high piezoelectric properties, with a piezoelectric coefficient $d_{33}$ reaching –63.5 pC/N. However, the literature on P (VDF-co-TrFE) copolymers containing approximately 50–60 mol% of VDF is limited, unlike the more extensively studied P(VDF-co-TrFE) copolymers containing around 70–80 % VDF for which the existing literature is both extensive and unanimous in attributing the crystal phases.

Therefore, the present study is focused on the deep investigation of the crystal phases of 55/45 P(VDF-co-TrFE) films in order to better understand the relationships between the structure and the copolymer high piezoelectric coefficient. The analysis was based on the comparison with 80/20 P(VDF-co-TrFE) copolymer, used as a reference as its crystal phases are well-established. In-situ WAXS (Wide-Angle X-ray Scattering) experiments as a function of temperature were conducted to track structural changes occurring below and above the Curie transition temperature. The temperature dependence of lattice parameters, Bragg peak width, and crystal phase fraction in these two copolymers was then studied. Subsequently, the impact of the copolymer stretching was evaluated from the evolution of the 55/45 P(VDF-co-TrFE) crystal structure probed by WAXS in-situ and ex-situ under uniaxial stretching. Finally, piezoelectric measurements were performed and correlated both to the crystal structure and to the film elaboration process to better understand the high piezoelectric response obtained for the 55/45 P (VDF-co-TrFE) copolymer.

# 2. Experimental section

## 2.1. Materials and sample preparation

### 2.1.1. Materials and film preparation

The commercial 80/20 P(VDF-co-TrFE) and 55/45 P(VDF-co-TrFE) copolymers were supplied by Piezotech. Tests were conducted on 300 µm thick films obtained from compression molding. The films

underwent hot pressing at 240 °C under a progressively increasing pressure, reaching up to 50 bars for 10 min, followed by a rapid cooling to ambient temperature under pressure.

### 2.1.2. Solvent casting film

Three different films were fabricated by solvent casting. Copolymer powder was dissolved in acetone and the solution was solvent casted into a silicon mold for 24h at room temperature. The first copolymer film was characterized as-obtained, the second one was annealed 62h at 130 °C and the third one was melt-molded at 240 °C under a progressively increasing pressure, reaching up to 50 bars for 10 min, followed by a rapid cooling to ambient temperature under pressure.

### 2.1.3. Stretched film

55/45 P(VDF-co-TrFE) films were stretched at a strain rate of 1 mm/min ($\dot{\epsilon}$ = $10^{-3}$ s$^{-1}$) using an Instron 4466 tensile testing machine. The samples used were in the form of dumbbells with dimension 22 × 5 mm² and a thickness of 0.3 mm.

### 2.1.4. Poled film

For the study of piezoelectric properties, the film underwent a poling at 35 kV/mm for 15 min at the polymer's Curie temperature, i.e., at 70 °C for 55/45 P(VDF-co-TrFE) and at 120 °C for 80/20 P(VDF-co-TrFE). Subsequently, the films were cooled to room temperature while maintaining the electric field for an additional time of 1h. Note, the poling was carried out at the Curie temperature, as it has been demonstrated in previous works that it is the optimal temperature for poling P (VDF-co-TrFE) copolymers [22].

## 2.2. Techniques

### 2.2.1. Differential scanning calorimetry (DSC)

Thermal characterization of copolymer films was performed on a DSC Q20 (TA instruments) calibrated with indium under nitrogen atmosphere. Samples of approximately 10 mg were put in aluminum pans and were analyzed between –70 °C and 200 °C at a heating rate of 10 °C/min under nitrogen gas flow.

### 2.2.2. Wide angle X-ray scattering (WAXS)

Wide-angle X-ray scattering (WAXS) measurements were carried out on a Xeuss 2.0 (Xenocs) operating under vacuum with a GeniX3D microsource ($\lambda$ = 1.54 Å) at 0.6 mA and 50 kV and with a 2D Pilatus 3 R 200 K detector. The WAXS patterns were acquired with a sample-to-detector distance of 160 mm. Analysis were performed in transmission mode. From the patterns, scattered intensities were integrated and plotted against the scattering angle $2\theta$. For the in-situ experiments as a function of temperature, a Linkam hot-stage was used. The thin films were heated from ambient temperature to 200 °C by step of 5 °C. The acquisition time was 600s.

Peak fit software was used for diffractogram deconvolution by using a Gaussian and Lorentzian deconvolution. The interplanar distance $d_{hkl}$ was determined from $2\theta_{hkl}$ using Bragg's law:

$$2d_{hkl} \sin \theta_{hkl} = \lambda \qquad (1)$$

The width of the Bragg peaks $\Delta 2\theta$ was taken to be the width at half the peak height. The full width at half maximum of the diffraction peak, when associated with a single family of planes (hkl), allows determining the crystal domain size $D_{hkl}$ perpendicular to the (hkl) planes, using the Scherrer formula [19,24]:

$$D_{hkl} = \frac{0.9 \lambda}{\Delta 2\theta_{hkl} \cos \theta_{hkl}} \qquad (2)$$

However, if the diffraction peak is the juxtaposition of two Bragg peaks corresponding to two families of crystallographic planes (hkl) and $(h'k'l')$, the width ($\Delta 2\theta_{hkl} + h'k'l'$) of the resulting peak is the sum of the intrinsic width of each peak with the angular separation ($\Delta 2\theta_{hkl}$-
$\Delta 2\theta_{h'k'l'}$ [19]:

$$ \Delta 2\theta_{hkl+h'k'l'} = \frac{1}{2}(\Delta 2\theta_{hkl} + \Delta 2\theta_{h'k'l'}) + 2\left[\text{Arcsin}\frac{\lambda}{2d_{hkl}} - \text{Arcsin}\frac{\lambda}{2d_{h'k'l'}}\right] \quad (3) $$

in this case, the use of the Scherrer equation to evaluate the size of crystal domains presents some limitations.

The interplanar distance $d_{hkl}$ and the Bragg peak widths $\Delta 2\theta$ are extracted from deconvoluted peaks within the $2\theta = 10^{\circ}$ and $2\theta = 46^{\circ}$ range in the WAXS diffractogram. The degree of crystallinity ($\chi_c$) was calculated for $2\theta$ values between $10^{\circ}$ and $46^{\circ}$ using the equation:

$$ \chi_c = \frac{Ac}{Ac + Aa} \quad (4) $$

where $A_c$ and $A_a$ represent the total integrated intensity of crystalline and amorphous peaks, respectively.

A homemade stretching device adaptable to WAXS experiments was used for the tensile tests. The samples were dumbbell-shaped, with a cross-sectional area of $14 \times 4 \text{ mm}^2$ and a thickness of 0.7 mm. The tests were performed at an initial strain rate of $\dot{\epsilon} = 10^{-3} \text{ s}^{-1}$.

