Jean Muller

Anik Charchit Kumar

Kumar Ghosh

Vaibhav Gupta

Michel Tschopp

Vincent Le Houerou

Andreas Fery

Gero Decher

Matthias Pauly

Olivier Felix

Anik Kumar Ghosh

Spray-Deposited Anisotropic Assemblies of Plasmonic Nanowires for Direction-Sensitive Strain Measurement

Keywords: oriented silver nanowire monolayer, direction-sensitive strain sensor, spray coating, anisotropic optical properties, polarized spectroscopy

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

INTRODUCTION

Anisotropic hybrid materials are emerging as a very promising class of materials owing to their unique functionalities derived from their nanoscale morphology and their applications in extremely diverse research fields such as optics, electronics, health, sensing, and energy. [START_REF] Hu | In-Plane Aligned Assemblies of 1D-Nanoobjects: Recent Approaches and Applications[END_REF] This class of materials presents direction-dependent physical and chemical properties. They offer unique possibilities to create novel materials properties by synergetic combination at the nanometer scale of two or more components exhibiting diverse but complementary properties. One key prerequisite for the fabrication of materials and devices with anisotropic properties is the control of the orientation of nanoscale objects during the material construction. In this context, nanoarchitectonics [START_REF] Ariga | Nanoarchitectonics Revolution and Evolution: From Small Science to Big Technology[END_REF] -based materials and devices 3 are emerging fields in the area of composites. In such materials, several subunits with different structures and properties are combined such that the macroscopic properties of these objects exceed the combined properties of the subunits (or the combined properties of the pure components). The individual components are spatially arranged by methods that allow to control their distance and their orientation over several orders of magnitude. Different strategies have already been applied to control the orientation of 1D nanoobjects in the materials, including the Langmuir-Blodgett technique, [START_REF] Tao | Langmuir-Blodgett Silver Nanowire Monolayers for Molecular Sensing Using Surface-Enhanced Raman Spectroscopy[END_REF] heat-assisted dip-coating, [START_REF] Shin | Alignment of Silver Nanowires Using Heat-Assisted Dip-coating Method[END_REF] substrate stretching, [START_REF] Dong | Simple Assembly of Long Nanowires Through Substrate Stretching[END_REF] capillary printing, [START_REF] Kang | Capillary Printing of Highly Aligned Silver Nanowire Transparent Electrodes for High-Performance Optoelectronic Devices[END_REF] shearing using a brush, [START_REF] Zhao | Clay Nanotubes Aligned with Shear Forces for Mesenchymal Stem Cell Patterning[END_REF] or the use of an electric field. [START_REF] Cao | A Technique for Controlling the Alignment of Silver Nanowires with an Electric Field[END_REF] Nevertheless, these methods are restricted to small groups of components, fail to produce compositional control along the z-direction, are limited in their ability to yield uniformly aligned monolayers and to control the density of anisotropic nano-objects over large areas or require the use of bulky equipment. [START_REF] Hu | In-Plane Aligned Assemblies of 1D-Nanoobjects: Recent Approaches and Applications[END_REF] To overcome these limitations, a deposition technique referred to as grazing incidence spraying (GIS), based on the flow-induced alignment in the spraying direction has been developed and used in our group to efficiently orient in the substrate plane various 1D nanoparticles such as silver nanowires (AgNWs), [START_REF] Hu | Spray-Assisted Alignment of Layer-by-Layer Assembled Silver Nanowires: a General Approach for the Preparation of Highly Anisotropic Nano-Composite Films[END_REF] gold nanorods, [START_REF] Sekar | Anisotropic Optical and Conductive Properties of Oriented 1D-Nanoparticle Thin Films made by Spray-Assisted Self-Assembly[END_REF] metal oxide nanowires, [START_REF] Taner Camci | Polarization-Dependent Optical Band Gap Energy of Aligned Semiconducting Titanium Oxide Nanowire Deposits[END_REF] and nanocellulose nanofibrils [START_REF] Blell | Generating in-Plane Orientational Order in Multilayer Films Prepared by Spray-Assisted Layer-by-Layer Assembly[END_REF] to form monolayer and multilayer films on solid substrates. One important field in which an anisotropic response of a nanostructured material is crucial is mechanical sensing. Indeed, stretchable and wearable strain sensors have attracted tremendous attention in recent years due to their facile applications on the human body for different purposes including health monitoring, [START_REF] Gao | Flexible Hybrid Sensors for Health Monitoring: Materials and Mechanisms to Render Wearability[END_REF] human motion detection, [START_REF] Amjadi | Highly Stretchable and Sensitive Strain Sensor Based on Silver Nanowire-Elastomer Nanocomposite[END_REF] artificial skins, [START_REF] Chossat | Wearable Soft Artificial Skin for Hand Motion Detection with Embedded Microfluidic Strain Sensing[END_REF] and soft robotics. [START_REF] Rus | Fabrication and Control of Soft Robots[END_REF] These sensors are all based on the conversion of a mechanical deformation into a measurable signal, but they are usually unable to distinguish stimuli from different directions, despite some recent developments for the fabrication of direction-sensitive sensors based on the formation of an anisotropic conductive network. [START_REF] Zhang | Anisotropic Conductive Networks for Multidimensional Sensing[END_REF] The sensing mechanisms in strain sensors is mainly based on the measurement of resistance, capacitance, or optical properties. [START_REF] Souri | Wearable and Stretchable Strain Sensors: Materials, Sensing Mechanisms, and Applications[END_REF] Unlike resistive and capacitive strain sensors, optical ones do not need to be connected to a power supply and the measurement is nondestructive and can be operated without touching the sample. In addition, they also display high resistance to temperature [START_REF] Lang | Temperature-Insensitive Optical Fiber Strain Sensor with Ultra-Low Detection Limit Based on Capillary-Taper Temperature Compensation Structure[END_REF] and humidity as well as a low sensitivity to electromagnetic interference. [START_REF] Sabri | Toward Optical Sensors: Review and Applications[END_REF] The preparation of high-performance strain sensors requires the combination of functional nanomaterials and stretchable supporting materials. Concerning the sensing components, due to the limited strains withstandable by metal foils and semiconductors, [START_REF] Zhou | Flexible Piezotronic Strain Sensor[END_REF] discrete isotropic and anisotropic nanomaterials such as carbon nanotubes (CNTs), [START_REF] Gu | Wearable Strain Sensors Using Light Transmittance Change of Carbon Nanotube-Embedded Elastomers with Microcracks[END_REF] graphene, [START_REF] Bae | Graphene-Based Transparent Strain Sensor[END_REF] conductive polymers, [START_REF] Lu | Ultrastretchable Conductive Polymer Complex as a Strain Sensor with a Repeatable Autonomous Self-Healing Ability[END_REF] metallic nanospheres, [START_REF] Huang | Highly Sensitive Strain Sensors Based on Molecules-Gold Nanoparticles Networks for High-Resolution Human Pulse Analysis[END_REF] and nanowires [START_REF] Wang | Quasi In Situ Polymerization To Fabricate Copper Nanowire-Based Stretchable Conductor and Its Applications[END_REF][START_REF] Liu | Highly Transparent and Flexible All-Solid-State Supercapacitors Based on Ultralong Silver Nanowire Conductive Networks[END_REF] have been widely used for the development of highly flexible and stretchable strain sensors. Among them, AgNWs are very promising candidates for the preparation of direction-sensitive sensors due to their intrinsically anisotropic optical and electronic properties. Independently from the type of strain sensors, these sensing materials have been incorporated in bulk or on the surface of various stretchable supporting materials such as silicone elastomers [START_REF] Wang | Network Cracks-Based Wearable Strain Sensors for Subtle and Large Strain Detection of Human Motions[END_REF][START_REF] Xu | Highly Stretchable Strain Sensors with Reduced Graphene Oxide Sensing Liquids for Wearable Electronics[END_REF] or natural fibers. [START_REF] Cai | Large-Scale Production of Highly Stretchable CNT/Cotton/Spandex Composite Yarn for Wearable Applications[END_REF][START_REF] Wang | Carbonized Silk Fabric for Ultrastretchable, Highly Sensitive, and Wearable Strain Sensors[END_REF] The incorporation of the sensing material has been completed using various fabrication strategies such as chemical vapor deposition (CVD), [START_REF] Liu | A Highly Sensitive Graphene Woven Fabric Strain Sensor for Wearable Wireless Musical Instruments[END_REF] electrospinning, [START_REF] Ding | A Highly Stretchable Strain Sensor Based on Electrospun Carbon Nanofibers for Human Motion Monitoring[END_REF] spray-assisted layer-by-layer (LbL) assembly, [START_REF] Cai | Stretchable Ti3C2Tx MXene/Carbon Nanotube Composite Based Strain Sensor with Ultrahigh Sensitivity and Tunable Sensing Range[END_REF] laser direct writing, [START_REF] Gao | Laser Direct Writing of Ultrahigh Sensitive SiC-Based Strain Sensor Arrays on Elastomer toward Electronic Skins[END_REF] or 3D-printing. [START_REF] Wang | Full 3D Printing of Stretchable Piezoresistive Sensor with Hierarchical Porosity and Multimodulus Architecture[END_REF] Although these strategies provide strain sensors with high stretchability, high sensitivity, and with various structures, they are not sensitive to the direction of stretching. To distinguish stimuli from different directions accurately, the design and fabrication of direction-sensitive sensors possessing anisotropic structures and properties are required. In this work, we introduce a direction-sensitive strain sensor by exploiting the anisotropic optical properties of a single oriented silver nanowire monolayer and their change upon mechanical stretching. For this purpose, we use grazing incidence spraying (GIS) as a simple and versatile method to control the in-plane alignment and the density of AgNWs on a flexible and transparent poly(dimethylsiloxane) (PDMS) substrate. The optical properties of the anisotropic AgNW thin films deposited on a PDMS substrate are monitored upon stretching by polarized UV-visible-NIR spectroscopy. By using a simple model, both the magnitude and angle of the in-plane local deformation can be accurately and directly determined from the polarized optical measurements.

