Jose Elias

Angulo Cervera

Mario Piedrahita-Bello

Baptiste Martin

Eric Dantras

Liviu Nicu

Thierry Leichlé

Kevin Dalla

Antonio Da Costa

Anthony Ferri

Rachel Desfeux

José Elías Angulo-Cervera

Thierry Leichle

Lionel Salmon

Gábor Molnár

Azzedine Bousseksou

The crystallinity and piezoelectric properties of spray-coated films of P(VDF70-TrFE30): effect of film thickness and spin-crossover nanofillers

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Poly(vinylidene fluoride), PVDF and its copolymers have been widely investigated for their appealing piezo-, pyro-and ferroelectric properties. Their ability to convert mechanical strain to electrical charge, and vice versa, have been already exploited in various applications, such as energy harvesting, sensing, monitoring and mechanical actuation [1][2][3]. Besides the attractive electromechanical properties, this family of piezopolymers possesses also high mechanical flexibility, low weight and good manufacturability. In particular, their good solubility and low melting point allows to manufacture them using various solution-and melt-based techniques, such as spin coating, electrospinning, Langmuir-Blodgett method, blade casting, hot pressing, screen-printing, inkjet printing roll-to-roll processing and 3D-printing [4][5][6] and integrate them into micromechanical devices [7][8]. In each case, a careful optimization of deposition conditions (speed, solvent, temperature, …) is mandatory and post-deposition treatments (annealing, poling) are usually indispensable to obtain films with good piezoelectric properties. Among the numerous crystalline polymorphs of PVDF [9][10][11][12], the so-called β-phase is the most attractive structure for electromechanical applications. It has an all-trans, planar zigzag conformation with natural electrical polarity [13]. This is the crystalline form with the highest spontaneous polarization, dielectric constant and piezoelectric coefficient. Although this all-trans phase is not favoured in PVDF, it can be directly obtained from a copolymerization process with the addition of tetrafluoroethylene, TrFE, units (from around 17 mol%). Due to the steric hindrance of the bulkier TrFE groups, P(VDF-TrFE) chains adopt more easily an all-trans (TTTT), low-temperature unit cell, being polar from the beginning and requiring no stretching or drawing to improve its ferroelectric properties [11,14]. This phase is often designated as β-phase owing to its strong similarity to the PVDF β-phase. The fact that the polar phase can be obtained in P(VDF-TrFE) copolymers without mechanical treatments is particularly important for applications requiring film coatings. Indeed, P(VDF-TrFE) has a semicrystalline structure, with crystallinity typically found between 35-70 %, depending on various parameters during the polymerization, the fabrication process and the TrFE content [4]. Recently, there have been a growing interest in using spray coating as a technologically relevant method for manufacturing P(VDF-TrFE)-based coatings. Spray coating refers to a family of Please do not adjust margins Please do not adjust margins techniques, which allow to turn a fluid into a mist (using, for example, a compressed gas) and spray it onto the target surface through a nozzle. Spray coating has the advantage of being able to achieve large-area, conformal deposition of various materials on non-flat, complex surfaces [15][16]. Notably, in situ coating of structural parts by piezoelectric polymers have been employed recently to fabricate ultrasonic transducers for structural health monitoring [17][18][19], strain actuators for adaptive optics [20], microelectromechanical systems (MEMS) [21] and piezo/ferroelectric coatings [22][23]. In the present work, we investigate the feasibility of high-quality P(VDF-TrFE) films by means of spray-coating. The piezoelectric behaviour of the films of different thicknesses (from ca. 200 nm to 30 m) is correlated with their crystallinity, which is the key material property in this context. Besides the investigation of the pure polymer films, we explore also the effect of inorganic, spin crossover (SCO) nanofillers on the piezoelectric properties. Indeed, the possibility of spray-coating electroactive composite films provides a first key step towards the development of useful product properties between the electromechanical behaviour of the polymer and the spontaneous strain in the SCO filler [24][25].

Experimental Section

Coating process

Samples were fabricated with a polymeric matrix of P(VDF-TrFE) with a ratio of vinilydene/trifluoroethylene of 70/30, provided by Piezotech. The inorganic SCO nanofillers with formula [Fe(Htrz)2.05(trz)0.75(NH2trz)0.2](BF4)1.25 were synthetized using a reverse micelle technique previously described in the literature [26]. The coating fluid was prepared by dissolving 1 g P(VDF-TrFE) in 20 ml 2-butanone at 50 °C, followed by stirring for 30 minutes and then adding acetone to the mixture until a total volume of 150 ml was achieved. For nanocomposite coatings, the fluid was prepared by dispersing the SCO nanofillers (0.5 g) in 15 ml 2-butanone via sonication during 10 minutes. A P(VDF-TrFE) solution (1g in 20ml 2butanone) was then added to the particle suspension, which was then homogenized by stirring. Finally, acetone was added to the mixture until a total volume of 150 ml was achieved. This mixture of solvents was found beneficial for the final film quality possibly due to a more appropriate dispersion or viscosity. The sample was then homogenized in an ultrasound bath for 30 minutes. The coating solutions were then sprayed over different types of substrates, including silicon, fused silica, Teflon and gold, using a SUSS MicroTec AltaSpray 8 manual spray coater. The substrates were pre-cleaned by rinsing them successively in acetone, deionized water and ethanol, followed by plasma cleaning in a PVA TePla 300 microwave plasma system with 1 l/min O2 flow and 800 watts power for 5 minutes. During the coating process, the substrates were held at 65 °C to ensure fast evaporation of the solvent. Spraying was carried out with flow rates between 1.1 and 3.3 ml min -1 , a gas pressure of 5 bar, a sample -nozzle distance of 20 cm, a pitch of 4 mm between adjacent scanning lines and a speed of 120 mm/s for the spray arm (see also Fig. S1 in the Supporting Information, SI). The asdeposited films were finally annealed at 105 ºC for 30 min.

Sample characterization

The thickness of the films was assessed using a Tencor P17 profilometer. The surface topography of the samples was characterized by means of a Cypher-ES (Oxford Instruments) atomic force microscope (AFM) in Tapping mode. Scanning electron microscopy (SEM) imaging was conducted by means of a HITACHI S-4800 instrument. Grazing incidence X-ray diffractograms (GIXRD) of thin films were acquired at room temperature on a PANanalytical X'Pert PRO MPD system in a parallel beam configuration using Cu-K radiation. The incident beam optics consisted of a mirror with a 1/32° divergence slit. A parallel plate collimator (0.18°) and Soller slits (0.04°) were mounted on the path of the diffracted beam. An X'Celerator detector in receiving slit mode was used for X-ray collection. The thickest films (30 m) were analysed using the same instrument in Bragg-Brentano geometry. Variable temperature Raman spectra were acquired using an XploRA micro-spectrometer (Horiba) with a spectral resolution of ca. 5 cm -1 . The laser beam (532 nm, 0.1 mW) was focused on the sample by a 50× magnification microscope objective, which was also used to collect the scattered light. The Rayleigh scattering was removed by an edge filter. The sample temperature was controlled by a THMS600 heating-cooling stage (Linkam Scientific). Differential scanning calorimetry (DSC) measurements were carried out using a Thermal Analysis DSC 2920 instrument with a heating ramp of 10 °C/min from 30 to 180 °C. Temperature and enthalpy were calibrated using the melting transition of a high purity indium sample.