### 2.2.3. Measurement of piezoelectric properties

Piezoelectric properties were investigated using poled P(VDF-co-TrFE) copolymer films. The $d_{33}$ coefficient was measured using a PM300 piezometer from Piezotest, which was previously calibrated with reference ceramics. The tests were performed at ambient temperature with an applied force of 10 N at a frequency of 110 Hz.

## 3. Results and discussion

### 3.1. Characterization of the crystal phases of P(VDF-co-TrFE) copolymer films

Differential Scanning Calorimetry (DSC) thermograms classically allow the observation of the thermal transitions such as the Curie transition associated to the transition from the ferroelectric phase to the paraelectric phase in P(VDF-co-TrFE) copolymers [25–27]. Consequently, the thermal behavior of both the 80/20 and 55/45 P (VDF-co-TrFE) films was investigated using DSC.

The thermogram of 80/20 P(VDF-co-TrFE) film (Fig. 1) reveals a first endothermic peak corresponding to the Curie transition temperature at $T_c = 132^{\circ}\text{C}$, and a second endothermic peak corresponding to the melt temperature at $T_m = 149^{\circ}\text{C}$. On the other hand, the thermogram of 55/45 P(VDF-co-TrFE) film indicates a significantly lower Curie transition

<figure><img src="image_2.png" /><figcaption>Fig. 1. DSC thermograms of 80/20 and 55/45 P(VDF-co-TrFE) during heating ramp. The region delimited with short segments represents the Curie transition zone, while the region delimited with small dots is the melting zone of the copolymer crystal phases.</figcaption></figure>

temperature at $T_c = 63^{\circ}\text{C}$ and a melt temperature of $T_m = 159^{\circ}\text{C}$. These results demonstrate a significant decrease in the Curie temperature and a slight increase of the melt temperature with increasing the molar fraction of TrFE, consistent with existing literature [12,28].

Wide-angle X-ray scattering (WAXS) experiments are classically performed to determine crystal phases of P(VDF-co-TrFE), providing additional information such as the unit cell symmetry and the interreticular distances of diffraction planes. Accordingly, WAXS analysis of 80/20 and 55/45 P(VDF-co-TrFE) copolymer films was carried out at room temperature. The diffraction patterns show the presence of rings for both copolymers (Fig. 2a-b) indicating the crystals present an isotropic distribution in the films.

The integrated intensity profile of 80/20 P(VDF-co-TrFE) (Fig. 2c) exhibits four peaks at $2\theta = 18.9^{\circ}$, $20.1^{\circ}$, $35.4^{\circ}$, $41.0^{\circ}$, which correspond to the inter-planar distances $d = 4.69 \AA$, $4.41 \AA$, $2.53 \AA$ and $2.19 \AA$ respectively. The three peaks of higher $2\theta$ are characteristic of the ferroelectric (FE) phase. The unit cell of the 80/20 ferroelectric copolymer is orthorhombic ($a = 8.90 \AA$; $b = 5.05 \AA$; $c = 2.55 \AA$) [29] and the macromolecular chain conformations are all-trans (TTTT) [12]. The peak at $2\theta = 20.1^{\circ}$ is associated with the superimposition of two closely spaced planes corresponding to diffraction crystal planes (110)/(200) [16] [30], indicative of the inter-chain order, i.e. of the order perpendicular to the macromolecular chains [19]. The peak at $2\theta = 35.4^{\circ}$ is attributed to the (001) plane, which corresponds to the intra-chain order, i.e. the order along the chains [19], and the peak at $2\theta = 41.0^{\circ}$ results from the superimposition of the four diffraction planes (111), (201), (220) and (400) [16] [30]. Regarding the peak at $2\theta = 18.9^{\circ}$, it corresponds to the Defective Ferroelectric (DFE) phase (also known as cooled phase [13]) and can be indexed with (200)/(110) planes, in an orthorhombic cell [19]. In this case, the macromolecular chains are predominantly in a trans conformation but exhibit some gauche conformational defects.

The integrated intensity profile of 55/45 P(VDF-co-TrFE) (Fig. 2d) exhibits only two crystal peaks, called P1 at $18.8^{\circ}$ and P2 at $19.4^{\circ}$, associated with inter-planar distance $d = 4.68 \AA$ and $4.57 \AA$, respectively. The disappearance of the peaks previously observed at $2\theta = 35^{\circ}$ and $2\theta = 41^{\circ}$ for 80/20 P(VDF-co-TrFE) suggests a loss of intra-chain order. For the indexation of these two peaks, several interpretations exist in the literature. Tashiro et al. [17] associated these two peaks with the (110) and (200) crystal planes, which are dissociated in the case of the 55/45 P(VDF-TrFE) copolymer and belong to the same phase called the cooled phase (or DFE). This cooled phase would be obtained in a monoclinic unit cell with parameters $a = 9.12 \AA$, $b = 5.25 \AA$, $c = 2.55 \AA$ and $\beta = 93^{\circ}$. However, Lovinger et al. attributed these peaks to a mixture of disordered trans-planar and 3/1-helical phases [21]. More recently, Liu et al. made a similar suggestion but also added that the competition takes place within the same macromolecular chain [22,23].

The deconvolution of the intensity profiles allows for the separation of the amorphous halo (green curve in Fig. 2) from the distinctive crystal peaks (blue curve in Fig. 2). Consequently, it is possible to estimate a crystallinity of approximately 48 % for 80/20 P(VDF-co-TrFE) and 44 % for 55/45 P(VDF-co-TrFE).

The in-situ evolution of the WAXS intensity profiles in the temperature range from $25^{\circ}\text{C}$ to $180^{\circ}\text{C}$ are presented in Fig. 3 for 80/20 P(VDF-co-TrFE) and 55/45 P(VDF-co-TrFE). For the 80/20 P(VDF-co-TrFE) copolymer (Fig. 3a,c), at room temperature, a peak is observed at $20.1^{\circ}$ with two additional peaks at $35.4^{\circ}$ and $41.0^{\circ}$ (Fig. 3a). These peaks have previously been identified as characteristic of the ferroelectric phase. The intensity and positions of the ferroelectric peaks remain constant up to a temperature of approximately $130^{\circ}\text{C}$. Above $130^{\circ}\text{C}$, the intensity of these peaks decreases progressively until the peaks fully disappears. A new single peak appears at $17.9^{\circ}$ from $130^{\circ}\text{C}$ up to the melt of the sample. The change observed at $130^{\circ}\text{C}$ is attributed to the presence of Curie transition, corresponding to the transition between the ferroelectric phase to the paraelectric phase. The peak of the paraelectric phase at $2\theta = 17.9^{\circ}$ (Fig. 3a,c) is associated with the exact superposition
<figure><img src="image_3.png" /><figcaption>b) 55/45 P(VDF-co-TrFE)</figcaption></figure>