EXPERIMENTAL SECTION

Materials. Poly(ethylene imine) (PEI, Mn = 60 000 g•mol -1 ) was purchased from Sigma-Aldrich (Lyon, France). Silver nanowires (AgNWs) were purchased from Novarials Corporation (Woburn, MA) at a concentration of 10 mg•mL -1 in isopropanol. Silicon wafers were purchased from WaferNet, Inc. (San Jose, CA). Poly(dimethylsiloxane) (PDMS) sheets with a thickness of 0.25 mm were purchased from Specialty Manufacturing Inc. (SMI) (Saginaw, MI). The PDMS sheets were cut into rectangular shape with a length of 3 cm and a width of 1 cm using a scalpel blade. A bicomponent and highly transparent silicon-based elastomer, Bluesil RTV 141 A/B, was purchased from Elkem France. Holcosil, a red dye suited for silicon-based elastomers, was purchased from Esprit Composite. All the chemicals were used without further purification. All aqueous solutions were prepared with ultrapure water (resistivity of 18.2 MΩ•cm at 25 °C, Milli-Q Advantage A10 water purification system, Merck-Millipore, Molsheim, France). PEI solutions were prepared at a concentration of 2.5 mg•mL -1 by dissolution of the polymer in ultrapure water. PEI layers were deposited on silicon wafers and on PDMS sheets by orthogonal spraying (5 s followed by a rinsing step with ultrapure water for 10 s) using a spray can (Carl Roth GmbH). AgNW solutions were prepared at a concentration of 0.2 mg•mL -1 by diluting the commercial solution 50 times in ultrapure water. Oriented Deposition of Silver Nanowires (AgNWs). An aqueous suspension of silver nanowires (0.2 mg•mL -1 ) was sprayed for 50 s on PEI-coated substrates (either silicon wafers or PDMS sheets) using a homemade spraying system equipped with two-fluid nozzles. The angle between the central axis of the cone of the spray jet and the receiving substrate was fixed at 10°, and the distance between the nozzle and the substrate was held at a constant distance of 1 cm. The liquid flow rate was fixed at 1 mL•min -1 with the air flow rate at 30 L•min -1 (see Figure S2). After the deposition of the oriented AgNW monolayer, the substrate was rinsed by orthogonally spraying ultrapure water to remove any weakly adsorbed nanoparticles and then dried using compressed air. Preparation of the Colored PDMS Substrates. To ascertain the density change during film stretching, a bicomponent silicon-based elastomer, Bluesil RTV 141 A/B, was used to prepare a colored PDMS film. The process consists of mixing the polymer base with the curing agent (weight ratio of monomer to curing agent of 10:1), which forms a transparent solution to which a few drops of a red silicone-based dye (Holcosil) are added and thoroughly mixed. The colored solution was then slowly poured onto a clean glass Petri dish and degassed in a vacuum desiccator multiple times (3-4 times) to remove the air bubbles from the mixture. Finally, the Petri dish filled up with solution was kept in a heating oven at 80 ± 5 °C for 2 h, which led to the reticulation of the polymer and the formation of PDMS. After curing, the PDMS film was carefully peeled off from the Petri dish and cut into a rectangular shape (see Figure S10a). Stretching Device and Spectroscopic Measurements. For the acquisition of the optical properties of oriented AgNW monolayers, a homemade stretching device was built with two metallic clamps whose movement was controlled by a single screw, providing the same displacement and strain in both directions, resulting in an eucentric setup. Each PDMS film coated with oriented AgNWs was fixed using the two jaws of the device as illustrated in Figure S8. The stretching device was mounted in a double-beam Cary 5000 UV-visible-near infrared spectrophotometer (Agilent Technologies France SAS, Les Ulis, France) that was used for recording the different optical extinction spectra. The extinction of the samples was measured through a circular aperture of 5 mm diameter, and a noncoated PDMS substrate was used as a reference. A spectrum was acquired for each applied strain, and a Glan-Taylor polarizer was used for performing UV-visible-NIR spectroscopy with linearly polarized light. Nanowire Characterization. The size distribution of silver nanowires was determined from images obtained with a scanning electron microscope (SEM) SU8010 (Hitachi, Japan) with a secondary electron detector at an acceleration voltage of 1.0 kV. Eighty-four individual nanowires were measured to get a representative statistical of the nanowire dimensions (see Figure S1). In Situ Electron Microscopy Imaging during Stretching. The AgNW-coated PDMS films were imaged during stretching using a custom-built stretching device that was incorporated into a NEON 40 FIB-SEM workstation (Carl Zeiss Microscopy GmbH, Oberkochen, Germany) under an accelerating voltage of 3.0 kV. This work was carried out in collaboration with the Leibniz-Institut für Polymerforschung in Dresden. All the micrographs were captured in SE2 mode. A constant clamping torque value of 4.5 cNm was applied to avoid bending upon stretching. The fabricated sample with a length of 3 cm and a width of 1 cm was stretched in situ at a constant speed of 1 mm/min from 0% to 40% of its length, with intermediate steps of 10%.