Piezoelectric properties

The piezoelectric properties of the samples have been assessed using two different approaches. Thick, freestanding samples were poled between gold-coated stainless steel disks using an Agilent 33220A waveform generator and a Trek high voltage amplifier. Several cycles of a sinusoidal poling electric field up to 60 MV/m were applied at a frequency of 100 mHz at room temperature. During poling, the samples were immerged in silicon oil to prevent arcing. The piezoelectric coefficient d33 was measured 24 h after the poling step, using a PM-200 piezometer (Piezotest), with an applied force of 0.25 N at 110 Hz frequency. Thin films, deposited on gold-coated silicon substrates, were locally investigated using piezo-force microscopy (PFM) technique. PFM analyses were carried out by means of an MFP-3D (Asylum Research/Oxford Instruments) microscope in dual AC resonance tracking (DART) mode [27] under ambient conditions using Pt/Ir-coated probes (PPP-EFM, NanoSensors) and stiff cantilevers (k ~ 3.9 N/m). PFM in spectroscopic mode (piezoloops recording) was conducted by grounding the conductive substrate and applying an AC driving voltage of 2 V to the probe. Piezoloops were recorded in remnant mode, i.e., DC voltage pulses are applied to the active layer and the PFM signal is measured at zero field. Poling experiments were performed by applying DC voltages of opposite polarity to the probe while scanning the sample surface.

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Results and discussion

Film preparation and morphology

Using the optimized coating parameters (see Experimental), we were able to deposit P(VDF-TrFE) layers with controlled thicknesses between 200 nm and 1 μm in a single spray-cycle. Thicker films, up to 30 μm thickness, were obtained by multilayer deposition. The resulting films are highly transparent and can be fixed on various substrates or exist as freestanding films (Fig. 1). Indeed, films above ca. 5 μm thickness, deposited on antiadhesive substrates (e.g. Teflon), can be peeled off and used as stand-alone samples. After film deposition, a recrystallization process is necessary in order to enhance the amount of the polar phase in the P(VDF-TrFE) matrix. To this aim, the films were annealed at 105 ºC, i.e. near the Curie temperature. This annealing temperature has been chosen in order to be able to compare the results with our previous report on ca. 0.1 mm thick blade casted films of similar composition [25]. One must note, however, that somewhat higher annealing temperatures could provide even better crystallinity [11] (see Fig. S2 for a case study). Nevertheless, a reasonably good crystallinity is reached already at 105 °C (vide infra), allowing for a straightforward comparison of the various samples. For the fabrication of P(VDF-TrFE) nanocomposites, we used an inorganic, spin crossover (SCO) filler. In brief, SCO compounds are phase change materials, which can give rise to high thermal strain at the phase transition [28]. This strain can be then used for mechanical actuation purposes [29]. In particular SCO@P(VDF-TrFE) composites were used to actuate MEMS [30] or other types of mechanical systems [31], but the strain can be also coupled to the piezoelectric properties of the P(VDF-TrFE) matrix to provide original (thermo-electrical) product properties [24][25]. In the present work, we charged the polymer matrix with 33 vol% nanocrystalline SCO compound with the chemical formula [Fe(Htrz)2.05(trz)0.75(NH2trz)0.2](BF4)1.25 (trz = 1,2,4-triazolato) [26]. Transmission electron microscopy (TEM) images revealed elongated, prolate-shaped particles with ca. 200 and 20 nm mean length and diameter, respectively (see Fig. S3). It is important to note that the particles were synthesized using a reverse-micelle based method. We found that this type of particles are less prone to aggregation, which is a primary concern in spray coating, implying relatively long transit times between the mixing of the constituents and their deposition on the surface. SEM images show that the films cover uniformly the whole substrate surface, including edges, which is an advantage for piezoelectric applications as short circuits and discharge are less prompt to occur (Fig. 1, see also Fig. S4). Locally the pure copolymer films appear very smooth and homogeneous, although one can note the formation of a few bubbles on largescale SEM images. AFM analysis indicates a mean surface roughness of ca. 1-2 nm for the entire thickness range both for the annealed and not-annealed copolymer films (Fig. S5), as measured over ca. 2 µm² scan area. For the composites, AFM reveals a statistically homogeneous distribution of the particles. Contrary to the pure copolymer films, a mean roughness of ca. 10-20 nm (measured over ca. 2 µm²) was observed in the composite films due to the inclusion of the particles (Fig. S6).

Crystallinity of the films

The crystalline composition of the samples has been assessed by means of a combination of XRD (Fig. 2 and Fig. S7), Raman spectroscopy (Fig. 3) and DSC (Fig. 4) techniques. The room temperature XRD patterns of the nanometric copolymer films consist of a well-defined, intense peak at 2θ = 19.75°, which has been described in the literature as the sum of the diffractions in planes (110) and (200), characteristic of the polar phase of P(VDF-TrFE) [32]. On the other hand, the 2.5 and 30 µm thick films of the pure P(VDF-TrFE) display some broader signals on the low-angle side of the main peak, which might be an indication for the formation of other polymorph(s), amorphous parts or defective phases [17,[33][34]. The XRD patterns of the composites consist of the superposition of diffraction peaks of the SCO particles (around ca. 2θ = 10.5° and 2θ = 18°) and that of the polar phase of P(VDF-TrFE) (around 2θ = 19.75°). When compared to the diffraction patterns of the neat powders [26], we remark the absence of diffraction peaks in the angular domain between 22-28° where intense Bragg peaks appear in the diffractograms of randomly oriented particles. We thus conclude that some preferential orientation must take place within the composite film. This kind of anisotropy is not surprising for strongly anisometric particles and may have important consequences on the (electro)mechanical Please do not adjust margins Please do not adjust margins properties of the composites. We note also that when normalizing the diffractograms of composite films of different thickness to the 2θ = 19.75° peak, the 2θ = 10.5° peaks closely overlap. This finding proves that the polar phase content is almost independent of the film thickness. From the diffraction patterns, we have estimated the apparent mean size of the crystalline domains (τ) of the low-temperature, polar phase in the different samples for different film thicknesses using the Scherrer formula [35]:

τ = kλ γ cos θ (1)
where k is a dimensionless shape factor, λ the X-ray wavelength, 𝛾 the line broadening at half the maximum intensity and θ the diffracted Bragg angle. The calculated values are shown in Figure 2c for different film thicknesses. Some caution must be taken concerning the absolute values of τ, because different factors may contribute to the peak broadening besides the crystallite size [35]. Nevertheless, the comparison of different samples and different film thicknesses is meaningful and demonstrates that neither the film thickness, neither the presence of the filler has a substantial impact on the apparent mean size (ca. 10 ± 1 nm) of the crystalline domains of the polar phase in the matrix. Representative Raman spectra acquired for pure copolymer and composite films at 20 °C and 110 °C are depicted in Figure 3.

For both samples, one can clearly observe the characteristic symmetric CF2 stretching modes of the crystalline polar and nonpolar phases around 840 and 800 cm -1 , respectively [36]. The (reversible) decrease of the former at the expense of the latter at 110 °C denotes the Curie transition from the polar, low-temperature phase to the paraelectric phase, both in the pure copolymer and in the composite films. At room temperature, both the pure polymer and composite films mainly present the expected polar phase. DSC analysis was performed on the different samples starting from ambient temperature up to the fusion temperature of the polymer. The corresponding thermograms are displayed in Figure 4 and the data extracted from the thermograms are summarized in Tables 12. For the pure copolymer, one can depict two endothermic peaks in the heating curve that can be assigned to the Curie transition from the ferroelectric phase to the paraelectric phase (TC ~110 °C) and to the melting of the crystalline paraelectric phase (Tm ~150 °C), respectively [37]. The well-defined melting peaks appear in each sample around the same temperature. Interestingly, the Curie transition is characterized actually by two overlapping peaks, which indicates the co-existence of two ferroelectric phases in the materialincluding possibly a defective ferroelectric phase [34]. A simple visual examination of the thermograms reveals that the Curie peaks in the 300 nm thick film downshift in temperature, decrease in area and change proportions. This behaviour indicates changes in the crystallinity of the film (e.g. formation of defects, microstructural changes, etc.). Please do not adjust margins Please do not adjust margins copolymer, one can note a significant modification of the Curie peak in the thinnest film (400 nm). Interestingly, in this sample the phase transition of the filler is shifted to higher temperatures, overlapping thus the Curie peak. This finding is obviously crucial as for the prospects of developing synergies between the electroactive matrix and the SCO-active filler [24][25]. In a more quantitative manner, crystallinity of P(VDF-TrFE) can be related to the enthalpies associated with the melting (ΔHm) and the Curie transition (ΔHC). Crystallinity (c) is then calculated using the following equation [37]:

𝜒 𝐶 = ∆𝐻 𝐶 +Δ𝐻 𝑚 ∆𝐻 ∞ × 100 ( 2
)
where ΔH∞ is the theoretical melting enthalpy value for the 100 % crystalline copolymer. By comparison with the pure PVDF and PTrFE, ΔH∞ has been estimated as 91.5 J/g for a 100% crystalline P(VDF-TrFE) copolymer with 70/30 monomer ratio [37]. As shown by Figure 5, the apparent crystallinity of the pure copolymer films falls around 50 %, albeit with a slight reduction (43%) for the thinnest (200 nm) film. The crystallinity of the copolymer in the composite films appears similar and shows no clear trend with the film thickness. One must note, however, that for the thinnest film the peak deconvolution introduces rather high uncertaintypossibly higher than the fitting error.

Piezoelectric properties of the films

Overall, the results above confirm for each sample a reasonable crystallinity, associated mostly with the presence of the polar phase, providing thus promise for electromechanical applications. As we are handling two decades difference of thickness among the samples, the piezoelectric properties need to be assessed by different methods. Poling the thicker films was undertaken between flat metallic electrodes and the piezoelectric coefficient d33 was assessed using the Berlincourt method [38] (direct piezoelectricity) (see Table 3). For the pure copolymer, the obtained d33 value is comparable with previous reports on thick P(VDF-TrFE) films made of the same starting material [25]. The composite displays a reduced piezoelectric coefficient as it can be expected in the presence of a non-piezoelectric filler of 33 vol%. Nevertheless, this d33 value remains surprisingly high when compared to previous work on blade casted composite films [25]. The major difference between the two works is the significantly higher poling field, which could be reached in the

P(VDF-TrFE) Composite

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Please do not adjust margins present case, arguably thanks to the best homogeneity of the spray-coated composites. The piezoelectric properties of the sub-micrometric films, spraycoated on gold substrates, were investigated by DART-PFM (converse piezoelectricity). Both poling and piezoloop measurements were conducted via the AFM tip acting as nanometric movable top electrode, giving access to local electrical behaviours. In addition, since the electromechanical activity d33 eff , determined locally by PFM, is strongly dependent on the probed area at the surface of the sample, each local analysis was repeated on (at least) 15 different zones over the free surface of each film in order to ensure the statistical relevance of the results. Representative phase and amplitude PFM loops are shown in Figure 6 (see Fig. S8 for other samples).

Well-defined, saturated and rectangular hysteresis loops are observed from the phase signal with an almost 180° phase difference, evidencing the local ferroelectricity in both the pure copolymer and the composite film. Piezoelectricity is also indicated by the characteristic "butterfly shape" of the simultaneously recorded amplitude signal [39]. The local piezoelectric coefficients d33 eff obtained from the amplitude response [40] are given in Table 4, together with the coercive voltage/field values. As previously mentioned, the detected PFM signal is amplified by the use of the contact resonance through the DART-PFM method. This requires taking into account the quality factor Q, in the following relation [40]:

𝐴 = 𝑑 33 𝑒𝑓𝑓 × 𝑉 𝐴𝐶 × Q (3)
Thus, we have determined the d33 eff values from the measured PFM amplitude A read on the piezoloops, while considering 2 V and ca. 50 for VAC and Q, respectively. It is important to stress that the local piezoelectric coefficients extracted from PFM experiments cannot be considered as fully quantitative values, mainly due to the very strong inhomogeneity of the electric field beneath the AFM tip, the complicated calibration procedure and the poor surface/tip contact [41][42]. Nevertheless, comparison of the estimated values, ca. 9-11 pm/V for the pure copolymer and ca. 4-6 pm/V for the composite films, can be done with confidence since all piezoloops were recorded the same day under similar experimental conditions. Similar to the thick films, a higher piezoelectric coefficient was found for the pure polymer when compared to the nanocomposite films. On the other hand, the composite films displayed a much smaller coercive voltage, which can be a decisive advantage for device operation [3]. This important observation has been confirmed for another series of composite samples (not shown here), in which the coercive voltage could be maintained below 10 V for film thicknesses up to 1.5 microns. The polarization switching process in ferroelectrics is affected by many factors. Notably, the presence of the inclusions inside the matrix may provoke an enhanced nucleation of ferroelectric domains in the crystal phase at the particle/polymer interface, which promotes the ferroelectric switching. Similar effect has been observed in previous works with inorganic particles inside P(VDF-TrFE) [43]. The ferroelectric switching behaviour of the films was also investigated by means of PFM lithography. Artificial domains were locally induced by applying positive and negative DC bias (exceeding the coercive voltage) to the AFM tip over rectangular areas at the free surface of the films. Out-of-plane PFM signals acquired on these areas are shown by Figure 7. Domains with "upward" (away from the substrate) and "downward" (toward the substrate) polarization, i.e. positively and negatively

Please do not adjust margins Please do not adjust margins polarized regions respectively, are clearly distinguished in the phase PFM images with strong contrasts. The influence of the non-polar, paraelectric phase on the switching behaviour, which was previously identified from the Raman spectra on both samples, can be ruled out since homogeneous contrasts are observed on the phase signal associated to the pure polymer (Figure 7b). This confirms the very low fraction of this non-polar phase. However, less sharply defined domains are observed in the case of composite films. This is mainly due to the concomitant effect of the higher surface roughness and the presence of non-piezoelectric fillers. Indeed, even if we do not observe fillers on the AFM topographies simultaneously recorded (Figure 7d), they are clearly visible on the surface of the films when characterized by a more suitable imaging mode, i.e. tapping mode AFM, where reduced damage or wear of the AFM tip and surface during scanning occur, as seen on Figure S6. In addition, this agrees with the nanometric lateral dimensions of the non-reversed areas observed on the PFM phase pattern (Figure 7e). However, it is worth noting that switched domains are still clearly distinguishable, denoting the good stability of the ferroelectric polarization at room temperature.

Conclusions

In this paper we have discussed the fabrication and properties characterization of piezoelectric P(VDF70-TrFE30) films obtained by a method. The films manufactured by this technologically relevant casting approach are dense, homogeneous and smooth over a thickness range of more than two decades (ca. 200 nm -30 m). Using X-ray diffraction and Raman spectroscopy, we have shown that the main crystalline phase of the matrix is the polar phase. DSC measurements revealed a crystallinity of the pure polymer and composite samples of ca. 50 %, which is slightly altered only for the thinnest films. The films display attractive electromechanical properties, characterized by high piezoelectric coefficients.

Interestingly, the composite films exhibit a marked reduction of the coercive field, which is of crucial importance for low voltage applications [3,43]. These results open up attractive perspectives for the development of P(VDF-TrFE) based electromechanical transducers. Notably, work is currently continued in our laboratories to investigate the coupling of the thermal strain arising from the SCO filler with the electromechanical properties of the copolymer matrix, which represents a promising scope for thermal energy harvesting applications.

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Figure 1 .

 1 Figure 1. Top panel: Representative photographs of a P(VDF-TrFE) coated glass substrate and a 10 m thick freestanding film. Bottom panel: SEM images of a 800 nm thick P(VDF-TrFE) coating deposited on a microstructure. (A scratch was made to reveal the coating.)

Figure 2 .

 2 Figure 2. GI-XRD patterns of spray-coated (a) P(VDF-TrFE) and (b) composite films of different thicknesses. (c) Apparent crystalline domain size of the low-temperature phase in the pure P(VDF-TrFE) and composite samples as a function of the film thickness. (N.B. The 30 m films were measured in Bragg-Brentano geometry.)