<figure><img src="image_4.png" /><figcaption>c)</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>d)</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>**Fig. 2.** WAXS patterns and integrated intensity profiles at room temperature for (a,c) 80/20 P(VDF-co-TrFE) and (b,d) 55/45 P(VDF-co-TrFE) films.</figcaption></figure>

of both diffraction planes (110) and (200) with an inter-planar distance of $d_{110} = d_{200} = 4.94$ Å. The symmetry corresponding to this crystal phase is hexagonal, with parameters $a = b\sqrt{3} = 9.80$ Å and $c = 2.30$ Å [29]. In this phase the macromolecular chains present a disorder of trans and gauche conformations along the chains [11,18]. The absence of the peaks at 35.4° and 41.0° in the paraelectric phase indicates a loss of intra-chain order [19] (Fig. 3a). It can be observed that the transition between the ferroelectric phase (blue arrow) and the paraelectric phase (purple arrow) at Curie transition is discontinuous in the 2D-map (Fig. 3e). This trend corresponds to a first-order transition, characterized by an order-disorder transition. In the same map, the defective ferroelectric phase (red arrow) is visible and, unlike the ferroelectric phase (blue arrow), continuously evolves towards the paraelectric phase (purple arrow). In this case, the transition is continuous and corresponds to a second-order transition.

For the 55/45 P(VDF-co-TrFE) copolymer (Fig. 3b,d), the two peaks observed at 18.9° and 19.4° at room temperature shift to smaller angles as the temperature increases. These two peaks gradually converge and become a single peak from a temperature of 70 °C, corresponding to the Curie temperature transition. The 2D-map (Fig. 3f) illustrates a continuous transition between the two phases P1 and P2 (red and blue arrows) and the PE phase (purple arrow), indicating a second-order transition. The peak of the paraelectric phase shifts to $2\theta = 17.8°$ until the melt of the copolymer film. This peak is associated with the exact superposition of both diffraction planes (110) and (200) with an inter-planar distance of $d_{110} = d_{200} = 4.98$ Å. The paraelectric crystal phase can be indexed with a rectangular unit cell of an hexagonal type, with parameters $a/b = \sqrt{3}$, $a = 9.75$ Å and $b = 5.63$ Å [20].

Physical parameters such as the inter-planar distance, the Bragg peak widths ($\Delta2\theta$), and the crystallinity, are extracted from deconvoluted

peaks of the WAXS diffractograms and are reported versus the temperature in Fig. 4. For the 80/20 P(VDF-co-TrFE) (Fig. 4a,c,e), the inter-planar distance of 4.40 Å (Fig. 4a) and the width of $\Delta2\theta = 0.46°$ (Fig. 4c) of the peak related to the FE phase (blue dots) remain quasi-constant (blue arrows) as the temperature increases to 140 °C. For the same temperature range, the inter-planar distance (Fig. 4a) and the peak width (Fig. 4c) attributed to the DFE phase (red triangles) increase (red arrows) up to 110 °C. The interplanar distance increases from approximately 4.61 Å to 4.75 Å, and the peak width changes from $\Delta2\theta = 1.00°$ to $\Delta2\theta = 1.34°$. The calculated crystallinity values (Fig. 4e) remain quasi-constant up to 110 °C with around 10 % of DFE phase (red triangles) and 37 % of FE phase (blue dots).

From 110 °C to 140 °C, 80/20 P(VDF-co-TrFE) goes through the Curie transition temperature. The interplanar distance (Fig. 4a) and the peak width (Fig. 4c) of the FE phase (blue dots) remain constant during this transition. In contrast, the interplanar distance (Fig. 4a) of the DFE phase (pink arrow) still increase from 4.82 Å to 4.90 Å and the peak width (Fig. 4c) of this phase (pink arrow) decreases from $\Delta2\theta = 1.34°$ to $\Delta2\theta = 0.20°$ during this transition. The reduction in peak width during the transition from the DFE phase to the PE phase is mainly due to the decrease in angular separation between the (110) and (200) planes, as in the PE phase, these planes are superimposed, whereas they are slightly offset in the DFE phase. The crystallinity (Fig. 4d) of the two phases evolves in opposite directions starting from the Curie transition. Indeed, the crystallinity of the DFE phase (pink triangles) increases from 10 % to 25 %, while the FE phase (blue dots) decreases from 35 % to 15 %.

From 140 °C, the Curie transition has been surpassed, and only the paraelectric phase remains up to the melting temperature. The inter-planar distance (Fig. 4a) remains approximately constant (green triangles), and the width of the peaks (Fig. 4c) still decrease until a value of
<figure><img src="image_7.png" /><figcaption>**Fig. 3.** WAXS integrated intensity profile during a temperature heating and 2D map of (a,c,e) 80/20 and (b,d,f) 55/45 P(VDF-co-TrFE) films. Figures c) and d) are a zoom of figures a) and b), respectively. The region delimited by two black lines with short segments represents the Curie transition zone, while the region between the two black lines with small dots concerns the melt zone of the crystal phases.</figcaption></figure>

$$ \Delta 2\theta = 0.16^{\circ} \text{ (green triangles).} $$

This temperature behavior is very similar to those reported by Bargain et al. on 72/28 P(VDF-co-TrFE) copolymer films [19]. The transition of the interplanar distance from the FE to the PE phases is discontinuous (Fig. 4a). This behavior is a well-known characteristic of the 1st-order Curie transition, where macromolecular chains in trans conformation are stable in temperature until the Curie transition where they instantaneously adopt dynamic gauche and trans conformations (PE phase) [11]. In contrast, the transition of the interplanar distance between the DFE and the PE phases is continuous, representing a second-order transition. Bargain et al. [19] explain that the DFE phase

contains trans conformations with some defects in gauche conformations. In this way, as the temperature rises, conformational disorder can appear progressively and the DFE phase cell parameters can gradually expand.

The increase (red arrow) and subsequent decrease (pink arrow) of Δ2θDFE as a function of temperature (Fig. 4c) would be related to the presence of two different behavior. Indeed, as previously presented, the diffraction peak of the DFE phase can be indexed with two (200) and (110) planes. From equation (3), in the approximation of small angle and considering an orthorhombic structure, Δ2θDFE can be written [19]:
<figure><img src="image_8.png" /><figcaption>Fig. 4. Physical parameters of 20 = 20.1° main peak, such as (a,b) inter-planar distances, (c,d) Bragg peak widths (Δ2θ) and (e,f) crystallinity for (a,c,e) 80/20 and (b,d,f) 55/45 P(VDF-co-TrFE). The two dotted vertical bars indicate the Curie temperature transition zone. The solid lines are a guide to the eye.</figcaption></figure>

$$ \Delta 2\theta_{DFE} = \Delta 2\theta_{110+200} \approx \frac{1}{2}(\Delta 2\theta_{110} + \Delta 2\theta_{220}) + \frac{\lambda}{a} \left[ \sqrt{1 + \left(\frac{a}{b}\right)^2} - 2 \right] \quad (5) $$

where a and b are the lattice parameters.