RESULTS AND DISCUSSION

Oriented Silver Nanowire Monolayers. The oriented deposition of AgNWs (length of 3.3 ± 1.5 μm and diameter of 47 ± 7 nm, Figure S1) was carried out by spraying the nanowire suspension at an angle of 10° on a receiving substrate from a distance of about 1 cm from the nozzle using GIS (see Figure S2 for more details). AgNW monolayers were deposited either on silicon wafers or on PDMS sheets that were precoated with a layer of poly(ethylene imine) (PEI) (Figure S3). As already reported, [START_REF] Hu | Spray-Assisted Alignment of Layer-by-Layer Assembled Silver Nanowires: a General Approach for the Preparation of Highly Anisotropic Nano-Composite Films[END_REF] AgNWs only adsorb on the PEI-coated areas and do not form an adlayer on top of already adsorbed AgNWs. The AgNW density in the monolayer can be easily controlled by varying the spraying time. A spraying time of 50 s allowed for the formation of monolayers presenting an extinction high enough to be easily measured by optical spectroscopy. The metallic monolayers deposited on PDMS and silicon wafers were imaged by SEM (Figure 1a and Figure S3) and the degree of orientation of AgNWs was characterized using OrientationJ,38 an ImageJ39 plug-in that determines the local orientation of nano-objects in the plane. A 2D nematic order parameter S2D was then calculated and used to compare quantitatively the degree of orientation of various samples (Figure S4). For all samples analyzed by SEM, an order parameter of about 0.8 was obtained (a value of 1 corresponding to perfectly aligned nanowires), showing the efficient in-plane alignment of the AgNWs by GIS. Optical Properties of Anisotropic AgNW Monolayers. The optical properties of the oriented AgNW monolayers on PDMS substrates were investigated by polarized UV-visible-near infrared spectroscopy. As for oriented AgNW monolayers deposited on quartz slides, 10 the extinction spectra of oriented AgNW monolayers on PDMS measured with unpolarized light display three characteristic peaks due to the localized surface plasmon resonances (LSPR) (Figure S7). While the two peaks in the UV-visible region (350 and 380 nm) are assigned to the transverse LSPR mode, the broadband starting at around 650 nm and extending toward the near infrared region is attributed to the longitudinal LSPR mode. The use of linearly polarized UV-visible-NIR light allows for the selective excitation of the transverse and longitudinal LSPR modes. [START_REF] Hu | Spray-Assisted Alignment of Layer-by-Layer Assembled Silver Nanowires: a General Approach for the Preparation of Highly Anisotropic Nano-Composite Films[END_REF] When the light polarization is parallel to the nanowire alignment direction, the longitudinal plasmon band is preferentially excited and is associated with a high extinction in the near-infrared region. On the other hand, the transverse mode is preferentially excited when the polarization is perpendicular to the AgNW orientation (Figure 1b) and leads to extinction in the UV-visible range (Figure S7). These anisotropic optical properties of oriented AgNW monolayers are used in this work for developing a directionsensitive sensor.

Development of a Direction-Sensitive Sensor.

Let us consider an oriented AgNW monolayer deposited on a PDMS sheet, having an initial length L0 and an initial width l0, which is stretched at an arbitrary angle α between the stretching direction and the nanowire orientation (Figures 1b and2c). The purpose of the proposed direction-sensitive strain sensor is to measure the stretching ratio !

!" " ! " # (also known as engineering strain, and referred to as strain in following) and its direction α from the extinction change

! (&) (&) ! " #
measured by spectroscopy (Figure 1c) (see Section S4 for more details). Therefore, it is necessary to first measure the extinction changes arising from deformations applied parallel ! "#$ "#$ ! " ∥ and perpendicular ! "#$ "#$ ! " % to the AgNW alignment direction. The experimental determination of the angle α between the AgNW orientation and the stretching direction is also required. Both stretching (S) and light polarization (P) are defined with respect to the average direction of the nanowire long axis (parallel (∥) or perpendicular (⊥)) and can be described by four main configurations: S⊥P∥, S⊥P⊥, S∥P∥, and S∥P⊥. The spectra measured upon stretching for these four configurations are given in Figure S9. Parts a and b of Figure 2 show the extinction spectra as a function of the applied strain for a strain applied parallel and perpendicular to the nanowire orientation and for a light polarization perpendicular to the AgNW orientation (corresponding to S∥P⊥ and S⊥P⊥ configurations, respectively, at 380 nm). The extinction decrease observed for all measured samples (Figure 2c) could be attributed at first sight to the decrease in the surface density of nanowires during stretching. Indeed, it is known that during uniaxial deformation PDMS stretches two times more in the stretching direction than it contracts in the perpendicular direction, as defined by its Poisson's ratio close to 0.5. [START_REF] Mihai | How to Characterize a Nonlinear Elastic Material? A Review on Nonlinear Constitutive Parameters in Isotropic Finite Elasticity[END_REF] This induces an increase in the PDMS area and a decrease in the surface density of AgNWs upon stretching as the number of AgNWs deposited on PDMS remains constant. The expected relative change of area

# # ! = "1 + $% % ! % &'𝜈 "#$%
(see Section S6 for more details). The relative extinction change, expressed as a function of the extinction prior to (Ext0) and during stretching (Ext), scales with the density of nano-objects or molecules and is thus inversely proportional to the area change (eq S11). Optical Properties of a Colored PDMS upon Stretching. In order to verify whether the decrease in extinction upon stretching is due solely to a decrease in the surface density of nanowires, the extinction change of a model sample, PDMS colored with a red dye, was monitored as a function of the applied strain and was compared to the extinction change of PDMS films coated with oriented AgNWs measured using the four configurations with respect to stretching direction and light polarization (Figure 2c). The experimental points measured for the colored PDMS are in good agreement with the theoretical variation obtained with eq S11 (Figure S11). If the extinction decrease of AgNW samples was only induced by a nanowire density change, we should get a similar decrease to the one observed for colored PDMS. As the extinction decrease is larger for all PDMS films coated with oriented AgNWs than for the colored PDMS (Figure 2c), the optical properties of AgNW monolayers upon deformation are not exclusively due to a density change. This decrease could be attributed to a reflectance change of the metallic network as its structure changes during the film stretching (see Figures S5 andS6). More importantly, the extinction change is proven to be dependent on both the stretching direction and light polarization with respect to NWs as four different variations of the optical properties are observed (Figure S9 and Figure 2c). If needed, the reader shall find the results of the Figure 2c in the finite strain formalism in Figure S12, which relates the extinction change to the true strain in the sample.

Direction-Sensitive Strain Determination from Polarized Extinction.

The different optical changes upon stretching depending on light polarization and direction of stretching is the basis for the design of an anisotropic strain sensor sensitive to the intensity and direction of the applied strain. The determination of these parameters from the optical measurements is based on the development of a model considering the geometry of the sample (length (L0, L) and width (l0, l) before and after deformation, respectively), the angle α between the nanowire orientation and the stretching direction, the measured extinctions before Ext0 and after stretching Ext, and the applied strain !" " ! .

We have focused so far our study on two idealized configurations (S∥ and S⊥) where α is equal to 0 or 90°, respectively. We generalize our approach by developing a model for any value of α comprised between 0° and 90°. The sample deformation transforms l0 in l, L0 in L, and α0 in α with α < α0 (Figure 3a). Based on geometrical considerations, the expected change of the tan(α)/tan(α0) ratio can be expressed in terms of film dimensions before (l0, L0) and after stretching (l, L) and the Poisson's ratio 𝜈 ()*+ (see Section S7, eq S15).

The variation of the angle thus depends on the applied deformation and the Poisson's ratio of PDMS, relating the contraction of the material in the direction perpendicular to the stretching direction.

Experimentally, it is possible to determine the angle f between the stretching direction and the polarization direction of the transverse mode of nanowires, reported as the polarizer angle, by monitoring the extinction change at 380 nm as a function of the polarizer angle. Indeed, the extinction at this wavelength is maximal when the AgNW orientation and the polarization direction are perpendicular. This extinction as a function of polarizer angle was completed for oriented AgNW monolayers with three different initial orientation angles (α0 close to 25°, 50°, or 75°) (Figure S13). The optical properties for α0 ∼ 25° are given as an example in Figure 3b. It is thus possible to determine the strain-dependent orientation angle as a function of the film stretching based solely on the measurement of the polarized extinction at a single wavelength without using any microscopy imaging of the sample (Figure 3c and Figure S14). As discussed previously, the strain applied at an angle α with respect to the AgNW alignment direction can be decomposed into a strain applied along the nanowire orientation and a strain applied across the nanowire orientation (eq S4). For both stretching directions, the extinction changes

! "#$ "#$ ! " ∥ and ! "#$ "#$ ! " %
as a function of the applied strain (Figure 2c) could be fitted to second order polynomials (see Section S8). The extinction change

! "#$ "#$ ! " &
can finally be expressed as a function of a fourth-order polynomial equation (see Section S9 and Table S1 for further details):

! "#$ "#$ ! " & = 𝑎 × ! '( ( ! " ∥ ) + 𝑏 × ! '( ( ! " ∥ * + 𝑐 × ! '( ( ! " ∥ + + 𝑑 × ! '( ( ! " ∥ + 𝑒 (1)
An Excel VBA Macro was then used to numerically solve the fourth-order polynomial equation for each extinction change measured by spectroscopy. Using this approach, the direction of the local strain α and the magnitude of the strain applied parallel and perpendicular to the nanowire orientation (and thus the effective strain applied at the angle α) can be determined solely from polarized spectroscopic measurements for any angle α.