Figure 3 .

 3 Figure 3. Raman spectra acquired at 20 °C (before heating), 110 °C and 20 °C (after heating) for pure P(VDF-TrFE) (left panel) and composite (right panel) films of 800 nm thickness. The dashed lines show the markers of the para-and ferroelectric phases at 800 and 840 cm -1 , respectively.

Figure 4 .

 4 Figure 4. DSC thermograms of the pure P(VDF-TrFE) (left panel) and a composite (right panel) films for different thicknesses.

Figure 5 .

 5 Figure 5. Crystallinity of P(VDF-TrFE) as a function of the film thickness for the pure copolymer as well as for the composite films.

Figure 6 .

 6 Figure 6. Local phase and amplitude PFM loops recorded on a 275 nm thick P(VDF-TrFE) film (a) and on a 400 nm thick composite film (b).

Figure 7 .

 7 Figure 7. AFM topography (a, d), out-of-plane PFM amplitude (b, e) and phase (c, f) signals recorded just after a poling experiment at ±40 V and ±20 V for a 200 nm thick pure copolymer (a-c) and for a 300 nm thick composite film (d-f), respectively. The difference in applied polarizing voltages is due to the different Vc values determined by spectroscopic PFM for the pure and composite films. (N.B. The inverted contrasts seen on the phase PFM patterns between the two samples are due to the jump in drive frequency on the other of the resonance during scanning.)

Table 1 .

 1 Thermal properties of the P(VDF-TrFE) films

	Thickness	TC	Tm	ΔHC	ΔHm	c
	(nm)	(°C)	(°C)	(J/g)	(J/g)	(%)
	200	98	152	10	32	43
	800	111	150	18	28	47
	4000	110	149	23	26	51
	30000	109	149	22	26	49

Table 2 .

 2 Thermal properties of the nanocomposite films

	Thickness	TSCO	TC	Tm	ΔHC	ΔHm	c
	(nm)	(°C)	(°C)	(°C)	(J/g)	(J/g)	(%)
	300	88*	101*	150	21*	19	61*
	900	76	106	150	12	20	49
	3500	77	107	150	13	18	49
	30000	76	106	149	10	27	58

* Estimated from peak deconvolution.

Table 3 .

 3 Poling field and piezoelectric coefficient of the 30 µm thick films.

	Sample	Poling field (MV/m)	d33 (pC/N)
	P(VDF-TrFE)	70	-18.7 ± 0.05
	Composite	67	-11.3 ± 0.05

Table 4 .

 4 Coercive voltage/field and local piezoelectric coefficient of the films analyzed by PFM.

	Sample	Thickness (nm)	Coercive voltage (V)	Coercive field (kV/mm)	Local d33 eff (pm/V)
		200	15 ± 3	73	-9.0
	P(VDF -	275	36 ± 2	140	-11 ± 2
	TrFE)	400	38 ± 11	90	-9.6
		800	>200	N/A	N/A
	Composite	300	5.8 ± 0.6	14.5	-3.6 ± 0.9
		900	12 ± 1	10	-6.3 ± 1.2

J. Name., 2013, 00, 1-3 | 3

J. Name., 2013, 00, 1-3 | 7

Acknowledgements

This work was supported by the CONACyT -Mexico (PhD grant 471690 of JEAC) and the Occitanie Region/Federal University of Toulouse (PhD grant of MPB), the ANR project NAGAM (ANR-19-CE09-0008), and by the LAAS-CNRS technology platform, a member of Renatech network. Chevreul Institute (FR 2638), Ministère de l'Enseignement Supérieur, de la Recherche et de l'Innovation, Hauts-de-France Region, Fonds Européen de Développement Régional (FEDER) and Major Domain of Interest (DIM) "Eco-Energy Efficiency" of Artois University are acknowledged for supporting and funding partially this work. Région Hauts-de-France and FEDER are acknowledged for funding the MFP-3D microscope under Program "Chemistry and Materials for a Sustainable Growth". We thank the technical assistance of Dr. Yuteng Zhang and Onkar Kulkarni. We acknowledge the referees for their careful reading and useful comments on the manuscript.

Supporting Information

Additional sample characterization details (TEM, SEM, AFM, XRD and PFM).

Author Contributions

JEAC and TL: spray coating and film characterization, MPB and LS: particle synthesis and characterization, BM and ED: DSC and piezometry, KDF, ADC, AF and RD: PFM analysis, GM, BM and JEAC: first draft, LN and AB: supervision and funding acquisition. All authors red the draft and discussed the results.

Conflicts of interest

There are no conflicts to declare.


Sami Mecheri
email: sami.mecheri@def.gouv.fr

Franck Mars
email: franck.mars@ls2n.fr

Régis Lobjois
email: regis.lobjois@ifsttar.fr

Gaze and Steering Strategies while Driving around Bends with Shoulders

Keywords: bends, paved shoulder, steering strategies, visual control of steering, driving simulator

Gaze and steering strategies while driving around bends with shoulders

Gaze and Steering Strategies while Driving around Bends with Shoulders

Non-motorway rural roads are known to put drivers at risk of death or injury. In Europe, 55% of all road accident fatalities occurred on such road networks in 2015 (European Road Safety Observatory [ERSO], 2017). A large proportion of these road fatalities involved single-vehicle accidents (ERSO, 2015; Observatoire National Interministériel de la Sécurite Routière [ONISR], 2010[ONISR], , 2019)), and most of them related to lane departures (see [START_REF] Najm | Pre-crash scenario typology for crash avoidance research[END_REF]. To combat the risk of single-vehicle accidents on rural roads, several experts have recommended installing paved shoulders adjacent to traffic lanes [START_REF] Garber | Evaluation of crash rates and causal factors for high-risk locations on rural and urban two-lane highways in Virginia[END_REF]; Organisation for Economic Co-operation and Development [OECD], 1999; Service d'Etudes sur les Transports, les Routes et leurs Aménagements [SETRA], 2002). This measure aims to provide drivers with a recovery area in cases of steering errors [START_REF] Ogden | The effects of paved shoulders on accident on rural highways[END_REF], but it is also designed to accommodate cyclists and slow-moving vehicles (American Association of State Highway and Transportation Officials [AASHTO], 2011; [START_REF] Armour | Effect of shoulder width and type on rural traffic safety and operations[END_REF][START_REF] Hall | Overview of cross section design elements[END_REF]SETRA, 2008). Roads both straight and curved that are equipped with paved shoulders have been proven to reduce accidents by about 30% for a wide range of traffic densities and shoulder widths [START_REF] Armour | Effect of shoulder width and type on rural traffic safety and operations[END_REF][START_REF] Zegeer | Accident relationships of roadway width on low-volume roads[END_REF][START_REF] Elvik | The handbook of road safety measures[END_REF] in comparison to unequipped roads (e.g., [START_REF] Turner | Effects of paved shoulders on accident rates for rural Texas highways[END_REF].

Researchers who have examined the influence of paved shoulders have reported beneficial effects in terms of lateral positioning on straight roads. Indeed, compared to a road without a shoulder, drivers shifted to the right1 of their lane when in the presence of a 1.50 m shoulder [START_REF] Bella | Driver perception of roadside configurations on two-lane rural roads: Effects on speed and lateral placement[END_REF]. Other studies showed that as the width of the shoulder increased, drivers moved more and more to the right of their lane [START_REF] Ben-Bassat | Effect of shoulder width, guardrail and roadway geometry on driver perception and behavior[END_REF][START_REF] Mecheri | The effects of lane width, shoulder width, and road cross-sectional reallocation on drivers' behavioral adaptations[END_REF]; see also [START_REF] Van Driel | The effects of an edgeline on speed and lateral position: a meta-analysis[END_REF]. These behavioural changes allow drivers to move away from oncoming traffic without getting closer to the edge of the road. Interestingly, while drivers gradually shifted to the edge line when the shoulder is enlarged, they systematically adjusted their lateral position to keep their vehicles within the lane boundaries and exhibited similar lateral-position variability across shoulder-width conditions [START_REF] Mecheri | The effects of lane width, shoulder width, and road cross-sectional reallocation on drivers' behavioral adaptations[END_REF]. This suggests that while drivers use the width of their lane differently in the presence of a shoulder on straight roads, they may not see a shoulder as an extra driving lane but only as a recovery area.