Bargain et al. demonstrated the evolution of Δ2θDFE mainly depend on the separation between the Bragg peaks 200 and 110 (second term of equation (5)), rather than an effect on the crystal size (first term of equation (5)) [19]. During heating, Δ2θDFE first increase because the ratio a/b increases with a predominant expansion of a-parameter. Then Δ2θDFE decreases while dDFE increases because of the predominant

expansion of b-parameter.

The temperature evolution of the crystallinity displays a significant amorphization of the copolymer film at the Curie temperature with a crystallinity variation from 47 % (37 % FE + 10 % DFE) to 25 % (PE) mainly related to the FE crystallinity decrease. Finally, the formation of the PE phase above the Curie transition occurs from the continuous transformation of DFE phase and the instantaneous transformation of a FE phase fraction.

The 55/45 P(VDF-co-TrFE) copolymer exhibits some differences compared to the 80/20 copolymer. Under heating, the interplanar
distance (Fig. 4b) increases (blue and red arrows) from 4.70 Å to 4.80 Å for P1 (red triangles) and from 4.58 Å to 4.71 Å for P2 (blue triangles) at temperatures up to 60 °C. It is interesting to note, there is no phase for which the interplanar distance remains constant with the temperature, as observed in the case of the FE phase of the 80/20 P(VDF-co-TrFE) copolymer (Fig. 4a).

The peak widths (Fig. 4d) remain quasi-constant (red and blue arrows) at approximately $\Delta\theta = 0.49^\circ$ for P1 (red triangles) and around $\Delta\theta = 0.61^\circ$ (blue triangles) for P2 up to around 50 °C. Upon reaching the Curie transition temperature, the peak widths of the two phases show opposite behaviors. The width of the P1 peak increases from $\Delta\theta = 0.61^\circ$ to $\Delta\theta = 0.71^\circ$ (red arrow), while the width of the P2 peak decreases from $\Delta\theta = 0.49^\circ$ to $\Delta\theta = 0.40^\circ$ (blue arrow). Therefore, there is no phase that exhibits a constant peak width as a function of

temperature, as observed for the FE phase of the 80/20 P(VDF-co-TrFE) copolymer (Fig. 4c).

Above the Curie transition temperature, the interplanar distance of the paraelectric phase (green triangles) increases from 4.85 Å to 4.99 Å (Fig. 4b), while the width of its peaks decreases from $\Delta\theta = 0.45^\circ$ to $\Delta\theta = 0.30^\circ$ (Fig. 4d).

Therefore, the evolution in temperature of the interplanar distance and peak widths of P1 and P2 is not constant, and the transition of the interplanar distance for both P1 and P2 phases to PE phase at the Curie transition (Fig. 4b) occurs continuously, indicating a second-order transition. As previously discussed, DFE phase contains trans conformations with some defects in gauche conformations. The temperature rise progressively implies the increase of conformational disorders associated to the expansion of copolymer cell parameters.

<figure><img src="image_9.png" /><figcaption>Fig. 5. a) WAXS patterns of 55/45 P(VDF-co-TrFE) film during in-situ stretching. b) Variation of the interplanar distances for P1 and P2 crystal phases and of the stress with the strain. c) WAXS intensity integrated profiles obtained during in-situ stretching at room temperature.</figcaption></figure>
During heating, as observed for 80/20 P(VDF-co-TrFE) copolymer, Δθ of both P1 and P2 phases first increase because the ratio a/b increases with a predominant expansion of a-of b-parameter.

At ambient temperature, the 55/45 P(VDF-co-TrFE) presents 16 % of crystallinity for the phase P1 (red triangles) and 30 % of crystallinity for the phase P2 (blue triangles) (Fig. 4f). After heating through the Curie transition temperature, P1 and P2 are completely transformed into a paraelectric phase (green triangles) with a crystallinity of around 41 %, which remains constant until the melting point. The formation of the PE phase above the Curie transition then occurs from the continuous transformation of P1 and P2 phases.

## 3.2. The impact of stretching on the crystal structure of 55/45 P(VDF-co-TrFE)

In the literature, some works have demonstrated that stretching a copolymer P(VDF-co-TrFE) leads to the formation of the FE phase from the DFE phase [13]. As previously discussed, the P1 and P2 phases of P (VDF-co-TrFE) 55/45 copolymer appear to exhibit a behavior characteristic of DFE phases. These phases are therefore expected to undergo a transformation into the FE phase upon stretching. To verify the crystal phase transformation of the 55/45 P(VDF-co-TrFE) copolymer, WAXS experiments have been performed *in-situ* and *ex-situ* under stretching.

### 3.2.1. *In-situ* structural analysis of stretched 55/45 P(VDF-co-TrFE) film

The structural evolution of 55/45 P(VDF-co-TrFE) was followed by WAXS *in-situ* under uniaxial stretching at ambient temperature. The *in-situ* structural analysis offers several advantages. Firstly, it avoids the relaxation effects found in *ex-situ* tests, which can interfere with the interpretation of diffractograms. Additionally, this approach enables the precise tracking of phase change kinetics.

Fig. 5a depicts diffraction patterns registered during the stretching of 55/45 P(VDF-co-TrFE) film. Initially, the film shows a ring characteristic of an isotropic distribution of the crystals and macromolecular chains in the films. However, at a deformation of ε = 0.20, there is localized intensity strengthening, indicating chain orientation. From a deformation of ε = 0.59, only spots at 70° are observed indicating complete chain alignment until the break of the film. The progression in strain is then characterized by the narrowing of the diffraction spots at 70°, indicative of the orientation of the (110)/(200) plans as already observed [31].

Fig. 5b presents the evolution of interplanar distance for both P1 and P2 phases of 55/45 P(VDF-co-TrFE) copolymer during stretching. In the elastic deformation domain, the interplanar distance decreases for both phases, from 4.73 Å to 4.68 Å for P1 (red dots) and from 4.60 to 4.57 for P2 (blue dots). The decrease of interplanar distance observed at low strain indicates a reduction of cell parameters associated to a decrease of gauche conformational defects within the macromolecular chains and

then an increase of trans conformations. Subsequently, in the plastic deformation domain, the interplanar distance becomes relatively constant for both phases.

Fig. 5c displays the WAXS diffractograms of 55/45 P(VDF-co-TrFE) *in-situ* during stretching and their deconvolution to observe the evolution of both P1 and P2 phases. During stretching, P1 (purple curve) presents a shift from 18.70° to 18.83° and gradually decreases until complete disappearance, and P2 (blue curve) also shifts from 19.23° to 19.44° and gradually increases in intensity. The attribution of these two phases will be discussed in the following part.