To summarize, the proposed approach can be decomposedinto three steps, with all measurements being made at a single wavelength (380 nm):

• Step 1: The measurement of the extinction variation for a stretch applied parallel and perpendicular to the orientation direction of the AgNWs on a sample with known nanowire orientation (which can be seen as a calibration, Figure 4b).

• Step 2: The determination of the orientation of the nanowires with respect to the direction of stretching on a sample whose direction is a priori unknown through the measurement of the variation of the extinction as a function of the polarizer angle (Figure 3b).

(&) (&) ! " # so that ! (&) (&) ! " 23.5°= ! (&) (&) ! " ∥ × ! (&) (&) ! " % and tan(19.6°) = 7 ,- -! 8 . 7 ,- -! 8 ∥
. The magnitude of the applied strain at angle α is then calculated from eq 1. The same procedure was repeated for different stretchings on the same sample, leading to the five green points in Figure 4c.

In order to probe the reproducibility and robustness of our approach, it was also applied to oriented AgNW monolayers with different initial orientation angles α0 close to 25°, 50°, and 70°, each one in triplicate (see Figure 4c and Figures S14 andS15). The strains measured using the procedure described above were compared with the strains applied experimentally with the stretching device (Figure 4c) to verify the accuracy of our approach. A good agreement was observed between the measured and applied strains, validating the proof of concept of this approach toward the development of a direction-sensitive sensor using the anisotropic optical properties of a silver nanowire monolayer. The differences observed between the applied and measured strains (see Figure 4c) can first be explained by the nonperfect alignment of the AgNWs on the PDMS substrate. In addition, uncertainties related to the determination of the applied strain using the stretching device can lead to discrepancies. Uncertainties on the extinction changes can finally also be responsible for the observed differences. The proposed approach allows for measuring directional strains over a wide range and with commendable sensitivity. Indeed, we have stretched several samples up to 130% strain, which caused the failure of the PDMS sheet, but the polarized optical properties were still measurable at the maximum strain, and thus, the sensors should, in theory, work beyond this range. As the extinction change can be measured easily with excellent accuracy, strain values of only a few percent can be detected, which demonstrates the very high sensitivity of the sensor. Finally, a single thin film has been stretched at 100% strain and released several times, and the optical properties are only slightly modified after a few cycles, which shows that the sensor can be reused several times (Figure S16). The presented model considers the variation of the optical properties at a single wavelength. This model could be modified in order to improve the performances of this sensor by considering the optical properties at different wavelengths for instance. Furthermore, the strain measurements determination is based on polarized transmittance measurements using a commercial spectrometer in which the measurement was made in the dark. However, it must be noted that such a measurement could also be performed in reflection and in an environment exposed to ambient light (Figure S17).

CONCLUSION

Oriented AgNW monolayers were successfully deposited on PEI-modified PDMS and silicon substrates by GIS. Their high degree of orientation was characterized by a 2D nematic order parameter close to 0.80. The resulting AgNW monolayers display highly anisotropic optical properties that were used to prepare a direction-sensitive strain sensor. The anisotropic contribution of AgNWs to extinction decrease upon deformation was confirmed by UV-visible-NIR spectroscopy in comparison to a colored PDMS. Spectroscopic studies performed with linearly polarized light upon sample stretching show that the optical properties of AgNW-coated PDMS films are highly dependent on the stretching direction and the light polarization. A simple model integrating all the required parameters (angle, extinction, strain, Poisson's ratio) was employed for determining both the magnitude and the direction of the deformation directly from the optical measurements. This anisotropic sensor, capable of detecting an induced strain and its direction, could be used in various applications where the measurement of multidirectional in-plane strains is required. Note that the spray-assisted deposition of AgNW films allows to modify existing objects and devices with a directional strain detector after their preparation. This could especially be interesting for turning thin foils into directional strain sensors. It must also be noted that the approach we introduce in this study could be used in theory with nano-objects that have anisotropic optical properties and that are oriented on a surface, with such a structure being reachable with several oriented deposition approaches. [START_REF] Hu | In-Plane Aligned Assemblies of 1D-Nanoobjects: Recent Approaches and Applications[END_REF] Finally, the proposed approach has the advantage of being nondestructive and allowing for contactless monitoring of strains in situ. Even if all optical measurements were carried out in transmission mode on a transparent substrate during that work, this approach could also be conducted in reflection mode with a nontransparent material.

Figure 1 .

 1 Figure 1. (a) SEM image of a AgNW monolayer deposited on PDMS obtained after 50 s of spraying using GIS (no stretching applied). (b) Schematic illustration of the experiment with the orange double arrow corresponding to the perpendicular polarization direction of the light (P⊥) used for the determination of the stretching direction α and strain ! !" " ! "

Figure 2 .

 2 Figure 2. UV-visible-NIR spectra upon film stretching for the configurations (a) S∥P⊥ and (b) S⊥P⊥ with the stretching directions (S) represented by the blue and red arrows and the polarization direction (P) by the orange double arrows. (c) Extinction change at 380 nm as a function of the applied strain for a colored PDMS film and oriented AgNW monolayers with different stretching directions and light polarizations: S∥P⊥, S⊥P⊥, S∥P∥, and S⊥P∥. The black line corresponds to the theoretical variation obtained with eq S11 while colored dashed lines are only guides to the eye.

Figure 3 .

 3 Figure 3. (a) Schematic drawing of a rectangular PDMS substrate before (l0, L0) and after a uniaxial stretching (l, L) showing the transformation of the angle between the stretching direction (blue arrows) and the AgNWs alignment direction (gray lines) from α0 to α. (b) Extinction change at 380 nm as a function of the polarizer angle upon stretching from 0 to 29% for an oriented AgNW monolayer with an initial orientation angle α0 ∼ 25°. (c) Variation of the orientation angle for an aligned AgNW monolayer with an initial orientation angle α0 ∼ 25° set during GIS deposition as a function of the applied strain.

• Step 3 :

 3 The determination of the stretching amplitude by measuring the polarized extinction before and after stretching. The numerical resolution of eq S10 is equivalent to finding the value of the magnitude of the deformation ! sample (blue and red dashed lines in Figure4b, respectively) and from the measured value! (&) (&) ! " #, in such a way that eqs S4 and S9 are simultaneously verified. This is exemplified for one measurement (green dot) in Figure4b: the local orientation of the AgNWs is first measured as being equal to 19.6° using extinction as a function of the polarizer angle (see Figure4a), and the values of ! red dots, respectively) are determined from the from the measured value !

Figure 4 .

 4 Figure 4. (a) Extinction change as a function of the polarizer angle for an oriented AgNW monolayer during its stretching with an initial orientation angle of 25.1°. (b) Extinction changes for strains applied across and along the AgNW alignment direction (these curves are the same as in Figure2c). (c) Strain applied on the stretching device as a function of the strain measured from the optical spectroscopy for initial orientation angles of 25°, 50°, and 70°.