In bends, it is well documented from real-world (e.g., [START_REF] Kandil | Driving is smoother and more stable when using the tangent point[END_REF] and simulator (e.g., [START_REF] Mars | Driving around bends with manipulated eye-steering coordination[END_REF] studies that drivers cut corners. Corner-cutting consists of steering to the outer lane's edge before entering the curve and moving towards the inner-lane boundary around the apex [START_REF] Boer | Tangent point oriented curve negotiation[END_REF]. This strategy is used to reduce the curvature of the trajectory so that driving speed can be maintained. Corner cutting is very common in negotiating turns [START_REF] Barendswaard | A classification method for driver trajectories during curve-negotiation[END_REF]. In fact, it has been shown that a path that cuts the corner is more likely to be attributed to a human driver, whereas driving in the centre of the lane is more readily associated with automated driving [START_REF] Bazilinskyy | What driving style makes pedestrians think a passing vehicle is driving automatically[END_REF]. This type of trajectory likely contributes to run-off-road crashes occurring in bends, as lateral vehicle placement is considered one of the critical safety-related characteristics in negotiating bends [START_REF] Steyer | Traffic safety on two-lane rural roads: New concepts and findings[END_REF]. In right-hand bends where the shoulder is installed on the inside of the curve, it has been observed that the presence of a shoulder increases corner-cutting. [START_REF] Bella | Driver perception of roadside configurations on two-lane rural roads: Effects on speed and lateral placement[END_REF] found that drivers shifted 40 cm towards the inside of a sharp curve in the presence of a 1.50 m wide shoulder. [START_REF] Ben-Bassat | Effect of shoulder width, guardrail and roadway geometry on driver perception and behavior[END_REF] observed that lateral deviation towards the inner lane boundary increased substantially with shoulder width (35, 53 and 70 cm from the centre of the lane in 0.50, 1.20 and 3.00-m shoulder-width conditions, respectively).

However, in left-hand bends, lateral positions were little affected by the presence of a shoulder. Although the results of these studies converge [START_REF] Bella | Driver perception of roadside configurations on two-lane rural roads: Effects on speed and lateral placement[END_REF][START_REF] Ben-Bassat | Effect of shoulder width, guardrail and roadway geometry on driver perception and behavior[END_REF], both studies were conducted using an applied perspective regarding roadway design elements. One can hardly infer from these data why drivers steered closer to the edge line in right-hand bends equipped with a shoulder. This question deserves to be investigated to better understand drivers' behavioural adaptations to shoulders.

From a road-safety perspective, it is recognized that paved shoulders make bends more forgiving [START_REF] Garber | Evaluation of crash rates and causal factors for high-risk locations on rural and urban two-lane highways in Virginia[END_REF]OECD, 1999;SETRA, 2002). In line with this, Ben-Bassat and Shinar (2011) demonstrated that drivers' perceived safety on undivided highways increased with the shoulder width and was higher on right-hand than left-hand bends regardless of shoulder width. One can assume that this greater sense of safety induces a change in drivers' perceptions of shoulders during right-curve negotiation in comparison to straight road sections; they may see the shoulder as a space that allows them to flatten out their path by cutting the corner to a greater extent. The differences in lateral deviation observed between shoulder conditions could then be the result of drivers planning their trajectories differently depending on whether a shoulder is present.

Since it has been robustly demonstrated that gaze and steering are tightly coupled in curve driving [START_REF] Lappi | Visuomotor control, eye movements, and steering: A unified approach for incorporating feedback, feedforward, and internal models[END_REF], one way to determine whether drivers plan their trajectories differently in the presence of shoulders is to examine whether the visual control of steering is affected by a shoulder concomitantly to the steering trajectories in right curves.

Several studies have indeed shown that when the gaze is manipulated so that it is laterally offset from the centre of the road, the trajectory tends to be deflected in the same direction. This has been observed in straight lines [START_REF] Readinger | Gaze eccentricity effects on road position and steering[END_REF] but also in bends with high (20 and 30°; [START_REF] Kountouriotis | Looking and thinking when driving: The impact of gaze and cognitive load on steering[END_REF] or low (5 to 11°; [START_REF] Robertshaw | Does gaze influence steering around a bend?[END_REF][START_REF] Kountouriotis | The role of gaze and road edge information during high-speed locomotion[END_REF]) gaze eccentricity. [START_REF] Robertshaw | Does gaze influence steering around a bend?[END_REF] found, however, that this effect is mainly valid for large lane widths (6 m). On narrow roads (3 m), lateral position error compensation mechanisms that are based on the peripheral view of lane edges come into play and limit this effect. Some studies have even found a trajectory shift in direction opposite to the deviation of the gaze [START_REF] Mars | Driving around bends with manipulated eye-steering coordination[END_REF][START_REF] Crisler | The effects of display location within simulated driving environments[END_REF]. Based on this literature, the hypothesis that installing or widening a shoulder affects drivers' gaze strategies in right-hand bends is a possible explanation for how shoulders affect drivers' behaviour. Specifically, in the presence of a shoulder, drivers may change the way they sample the road scene by directing their gaze more towards the inside of a curve (towards the shoulder) and, as a result, steer further inside. However, it is not known whether drivers' gaze strategies in right-hand bends are affected by the presence and width of shoulders.

The present study aims to examine drivers' visual strategies in relation to their steering trajectories in right-hand bends that are equipped with paved shoulders. For this purpose, drivers negotiated a series of bends on a simulated two-lane rural road with or without a shoulder while their gaze and steering behaviour were recorded. The widths of the shoulder (0, 0.75 and 1.25 m) and the lane (2.75 and 3.50 m) were manipulated. Based on previous findings, a series of hypotheses were formulated. H1. Shoulder presence hypothesis: If the extra space provided by a shoulder is seen as an opportunity to straighten a trajectory, the presence of a shoulder would cause drivers to look further inside the curve and steer in the same direction as a result.

H2. Shoulder width hypothesis: Following Ben-Bassat and Shinar (2011), it was hypothesized that the wider the shoulder, the more the gaze and the trajectory would deviate towards the inside of a curve. H3. Lane width hypothesis: On a narrow lane, the presence of a shoulder may induce a greater orientation of the gaze toward the inside of a curve, but steering trajectories could remain relatively unchanged. According to [START_REF] Robertshaw | Does gaze influence steering around a bend?[END_REF], this would be due to the information provided by inner edge line that provides a stronger feedback for the compensation of lateral position errors.

Method Participants

Eighteen participants aged between 23 and 50 years (mean age = 36 years; SD = 10 years; 9 females), all with normal or corrected vision, were recruited for this experiment via web advertisements. The experiment was approved by the ethics committee of Université Gustave Eiffel. The participants had been fully licensed for at least two years. No professional drivers were involved. The self-reported total mileage ranged from 22,000 to 490,000 km (mean = 229,611 km; SD = 205,480 km). All participants provided their informed consent to be included in the study and did not know about the purpose of the experiment.

Experimental Setup

The experiment was carried out using a low-cost driving simulator (Figure 1) that was equipped with a force-feedback steering wheel (Logitech G25). A virtual full-scale vehicle cab (vehicle width = 1.86 m, including mirrors) was displayed on the screen (Figure 1), as it has been shown that that providing a virtual full-scale cab increases the drivers' ability to adjust steering to the width of the lane in low-cost simulators [START_REF] Mecheri | Steering control in a low-cost driving simulator: a case for the role of virtual vehicle cab[END_REF].