### 3.2.2. *Ex-situ* structural analysis of stretched 55/45 P(VDF-co-TrFE) film

Subsequently, an *ex-situ* analysis of stretched 55/45 P(VDF-co-TrFE) films was conducted using WAXS experiments to investigate the evolution of crystal phases *in-situ* in temperature. This approach will allow for comparison of these results with those previously obtained for unstretched P(VDF-co-TrFE) films. The film was uniaxially stretched at room temperature.

Fig. 6a shows the diffraction pattern registered at 25 °C for the stretched 55/45 P(VDF-co-TrFE) film. Diffraction spots are observed, indicating an orientation of the chains characteristic of a stretched film [32]. The deconvolution of the 55/45 P(VDF-co-TrFE) intensity profile (Fig. 6b) reveals four peaks at 2θ = 18.8°, 19.5°, 35.4° and 41.0° after stretching. A comparison with the unstretched 80/20 P(VDF-co-TrFE) film (Fig. 2c) reveals notable similarities and suggests that the P2 phase of 55/45 P(VDF-co-TrFE) could become a FE phase after stretching. Note that after *ex-situ* stretching, the presence of a small fraction of P1' phase is observed. This phase can be attributed to relaxation effects consecutive to the stretching experiments. The crystallinity of 55/45 P (VDF-co-TrFE) copolymer slightly increased, from 44 % to 48 % after stretching.

Fig. 7 presents the evolution of WAXS intensity profiles *in-situ* in temperature for the stretched 55/45 P(VDF-co-TrFE) sample. The three peaks observed at 19.5°, 35.4° and 41.0°, are visible up to the Curie temperature of 70 °C (Fig. 7a) and then disappear to give a new peak at 2θ = 17.8°, indicative of the PE phase. In Fig. 7c, the transition between the peaks at 19.5° (blue arrow) and 17.8° (green arrow) corresponding to the PE phase, is discontinuous, indicating a first order phase transition. As previously observed in the case of unstretched 80/20 P(VDF-co-TrFE) (Fig. 3c-e), the discontinuity is characteristic of a transition from a FE to a PE phase. In addition, the transition between the peak at 18.8° (indicated by the red arrow) and 19.5° (indicated by the green arrow) is continuous (second-order phase transition). The P2 phase of P(VDF-co-TrFE), which initially exhibited characteristics of a DFE phase, reveals ferroelectric phase behavior after stretching. Meanwhile, P1' phase of 55/45 P(VDF-co-TrFE) exhibits DFE phase behavior.

In Fig. 8, the evolution of physical parameters such as interplanar

<figure><img src="image_10.png" /><figcaption>Fig. 6. (a) WAXS pattern at room temperature and (b) the corresponding WAXS diffractogram of 55/45 P(VDF-co-TrFE) film after stretching.</figcaption></figure>
<figure><img src="image_11.png" /><figcaption>Fig. 7. (a) WAXS diffractograms during a temperature rise for the stretched 55/45 P(VDF-co-TrFE) film and (b) a zoom in 2θ-range. (c) 2D-map of WAXS experiment during heating for the stretched 55/45 P(VDF-co-TrFE). The region delimited by two black lines with short segments represents the Curie transition zone, while the region between the two black lines with small dots signifies the melt zone.</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>Fig. 8. Parameters from WAXS experiments during heating ramp for stretched 55/45 P(VDF-co-TrFE): (a) inter-planar distances, (b) Bragg peak widths (Δ2θ), (c) crystallinity. The two dotted vertical bars indicate the Curie transition zone.</figcaption></figure>

distance, Bragg peak width (Δ2θ), and crystallinity, are presented during heating for the stretched 55/45 P(VDF-co-TrFE) copolymer. The interplanar distance and the Δ2θ of P2 peak are constant at 4.55 Å and 0.58° on the temperature range (blue arrow in Fig. 8a). Therefore, the P2 phase of the stretched 55/45 P(VDF-co-TrFE) polymer (blue arrow in Fig. 8a-b) exhibits the same characteristic behavior as the FE phase of the unstretched 80/20 P(VDF-co-TrFE) film (Fig. 4a-c), confirming that the P2 phase of 55/45 P(VDF-co-TrFE), initially classified as a DFE phase, transforms into a FE phase after stretching.

Under heating, the interplanar distance of P1' phase slightly increases from 4.72 Å to 4.84 Å up to the paraelectric phase (red and black arrows in Fig. 8b). The width of P1' peak shows a slight increase from

0.95° to 1.04° (red arrow in Fig. 8b), following by a decrease to 0.52° during the Curie transition (black arrow in Fig. 8b). This observed trend confirms the presence of a DFE phase behavior after stretching. Due to relaxation phenomena, part of the P2 phase transforms into P1', giving a crystallinity of 4 % for this phase.

The stretching of 55/45 P(VDF-co-TrFE) results in the emergence of a ferroelectric phase, confirming the presence of two initially defective ferroelectric phases in the copolymer. Specifically, 55/45 P(VDF-co-TrFE) possesses two defective ferroelectric phases with predominantly trans conformation chains and some gauche conformations as presented in Fig. 9. P1 has more gauche conformational defects than P2, given its larger lattice parameters. During stretching, chain reorganization

<figure><img src="image_13.png" /><figcaption>Fig. 9. Schematic representation of the evolution of crystal phases and macromolecular chain conformations in 55/45 P(VDF-co-TrFE) during stretching and after relaxation.</figcaption></figure>
occurs, removing gauche conformational defects and maintaining only trans conformations. It implies a smaller lattice parameter and a single phase known as the FE phase. The FE phase of stretched 55/45 P(VDF-co-TrFE) exhibits the same characteristics as the FE phase of 80/20 P (VDF-co-TrFE), namely a first-order transition (discontinuous transition) at the Curie transition with an interplanar distance and Bragg peak width evolution constant with the temperature, and the presence of two peaks at approximately 35.5° and 41.0°, indicative of intrachain order.

### 3.3. Structure-properties relationships

To better understand the impact of different crystal phases on the piezoelectric properties of P(VDF-co-TrFE) copolymers, piezoelectric coefficient measurements were performed on unstretched 80/20 and 55/45 P(VDF-co-TrFE) copolymers, as well as on stretched 55/45 P (VDF-co-TrFE) copolymer. These three films were poled for 15 min under a field of 35 kV/mm at around their respective Curie temperatures (70 °C for 55/45 and 120 °C for 80/20 P(VDF-co-TrFE)) before measuring their $d_{33}$ piezoelectric coefficients at ambient temperature. Table 1 presents the values of the $d_{33}$ piezoelectric coefficients for the three copolymers. The piezoelectric coefficient of unstretched 80/20 P (VDF-co-TrFE) is -22 pC/N while for unstretched 55/45 P(VDF-co-TrFE) it reaches a value as high as -41 pC/N. After stretching, the piezoelectric coefficient of 55/45 P(VDF-co-TrFE) decreases to -22 pC/N, with a value similar to the value for 80/20 P(VDF-co-TrFE). It was previously observed that stretched 55/45 and 80/20 P(VDF-co-TrFE) exhibit similarities, with the presence of a FE phase and a DFE phase, whereas unstretched 55/45 P(VDF-co-TrFE) possesses two DFE phases. Therefore, to achieve high piezoelectric properties, it seems preferable to have copolymers with two DFE phases rather than a mixture of high fraction of FE phase with DFE phase.