ACKNOWLEDGMENTS

The authors acknowledge the excellence network Chemistry of Complex Systems (LabEx CSC) and the CNRS for the financial support, the microscopic platforms at ICS (A. Carvalho) and at Leibniz-IPF for SEM investigations, the characterization platform at ICS for NIR-UV-vis spectroscopic studies, and the mechanical workshop (F. Courtier) at ICS for the design of the stretching device. A.K.G. and A.F acknowledge funding by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)-CRC-1415-417590517 as well as the LaSensA project carried out under the M-ERA.NET 2 scheme (European Union's Horizon 2020 research and innovation programme, grant No. 685451), cofunded by the Research Council of Lithuania (LMTLT), agreement No. S-M-ERA.NET-21-2, the National Science Centre of Poland, project No. 2020/02/Y/ST5/00086, and the Saxon State Ministry for Science, Culture and Tourism (Germany), grant No. 100577922, as well as from the tax funds on the basis of the budget passed by the Saxon state parliament.

SUPPORTING INFORMATION

The Supporting Information is available free of charge at: https://pubs.acs.org/doi/10.1021/acsami.2c14526. Discussions of AgNW size distribution, orientation of AgNWs, distance change between AgNWs upon film stretching, model used for the development of a direction-sensitive sensor, optical properties of oriented AgNW thin monolayers, optical properties of colored PDMS films, orientation of AgNWs upon stretching, schematic drawings of the oriented AgNW monolayers with initial orientation angles, determination of the macroscopic applied strain, and polarized microscopy of an oriented AgNW substrate, figures of SEM images, length and diameter distributions, schematic representation of the GIS setup and the experimental conditions, schematic illustration of a uniaxial stretching applied parallel and perpendicular to the nanowire orientation, schematic illustration of polarized UV-visible-NIR measurements, UV-visible-NIR spectra, schematic drawing of an orientedAgNW monolayer deposited, optical photograph of the red-colored PDMS film, schematic illustration of the uniaxial stretching of a PDMS film, extinction spectra, comparison between the expected and experimental extinction changes upon stretching, schematic drawings of the oriented AgNW monolayers with initial orientation angles, and optical scheme of the crossed polarizer configuration, and table of solving of the fourth-degree polynomial equations.


domain: chim phys

text:
Souria Benallou

Salima Saïdi-Besbes

Abdelatif Bouyacoub

Eric Grelet
email: eric.grelet@crpp.cnrs.fr

Synthesis of achiral rod-shaped triazolic molecules and investigation of their striped texture and propeller-patterned nematic droplets

Keywords: Bis-triazole derivatives, striped patterns, chiral symmetry breaking, surface symmetry breaking

In this study, novel achiral mesogens containing 4,4'-biphenyl central core connected on both sides through an ester function to 1-(4-(alkyloxy)phenyl)-1H-[1,2,3]-triazolyl group have been synthesized and characterized. Different mesophases have been identified, with the appearance of both a periodic striped pattern and propeller-patterned droplets close to the transition between the nematic and the smectic-C phases. This periodic texture has been found to be independent of the geometry of the sample cell. These observations suggest a spontaneous symmetry breaking which can result either from an intrinsic enantioselective self-sorting process with a chirality synchronization mechanism, or from an extrinsic surface mechanism at the interface between the two phases.

Introduction

Liquid crystals (LCs) are ubiquitous in our daily lives, found in a wide range of technological applications including display, optics, light-emitting diodes, photovoltaics, nanophotonics and biosensors [START_REF] Geelhaar | 25 Years of liquid crystals-a scientific revolution in the home[END_REF][START_REF] Bahadur | Liquid Crystals: Applications and Uses[END_REF]. These outstanding states of matter, which combine orientational and positional orders, continue to arouse the interest of the scientific community due to their potential for strategic applications. Numerous self-assembling systems built-up from functional organic molecules have been synthetized and investigated for their LC properties. The nature and stability of the resulting mesophases are closely dependent on the extent of intermolecular interactions and can be tuned and controlled through a suitable design of the molecular architecture and shape.

Rod-like (calamitic) mesogens have contributed extensively to LC development [START_REF] Demus | A, Low Molecular Weight Liquid Crystals I: calamitic liquid crystals[END_REF]. They are generally composed of a central rigid core containing at least two aromatic rings and one or more flexible alkyl chains and/or polar groups in terminal positions. Flexible connecting groups and lateral substituents can also be introduced to achieve the required criteria for liquid crystalline behaviour. Such anisotropic molecules usually give rise to the formation of typical nematic and smectic organizations.

The use of heterocyclic rings as a core unit in the molecular structure of LC materials is an efficient and convenient way to modify the physical, optical and electronic properties of LCs [START_REF] Ghosh | Recent advances in heterocycle-based metal-free calamitics[END_REF][START_REF] Titov | Thermotropic liquid crystals in the heterocyclic series (review)[END_REF]. The presence of electronegative heteroatoms such as oxygen, nitrogen or sulphur can impart lateral and/or longitudinal dipoles to the designed LC compounds and affect substantially their geometry and shape, which in turn can modify their mesomorphic behaviour. N-heterocyclic compounds also have the ability to induce specific interactions such as hydrogen bonding, donor-acceptor assemblies or metal complexation favouring the formation of supramolecular mesogens [START_REF] Roy | Advances in Metal-Free Heterocycle-Based Columnar Liquid Crystals[END_REF][START_REF] Han | Synthesis and mesomorphic behaviour of heterocyclebased liquid crystals containing 1, 3, 4-oxadiazole/thiadiazole and thiophene units[END_REF][START_REF] Rodrigues | 1,2,3/1,2,4-Triazole containing liquid crystalline materials: An up-to-date review of their synthetic design and mesomorphic behavior[END_REF].

[1,2,3]-triazole is a key building block in materials science for electronic, biomedical and supramolecular applications [START_REF] Juríček | Triazole: a unique building block for the construction of functional materials[END_REF][START_REF] Hua | Click chemistry generates privileged CH hydrogen-bonding triazoles: the latest addition to anion supramolecular chemistry[END_REF]. This five-membered N-heterocycle presents remarkable features in terms of chemical and thermal stability, polarity and the ability to interact with different biological, organic and inorganic targets [START_REF] Schulze | Beyond click chemistry -supramolecular interactions of 1,2,3triazoles[END_REF][START_REF] Pedersen | 1,2,3-Triazoles in Peptidomimetic Chemistry[END_REF]. In recent years, a growing number of thermotropic triazole based liquid crystalline materials have been designed, synthesized and characterized to highlight the structure-property correlation [START_REF] Xiong | Mesophase behaviour of 1,2,3-triazole-based nematic liquid crystals influenced by varying alkyl chains and halogen atom substitution[END_REF][START_REF] Dhingra | An electron-deficient tris(triazole)-based discotic liquid crystal that exhibits fast electron transport[END_REF][START_REF] Gimeno | Click chemistry as a versatile route to synthesize and modulate bent-core liquid crystalline materials[END_REF][START_REF] Cristiano | 1,4-Diaryl and Schiff's base [1,2,3]triazole derivative liquid crystalline compounds[END_REF]. Several studies emphasized the role of the linking groups in influencing the molecular architecture and polarity of LC materials and consequently their mesomorphic properties. For instance, ester and alkene groups have been shown to promote more layer organization than the oxymethylene group. This arises from the lack of linearity of the related mesogen, which disrupts the lamellar ordering [START_REF] Benbayer | Synthesis and mesomorphic properties of novel [1,2,3]-triazole mesogenic based compounds[END_REF][START_REF] Benallou | 1,2,3]-triazole derivatives: Mesomorphic property dependence on the molecular shape[END_REF]. It is also generally noticed that liquid crystalline organizations and mesophase thermal stability are improved by the insertion of a polar connector due to the enhancement of the dipole moment in the mesogen [START_REF] Benbayer | Structure-property study of new [1,2,3]triazole liquid crystalline derivatives[END_REF].