Images were displayed on three screens that were 1.22 m wide and 0.70 m high (60 Hz refresh rate; resolution of 3840 × 2160 pixels). The distance between the participant's head and the centre of each screen was 1.05 m, making the field of view 180° horizontally and 37° vertically. Three loudspeakers generated realistic engine and environmental noises. The data were collected at a sampling rate of 60 Hz.

The visual scene represented a two-lane rural road in a traffic-free environment with one lane going in each direction. The road surface was textured and marked by a discontinuous line 0.18 m wide on the edges and 0.15 m wide in the centre. The surrounding terrain was depicted as a flat rural landscape. The participants drove on the right side of the road. A Pertech head-mounted monocular eye tracker was used to record the participants' eye movements at a sampling rate of 50 Hz. This monocular eye-tracker has 0.25° of accuracy (according to the manufacturer's specifications) and uses pupil-tracking technology with an image processing algorithm to define ocular direction. It was calibrated using a 7-point grid.

Data from the simulator, including the tangent point position in the coordinate system of the screen (in pixels), were sent to the eye-tracker software. Gaze positions were automatically calculated and expressed (in pixels) in the same coordinate system. The synchronisation between the two data sets was achieved through a Network Time Protocol server/client application.

Experimental Design and Task

Six experimental rural roads that corresponded to two lane widths (3.50 and 2.75 m)

and three shoulder widths (0, 0.75 and 1.25 m) were used in this study (Figure 2). The lane widths were selected from typical lane designs in France (see [START_REF] Hall | Overview of cross section design elements[END_REF]SETRA, 1994). The shoulder widths were determined using French regulations for shoulders on rural roads; 0.75 m and 1.25 m corresponded to the minimum and recommended widths, respectively.

Figure 2. Screenshots of the six experimental roads used in the experiment. The point of view is that of the participants at the beginning of the curve.

On each experimental road, the participants had to perform a repetitive cornering task in a right-hand bend which had a radius and arc length of 200 m as measured from the centre of the road. At the beginning of each trial, the participants were positioned in the centre of their (straight) lane at 50 m from the bend entry and steered with an initial speed of 90 km/h (i.e., the legal speed limit for two-lane rural roads in France). Their speed was maintained constantly by the simulator software so that the trajectories in the bend were not influenced by any individual speed reduction strategies. Given the constant speed and road portion length (250 m), each experimental trial lasted 12 s.

Procedure

Upon their arrival, the participants filled out biographical and consent forms. They were then invited to sit down in the simulator and were encouraged to adjust the driving seat before the nature and requirements of the task were explained. They were told that they would have to drive repeatedly on a right-hand bend on a two-lane rural road while their driving speed would be kept constant. Participants were asked to drive as they would normally do with their own car on a two-lane rural road while obeying traffic rules. They were then informed that each trial would begin with a black screen, which would be replaced with the visual scene. At this point, they had to drive until they reached the end of the bend, at which point the black screen reappeared. The participants were then allowed to get used to the simulator by driving on a winding rural road that featured several different curves. Before performing the experimental trials, the participants carried out six practice trials to familiarize themselves with the experimental task. After that, they were equipped with the eye tracker, and the device was calibrated (this was done before each experimental session). During the experiment proper, the participants completed one block of eight successive trials on every experimental road; the order of presentation was random. The participants did not receive feedback on their driving performance. They took a short break every two roads, during which they were free to leave the simulator, if necessary. The experimental session lasted about one hour. Gaze measures. Given our hypothesis that drivers would look more towards the inside of a curve when in the presence of a shoulder, we examined gaze behaviour by computing the deviation of the gaze on the horizontal axis relative to the tangent point (TP;

Data and Statistical

i.e., the point in the bend where the direction of the inside edge line seems to reverse from the driver's viewpoint, see Figure 3B) [START_REF] Kandil | Driving is smoother and more stable when using the tangent point[END_REF][START_REF] Land | Where we look when we steer[END_REF][START_REF] Wilson | Eye movements coordinated with steering benefit performance even when vision is denied[END_REF]. The TP was used as a dynamic spatial reference to analyse visual strategies as it was found that gaze points in the vicinity of the TP capture a large proportion of guiding fixations regardless of whether they are future path fixations (e.g., [START_REF] Mars | Where we look when we drive with or without active steering wheel control[END_REF][START_REF] Robertshaw | Does gaze influence steering around a bend?[END_REF] or fixations to the TP itself (e.g., [START_REF] Kandil | Driving is smoother and more stable when using the tangent point[END_REF]. As the TP was located on the edge line, this provided a straightforward view of gaze orientation as being either in the lane or beyond the edge line. In practical terms, the visual scene was divided into twenty intervals of 1° of angular deviation from the TP (from -10° to +10°), and the proportion of gaze points falling within each interval was computed for each bend (the straight-line approach has been excluded). Gaze points that fell beyond 10° of eccentricity were distributed between two additional classes (<-10° or >+10°).

These variables were analysed with repeated measure analyses of variance (ANOVAs). The effects of lane width and shoulder width on driving measures were assessed using 2 (lane width: 2.75, 3.50) × 3 (shoulder width: 0, 0.75, 1.25) ANOVAs. For gaze distribution, we performed a three-way ANOVA and used lane width, shoulder width and angular deviation from the TP as within-participant factors. All tests were done with p set at .05. Mauchly's test of sphericity was conducted to determine whether the sphericity assumption was violated. In cases of violation, the Greenhouse-Geisser correction was used and modified degrees of freedom were reported. To follow up on significant effects, Newman-Keuls post hoc tests were run when necessary. For each effect, partial eta-squared (ηp 2 ) was calculated to determine the proportion of total variability accounting for the effect.

Descriptive statistics were reported using means and standard deviations (mean ± SD).

Results

Driving Measures

The 2 × 3 repeated measures ANOVA on LPEntry revealed only a main effect of shoulder width (F1.44, 24.57 = 4.21, p = .03, ηp 2 = 0.20). Under the no-shoulder condition, the drivers entered the bend with a mean deviation toward the outside edge (-4 ± 31 cm), whereas they drove more in the right half lane in presence of a shoulder (5 ± 28 and 6 ± 29 cm from the centre of the lane in the 0.75-and 1.25-m shoulder-width conditions, respectively).

Similarly, only a main effect of shoulder width was found for LPApex (F1.34,22.88 = 5.71, p = .02, ηp 2 = 0.25). Under the no-shoulder condition, the drivers maintained a middle-lane position on average (0 ± 30 cm). By contrast, a mean inward deviation was observed when a shoulder was present (9 ± 29 and 11 ± 34 cm from the centre of the lane in the 0.75-and 1.25m shoulder-width conditions, respectively).

The ANOVA on LPMax indicated a main effect of lane width (F1,17 = 7.751, p = .01, ηp 2 = 0.31) due to a smaller lateral deviation on the narrow lane (40 ± 26 and 48 ± 30 cm for the 2.75 and 3.50 m wide roads, respectively) and a main shoulder-width effect (F1.43,24.31 = 12.19, p < .001, ηp 2 = 0.42). A post hoc test for the shoulder effect revealed that the innermost lateral position in the bend was further down the inside edge line when a shoulder was present (34 ± 27, 48 ± 27 and 49 ± 28 cm in the 0, 0.75-and 1.25-m shoulder-width conditions, respectively). The effects of shoulder width on the lateral position at the three key points in the bend are depicted in Figure 4.

The ANOVA performed on the amplitude of corner-cutting demonstrated only the main effect of lane width (F1,17 = 11.07, p = .01, ηp 2 = 0.39). The amplitude of corner cutting was significantly larger on a wide lane (46 ± 17 cm) than on a narrow lane (37 ± 13 cm).