However, it might be considered that a crystal phase composed of chains with gauche conformation defects offers reduced piezoelectric properties due to a lower dipole moment compared to chains adopting an all-trans conformation. But a defective ferroelectric phase exhibits higher mobility due to the presence of these gauche conformation defects, thereby facilitating its orientation along the direction of the electric field and subsequently enhancing the piezoelectric properties of P(VDF-co-TrFE). Choi et al. [35] investigated structural changes of a 55/45 P(VDF-co-TrFE) using in-situ X-ray diffraction during poling. They demonstrated that the DFE phase of the 55/45 P(VDF-co-TrFE) copolymer exhibited higher reactivity to the electric field due to its greater facilities in accommodating trans and gauche conformations of monomer units. Indeed, if the chain dipoles are not aligned with the field, they must easily flip to align under the application of an electric field. However, this process must pass through an intermediate step during which some units adopt gauche conformations before reverting to trans conformation. Since the FE phase has an entirely trans conformation, the

<table><caption>**Table 1**
Comparison of $d_{33}$ piezoelectric coefficients of P(VDF-co-TrFE) copolymers.</caption><thead><tr><th>Processing conditions</th><th>d<sub>33</sub> (pC/N)</th><th></th><th>Reference</th></tr></thead><tbody><tr><td>melt-molding</td><td>55/45 P(VDF-co-TrFE)<br/>-41 [±0.5]</td><td>80/20 P(VDF-co-TrFE)<br/>-22 [±0.5]</td><td>our work</td></tr><tr><td>melt-molding and stretching</td><td>55/45 P(VDF-co-TrFE)<br/>-22 [±0.5]</td><td>-</td><td>our work</td></tr><tr><td>solvent casting and stretching</td><td>52/48 P(VDF-co-TrFE)<br/>-28</td><td>-</td><td>[33]</td></tr><tr><td>solvent casting</td><td>52/48 P(VDF-co-TrFE)<br/>-30</td><td>73/27 P(VDF-co-TrFE)<br/>-12</td><td>[34]</td></tr><tr><td>solvent casting and annealing at 130 °C</td><td>50/50 P(VDF-co-TrFE)<br/>-63.5</td><td>70/30 P(VDF-co-TrFE)<br/>-22</td><td>[22]</td></tr></tbody></table>

transition through gauche conformations is more energetically unfavorable than in a DFE phase, which already contains gauche conformations. Consequently, the chain alignment of the FE phase to the electric field is less favorable. This implies that maximizing the presence of DFE phases seems preferable to achieve higher piezoelectric coefficient.

However, it is essential to note that crystal phases can evolve under the influence of an electric field and that poling conditions, particularly the applied field [36] and the poling temperature [37], play a crucial role in these phase transformations. Consequently, they can impact the final piezoelectric response. Furthermore, it should be emphasized that a DFE phase can correspond to an RFE phase, meaning a non-polarizable phase that does not transform into an FE phase under an applied field [38]. The investigation of these features will be the subject of future works.

The film elaboration is a crucial step to obtain the presence of defective ferroelectric phase and then to optimize the piezoelectric response. In the framework of this article, the DFE phase is obtained from the melt by rapid cooling under pressure. Moreover, other process and/or treatment can be used to induce a DFE phase. Upon reviewing the literature (Table 1) on P(VDF-co-TrFE) copolymers with compositions between 49 and 55 mol% VDF, it is observed that the solvent casting is widely used. However, the copolymer film exhibiting the highest piezoelectric coefficient $d_{33}$ is those elaborated by solvent casting following by an annealing step [22]. To confirm the impact of the film process on the presence of DFE phase, the structure of three films of 55/45 P(VDF-co-TrFE) was compared. The three films were fabricated by solvent casting in acetone (polymer powder was dissolved in acetone and the solution was evaporated for 24h at room temperature). The first copolymer film was characterized as-obtained, the second one was annealed 62h at 130 °C and the third one was melt-molded. The films were then analyzed by WAXS (Fig. 10).

For the 55/45 P(VDF-co-TrFE) film made by solvent casting, the P1

<figure><img src="image_14.png" /><figcaption>**Fig. 10.** WAXS diffractograms of 55/45 P(VDF-co-TrFE) films obtained by solvent casting, by solvent casting melt molding, and by solvent casting and annealing at 130 °C.</figcaption></figure>
phase is significantly less intense than the P1 phase obtained after melt molding or after annealing at 130 °C. Additionally, the peak of the P2 phase shifted from 19.5° to 19.3° after melt molding or after annealing at 130 °C, indicating an increase in gauche conformational defects in this phase. Finally, peaks at 25.4° and 41.0°, associated to the FE phase, were slightly observable after solvent casting but completely disappeared after melt molding or after annealing at 130 °C. Therefore, annealing above the Curie temperature facilitates the introduction of gauche conformational defects and increases the fraction of DFE phase, as highlighted by Bargain et al. [19]. In summary, to achieve high chain mobility, P(VDF-co-TrFE) copolymer should contain between 49 and 55 mol% of VDF. Furthermore, the copolymer film should undergo either a melt-molding or an annealing step during its fabrication to optimize the $d_{33}$ coefficient since these processes favor a high fraction of the DFE phase, as illustrated in Table 1. This investigation highlights the importance of the DFE phase presence impacted by the film elaboration process to enhance a high piezoelectric response in copolymers. This study contributes to a better understanding of the relationships between elaboration, structure and properties of P(VDF-co-TrFE) films, which is a key issue for the design of advanced electroactive organic devices.

## 4. Conclusions

In this study, we have demonstrated that the 55/45 P(VDF-co-TrFE) film under investigation exhibits two phases with behavior analogous to the DFE phase observed in the 80/20 P(VDF-co-TrFE) film [19]. Specifically, both phases display a continuous transition to the paraelectric phase (second-order transition).

The DFE phase of 80/20 P(VDF-co-TrFE), as described in the literature, presents a crystal phase where the macromolecular chains predominantly adopt trans conformations with gauche conformational defects. This is in contrast to the description of the FE phase, which exclusively features trans conformations. The two phases of 55/45 P (VDF-co-TrFE) consequently exhibit DFE behavior, with one phase (P1) containing a higher prevalence of gauche conformational defects compared to the other phase (P2). Upon stretching the 55/45 P(VDF-co-TrFE) film, macromolecular rearrangement take place, leading to the transformation of some gauche conformational defects into trans conformations. Consequently, the stretched 55/45 P(VDF-co-TrFE) film exhibits characteristics similar to the unstretched 80/20 P(VDF-co-TrFE), featuring both FE and DFE phases.