In this study, we develop a new molecular design approach to obtain mesogenic molecules composed of a 4,4'-biphenyl central core connected on both sides through an ester function to a 1-(4-(alkyloxy)phenyl)-1H-[1,2,3]-triazolyl group with varying number carbon atoms in the terminal alkyl chains n = 8-12 (1a-c) as shown in Scheme 1. The mesomorphic properties of these compounds are investigated by means of X-ray scattering, optical microscopy and calorimetry. These mesogens, which do not exhibit any asymmetric tetrahedral carbons (i.e. do not have any chiral center), show a periodic striped pattern phase between the nematic and smectic-C states, as well as unusual propeller-patterned droplets. The mechanisms at the origin of these unusual features will be discussed.

Experimental section

Synthesis and chemical characterization

All the reagents have been purchased from Aldrich and used as received. The solvents are of commercial grade quality and have been dried and distilled before use. 1-(4-Alkyloxyphenyl)-1-H-[1,2,3]-triazole-4-carboxylic acid have been prepared according to a recently described procedure [START_REF] Benallou | Synthesis and mesomorphic behaviour of unsymmetrical tetracatenar [1,2,3]-triazole derivatives[END_REF]. 1 H and 13 C NMR spectra have been recorded on a Bruker 300 MHz spectrometer (Wissembourg, France). Tetramethylsilane has been used as an internal reference for chemical shifts. Column chromatographies have been carried out using Merck silica gel (Kieselgel 60, 230-400 mesh) as the stationary phase (Merck Millipore, Gernsheim, Germany).

High resolution mass spectroscopy (HRMS) has been carried out using a Bruker Daltonics -micrOTOF-Q mass spectrometer coupled to LC system in ESI mode. 1a-c: 2.5 mmol of 4-(alkyloxyphenyl)-1H-[1,2,3]-triazole-4-carboxylic acid and 25 mmol of thionyl chloride are stirred at 85°C under nitrogen atmosphere for 5-6 hours. Thereafter, the excess of thionyl chloride is evaporated and a solution of triethylamine (7.2mmol) in 10 mL of freshly distilled dichloromethane is added. The mixture is cooled using an ice bath and the reaction is stirred under nitrogen atmosphere until a homogeneous solution is obtained. 4,4'biphenol (1.25mmol) dissolved in 5 mL of dry dichloromethane is then added dropwise and the mixture is stirred at 40°C for 48-72 hours. After cooling the mixture, water is added and the organic layer is extracted, washed three times with 1M HCl solution then with water until neutrality and finally dried under anhydrous MgSO4. The solvent is evaporated under reduced pressure and the crude product is purified by column chromatography using as eluent dichloromethane/ethyl acetate (20/1).

bis (1-(4-octyloxyphenyl)-1H-[1,2,3]-triazole)-4,4'-biphenyl dicarboxylates (1a)

Yield (56%); 1 H NMR (300 MHz, CDCl3):δ = 0.92 (t, 6H, CH3, 3 J= 6.71 Hz), 1.32 (m, 20H, CH3(CH2)5), 1.85 (m, 4H, OCH2CH2), 4.07 (t, 4H, OCH2, 3 J = 6.58 Hz), 7.06 (d, 4H, Ar-H, 3 J = 9.04 Hz), 7.39 (d, 4H, Ar-H, 3 J = 8.65 Hz), 7.72 (m, 8H, Ar-H), 8.61 (s, 2H, H5-triazole); 13

bis (1-(4-decyloxyphenyl)-1H-[1,2,3]-triazole)-4,4'-biphenyl dicarboxylates (1b)

Yield (48%); 1 H NMR (300 MHz, CDCl3):δ = 0.91 (t, 6H, CH3, 3 J = 6.71 Hz), 1.30 (m, 28H, CH3(CH2)7), 1.85 (m, 4H, OCH2CH2), 4.05 (t, 4H, OCH2, 3 J = 6.58 Hz), 7.09 (d, 4H, Ar-H, 3 J = 9.04 Hz), 7.39 (d, 4H, Ar-H, 3 J = 8.65 Hz), 7.69 (m, 8H, Ar-H), 8.61 (s, 2H, H5-triazole); 13

bis (1-(4-dodecyloxyphenyl)-1H-[1,2,3]-triazole) 4,4'-biphenyl dicarboxylates (1c)

Yield (61%); 1 H NMR (300 MHz, CDCl3):δ = 0.90 (t, 6H, CH3, 3 J = 6.71 Hz), 1.29 (m, 36H, CH3(CH2)9), 1.87 (m, 4H, OCH2CH2), 4.05 (t, 4H, OCH2, 3 J = 6.58 Hz), 7.09 (d, 4H, Ar-H, 3 J = 9.04 Hz), 7.36 (d, 4H, Ar-H, 3

Methods for mesomorphic property determination

The melting points, transition temperatures and phase transition enthalpies have been determined using a differential scanning calorimetry (DSC Q200®, TA Instruments). The mesomorphic textures have been observed using BH-2 and BX-51 Olympus microscopes equipped with a Linkam THM600 heating stage and with a colored JAI CV-M7 and CoolSNAP ES (Photometrics) cameras, respectively. X-ray diffraction experiments have been performed by using a rotating anode generator (Rigaku Nanoviewer MicroMax 007HF) coupled to a confocal Max-Flux® Osmic mirror (Applied Rigaku Technologies, Austin, USA) producing a beam with a wavelength of 1.54 Å together with a homemade heating stage with a thermal stability of 0.1°C. The spectra have been recorded with a bi-dimensional detector (MARResearch-345). All samples were introduced as a powder in glass capillary tubes (Glas, Muller, Germany) having a diameter of 1.5mm. The spectra were analyzed using FIT2D software (ESRF; http://www.esrf.eu/).

Results

The targeted compounds have been synthetized according to the synthetic strategy outlined in Scheme 1. They were obtained from 1H-[1,2,3]-triazole-4-carboxylic acid intermediates, reported in a previous published work [START_REF] Benallou | Synthesis and mesomorphic behaviour of unsymmetrical tetracatenar [1,2,3]-triazole derivatives[END_REF], which have been transformed into the corresponding triazoyl chloride compounds. The condensation with 4,4'-biphenol affords the final compounds with good yields. The purity and more specifically the absence of chiral impurities has been checked by NMR spectroscopy and HRMS (See Experimental section).

The phase behavior and mesomorphic properties of the series 1a-c have been determined by the combination of different experimental techniques, from X-ray diffraction (Figure 1) and optical microscopy (Figure 2) to calorimetry (Figures S1,S2,S3 and Table 1).

Beyond a set of crystalline states at low temperature, all compounds 1a-c exhibit a smectic phase above which appears a nematic mesophase. The physical signature of the smectic phase has been obtained by X-ray diffraction, where the X-ray scattering spectra show a first sharp Bragg peaks in the range of q100 = 1.95 ̶ 2.00 nm -1 and the second-order reflection (200) confirming the lamellar organization (Figure 1). The signal of the disordered aliphatic chains corresponds to the broad reflection at about 13.6 nm -1 . The increase of the smectic layer spacing d = 2π/q100 with temperature (Inset of Figure 1) stems from the rise of the tilt angle of the molecular director due to thermal fluctuations, and therefore suggests a smectic-C like order.

The lamellar spacing value of about d = 3.2 nm is about the same size as the rigid core of the mesogen (See Scheme 2 for the theoretical calculation considering the energy minimized structure obtained by DFT calculations). Above the smectic range, the recorded scattered X-ray spectra do not show sharp Bragg reflections but exhibit a very broad peak at low range of scattering wavevectors q, which is the hallmark of molecular liquid-like order consistent with the reported nematic and isotropic liquid phases at high temperature.

Polarized-light optical microscopy analysis has been carried out to complete the identification of the different mesophases. The micrographs for compound 1b sandwiched between a glass slide and a cover slip are shown in Figure 2. Upon cooling down from the isotropic liquid, characteristic nematic swarming is observed that evolves to birefringent nematic texture with Schlieren defects (Fig. 2(a)). At lower temperature, a striped pattern texture appears as depicted in Figures 2(c) below which the fan shape texture or Schlieren pattern characteristic of a tilted smectic phase is seen (Fig. 2(e)).