Regarding the lane departure duration, the statistical analysis revealed the main effect of lane width (F1,17 = 12.93, p < .01, ηp 2 = 0.44) and the main effect of shoulder width (F1.51,25.81 = 12.19, p = .03, ηp 2 = 0.21). Participants spent more time off the lane on the narrow lane (7 ± 10%) than on the wide lane (2 ± 6%) and in presence of a shoulder (5 ± 8 and 6 ± 12% in the 0.75 and 1.25 m conditions, respectively) than in the absence of one (2 ± 4%).

Gaze Measures

The 2 x 3 x 22 repeated measures ANOVA on the proportion of gaze points revealed the main effect of angular deviation (F21,294 = 24.33, p < .001, ηp 2 = 0.63) and a significant interaction between shoulder width and angular deviation (F42,588 = 2.28, p < .001, ηp 2 = 0.14).

Most visual sampling was concentrated in the vicinity of the TP (85% between -3° and 3°),

with almost two-thirds of these gaze points that were oriented towards the lane (i.e., from -3° to 0°). The peak of the distribution (23%) occurred at the [-1°; 0°[ interval.

The post hoc test for the interaction between shoulder width and angular deviation revealed that this overall distribution of gaze differed as a function of shoulder width with a larger proportion of gaze points directed beyond the TP in the presence of a shoulder (Figure 5). A higher proportion of gaze points falling within the [-2°; -1°[ interval was found in the no-shoulder condition than in the two shoulder conditions, which also differed between each Figure 5. The proportion of the gaze points (%) as a function of shoulder width and angular deviation from the tangent point on the horizontal axis (degree). Negative angular deviations indicate that drivers' gaze is directed toward the lane.

Discussion

The objective of this study was to examine whether the presence of a shoulder influences the distribution of a drivers' visual strategies in relation to their trajectories in right-hand bends. For this purpose, the participants repeated a cornering task on a simulated two-lane rural road with or without a paved shoulder while their free gaze and steering strategies were recorded. Gaze behaviour was analysed as the horizontal angular deviation of gaze points from the TP. This made it possible to characterize the gaze as being oriented either towards the lane or towards the shoulder. Three hypotheses were formulated as follows:

H1. Drivers may look further inside the curve and steer in the same direction when a shoulder is present; H2. The gaze and the trajectory may deviate more towards the inside of a curve when the shoulder is widened; H3. When it is installed on a narrow lane, the shoulder may induce changes in gaze but not in steering due to a stronger edge-line feedback that comes into play.

Gaze and driving measures revealed significant effects of the shoulder on driver behaviour in right-hand bends. Under the no-shoulder condition, significantly more gaze points were directed in the interval [-2°; -1°[ in comparison to the shoulder conditions. The drivers thus looked more within the lane boundaries and steered accordingly at a significantly smaller distance from the centre of their lane and with significantly lower lane departure duration. It is worth noting that a similar pattern of gaze distribution and steering trajectories was found in prior curve-driving studies that used a similar method [START_REF] Mars | Where we look when we drive with or without active steering wheel control[END_REF][START_REF] Schnebelen | Looking at the road when driving around bends: Influence of vehicle automation and speed[END_REF]. In the presence of a shoulder, the participants gazed more at the interval [0°; 1°[. As a result, they steered further towards the inside of the curve, in accordance with previous studies [START_REF] Bella | Driver perception of roadside configurations on two-lane rural roads: Effects on speed and lateral placement[END_REF][START_REF] Ben-Bassat | Effect of shoulder width, guardrail and roadway geometry on driver perception and behavior[END_REF]. Consequently, the trajectories taken by the participants were not always well-suited to the manoeuvring space as more time was spent off the lane. This pattern of results supports the hypothesis H1 that the shoulder is seen by drivers as an opportunity to increase corner cutting and has an influence on path planning. Although the drivers steered closer to the edge line, the results revealed that the amplitude of corner-cutting was not affected by the presence of a shoulder.

The drivers adopted roughly equivalent path curvatures in the three shoulder width conditions, but the presence of a shoulder led to a rightward shift of the trajectory, which was observed at the three measurement points. This suggests that the tight coupling between gaze and steering control in bends is preserved when a shoulder is added, but the driver's path planning is changed.

The fact that the drivers used the extra space provided by the shoulder is consistent with Ben-Bassat and Shinar's results (2011). In accordance with the "steer where you look" strategy whereby drivers look at successive waypoints [START_REF] Lappi | Visuomotor control, eye movements, and steering: A unified approach for incorporating feedback, feedforward, and internal models[END_REF][START_REF] Wann | Why you should look where you are going[END_REF][START_REF] Wilkie | Eye-movements aid the control of locomotion[END_REF], the participants in the present study looked more or less towards the inside of the curve depending on the presence or absence of a shoulder.

Nevertheless, based on this visual strategy and the increased feeling of safety, one might have expected that the wider the shoulder, the more the gaze and the trajectory would deviate towards the inside of the curve. This was not observed. Contrary to the hypothesis H2, the effects of the shoulder on gaze and steering behaviour did not depend on shoulder width, which operated in an all-or-nothing mode. The functional significance of this observation may be found in the hypothesis formulated by [START_REF] Mars | Where we look when we drive with or without active steering wheel control[END_REF]. These authors assumed that drivers' gaze is not directed towards points on the future path but rather to a safety line that they do not want to cross. According to this perspective, maintaining some distance from the inside edge line under the no-shoulder condition makes sense since drivers cannot risk losing control of their vehicles by driving on the side of the road. In contrast, the presence of a shoulder could increase the acceptable trajectory envelope, which would explain why drivers gazed more beyond the TP and why they spent more time off the lane. However, when the width of a shoulder increases, drivers limit this behaviour because they know the shoulder is not a drivable area.

From a more theoretical point of view, these findings can be comprehensively accounted for by the concept of field of safe travel [START_REF] Gibson | A theoretical field-analysis of automobile-driving[END_REF]. The boundaries of the field of safe travel are determined by objects or features of the terrain that have a negative 'valence' from the driver's viewpoint, such as obstacles or low-grip surfaces.

According to [START_REF] Gibson | A theoretical field-analysis of automobile-driving[END_REF], a positive or negative valence refers to the propensity of an object to induce a movement towards or away from it. In the present case, the inner edge line, which coincided with the road edge in the absence of a shoulder, was equated to an obstacle. In the presence of a shoulder, the inner edge line may take on a less negative valence and no longer be considered as an obstacle as the shoulder opens a new field of safe travel that did not exist before. In this case, the inner edge line is no longer a reliable indicator of the objective possibilities of locomotion and becomes a purely legal limit. From the driver's point of view, this may lead to a compromise between the legal interdiction of crossing the edge line and the possibility of extending the field of safe and efficient travel. As stated by [START_REF] Gibson | A theoretical field-analysis of automobile-driving[END_REF], the possibilities for opening up a new field of safe travel depend on a driver's sensitivity to the pertinence of this field for locomotion and upon the degree to which this field is imbued with meaning for locomotion. In the present study, one can assume that drivers considered driving on the shoulder to be pertinent insofar as only 3 participants out of 18 did not encroach into this road space. However, they seemed to have made some kind of compromise with the meaning of such behaviour that contravened the traffic rules to keep this behaviour within a satisfying limit.

The present results also revealed that the shoulder effects on the driving behaviour were similar between the two lane-width conditions. Although the lane departure duration was higher with a shoulder than withoutand the amplitude of corner-cutting was similarthese shoulder-related effects did not vary with the width of the lane. This goes against the hypothesis H3 that was based on the results of [START_REF] Robertshaw | Does gaze influence steering around a bend?[END_REF]. Indeed, if the compensation of lateral deviations were stronger in narrow lanes, then the shoulder effect on the lane departure duration would have been mitigated. This discrepancy between studies may be due to the fact that the participants drove freely and did not have to keep their vehicles as close to the centre of the lane as possible, a condition in which the influence of the edge lines in compensatory control may play a more determining role (e.g., [START_REF] Kountouriotis | The role of gaze and road edge information during high-speed locomotion[END_REF].