After poling, the piezoelectric coefficients of unstretched 55/45 P (VDF-co-TrFE), stretched 55/45 P(VDF-co-TrFE), and unstretched 80/20 P(VDF-co-TrFE) films were measured. The unstretched 55/45 P(VDF-co-TrFE) film exhibited a notably high piezoelectric coefficient of -41 pC/N. In comparison, both stretched 55/45 P(VDF-co-TrFE) and unstretched 80/20 P(VDF-co-TrFE) films share the same piezoelectric coefficient at -22 pC/N, which is significantly lower than that of the unstretched 55/45 P(VDF-co-TrFE) film. This can be explained by the fact that the unstretched P(VDF-co-TrFE) film has two DFE phases, whereas the stretched 55/45 P(VDF-co-TrFE) and unstretched 80/20 P (VDF-co-TrFE) films each have one FE phase and one DFE phase. The unstretched 55/45 P(VDF-co-TrFE) film exhibits significantly greater mobility in the crystal phases compared to the two other films. As a result, the poling is easier, leading to a much higher piezoelectric coefficient. The study then demonstrates the presence of DFE phases is preferable to achieve high piezoelectric coefficient.

### CRediT authorship contribution statement

**Mélanie Girardot:** Writing – original draft, Visualization, Methodology, Investigation.
**Jean-François Tahon:** Investigation.
**Joël Lyskawa:** Supervision, Funding acquisition.
**Sophie Barrau:** Supervision, Methodology, Funding acquisition, Conceptualization.

### Declaration of competing interest

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

### Acknowledgments

The authors are grateful to Région Hauts-de-France and University of Lille for granting a PhD fellowship to M. Girardot. Financial support from Région Nord – Pas de Calais and European Regional Development Fund (FEDER) for implementing the SAXS-WAXS laboratory equipment is gratefully acknowledged.

### Data availability

Data will be made available on request.

### References

[1] S. Bauer, Poled polymers for sensors and photonic applications, J. Appl. Phys. 80 (10) (1996) 5531–5558, https://doi.org/10.1063/1.363604.

[2] A.J. Lovinger, Ferroelectric polymers, Science 220 (4602) (1983) 1115–1121, https://doi.org/10.1126/science.220.4602.1115.

[3] R.G. Kepler, R.A. Anderson, Ferroelectric polymers, Adv. Phys. 41 (1) (1992) 1–57, https://doi.org/10.1080/00018739200101463.

[4] J.B. Lando, W.W. Doll, The polymorphism of poly(vinylidene fluoride). I. The effect of head-to-head structure, J. Macromol. Sci., Part B 2 (2) (1968) 205–218, https://doi.org/10.1080/00222346808212449.

[5] K. Matsushige, K. Nagata, S. Imada, T. Takemura, The II-I crystal transformation of poly(vinylidene fluoride) under tensile and compressional stresses, Polymer 21 (12) (1980) 1391–1397, https://doi.org/10.1016/0032-3861(80)90138-X.

[6] J. Defebvin, S. Barrau, G. Stoclet, C. Rochas, J.-M. Lefebvre, In situ SAXS/WAXS investigation of the structural evolution of poly(vinylidene fluoride) upon uniaxial stretching, Polymer 84 (2016) 148–157, https://doi.org/10.1016/j.polymer.2015.12.041.

[7] H.-J. Ye, L. Yang, W.-Z. Shao, S.-B. Sun, L. Zhen, Effect of electroactive phase transformation on electron structure and dielectric properties of uniaxial stretching poly(vinylidene fluoride) films, RSC Adv. 3 (45) (2013) 23730, https://doi.org/10.1039/c3ra43966f.

[8] V. Sencadas, R. Gregorio Filho, S. Lanceros-Mendez, Processing and characterization of a novel nonporous poly(vinylidene fluoride) films in the β phase, J. Non-Cryst. Solids 352 (21–22) (2006) 2226–2229, https://doi.org/10.1016/j.jnoncrysol.2006.02.052.

[9] R. Gregorio Jr., M. Cestari, Effect of crystallization temperature on the crystalline phase content and morphology of poly(vinylidene fluoride), J. Polym. Sci. B Polym. Phys. 32 (5) (1994) 859–870, https://doi.org/10.1002/polb.1994.090320509.

[10] V. Sencadas, R. Gregorio, S. Lanceros-Méndez, α to β phase transformation and microstructural changes of PVDF films induced by uniaxial stretch, J. Macromol. Sci., Part B 48 (3) (2009) 514–525, https://doi.org/10.1080/00222340902837527.

[11] A.J. Lovinger, T. Furukawa, G.T. Davis, M.G. Broadhurst, Crystallographic changes characterizing the Curie transition in three ferroelectric copolymers of vinylidene fluoride and trifluoroethylene: 1. As-crystallized samples, Polymer 24 (10) (1983) 1225–1232, https://doi.org/10.1016/0032-3861(83)90050-2.

[12] K. Tashiro, M. Kobayashi, Structural phase transition in ferroelectric fluorine polymers: X-ray diffraction and infrared/Raman spectroscopic study, Phase Transitions 18 (3–4) (1989) 213–246, https://doi.org/10.1080/0141159808026864.

[13] K. Tashiro, K. Takano, M. Kobayashi, Y. Chatani, H. Tadokoro, Structural study on ferroelectric phase transition of vinylidene fluoride-trifluoroethylene copolymers (III) dependence of transitional behavior on VDF molar content, Ferroelectrics 57 (1) (1984) 297–326, https://doi.org/10.1080/00150198408012770.

[14] R. Su, J.-K. Tseng, M.-S. Lu, M. Lin, Q. Fu, L. Zhu, Ferroelectric behavior in the high temperature paraelectric phase in a poly(vinylidene fluoride-Co-trifluoroethylene) random copolymer, Polymer 53 (3) (2012) 728–739, https://doi.org/10.1016/j.polymer.2012.01.001.

[15] C. Bourgaux-Leonard, J.F. Legrand, A. Renault, P. Delzenne, Annealing effects in ferroelectric poly(vinylidene fluoride-trifluoroethylene) copolymers: real-time studies using synchrotron radiation, Polymer 32 (4) (1991) 597–604, https://doi.org/10.1016/0032-3861(91)90470-4.

[16] E. Belletamlicric, Ferroelectric transition under hydrostatic pressure in poly (vinylidene fluoride-trifluoroethylene) copolymers, Polymer 35 (1) (1994) 34–46, https://doi.org/10.1016/0032-3861(94)90046-9.

[17] K. Tashiro, K. Takano, M. Kobayashi, Y. Chatani, H. Tadokoro, Structural study on ferroelectric phase transition of vinylidene fluoride-trifluoroethylene random copolymers, Polymer 22 (10) (1981) 1312–1314, https://doi.org/10.1016/0032-3861(81)90226-3.