The presence of transient state between nematic and smectic mesophases, i.e. in the temperature range where the striped patterns are observed, can be inferred from some but not all differential scanning calorimetry thermograms (Figs. S1 to S3). Indeed, a small endothermic peak can be barely guessed from a rugged line with structureless broad features only in the first heating cycles at 225 and 228 °C, for compounds 1a (Figure S1) and 1b (Figure S2), respectively. However, this peak is more difficult to detect during the second cycle, which seems to indicate some thermal damage to the sample (Figs. S1, S2, S3).

Despite its lack of clear thermodynamic signatures, the striped textures have been observed enantiotropic ally, i.e. on both heating and cooling and appear to be independent of the nature of the substrates used (glass, silicon wafer, rubbed Teflon coating), and the sample geometry (glass cell or open droplets, thin or thick samples from a few to tens of µm). Note that these periodic structures have been found over many heating-cooling cycles. Furthermore, the striped pattern stands out for its high fluidity (see supplementary movie) particularly on heating.

Similar behavior has been seen for each compound of the investigated series. The repeat distance between parallel bright and dark lines corresponding to the periodicity of the stripes does not show significant variation within observation times of a few minutes, regardless of the studied domain. The stripe period p is shown to be temperature dependent and increases with decreasing temperature, as reported in Figure 3, in agreement with the behavior commonly encountered for the chiral nematic (cholesteric) mesophase. However, the usual divergence of the cholesteric periodicity scaling with 𝑝𝑝 ∝ (𝑇𝑇 -𝑇𝑇 𝑐𝑐 ) -𝜈𝜈 with 𝜈𝜈 > 0 and 𝑇𝑇 𝑐𝑐 , an effective critical temperature related to the phase transition temperature, is not observed here when approaching the smectic phase transition [START_REF] Yoon | Cholesteric pitch divergence near smectic phase transitions[END_REF]. Instead of a convex diverging function, a concave one fits our data with 𝑝𝑝 ∝ (𝑇𝑇 𝑐𝑐 -𝑇𝑇) 𝜈𝜈 (Eq. ( 1)) and 𝜈𝜈 ≈ 0.6, demonstrating an anomalous behavior for the stripe periodicity.

To further investigate this striped pattern, a very thin supported droplet geometry has been employed for compound 1a (Figure 4). Upon cooling from the nematic phase, right-handed and left-handed propeller patterns appear in these droplets, as illustrated in Figure 4. They are observed in a temperature range from 207 to 220°C, which is within the striped texture range obtained during very slow cooling processes, where supercooling shifts all transition to lower temperatures by a few °C. It is worth mentioning here that no coexistence of adjacent domains with opposite handedness has been detected by optical microscopy.

Discussion

A striped texture is a common feature observed at the N-SmC phase transition, as well as at the Iso-SmC transition. These so-called transition bars were discovered in the 1970s and attributed to spontaneous undulations at the SmC-N interface [START_REF] Demus | Textures of Liquid Crystals[END_REF][START_REF] Allet | Striped patterns in a thin droplet of a smectic C phase[END_REF][START_REF] Fournier | Undulation Instability of the Interface Between a Smectic-C Liquid Crystal and its Isotropic or Nematic Melt[END_REF][START_REF] Seul | Domain Shapes and Patterns: The Phenomenology of Modulated Phases[END_REF]. The stripes stem from the coupling between the surface tension anisotropy and the director orientation in the SmC layers [START_REF] Demus | Textures of Liquid Crystals[END_REF][START_REF] Allet | Striped patterns in a thin droplet of a smectic C phase[END_REF][START_REF] Fournier | Undulation Instability of the Interface Between a Smectic-C Liquid Crystal and its Isotropic or Nematic Melt[END_REF][START_REF] Seul | Domain Shapes and Patterns: The Phenomenology of Modulated Phases[END_REF][START_REF] Galatola | Spontaneous undulation of equilibrium interfaces with positive surface stiffness[END_REF][START_REF] Okano | Photoresponsive Stripe Pattern in Achiral Azobenzene Liquid Crystals[END_REF][START_REF] Maclenna | Textures in hexatic films of nonchiral liquid crystals: Symmetry breaking and modulated phases[END_REF][START_REF] Demikhov | Length scale dependence of chiral symmetry breaking in free-standing films of achiral smectic C[END_REF].

In such a mechanism, the undulation repeat distance depends on the sample thickness, the thermal gradient and the presence of impurities [START_REF] Allet | Striped patterns in a thin droplet of a smectic C phase[END_REF][START_REF] Galatola | Spontaneous undulation of equilibrium interfaces with positive surface stiffness[END_REF]. The less pure the product is, the broader the two-phase coexistence region is and the more pronounced the stripes are. Even if the purity of the compounds has been carefully checked by NMR and HRMS, the formation of impurity traces at high temperature for which the striped patterns are observed cannot be formally excluded. Such impurities may be generated, especially during prolonged and repeated heating steps. Moreover, the high temperatures of the N-SmC phase coexistence favor the presence of (vertical) thermal gradients from the heating stage. Combined with both the lack of a clear transition peak in the DSC thermograms and the unusual stripe periodicity dependence (Figure 3), this suggests that the striped patterns of 1a-c mesogens could have an extrinsic origin, based on surface induced symmetry breaking. Nevertheless, the unambiguously observed propeller-patterned droplets as shown in Figure 4 also suggests another mechanism based on an intrinsic mirror symmetry breaking of the achiral mesogens to form chiral nematic domains. Furthermore, the striped texture could then be interpreted as cholesteric fingerprints, providing a measurement of the helical pitch of the sample. In recent decades, the phenomenon of mirror-symmetry breaking has been reported in several liquid crystalline phases and particularly in layered phases [START_REF] Tschierske | Mirror Symmetry Breaking by Chirality Synchronisation in Liquids and Liquid Crystals of Achiral Molecules[END_REF][START_REF] Tschierske | Mirror symmetry breaking in liquids and liquid crystals[END_REF][START_REF] Goodby | Chirality in liquid crystals[END_REF][START_REF] Salamończyk | Multi-level chirality in liquid crystals formed by achiral molecules[END_REF][START_REF] Darren | Spontaneous formation of macroscopic chiral domains in a fluid smectic phase of achiral molecules[END_REF][START_REF] Takezoe | Spontaneous achiral symmetry breaking in liquid crystalline phase[END_REF][START_REF] Alasaar | A liquid crystalline phase with uniform tilt, local polar order and capability of symmetry breaking[END_REF][START_REF] Dantlgraber | Chirality and macroscopic polar order in a ferroelectric smectic liquidcrystalline phase formed by achiral polyphilic bent-core molecules[END_REF][START_REF] Hough | Chiral isotropic liquids from achiral molecules[END_REF][START_REF] Görtz | Enantioselective segregation in achiral nematic liquid crystals[END_REF][START_REF] Heppke | Chiral order from achiral molecules[END_REF]. Even if the archetypal mesogens inducing such enantioselective segregation are achiral bent-core molecules and bent-shape mesogenic dimers that can acquire conformational chirality in layered smectic mesophases [START_REF] Reddya | Bent-core liquid crystals: polar order, superstructural chirality and spontaneous desymmetrisation in soft matter systems[END_REF][START_REF] Eremina | Polar bent-shape liquid crystals-from molecular bend to layer splay and chirality[END_REF][START_REF] Pelzl | Spontaneous chiral ordering in the nematic phase of an achiral banana-shaped compound[END_REF], propeller-like molecular conformation has also been found with achiral molecules through specific non covalent interactions like hydrogen bonding [START_REF] Jeong | Construction of chiral propeller architectures from achiral molecules[END_REF], coordinative interactions and π-π interactions between aromatic cores [START_REF] Jeong | Construction of chiral propeller architectures from achiral molecules[END_REF][START_REF] Jakli | Macroscopic chirality of a liquid crystal from nonchiral molecules[END_REF][START_REF] Nagayama | Spontaneous Deracemization of Disc-like Molecules in the Columnar Phase[END_REF].