These results reinforce the idea that shoulder effects are the result of different trajectory planning and further suggest that creating or widening a shoulder can be done equally well on wide and narrow rural roads without increasing the amplitude of corner-cutting.

These results lead us to consider road layout that would prompt drivers to keep their vehicles in the lane in right-hand bends equipped with shoulders. The objective would be to preserve the safety benefits of the shoulder without inducing deleterious changes in the trajectory (e.g., encroachment on the shoulder or reduction of the lateral clearance while overtaking cyclists riding on the shoulder). Since the present results demonstrated that drivers' trajectory follows their gaze, the objective would also be to prevent drivers from shifting their gaze towards the shoulder. One method would consist of implementing perceptual countermeasures such as a continuous, wider or double edge line (e.g., [START_REF] Charlton | The role of attention in horizontal curves: A comparison of advance warning, delineation, and road marking treatments[END_REF], peripheral transverse bars (e.g., [START_REF] Calvi | Evaluating the effectiveness of perceptual treatments on sharp curves: a driving simulator study[END_REF] or herringbones (e.g., [START_REF] Charlton | The role of attention in horizontal curves: A comparison of advance warning, delineation, and road marking treatments[END_REF][START_REF] Awan | Impact of perceptual countermeasures on driving behavior at curves using driving simulator[END_REF]. Such delineation devices would be aimed at strengthening guidance signals dedicated to trajectory planning and/or inducing a negative valence from the driver's viewpoint. In the studies of [START_REF] Bella | Driver perception of roadside configurations on two-lane rural roads: Effects on speed and lateral placement[END_REF] and Ben-Bassat and Shinar (2011), experimental roads had continuous edge lines. Since the drivers still deviated to the inside of the bend in the presence of a shoulder, it can thus be assumed that implementing continuous lateral marking is not effective in counteracting the influence of the shoulder on gaze and steering behaviour.

Out of all the countermeasures that have been tested to make bends safer, herringbones have a good potential to influence lateral positions around bends with shoulders. Indeed, drivers were found to move further towards the outer part of their lane at curve entry [START_REF] Charlton | The role of attention in horizontal curves: A comparison of advance warning, delineation, and road marking treatments[END_REF][START_REF] Awan | Impact of perceptual countermeasures on driving behavior at curves using driving simulator[END_REF] and to maintain a more central position in the bend [START_REF] Awan | Impact of perceptual countermeasures on driving behavior at curves using driving simulator[END_REF] see [START_REF] Ariën | The effect of pavement markings on driving behaviour in curves: a simulator study[END_REF] in the presence of herringbones in comparison to a control condition without altering corner-cutting behaviour. Additionally, this pavement treatment could be coupled with advanced warning signs that are known to reduce speed [START_REF] Charlton | The role of attention in horizontal curves: A comparison of advance warning, delineation, and road marking treatments[END_REF] insofar as corner-cutting and time spent out of the lane are reduced at a slower speed [START_REF] Raw | Movement control in older adults: Does old age mean middle of the road?[END_REF][START_REF] Xu | Vehicle trajectory at curved sections of two-lane mountain roads: a field study under natural driving conditions[END_REF].

It warrants mentioning that the choice was made to hold drivers' speed constant in this study, preventing the ability of drivers to modulate their speed to negotiate bends. This method is commonly used in studies investigating the relationship between gaze and steering control (e.g., [START_REF] Kountouriotis | The role of gaze and road edge information during high-speed locomotion[END_REF][START_REF] Robertshaw | Does gaze influence steering around a bend?[END_REF][START_REF] Schnebelen | Looking at the road when driving around bends: Influence of vehicle automation and speed[END_REF], as it facilitates comparison between experimental conditions. However, it limits the ecological validity of the study. Therefore, it would be relevant to replicate this experiment with participants driving at a self-determined speed and to extend the analysis to curves of various radii in order to generalize the findings of this study.

In conclusion, this study showed in accordance with previous research that drivers steer further inside right-hand bends with the presence of a shoulder, and that this was observed at three points in the curve. Although the amplitude of corner-cutting was not affected by the presence of a shoulder, the increases in lateral deviation resulted in more time spent out of the lane. Importantly, the analysis of visual strategies provided compelling evidence that this driving behaviour is due to a modification of the visual sampling of the road ahead. In the presence of a shoulder, the drivers' gaze deviated towards the inside of the curve, and the steering trajectories followed, regardless of the shoulder width. This alteration of behaviour can be viewed as the product of the drivers' sensitivity to the shoulder as a new field of safe travel [START_REF] Gibson | A theoretical field-analysis of automobile-driving[END_REF]) that induces a compromise, from the driver's point of view, between the legal interdiction of crossing the edge line and the possibility of steering more efficiently (shorter path length through the curve). Based on our findings, it would be worth examining the effects of delineation treatments to better define travel paths on roads that are equipped with shoulders in order to bring the drivers' gaze and vehicle back to the lane. As shoulders are also suitable for cycle use, another valuable future direction might be to examine drivers' steering trajectories when overtaking cyclists in right-hand bends.

Figure 1 .

 1 Figure 1. Illustration of the low-cost driving simulator with a virtual full-scale cab displayed in the visual scene.

  AnalysisDriving measures. Driver behaviour was assessed in terms of lateral position in the lane. The lateral position was defined as the distance in centimetres between the centre of the participant's vehicle and the centre of his or her driving lane. To obtain a straightforward view of the trajectories taken by participants along the curve, we computed the lateral position at three points in the bend (Figure3A). LPEntry corresponded to the instantaneous position in the lane at curve onset. LPApex indicated the instantaneous position in the lane when the driver reached half of the curve. LPMax corresponded to the vehicle's closest position to the inside edge of a curve. Negative values indicated deviation toward the outside edge line, whereas positive values indicated deviation toward the inside edge line. Based on these variables, we also calculated the amplitude of corner-cutting as measured by the difference between LPMax and LPEntry. Finally, we computed the lane departure duration, which we defined as the percentage of the total time that the participant's vehicle was outside the lane. A departure began when any wheel touched the inner lane marking.

Figure 3 .

 3 Figure 3. Schematic representation of the dependent variables computation according to the geometry of a bend. (A) The first 50 m of each trial consisted of a straight road followed by a bend of 200 m. Three lateral-position variables were calculated: LPEntry (position at 0 m into the curve), LPApex (position at 100 m into the curve), and LPMax (innermost position). Lateral position was calculated relative to the lane centre, with positive values corresponding to a deviation toward the inside edge of the curve. (B) The gaze behaviour was analysed as the horizontal angular deviation from the tangent point. As an approximation, gaze deviation was considered to be either in the driving lane (negative angular deviations) or beyond the edge line (positive angular deviations).

Figure 4 .

 4 Figure 4. Lateral position at the three measurement points in the bend (the entry, the apex and the innermost position) as a function of lane width and shoulder width. Zero represents the centre of the lane.

  , a higher proportion of gaze points was observed within the [0°; 1°[ interval in the presence of a shoulder, regardless of its width, compared with the no-shoulder condition.

The arguments are developed for countries with right-hand traffic lanes. Driving on the right side of the road implies that oncoming traffic is located on the left of the vehicle while the shoulder adjacent to the travel lane is located on the right of the vehicle.

Acknowledgments

This research was supported by a grant from the Road Safety Department of the French Government (contract n° 2201141611). The authors would like to thank Matthieu Adam (CEREMA) for designing the simulated roads, and Stéphane Caro and Fabrice Vienne (IFSTTAR) for their help in preparing the simulator and communication with the eye-tracker.