[18] J.F. Legrand, P.J. Schuele, V.H. Schmidt, M.N.m.r. Minier, Study of the ferroelectric phase transition in a 7030mol% copolymer of vinylidene fluoride
(VF2) and trifluoroethylene (TrFE), Polymer 26 (11) (1985) 1683-1688, https://doi.org/10.1016/0032-3861(85)90286-1.

[19] F. Bargain, P. Panine, F. Domingues Dos Santos, S. Tencé-Girault, From solvent-cast to annealed and poled poly(VDF-Co-TrFE) films: new insights on the defective ferroelectric phase, Polymer 105 (2016) 144-156, https://doi.org/10.1016/j.polymer.2016.10.010.

[20] K. Tashiro, K. Takano, M. Kobayashi, Y. Chatani, H. Tadokoro, Structure and ferroelectric phase transition of vinylidene fluoride-trifluoroethylene copolymers: 2. VDF 55% copolymer, Polymer 25 (2) (1984) 195-208, https://doi.org/10.1016/0032-3861(84)90326-4.

[21] A.J. Lovinger, G.T. Davis, T. Furukawa, M.G. Broadhurst, Crystalline forms in a copolymer of vinylidene fluoride and trifluoroethylene (52/48 mol %), Macromolecules 15 (2) (1982) 323-328, https://doi.org/10.1021/ma00230a024.

[22] Y. Liu, H. Aziguli, B. Zhang, W. Xu, W. Lu, J. Bernholc, Q. Wang, Ferroelectric polymers exhibiting behaviour reminiscent of a morphotropic phase boundary, Nature 562 (7725) (2018) 96-100, https://doi.org/10.1038/s41586-018-0550-z.

[23] Y. Liu, B. Zhang, A. Haibibu, W. Xu, Z. Han, W. Lu, J. Bernholc, Q. Wang, Insights into the morphotropic phase boundary in ferroelectric polymers from the molecular perspective, J. Phys. Chem. C 123 (14) (2019) 8727-8730, https://doi.org/10.1021/acs.jpcc.9b01220.

[24] Edwards, A.J.H.P. Klug, L.E. Alexander, X-ray diffraction procedures for polycrystalline and amorphous materials, Anal. Chim. Acta 77 (1975) 349, https://doi.org/10.1016/S0003-2670(01)95199-2.

[25] K. Koga, H. Ohigashi, Piezoelectricity and related properties of vinylidene fluoride and trifluoroethylene copolymers, J. Appl. Phys. 59 (6) (1986) 2142-2150, https://doi.org/10.1063/1.336351.

[26] G. Teyssedre, A. Barnes, C. Lacabanne, DSC and TSC study of a VDF/TrFE copolymer, Thermochim. Acta 226 (1993) 65-75, https://doi.org/10.1016/0040-6031(93)80207-Q.

[27] J. Menegotto, L. Ibos, A. Barnes, P. Demont, C. Lacabanne, Dielectric relaxation spectra in ferroelectric P(VDF-TrFE) copolymers, Ferroelectrics 228 (1) (1999) 1-22, https://doi.org/10.1080/00150199908226122.

[28] R. Gregorio, M.M. Botta, Effect of crystallization temperature on the phase transitions of P(VDF/TrFE) copolymers, J. Polym. Sci. B Polym. Phys. 36 (3) (1998) 403-414, https://doi.org/10.1002/(SICI)1099-0488(199802)36:3<403::AID-POLB2>3.0.CO;2-S.

[29] E. Bellet-Amalric, J.F. Legrand, Crystalline structures and phase transition of the ferroelectric P(VDF-TrFE) copolymers, a neutron diffraction study, Eur. Phys. J. B 2 (2) (1998) 225-236, https://doi.org/10.1007/s100510050307.

[30] M.-C. García-Gutiérrez, A. Linares, I. Martín-Fabiani, J.J. Hernández, M. Soccio, D. R. Rueda, T.A. Ezquerra, M. Reynolds, Understanding crystallization features of P (VDF-TrFE) copolymers under confinement to optimize ferroelectricity in nanostructures, Nanoscale 5 (13) (2013) 6006, https://doi.org/10.1039/c3nr00516j.

[31] K. Tashiro, R. Tanaka, Structural correlation between crystal lattice and lamellar morphology in the ferroelectric phase transition of vinylidene fluoride-trifluoroethylene copolymers as revealed by the simultaneous measurements of wide-angle and small-angle X-ray scatterings, Polymer 47 (15) (2006) 5433-5444, https://doi.org/10.1016/j.polymer.2005.06.128.

[32] R. Tanaka, K. Tashiro, M. Kobayashi, Annealing effect on the ferroelectric phase transition behavior and domain structure of vinylidene fluoride (VDF)-Trifluoroethylene copolymers: a comparison between uniaxially oriented VDF 73 and 65% copolymers, Polymer 40 (13) (1999) 3855-3865, https://doi.org/10.1016/S0032-3861(98)00609-0.

[33] T. Furukawa, J.X. Wen, Electrostriction and piezoelectricity in ferroelectric polymers, Jpn. J. Appl. Phys. 23 (9A) (1984) L677, https://doi.org/10.1143/JJAP.23.L677.

[34] T. Furukawa, J.X. Wen, K. Suzuki, Y. Takashina, M. Date, Piezoelectricity and pyroelectricity in vinylidene fluoride/trifluoroethylene copolymers, J. Appl. Phys. 56 (3) (1984) 829-834, https://doi.org/10.1063/1.334016.

[35] A.C. Choi, A. Pramanick, S.T. Mixture, A.R. Paterson, J.L. Jones, O.C. Borkiewicz, Y. Ren, Polarization mechanisms in P(VDF-TrFE) ferroelectric thin films, Physica. Rapid. Res. Ltr. 12 (10) (2018) 1800340, https://doi.org/10.1002/pssr.201800340.

[36] C. Revenant, S. Toinet, E. Lawrence Bright, M. Benwadih, The longitudinal and transverse piezoelectric effects of the ferroelectric polymer P(VDF-TrFE), Macro. Mater. Eng. (2025) 2400420, https://doi.org/10.1002/mame.202400420.

[37] M. Mai, A. Leschhorn, H. Kliem, The field and temperature dependence of hysteresis loops in P(VDF-TrFE) copolymer films, Phys. B Condens. Matter 456 (2015) 306-311, https://doi.org/10.1016/j.physb.2014.09.017.

[38] F. Bargain, D. Thuau, G. Hadziioannou, E. Domingues Dos Santos, S. Tencé-Girault, Phase diagram of poly(VDF-ter-TrFE-ter-CTFE) copolymers: relationship between crystalline structure and material properties, Polymer 213 (2021) 123203, https://doi.org/10.1016/j.polymer.2020.123203.