The existence of propeller-pattern droplets in the series of achiral compounds 1a-c with only homochiral domains may indicate the spontaneous formation and resolution of enantiomeric species from the nematic phase with a dynamic process of chirality synchronization. That would imply a stochastic generation of an excess of one enantiomer in the liquid crystalline state and a subsequent chirality amplification to a given homochiral domain or droplet, thanks to collaborative effect that stabilize the molecules with identical chiral conformation.

The unusual formation of propeller-patterned droplets for the series reported here is unexpected since these mesogens are achiral molecules having neither a chiral center nor any functional group likely to induce self-assembly through hydrogen bonding interactions. Interestingly, analogous compounds described in a previous work bearing oxymethylene connector function instead of the ester one, reveal neither striped structures nor propeller-patterned droplets (only the enantiotropic smectic-C mesophase is seen above 220°C without any nematic state) [START_REF] Benallou | 1,2,3]-triazole derivatives: Mesomorphic property dependence on the molecular shape[END_REF]. This result may suggest the key-contribution of the ester group on the induction of such features.

Previous reports have shown peculiar behavior of ester molecules in chirality amplification [START_REF] Jeong | Spontaneous Chirality Induction and Enantiomer Separation in Liquid Crystals Composed of Achiral Rod-Shaped 4-Arylbenzoate Esters[END_REF]. Takezoe et al. proved that rod-shape molecules bearing an ester function can act as a chiral dopant in a cholesteric guest phase and induce more than a 10% increase of the twisting power [START_REF] Choi | Amplification of twisting power in chiral mesophase by introducing achiral rod-like compound with ester group[END_REF][START_REF] Kawauchi | Why achiral rod-like compound with ester group amplifies chiral power in chiral mesophase[END_REF]. Enantioselective segregation of achiral nematic phase into chiral domains of opposite handedness has been also reported for achiral bent-core systems based on bis(phenyl)oxadiazole compounds with two ester linkages [START_REF] Görtz | Enantioselective segregation in achiral nematic liquid crystals[END_REF]. For our investigated compounds, a collective effect implying the specific role of ester groups in the intermolecular interactions could be invoked for the stabilization of one of the axial chiral conformers in series 1a-c (Scheme 2).

Conclusion

In this work, the synthesis and the mesomorphic characterization of achiral bis-triazole substituted biphenyl derivatives have been performed, from which two liquid crystalline phases, i.e. nematic and smectic-C mesophases, have been identified. At the transition between the two mesophases, a spontaneous striped texture is shown. This periodic structure could be associated with a spontaneous symmetry breaking, having either an extrinsic origin resulting from the instability of the interface at the phase coexistence, or an intrinsic one, promoting the stochastic emergence of one chiral conformer as well as the development of macroscopic homochiral nematic domains. The latter interpretation is supported by the formation of thin propeller-like patterned droplets, whose helicity can be inverted through thermal annealing.

Further experimental studies are required to fully explore the mechanism of this spontaneous symmetry breaking evidenced in this series, implying the design of compounds with lower transition temperatures.

OH HO

N N N O O N N N N N N OCnH 2n+1 H 2n+1 CnO O O ii 1a-c n = 8,

1a-c

  determined by DSC (10°C/min) during the first cycle. X stands for the striped pattern phase.

Figure 1 .

 1 Figure 1. X-ray diffractograms showing the main phases found on the compound 1a at different temperatures. The crystalline phase displays many sharp reflections, as indicated by the black line. The smectic mesophase (red line) has two main Bragg reflections related with the layer periodicity (d=2π/q100) and a broad peak stemming from the disordered aliphatic chains at about 14 nm -1 . At higher temperature, the spectrum (blue line), typical of the liquid-like order characteristic of a nematic phase is shown. Inset: Increase of the smectic layer spacing d with temperature indicating tilted molecules in the layers i.e. a smectic-C like local order.

Figure 2 .

 2 Figure 2. Optical textures observed between crossed polarizers on cooling at 5°C/min with the compound 1b prepared in a glass cell. Both nematic N (a) and smectic-C (e) phases exhibit a Schlieren texture, whereas the X phase (c) displays a striped texture from which the period can be measured. Note the phase coexistence between all the different phases; (b): N-X; (d): X-SmC; (f): SmC-Cr. Image size: 330 X 330 µm 2 .

Figure 3 .

 3 Figure 3. (Up) Pictures of liquid crystalline phase sequence observed between crossed polarizers on cooling at 0.2°C/min the sample 1a in the geometry of open droplet. The sample starts from a nematic phase (223.6°C) with a typical Schlieren texture to a smectic-C phase (198.6°C) via the striped pattern phase (X), whose periodicity increases with decreasing temperature. Image size: 150 X 90 µm 2 . (Bottom) Temperature dependence of the undulation period measured on cooling sample 1a (black circles). The gaps in the measurements stem from microscope focus tuning of the observation region when temperature is changed during the experiment. The fit to Eq. (1) is shown by the solid red line.

Figure 4 .

 4 Figure 4. Propeller-patterned droplets observed for compound 1a between crossed polarizers by optical microscopy. (a) Mixture of left and right-handed droplets obtained in a few µm thick sample on slow cooling at T=210°C. (b) Same droplets after a thermal annealing in the isotropic liquid phase and cooled down back at 210°C. The handedness of the propeller-pattern has been inverted for two droplets (indicated by white arrows) while the others do not exhibit chiral inversion. Image size: 280 X 210µm 2 .

C

  NMR (75MHz, CDCl3): δ = 14.11, 22.67, 26.00, 29.34, 31.81, 68.58, 115.51, 122.00, 122.52, 128.34, 129.38, 137.41, 139.79, 149.78, 154.66, 159.12; HRMS (ESI) m/z calculated for C46H53N6O6 ([M+H] + ): 785.3985; found: 785.4021.

  J = 8.65 Hz), 7.69 (m, 8H, Ar-H, 3 J=9.17); 8.61 (s, 2H, H5triazole); 13 C NMR (75MHz, CDCl3): δ = 14.13, 22.70, 26.00, 29.36, 31.92, 68.58, 115.51, 122.02, 122.50, 128.33, 129.37, 138.54, 139.77, 147.14, 159.12, 160.13; HRMS (ESI) m/z

	calculated for C54H69N6O6 ([M+H] + : 897.5261; found: 897.5273; C54H68N6NaO6 ([M+Na] + :
	919.5080; found: 919.5093.

10, 12

				COOH
	Compound	n	Transitions temperatures (°C) [transition enthalpies ∆H (kJ.mol -1 )]
	1a		8	Cr(193)[32.6] SmC(225)[2.5] X(252)[0.49] N(283)[0.5] I
	1b	H 2n+1 CnO 10	i Cr(147)[7.8] SmC(228)[3.3] X(242)[1.57] N(272)[0.3] I
	1c		12	Cr (168)[42.11] SmC(258)[4.8] X(281)[5.1] N+I
				COCl
				N	N
				N
		H 2n+1 CnO
	Scheme 1. Conditions for the synthesis of triazole derivatives (1a-c) (i) SO2Cl2, 85°C, 5-6 h (vi)
	N(C2H5)3, DCM, 40°C, 48-72 h.

Table 1 .

 1 Transition temperatures (°C) and related enthalpy values ∆H (kJ.mol -1 ) of compounds

Acknowledgements

This work was supported by DGRSDT and CNRS.

Author contributions

SB and SSB designed and synthesized the compounds, AB performed the molecular simulations, EG and SSB performed the physical characterizations, interpreted the data and wrote the manuscript.

The authors report there are no competing interests to declare.

Scheme 2. Energy minimized structure of compound 1a-c for which the aliphatic chains have not been represented, and its mirror image conformer according to density functional theory

(DFT) calculations. The activation energy for enantiomerization of the helical conformers is 8 kJ.mol -1 . Note that this energy barrier is rather weak, and is not a priori expected to prevent the chiral conformational interconversion.